Answer: 44 miles
Step-by-step explanation:
Let's call the number of miles Kevin can travel "m". We can set up an equation using the given information:
4.25 + 0.47m ≤ 25
Solving for "m", we can begin by subtracting 4.25 from both sides:
0.47m ≤ 20.75
Then, divide both sides by 0.47:
m ≤ 44.15
Therefore, Kevin can travel at most 44 miles without exceeding his spending limit.
Can you help me to solve these two questions?
The equation of the tangent line is y = (-1/49)x + 8/49. 2. The equation of the normal line is y = 49x - 342.
What do a curve's tangent and normal lines represent?A line that meets a curve at a point and has the same slope as the curve there is said to be the tangent line to that curve. A line that is perpendicular to the tangent line at a given position is the normal line to a curve at that location. In other words, the normal line's slope equals the tangent line's slope's negative reciprocal. The normal line is helpful for determining the direction of greatest change of the curve at a place whereas the tangent line gives information about the instantaneous rate of change of the curve at that point.
The given function is f(x) = 1/x.
The slope of the function is the derivative of the function thus,
f(x) = 1/x
f'(x) = -1/x²
f'(7) = -1/49
The equation of the line is given as:
y - y1 = m(x - x1)
where, m is the slope of the equation.
The equation of the tangent line is:
y - f(7) = f'(7)(x - 7)
y - 1/7 = -1/49(x - 7)
y = (-1/49)x + 8/49
b. The equation of the normal line to the graph is given as:
The slope of the normal line is negative and opposite of the tangent line.
That is,
m = 49.
y - f(7) = 49(x - 7)
y - 1/7 = 49(x - 7)
y = 49x - 342
Hence, the equation of the tangent line is y = (-1/49)x + 8/49. 2. The equation of the normal line is y = 49x - 342.
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begin by finding the area under the curve from to , . this area can be written as the definite integral
The area under the curve y = 1/ (x^2 + 6x -16) from x = t to x = 6 is 1/10( ln(4) - 1/10 ln(t+8))
To find the area under the curve y = 1/ (x^2 + 6x -16) from x = t to x = 6, where t > 2, we need to evaluate the definite integral:
∫[t,6] 1/ (x^2 + 6x -16) dx
To solve this integral, we can use partial fraction decomposition. First, we factor the denominator:
x^2 + 6x -16 = (x+8)(x-2)
Then, we can write:
1/ (x^2 + 6x -16) = A/(x+8) + B/(x-2)
Multiplying both sides by (x+8)(x-2), we get:
1 = A(x-2) + B(x+8)
Setting x = -8, we get:
1 = A(-10)
So, A = -1/10.
Setting x = 2, we get:
1 = B(10)
So, B = 1/10.
Therefore, we can write:
1/ (x^2 + 6x -16) = -1/10(x+8) + 1/10(x-2)
Substituting this into the integral, we get:
∫[t,6] 1/ (x^2 + 6x -16) dx = ∫[t,6] (-1/10(x+8) + 1/10(x-2)) dx
Integrating, we get:
= [-1/10 ln|x+8| + 1/10 ln|x-2|] from t to 6
= 1/10 ln|6-2| - 1/10 ln|t+8|
= 1/10 ln(4) - 1/10 ln(t+8)
Therefore, the area is: 1/10( ln(4) - 1/10 ln(t+8))
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_____The given question is incomplete, the complete question is given below:
begin by finding the area under the curve from to y = 1/ (x^2 + 6x -16) from x = t to x = 6, t>2 this area can be written as the definite integral
Find x, if √x +2y^2 = 15 and √4x - 4y^2=6
Answer:
x = 52.2
Step-by-step explanation:
Add 4x - 4y^2 = 36 and x + 2y^2 = 225
x + 2y^2 + 4x - 4y^2 = 225 + 36
5x = 261
x = 261/5=52.2
Question 12 (2 points)
Among the seniors at a small high school of 150 total students, 80 take Math, 41
take Spanish, and 54 take Physics. 10 seniors take Math and Spanish. 19 take Math
and Physics. 12 take Physics and Spanish. 7 take all three.
