The two numbers are x = 3.43 and y = 22.57.
What is a linear equation in two variables?
An equation is said to be a linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.
Let the first number be x and the second number be y. Then we can write the given information as a system of equations:
x + y = 26
(2/5)x + (3/8)y = 10
To solve this system, we can eliminate one of the variables by multiplying the first equation by 8 and the second equation by 5, then subtracting the resulting equations:
8x + 8y = 208
10x + 15y = 50
Subtracting these equations gives us:
-2x - 7y = -158
Dividing both sides by -7, we get:
x + y = 22.57
Substituting this back into the first equation, we get:
x + 22.57 = 26
Solving for x, we get:
x = 26 - 22.57
= 3.43
Substituting this back into the original equation x + y = 26, we get:
3.43 + y = 26
Solving for y, we get:
y = 26 - 3.43
= 22.57
Hence, the two numbers are x = 3.43 and y = 22.57.
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What is the value of y in the equation?
6y + 2 = 4p - 10
Two angles are complementary. The measure of the larger angle is 26 degrees less than 3 times the measure of the smaller angle. The measure of the smaller angle is ________ degrees, and the larger angle is ________ degrees.
Answer:
29, 61
Step-by-step explanation:
x = smaller
y = larger
y = 3x - 26
x + y = 90
x + 3x - 26 = 90
4x - 26 = 90
4x = 116
x = 29
x + y = 90
29 + y = 90
y = 90 - 29
y = 61
Answer:
smaller angle = 29°
larger angle = 61°
Step-by-step explanation:
Let x be the larger angle and y be the smaller angle
Larger angle is 26° less than 3 times the smaller angle
i. e x = 3y-26°
Since x and y are complementary angles, we can write,
x + y = 90°
or, (3y - 26°) + y = 90°
or, 4y = 90° + 26°
or, y = 116°/4
or, y = 29°
So,
x = 3 * 29° - 26° = 61°
What i cot of tiling a rectangular plot of land 500m long and 200m wide at the rate r 8 per q m
The cost of tilling a rectangular plot of land 500m long and 200m wide at the rate of rs 8 per sq m is Rs. 8,00,000.
Area of rectangle = length × breadth
Area of rectangular plot = 500× 200 = 1,00,000 sq m
Cost of tilling 1 sq m of land = Rs. 8
Cost of tilling 1,00,000 sq m of land = 8 × 1,00,000 = Rs. 8,00,000
Thus, The cost of tilling a rectangular plot of land 500m long and 200m wide at the rate of rs 8 per sq m is Rs. 8,00,000.
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Please help me !!!??
Answer:
I think it's 100.8
Step-by-step explanation:
I'm pretty sure
Answer: 100.8666666666667 (rounded to the nearest hundredth: 100.87)
Tabatha and Horatio each leave their separate houses and drive to a restaurant to meet for dinner. Tabatha lives 15 miles from the restaurant, and she drives at a rate of 3 miles every 2 minutes. The graph represents Horatio’s distance, in miles, y, from the restaurant after driving for x minutes.
Tabatha drives 1/12 mile more per minute than Horatio drives.
Tabatha drives 1/6 mile more per minute than Horatio drives
Tabatha drives 3 miles more per minute than Horatio drives.
Tabatha drives 9 miles more per minute than Horatio drives.
Answer:
Tabatha drives 1/6 mile more per minute than Horatio drives
Step-by-step explanation:
a vocational counselor wishes to compare the mean scores on a paper-and-pencil test of anxiety for groups of physicians, lawyers, and accountants. the appropriate test is a
A vocational counselor wishes to compare the mean scores on a paper-and-pencil test of anxiety for groups of physicians, lawyers, and accountants. the appropriate test is a two factor chi Square test.
The Pearson chi-square (χ²) test, often simply called the chi-square test, is one of the most common non-parametric tests. Nonparametric tests are used for data that do not follow the assumptions of parametric tests, especially the assumption of normal distribution.