How many seniors were taking none of these courses?
Note: Consider making a Venn Diagram to solve this problem.
0
5
9
22
150 - 141 = 9 seniors are not enrolled in any classes.
What is statistics, and how can it be used?The area of mathematics known as statistics is used to gather, analyse, and interpret data. To predict the future, determine the likelihood that a specific event will occur, or learn more about a survey, statistics can be employed.
The Venn diagram reveals the amount of seniors enrolling in at least one of the courses as follows:
80 + 41 + 54 - 10 - 19 - 12 + 7
= 141
Therefore, 150 - 141 = 9 seniors are not enrolled in any classes.
= 9
So, there are 9 seniors taking none of the courses. Answer: 9.
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Andres Michael bought a new boat. He took out a loan for $24,420 at 3.5% interest for 2 years. He made a $4,330 partial payment at 2 months and another partial payment of $2,600 at 6 months. How much is due at maturity?
If Andres Michael bought a new boat. He took out a loan for $24,420 at 3.5% interest for 2 years. Andres Michael owes $18806.6 at maturity.
How to find the amount?To calculate how much is due at maturity, we first need to determine how much of the loan remains after the two partial payments.
To do this, we can use the formula for simple interest:
I = P * r * t
Where:
I = Interest
P = Principal (original loan amount)
r = Annual interest rate
t = Time (in years)
The interest for the first two months can be calculated as:
I1 = P * r * t1
= 24420 * 0.035 * (2/12)
= 142.45
So after the first two months, the amount owing on the loan is:
P1 = P + I1 - 4330
= 24420 +142.45 - 4330
= 20,232.45
The interest for the next four months can be calculated as:
I2 = P1 * r * t2
= 20,232.45 * 0.035 * (4/12)
= 236.05
So after six months, the amount owing on the loan is:
P2 = P1 + I2 - 2600
= 20,232.45 + 236.05- 2600
= 17868.50
Now we can calculate the interest for the remaining 18 months:
I3 = P2 * r * t3
= 17868.50* 0.035 * (18/12)
= 938.10
So the total amount owing at maturity (after 2 years) is:
Total amount owing = P2 + I3
= 17868.50 + 938.10
= 18806.6
Therefore, Andres Michael owes $18806.6 at maturity.
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Using the Distributive Property as a good first step to solving the equation, you could simplify to get which of these choices?7(5x + 2) = -4(6 - 5x)35x + 14 = -24 - 20x35x + 14 = -24 + 20x5x + 14 = 6 + 20x35x + 2 = -24 - 5x35x + 2 = 24 - 20x
In equation 7(5x + 2) = -4(6 - 5x), Using the Distributive Property, we get 35x + 14 = -24 + 20x. So, the correct option is D).
To solve the equation 7(5x + 2) = -4(6 - 5x), a good first step is to use the Distributive Property to simplify both sides of the equation. Distributing the 7 and -4 on the left and right sides, respectively, we get
35x + 14 = -24 - 20x.
Next, we can combine like terms by adding 20x to both sides to get 55x + 14 = -24. Then, subtracting 14 from both sides, we get 55x = -38. Finally, we can solve for x by dividing both sides by 55, giving us x = -38/55. Therefore, the solution to the equation is x = -38/55.
The evaluation process involves performing arithmetic operations in a logical order to simplify the equation step-by-step until a solution is reached. So, the correct answer is D).
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Find two real numbers between −2π and 2π that determine each of the points on the unit circle given to the right. MNPQ1 A graph has a horizontal x-axis and a vertical y-axis. A circle with its center at the origin has radius 1. The circle is divided into sixteen parts by the axes and by three tick marks in each quadrant. The tick marks are one third, one half, and two thirds of the way into each quadrant. The circle includes four points, all either on a tick mark or on an axis. The point labeled "M" is on the tick mark at approximately (0.5,negative 0.9). The point labeled "N" is on the tick mark at approximately (negative 1,0). The point labeled "P" is on the tick mark at approximately (negative 0.7,0.7). The point labeled "Q" is on the tick mark at approximately (negative 0.5,negative 0.9). The two real numbers that determine M are nothing. (Simplify your answer. Type exact answers, using π as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers.)
For point M, we have x-coordinate cos( 5π/ 6) ≈0.5 y- match sin( 5π/ 6) =0.9
Since thex-coordinate is positive and the y- match is negative, we know that the angle lies in the alternate quadrant.
We can find another angle in the alternate quadrant that has the same sine and cosine values by abating 2π from the angle. thus, the two real figures that determine point M are 5π/ 6 and 5π/ 6- 2π = -7 π/ 6 Simplifying, we get
Two real figures that determine M 5π/ 6,-7 π/ 6 For the other points, we can use the same system
Two real figures that determine N π, π Two real figures that determine P 5π/ 4, 5π/ 4- 2π = -3 π/ 4 Two real figures that determine Q 7π/ 6, 7π/ 6- 2π = -5 π/ 6 .
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Joann had a vegetable stand where she sold tomatoes. She sold 15 tomatoes the first day. The second day she sold half of what was left. On the third day she sold 12 and sold half of what was left on the fourth day. On the fifth day there were 4 tomatoes left to be sold. How many tomatoes did she have to begin with?
On the fifth day there were 4 tοmatοes left tο be sοld. Jοann had 71 tοmatοes tο begin with.
What is prοbability?Prοbability is a measure οf the likelihοοd οr chance οf an event οccurring. It is a number between 0 and 1, where 0 indicates that the event is impοssible, and 1 indicates that the event is certain tο οccur.
Let's wοrk backwards frοm the last day and figure οut hοw many tοmatοes Jοann had οn the fοurth day.
On the fifth day, there were 4 tοmatοes left tο be sοld, which means she sοld half οf what was left οn the fοurth day. Sο she must have started with 8 tοmatοes οn the fοurth day (since half οf 8 is 4).
On the fοurth day, she sοld half οf what was left, which means she had 16 tοmatοes befοre she sοld any.
On the third day, she sοld 12 tοmatοes, which means she had 28 tοmatοes befοre she sοld any.
On the secοnd day, she sοld half οf what was left, which means she had 56 tοmatοes befοre she sοld any.
Finally, οn the first day, she sοld 15 tοmatοes.
Therefοre, Jοann had 71 tοmatοes tο begin with.
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A dietician is planning a snack package of fruit and nuts. Each ounce of fruit will supply zero units of protein, 3 units of carbohydrates, and 2 unit of fat, and will contain 40 calories. Each ounce of nuts will supply 4 units of protein, 2 unit of carbohydrate, and 4 units of fat, and will contain 50 calories. Every package must provide at least 4 units of protein, at least 11 units of carbohydrates, and no more than 16 units of fat. Find the number of ounces of fruit and number of ounces of nuts that will meet the requirement with the least number of calories. What is the least number of calories?
Let x be the ounces of fruit and y be the ounces of nuts. What is the objective function that must by minimized?
z = __x + __y
The dietician should use ___ ounce(s) of fruit and ___ ounce(s) of nuts. These amounts will have a total of ___calories.
(Type your answer in whole numbers)
The objective function that must be minimized is:
z = 40x + 50y
subject to the constraints:
0x + 4y ≥ 4 (protein constraint)
3x + 2y ≥ 11 (carbohydrate constraint)
2x + 4y ≤ 16 (fat constraint)
We want to find the number of ounces of fruit (x) and nuts (y) that will meet the requirement with the least number of calories.
Solving the system of inequalities, we get:
x = 2 ounces
y = 2 ounces
Therefore, the dietician should use 2 ounces of fruit and 2 ounces of nuts. These amounts will have a total of 180 calories (402 + 502).