To test hypotheses about the distribution of a categorical variable, you should use the chi-square test or another non-parametric test. Categorical variables can be nominal or ordinal and represent groups such as species or nationality. They can only have a small number of specific values, so they cannot have a normal distribution.
Bidirectional chi-square is one of several tests of goodness of fit between the actual values of two nominal or ordinal variables and the values expected if the variables were unrelated or independent. Chi-square is also known as Pearson Chi-square and Chi-square test of independence. The symbol for the chi-square test is the lowercase Greek letter chi (χ) with a superscript 2, such as χ2. χ2 is a test of significance and should be accompanied by an appropriate test of strength. The strength test should be chosen based on the number of rows and columns in the table of observations. In particular, one of the most commonly used strength tests is the π coefficient.
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Which is equal to 1/58^8 ? a.58^-8 b.-1/58^-8 c.58^8 d.1/(58)^-8
a) 58^-8 is the same as 1/58^8. we can also simplify the expression by applying the rule for negative exponents to the entire fraction.
How to evaluate this expression ?To evaluate this expression, we can use the rule that any number raised to a negative exponent is equal to the reciprocal of the same number raised to the same positive exponent. In other words, x^-n = 1/x^n.
Applying this rule to the expression 1/58^8, we get:
1/58^8 = 1/(58^8) = 58^-8
Therefore, the correct answer is 58^-8.
It is important to note that the exponentiation operator (^) has higher precedence than the division operator (/), so we need to use parentheses to indicate that the exponent should be applied to the entire denominator before the division is performed. In this case, we can also simplify the expression by applying the rule for negative exponents to the entire fraction:
1/58^8 = (1/58)^8 = 58^-8
This simplification shows that the correct answer is still 58^-8.
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Last winter, a store sold 408 coats in
3 months. This winter, the store plans to sell
coats for 4 months. Based on the average
number of coats sold each month last winter,
how many total coats should the store plan to
sell this winter?
Total coats should the store plan to sell this winter is 952.
Last winter, a store sold 408 coats in 3 months. This winter, the store plans to sell coats for 4 months.
What is sell?
Determine the total cost of all the purchased units. To find the cost price, divide the total cost by the quantity of units purchased. To get the final price, use the formula for selling price (SP), which is: SP = CP + Profit Margin. The cost of the commodity will then be increased by the margin to determine the proper pricing. Retail math describes the mathematical techniques or formulae utilised in the sales industry. It is earning money or receiving change in the most basic sense. Business owners, retailers, managers, and sales representatives all utilise retail math in their daily work.
3month = 408 coats
1 month = 408/3 =136 coats
Then, 4 months = 136*4 = 544 coats
Total coats should the store plan to sell this winter = 544+408 = 952.
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3. The vertices for A LML are L(-4,0), M(-2,0) and N(-3,-3). Its image is L'(1,1), M'(3,1) and
N'(2,-2). What is the translation rule that maps the preimage to the image?
The translation rule that maps the preimage to the image is (x, y) ⇒ (x + 5, y + 1)
How to determine the translation rule of the transformationFrom the question, we have the following parameters that can be used in our computation:
Pre-image: L(-4,0), M(-2,0) and N(-3,-3)
Image: L'(1,1), M'(3,1) and N'(2,-2)
The translation rule is calculated as
(x, y) = L' - L
Substitute the known values in the above equation, so, we have the following representation
(x, y) ⇒ (x + 1 + 4, y + 1 - 0)
Evaluate
(x, y) ⇒ (x + 5, y + 1)
Hence, the translation is (x, y) ⇒ (x + 5, y + 1)
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1. 5x - 8 < 17
It needs to be graphed on a number line.
Answer: x < 5
What does this mean?
This simply means that any point that is five or below is going to be outlined.
How do I do it?
It's as simple as drawing a point at value 5, and everything below is going to contain a line.
Representation
-----------------------------------------------o
11. Engineering The maximum load for a certain elevator is 2000 pounds. The total
weight of the passengers on the elevator is 1400 pounds. A delivery man who weighs
243 pounds enters the elevator with a crate of weight w. Write, solve, and graph an
inequality to show the values of w that will not exceed the weight limit of the elevator.