Answer:
Step-by-step explanation:
Let's assume we need x ounces of fruit and y ounces of nuts to meet the requirements with the least number of calories. Then, the problem can be expressed as an optimization problem:
Minimize: 40x + 50y (since we want to minimize the number of calories) Subject to:
0x + 4y ≥ 4 (we need at least 4 units of protein)3x + 2y ≥ 11 (we need at least 11 units of carbohydrates)2x + 4y ≤ 16 (we cannot have more than 16 units of fat)
To solve this problem, we can use the simplex method. First, we convert the problem to standard form by introducing slack variables:
Minimize: 40x + 50y Subject to:
0x + 4y + s1 = 43x + 2y + s2 = 112x + 4y + s3 = 16
Now we can create the initial simplex tableau:
xys1s2s3RHSs1041004s23201011s32400116z-40-500000
We want to find the minimum value of z, so we need to choose the variable with the most negative coefficient in the bottom row as the entering variable. In this case, that is y. We then choose the variable with the smallest non-negative ratio between the right-hand side and the coefficient of the entering variable in its row as the leaving variable. In this case, that is s3, since 16/4 = 4 is the smallest non-negative ratio.
We then perform the pivot operation to eliminate the coefficient of y in the other rows:
x y s1s2s3RHSs1001-214y3/2101/2-1/24s2-1001-1/25z-100025-15200
We repeat this process until all the coefficients in the bottom row are non-negative. The final tableau is:
x
In the year 1985, a house was valued at $108,000. By the year 2005, the value had appreciated to $148,000. What was the annual growth rate percentage between 1985 and 2005? Assume that the value continued
to grow by the same percentage. What was the value of the house in the year 2010?
Answer:
To find the annual growth rate percentage, we can use the formula:
annual growth rate = [(final value / initial value)^(1/number of years)] - 1
where "final value" is the value in the ending year, "initial value" is the value in the starting year, and "number of years" is the total number of years between the starting and ending years.
Using the given values, we have:
annual growth rate = [(148,000 / 108,000)^(1/20)] - 1
= 0.0226 or 2.26%
So the house appreciated at an annual growth rate of 2.26%.
To find the value of the house in 2010, we can use the same growth rate to project the value from 2005 to 2010:
value in 2010 = 148,000 * (1 + 0.0226)^5
= $175,465.11 (rounded to the nearest cent)
Therefore, the value of the house in the year 2010 was $175,465.11.
determine if the transformation is one to one and/or onto. justify your answers. give an explanation for each of these properties.
To determine whether a transformation is one-to-one or onto, one must analyze its behavior and properties, such as passing the horizontal line test for one-to-one or checking if the range equals the codomain for onto.
In mathematical terms, a transformation refers to a function that maps elements from one set, called the domain, to another set, called the range. A transformation is said to be one-to-one if no two distinct elements in the domain are mapped to the same element in the range. This means that each element in the range is associated with a unique element in the domain.
On the other hand, a transformation is onto if every element in the range is mapped to by at least one element in the domain. In other words, for each element in the range, there exists at least one element in the domain that maps to it.
To determine whether a transformation is one-to-one or onto, one can analyze its properties and behavior. For example, a transformation is one-to-one if and only if it passes the horizontal line test. This means that no two points in the domain map to the same point on a horizontal line. To determine if a transformation is onto, one can check if the range of the transformation equals the codomain.
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The given question is incomplete, the complete question is:
How to determine the transformation is one to one and/or onto?
if cot0=3/4 and the terminal point determined by 0 is in quadrant 3, then
If cotθ = 3/4 then cosθ = -3/5 is the right option according to the rules of trigonometry.
What is Trigonometry?Trigonometry is a branch of mathematics that deals with the study of relationships between the sides and angles of triangles. It is primarily concerned with the study of the six trigonometric functions: sine, cosine, tangent, cosecant, secant, and cotangent, and their applications in various fields such as engineering, physics, and navigation.
What are angles of triangle?A triangle is a three-sided polygon, and its angles are the angles formed by the intersection of its sides. The sum of the angles in a triangle is always 180 degrees.
First, we know that cot(0) = adjacent / opposite = 3/4.
In quadrant 3, the adjacent side is negative and the opposite side is positive, so we can draw a right triangle in quadrant 3 with adjacent side -3 and opposite side 4.
The hypotenuse can be found using the Pythagorean theorem.
h² = adjacent²+ opposite²
h² = (-3)^2 + 4^2
h²= 9 + 16
h² = 25
h = 5
So we have a right triangle in quadrant 3 with adjacent side -3, opposite side 4, and hypotenuse 5.
Using the definitions of the trigonometric functions, we can find the values of the other functions:
sin(0) = opposite / hypotenuse = 4/5
cos(0) = adjacent / hypotenuse = -3/5
tan(0) = opposite / adjacent = -4/3
csc(0) = hypotenuse / opposite = 5/4
sec(0) = hypotenuse / adjacent = -5/3
cot(0) = adjacent / opposite = 3/4 (given)
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jerome haw 1,040 songs downloaded on his spotify account and 30% of the songs are country songs. How many of the songs are not country
Use the product of powers property to simplify the numeric expression. 2^2/5/2^1/10
Answer:
[tex] 2^\frac{3}{10} [/tex]
Step-by-step explanation:
[tex] \dfrac{2^\frac{2}{5}}{2^\frac{1}{10}} = [/tex]
[tex]= 2^{\frac{2}{5} - \frac{1}{10}}[/tex]
[tex]= 2^{\frac{4}{10} - \frac{1}{10}}[/tex]
[tex] = 2^\frac{3}{10} [/tex]
one ticket is drawn at random from each of the two boxes below: 1 2 6 1 4 5 8 find the chance that the both numbers are even numbers.
The chance that both numbers drawn are even numbers is 8/21.
The probability refers to the measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain.
There are 4 even numbers and 3 odd numbers in the first box, and 2 even numbers and 1 odd number in the second box.
The probability of drawing an even number from the first box is 4/7, and the probability of drawing an even number from the second box is 2/3.
By the multiplication rule of probability, the probability of drawing an even number from both boxes is
(4/7) × (2/3) = 8/21
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QUESTION THREE (30 Marks) a) For a group of 100 Kiondo weavers of Kitui, the median and quartile earnings per week are KSHs. 88.6, 86.0 and 91.8 respectively. The earnings for the group range between KShs. 80-100. Ten per cent of the group earn under KSHs. 84 per week, 13 per cent earn KSHs 94 and over and 6 per cent KShs. 96 and over. i. Put these data into the form of a frequency distribution and obtain an estimate of the mean wage. 15 Marks
Answer:
the answer would be 100 I guess
What is the missing value in the equation shown below?
4/10+ ?/100= 7/10
A 1
B 3
C 10
D 30
Answer: D 30
Step-by-step explanation:
4/10 + 30/100
2/5 + 3/10
7/10
NB: LEFT-HAND SIDE IS EQUAL TO THE RIGHT-HAND SIDE
Lori is moving and must rent a truck. There is an initial charge of $60 for the rental plus an additional fee per mile driven. Would a linear, quadratic or exponential function be the best type of equation to model this function? Exponential Quadratic Linear
Answer:
A linear function would be the best type of equation to model this situation. The total cost of renting the truck increases linearly with the number of miles driven. The initial charge of $60 can be considered as the y-intercept of the linear function, and the additional fee per mile driven can be considered as the slope of the line. Therefore, the equation that models this situation can be written in the form y = mx + b, where y is the total cost of renting the truck, x is the number of miles driven, m is the additional fee per mile driven (the slope of the line), and b is the initial charge of $60 (the y-intercept).
Answer:
A linear function would be the best type of equation to model this function.