The inequality to show the values of [w] that will not exceed the weight limit of the elevator is w + 1643 ≤ 2000. On solving the inequality, we get w ≤ 357. The graph of the inequality is attached.
What is inequality?In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.An inequality is a mathematical relationship between two expressions and is represented using one of the following -≤ : less than or equal to
≥ : greater than or equal to
< : less than
> : greater than
≠ : not equal to
Given is the maximum load for a certain elevator is 2000 pounds. The total weight of the passengers on the elevator is 1400 pounds. A delivery man who weighs 243 pounds enters the elevator with a crate of weight [w].
We can write the inequality as follows -1400 + 243 + w ≤ 2000
w + 1643 ≤ 2000
Solving the inequality, we get -w + 1643 ≤ 2000
w ≤ 2000 - 1643
w ≤ 357
Refer to the graph attached.Therefore, the inequality to show the values of [w] that will not exceed the weight limit of the elevator is w + 1643 ≤ 2000. On solving the inequality, we get w ≤ 357. The graph of the inequality is attached.
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Explain how to solve 2^(x + 1) = 9 using the change of base formula log base b of y equals log y over log b. Include the solution for x in your answer. Round your answer to the nearest thousandth
The solution of the given expression is equal to 2.17.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is [tex]2^{x+1} = 9[/tex]. The expression will be solved by using the logarithmic property below,
[tex]2^{x+1}=9[/tex]
Take logs on both sides,
(x+1) ln(2) = ln(9)
(x+1) = ln(9) / ln(2)
x + 1 = 3.17
x = 2.17
Hence, the expression will be solved by taking log on both sides.
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What is the slope of the line passing through (9,4) and (3,9)
Answer:
[tex]\sf m=-\frac{5}{6}[/tex]
Step-by-step explanation:
The formula to find the slope is :
[tex]\sf m=\frac{y_1-y_2}{x_1-x_2}[/tex]
For that, let us use the given two coordinates.
( 9 , 4 ) ⇒ ( x₁ , y₁ )
( 3 , 9 ) ⇒ ( x₂ , y₂ )
Let us solve it now.
[tex]\sf m=\frac{y_1-y_2}{x_1-x_2}\\\\\sf m=\frac{4-9}{9-3}\\\\\sf m=-\frac{5}{6}[/tex]
Simplify 4x - 7 + 12x - 3.
Answer:2(8x-5)
Hope this helps!
2. How many points of inflection will f(x) = 3x5+2x4 - 5x - 12 have?
5
3
2
4
2 points of inflection will f(x) = 3x5+2x4 - 5x - 12 have.
What is Inflection points definition?
An inflection point is a point on the graph at which the second derivative is equal to zero or undefined and changes sign.
The characteristic that every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. A mapping from A to B will only be a function if every element in set A has one end and only one image in set B. Let A & B be any two non-empty sets.
If [tex]$f^{\prime \prime}(x) > 0$[/tex]then f(x) concave upwards.
If [tex]$f^{\prime \prime}(x) < 0$[/tex]then f(x) concave downwards.
[tex]$$f^{\prime \prime}(x)=126 x^5+40 x^3$$[/tex]
Show Steps
Find intervals: Concave Downward: [tex]-\infty < x < 0$, Concave Upward: $0 < x < \infty$[/tex]
Plug x=0 into [tex]$3 x^7+2 x^5-5 x-12: \quad-12$[/tex]
(0,-12)
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What is an equation of a line that passes through the points (1, 4) and (2, 9) in
5)
point-slope form? Analyze the steps and fill in the blanks. (4pts)
First, use the two given points to find the slope.
m=
Уг-У1
Use the slope and one point to write an equation of the line in
point-slope form.
Point-slope form of a linear equation.
Substitute
The equation of line in point-slope form of the line, is y = 5x - 1.
What is point - slope form of the line?