Step-by-step explanation:
The total cost of renting the truck is composed of two parts:
Initial charge of $60.Additional fee per mile driven.The initial charge of $60 is the fixed charge, and the additional fee is the variable charge that is proportional to the number of miles driven.
Let "x" be the number of miles driven and "y" be the total cost of the rental (in dollars), then the linear equation is:
y = mx + 60
where "m" is the additional fee (in dollars) per mile driven.
Therefore, a linear function, in the form y = mx + b, where m represents the slope or rate of change, and b represents the initial fixed charge, is the most appropriate function to model this situation.
Trains Two trains, Train A and Train B, weigh a total of 188 tons. Train A is heavier than Train B. The difference of their
weights is 34 tons. What is the weight of each train?
Step-by-step explanation:
A + B = 188
A = 188 - B - (1)
Now,
A - B = 34
188 - B - B = 34 (Substituting eqn 1 in A)
188 - 34 = 2B
154 = 2B
• B = 77 tons
Now
A = 188 - B
A = 188 - 77
A = 111 tons
Suppose you are trying to estimate the average age of the entire CSU student population. You collect a sample of size n-163, and from your data you calculate x =20.1 s 1.8 round your answers to 3 decimal places) 1. The standard error of the mean for this data set is: 2. The approximate 95% margin of error is (Use the approximation method from the notes, in which the critical value is approximately 2.) 3. The approximate 95% CI for lage is
a) The standard error of mean for this data set is approximately 0.141.
b) The approximate 95% margin of error is approximately 0.282.
c) The approximate 95% confidence interval for the population mean age is 19.824 to 20.376.
a) The standard error of mean (SEM) is given by the formula: SEM = s / sqrt(n), where s is the sample standard deviation and n is the sample size. Plugging in the values given, we have:
SEM = 1.8 / sqrt(163) ≈ 0.141
So the standard error of the mean is approximately 0.141.
b) The approximate 95% margin of error (MOE) can be calculated using the formula: MOE ≈ 2 * SEM. Plugging in the SEM value from part 1, we get:
MOE ≈ 2 * 0.141 ≈ 0.282
So the approximate 95% margin of error is approximately 0.282.
c) The approximate 95% confidence interval (CI) for the population mean age can be calculated using the formula: CI = x ± (z*SEM), where x is the sample mean, z is the critical value from the standard normal distribution corresponding to the desired level of confidence (95% in this case), and SEM is the standard error of the mean. The critical value for 95% confidence is approximately 1.96. Plugging in the values, we get
CI = 20.1 ± (1.96 * 0.141) ≈ 19.824 to 20.376
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Each license plate in a certain state has five characters (with rep Here are the possibilities for each character. Character Possibilities The digits 1, 2, 3, or 4 The 26 letters of the alphabet The 26 letters of the alphabet The 10 digits 0 through 9 Fifth The 10 digits 0 through 9 How many license plates are possible in this state? First Second Third Fourth
The state in question is using a five-character license plate system, with each character having 36 possible combinations. Multiplying the possible combinations of each character gives us a total of 60,466,176 possible license plates.
What is multiplication?Multiplication is an iterative process of addition where the multiplier is the quantity of times the multiplicand is added to itself. When a number is multiplied, it is multiplied by itself a predetermined amount of times.
This implies that each license plate will have five distinct characters, each of which can be any of the following: the 26 characters of the alphabet, the digits 1, 2, 3, or 4, or the numbers 0 through 9. It provides us with a total of 5 characters, each of which has 36 different potential combinations (4 digits + 26 letters + 10 digits).
The number of character combinations is multiplied to determine the total number of potential license plates. In this instance, the result is 36 times itself.
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270,400 license plates are possible from the combinations of each character given in the question.
What are Combinations?Combinations are used to calculate the number of ways a certain number of items can be selected from a given set of items.
To calculate the total possible license plates in the state, we need to consider the total number of possible combinations of the five characters.