The general form of a linear equation is y - y1 = m(x - x1).
It draws attention to the line's slope and one of the line's points (that is not the y-intercept).
Given:
The line passes through the points (1, 4) and (2, 9).
We have to find the equation of line in point - slope form.
First to find the slope from the given points.
Since,
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
Here, [tex](x_1, y_1) = (1, 4), (x_2, y_2) = (2, 9)[/tex]
So, [tex]m = \frac{9-4}{2-1} = 5[/tex]
Now consider, the point slope form of the line
[tex]y-y_1=m(x-x_1)[/tex]
Plug [tex]m = 5, (x_1, y_1) = (1, 4)[/tex]
⇒
[tex]y - 4=5(x-1)\\y-4=5x-5\\y=5x-5+4\\y=5x-1[/tex]
Hence, the equation of line in point-slope form of the line, is y = 5x - 1.
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HELPPPPP ME NOW PLEASE
Write y=1/8x+7 in standard form unsung integers.
A. 8x-y=56
B. -x+8y=56
C. -x-8y=56
D. -x+8y=56
Answer:
-x + 8y = 56
Step-by-step explanation:
.................
One of the tallest ferris wheels in the world is in las vegas. It has a diameter, , of 520 feet. The circumference of the ferris wheel represents the distance traveled by a passenger after one full rotation. The circumference can be determined using the expression. What is the distance traveled, in feet, by passengers on each rotation of the ferris wheel? record your answer to the nearest tenth of a foot.
Answer:
Below
Step-by-step explanation:
Circumference of a circle = pi * diameter
circumference of ferris wheel = 3.14159 * 520=1633.6 ft
give a point estimate (mean) for the average height of all people at the place where you work. start by putting the 20 heights you are working with into the blue data column of the spreadsheet. what is your point estimate, and what does this mean?
A point estimate (mean) for the average height of all people at the place where you work is 62.26
Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.
In statistics, the mean is one of the measures of central tendency, apart from the mode and median. Mean is nothing but the average of the given set of values. It denotes the equal distribution of values for a given data set.
Given,
Number of observations = 20
Mean = sum of all observation / number of observations
Mean = 66 +65 +66+ 67+ 62+ 70+ 69+ 68+ 71+ 78+ 61+ 62.5+ 64+ 64.2+ 64.3+ 58+ 60+ 63+ 65+ 66.2 / 20
Mean = 1245.2 / 20 = 62.26
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1. Simplify the following expressions:
10
a. 2¹⁰.2
-4
Answer:1020.2
Step-by-step explanation:
When Lisa increased her speed in letter c,
the increase took two seconds. What was her acceleration?
Lisa's change in speed is 4 miles per hour.Lisa's acceleration is 2 miles per hour.
What was her acceleration?According to the question,
The speed of Lisa is = 3 miles per hour
A dog starts to chase her, and she speeds up to seven miles per hour.
The change in speed after dog chase her is,
= 7 miles per hour - 3 miles per hour
= 4 miles per hour
Lisa's change in speed is 4 miles per hour.
When Lisa increased her speed in letter c, the increase took two seconds.
Then,
The Lisa acceleration is,
Acceleration = Change in speed/Change in time
Acceleration = 4/2
Acceleration = 2 per mail.
Hence, Lisa's acceleration is 2 miles per hour.
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A taxi company charges $1.00 for a ride, and an additional $0.30 for each mile traveled. Write the equation that describes the relationship between the number of miles M and the total cost of each ride C.
Answer:
C = 0.30m + 1.00
Answer:
C= $1,00 +(M×$0,30)=$1.00+$.30M
Step-by-step explanation:
How do you answer this question?
The value of x for the given function at the value of y = 4 will be 2.536.
What is coordinate geometry?A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.
Given that the function is y = x² - x. On drawing the graph of the function y = x² - x we get the parabola at the vertex of ( 0.5,-0.25).
When we plot the coordinate y = 4, the value of the coordinate x on the graph will be x = 2.536. The graph of the function is attached with the answer below.
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A sporting goods manager was selling a ski set for a certain price. The manager offered the markdowns shown, making the one-day sale price of the ski set $327. Find the original selling price of the ski set.
The original selling price of the ski is $385.
How to calculate the price?From the information, the sporting goods manager was selling a ski set for a certain price. The manager offered the markdowns as 15% making the one-day sale price of the ski set $327.
Let the original selling price of the ski be x.
This will be:
x - (15% × x) = 327
0.85x = 327
Divide
x = 327 / 0.85
x = 385
The original price is $385.
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Complete question
A sporting goods manager was selling a ski set for a certain price. The manager offered the markdowns as 15% making the one-day sale price of the ski set $327. Find the original selling price of the ski set.
suppose a juice box contains 30% juice with the remaining portion of the drink composed of water. what is the solute in this type of juice box?
Suppose a juice box contains 30% juice with the remaining portion of the drink composed of water alcohol is the solute in this type of juice box.
Ethanol; Ethanol, a drab liquid with a pleasing scent this is produced evidently from fermentation through yeasts and different microorganisms. It is utilized in alcoholic beverages, as a solvent, and withinside the manufacture of different chemicals. Ethanol is a fairly poisonous and colorless compound.
Alcohol is the solute in this type of juice box is the solvent as alcohol is easily soluble as the solvent and has best property of a solute and csn pass through the semipermeable permeability and others solvent also. The alcohol is actually acting as the solute here to dissolve the solvent.
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What is the value of 24 + x ÷ 12 when x = −180?
17
9
−13
−178
If you don't know the answer please do not type random stuff or you'll see what ima do
The value of the expression 24 + x ÷ 12 when x = −180 is (b) 9
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the value of the expression?From the question, we have the following parameters that can be used in our computation:
24 + x ÷ 12
Also, we have the value of the variable to be
x = −180
Substitute the known values in the above equation, so, we have the following representation
24 - 180 ÷ 12
Evaluate the quotient in the above equation
So, we have the following representation
24 - 180 ÷ 12 = 24 - 15
Evaluate the difference in the above equation
So, we have the following representation
24 - 180 ÷ 12 = 9
Hence, the value of the expression is (b) 9
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Help me pls pls I been stuck om this question for 5 hours now help me pls
The volume of the tunnel is 225.476cm³
How to find volume of objects?We should know that the volume of an object entails the quantity of things it can hold at a particular time.
The volume of the tunnel = Volume of semi circle + volume of the rectangle
This is given by
V=3/4[tex]\frac{4}{3} \pi r^{3}[/tex] + lbh
volume of the tunnel = 4/3*3.142*(5/2)³ + 4*5*8
Simplifying the expression
(65.476 + 160)cm³
Volume = 225.476cm³
Given that the car exhaust at 10m³
226cm = 2.26m
Note that 60 seconds = 1 Minute
Therefore 10*2.26=22.6m
=22.6/60 = 3 hours, 46 mins and 2 seconds.
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Rectangle ABCD is dilated with a center at (0, 0) and a scale factor of 1. What is the perimeter of the dilated rectangle? Enter the answer as a whole number in the box.
units
Answer:
12 units
Step-by-step explanation:
You want to know the perimeter of rectangle ABCD after it has been dilated by a factor of 1.
PerimeterThe original rectangle ABCD has a perimeter of ...
P = 2(L +W) = 2(4 +2) = 12
The perimeter of the dilated rectangle is the original perimeter multiplied by the dilation factor:
P' = 12·1 = 12
The dilated rectangle has a perimeter of 12 units.
__
Additional comment
Dilation by a factor of 1 changes nothing at all. The center of dilation is irrelevant.
If Santa Claus ate two cookies from every child on Earth, how many cookies would he eat over one Christmas Eve?
Answer:
three billion eight hundred million
Step-by-step explanation:
Find the y intercept y = – 17 x + 12.
Answer: 12
Step-by-step explanation:
The y-intercept in the equation that is in slope-intercept form is the constant.