For the first character, there are four possible digits (1, 2, 3, or 4).
For the second character, there are 26 letters of the alphabet. (A-Z)
For the third character, there are again 26 letters of the alphabet.
For the fourth character, there are 10 possible digits (0 through 9).
For the fifth character, there are again 10 possible digits.
We can calculate the number of possible license plates by multiplying the number of possibilities for each character.
4 x 26 x 26 x 10 x 10 = 270,400 possible license plates.
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Select all the expressions that are equivalent to (12 + x)10.5.
It’s multiple choice and these are the answers
10.5(12x)
(10.5 + 12 + x)
10.5(12 + x)
126x
126 + 10.5x
22.5 + x
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Given parallelogram STUV, what is the length of TV?
TW = y2
WV = 2y − 1
A) 2
B) 8
C) 4
The required value of TV is 2 units.
What is parallelogram?
A parallelogram is a straightforward quadrilateral with two sets of parallel edges in Euclidean geometry. A parallelogram's confronting or opposing sides are of equal length, and its opposing angles are of equal size.
According to question:
We have given that;
TW = y²
WV = 2y − 1
We know that in parallelogram
TW = WV
y² = 2y − 1
y² - 2y + 1 = 0
y² - y - y + 1 =0
y(y - 1)-1(y - 1) = 0
(y - 1)(y - 1) = 0
(y - 1)² = 0
y - 1 = 0
y = 1
So;
TV = TW + WV
TV = y² + 2y − 1
TV = 1² + 2(1) - 1
TV = 1 + 2 - 1
TV = 2 units
Thus, required value of TV is 2 units.
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8. The diagram shows the triangle PQR. In the diagram, all the angles are in degrees. RP = RQ Find the value of y. Show clear algebraic working. P= 2x + 10, R=y, Q= X + 15
The value of y in the given isosceles triangle is 140°.
What is isosceles triangle?A triangle with two equal edges is said to be isosceles. Also equal are the two angles that face the two identical sides. In other terms, an isosceles triangle is a triangle with two sides that are the same length.
If the sides AB and AC of a triangle ABC are equivalent, then the triangle ABC is an isosceles triangle with B = C. "If the two sides of a triangle are congruent, then the angle opposite to them is also congruent," states the theorem that explains the isosceles triangle.
What is an angle?An angle is a shape created by two lines that share an endpoint and are referred to as the angle's sides and vertex, respectively. Angles created by two beams are in the plane where the rays are located. The meeting of two surfaces also creates angles.
In the given question,
∠P=∠Q
2x+10=x+15
x=5
Therefore,
∠P=2(5)+10=20°
∠Q=5+15= 20°
∠P+∠Q+∠R= 180°
20+20+∠R= 180°
∠R= 140°
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Find X using the picture below.
Answer: 37.5
Step-by-step explanation:
75 - 180 = 105
105 degrees = the obtuse angle, bottom triangle.
75/2= 37.5 (since both sides of the bottom triangle are equal angles)
A triangle has an area of 144 square feet. The height is 24 feet. What is the length of the base (in feet)?
During a manufacturing process, a metal part in a machine is exposed to varying temperature conditions. The manufacturer of the machine recommends that the temperature of the machine part remain below 135°F. The temperature T in degrees Fahrenheit x minutes after the machine is put into operation is modeled by T=-0.005x^2+0.45x+125. Will the temperature of the part ever reach or exceed 135°F? Use the discriminant of a quadratic equation to decide.
Using the discriminant of the quadratic equation, the temperature will part after 50 minutes
Will the temperature of the part ever reach or exceed 135°F?The temperature of the machine part is given by the equation:
T = -0.005x^2 + 0.45x + 125
We need to find out if the temperature will ever reach or exceed 135°F, which means we need to check if there exists a value of x for which T = 135.
Substituting T = 135 in the above equation, we get:
135 = -0.005x^2 + 0.45x + 125
Simplifying the equation, we get:
0.005x^2 - 0.45x + 10 = 0
This is a quadratic equation of the form ax^2 + bx + c = 0, where a = 0.005, b = -0.45, and c = 10.
The discriminant of this quadratic equation is given by:
D = b^2 - 4ac
= (-0.45)^2 - 4(0.005)(10)
= 0.2025 - 0.2
= 0.0025
Since the discriminant is positive, the quadratic equation has two real roots. Therefore, the temperature of the machine part will cross 135°F at some point during the operation.
We can also find the roots of the quadratic equation using the formula:
[tex]x = (-b \± \sqrt(D)) / 2a[/tex]
Substituting the values of a, b, and D, we get:
[tex]x = (0.45 \± \sqrt(0.0025)) / 2(0.005)\\= (0.45 \± 0.05) / 0.01[/tex]
Taking the positive value, we get:
x = 50
Therefore, the temperature of the machine part will cross 135°F after 50 minutes of operation.
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michael scott picks up the donut and coffee order for hos office. yesterday he bought 6 donuts and 8 cups of coffee for $21. today he bought 10 donuts and 5 cups of coffee for $16.25. what is the cost of each item?
The cost of each item would be = $1.5 each of cup of coffee and donuts.
How to calculate the cost of each item bought by Michael?For yesterday, the number of donut he ordered = 6
The number of cup of coffee he ordered = 8cup
Total cost = $21
The total number of items he ordered = 6+8 = 14
The cost for donuts alone,
= 6/14× 21/1
= 126/14
= $9
The cost of each donut = 9/6 = $1.5
The cost of cup of coffee ;
= 8/14× 21/1
= 168/14
= 12
for each cup of coffee;
= 12/8
=$1.5
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AA contestant on a game show has a 1 in 6 chance of winning for each try at a certain game. Which probability models can be used to simulate the contestant’s chances of winning?
Select ALL of the models that can be used to simulate this event.
A) a fair six-sided number cube
B) a fair coin
C) a spinner with 7 equal sections
D) a spinner with 6 equal sections
E) a bag of 12 black chips and 60 red chips
Answer:
Model D) a spinner with 6 equal sections can be used to simulate the contestant's chances of winning.
Step-by-step explanation:
A spinner with 6 equal sections represents the possible outcomes of the game show, where each section represents a possible win or loss. Since the contestant has a 1 in 6 chance of winning, the spinner would have one section representing a win and five sections representing a loss. Each spin of the spinner would represent one try at the game show, and the probability of winning can be determined by calculating the theoretical probability of landing on the win section.
Workers are preparing an athletic field by mixing soil and sand
in the correct ratio. The table shows the volume of sand to mix
with different volumes of soil. Which statement is correct?
A For 1,425 m³ of soil, the workers should use 375 m³ of sand.
B The ratio of the volume of soil to the volume of sand is 1:4.
C A graph of the relationship includes the point (900, 225).
D The equation y = 4x models the relationship.
Option B: The ratio of the volume of soil to the volume of sand is 1:4.
Looking at the table, we can see that for every 100 m³ increase in soil, the sand volume increases by 25 m³. This gives us a ratio of 4:1, which means that the volume of sand is one-fourth of the volume of soil. Therefore, option B is correct.
Option D: The equation y = 4x models the relationship.
We can see that the volume of sand is always one-fourth of the volume of soil. Therefore, we can write y = (1/4)x or y = 0.25x. This equation is the same as y = 4x. Therefore, option D is also correct.
So, the correct statements are B and D.
What is a graph?In mathematics, a graph is a visual representation of data or a mathematical function. It consists of a set of points or vertices connected by lines or curves called edges or arcs, which represent the relationships between the points. Graphs can be used to show trends, patterns, and relationships in data, and they are commonly used in fields such as statistics, economics, and computer science. Some common types of graphs include line graphs, bar graphs, pie charts, scatterplots, and network graphs.
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The table mentioned in the question has been attached below.
