This equation x + (x + 1) + (x + 2) = negative 21 will be used.
Let the first Number is x.
We have to take 3 consecutive integers.
second Number is x+1
third Number is x+2.
Sum of these 3 consecutive integers is x+(x+1)+(x+2).
Sum of these 3 consecutive integers is given as negative21.
so we can write x+(x+1)+(x+2)=negative 21.
by using above equation we can find the value of 3 numbers.
So the final equation will be x + (x + 1) + (x + 2) = negative 21.
Given Question is incomplete, Complete Question here:
Three consecutive integers have a sum of –21. Which equation can be used to find the value of the three numbers? x + x + x = negative 21 x + 2 x + 3 x = negative 21 x + (x + 1) + (x + 2) = negative 21 x + (x + 2) + (x + 4) = negative 21
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please help!! easy question but cant seem to figure out
Viv and Ian were trying to describe parts of the expression 5(x+7)
Viv said, "The entire expression is the product of 3 factors."
Ian said, "On its own, (x+7) sum with 2 terms."
The expression 5(x + 7) has a sum of two terms 5x and 35.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, an expression 5(x + 7).
Now distributing 5 to x and 7 we get 5x + 35.
So, The expression 5(x + 7) has the sum of two terms.
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what is the ratio of cups to flour to eggs
Answer:
Step-by-step explanation:
Answer= use 2 eggs per 1 cup of flour to make 1 serving.
Need help ASAP
2^7x2^-2 +2^9/2^4 +2^3/2^-2
Show that C = a×2^b where a and b are two integers to be determined
The problem is based on laws of exponents and answer to this Question is a = 2 and b = 14
What are laws of exponents?
Laws which are used to solve the problems including the exponents are called laws of exponents
Solution:
As we can clearly see in whole expression 2 is present in every term
By laws of Exponents we can take 2 common out and we can easily express this thing in given form that a multiplied 2 rays to power b
When we solve this expression we get
this expression equal to 2^15
which we can write 2×2^14
hence on comparing we get a = 2 and b = 14
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Help I don't know how to do this
Answer:
Step-by-step explanation:
a(n) = a(1) + (n-1)d
a(n) = -9 + (n-1) x (-6-(-9)
a(n) = -9 + (n-1) x (-6 +9)
a(n)= -9 + (n-1) x 3
a(n) = -9 + 3n - 3
a(n) = 3n - 12
a(30) = 3 x 30 - 12
a(30) = 90 - 12
a(30) = 78
solve the system of equations using any method
3x-3= y
6x-5y=12
(please i need help im begging you)
Answer:
(1/3, - 2)-------------------------------
Given system3x - 3 = y6x - 5y = 12Solve by substitution6x - 5(3x - 3) = 126x - 15x + 15 = 12- 9x = 12 - 15- 9x = - 3x = - 3 / - 9x = 1/3Find y:
y = 3 * 1/3 - 3y = 1 - 3y = - 2Identify the sampling technique used in the given scenario. The English department is interested in overall performance in its entry-level 101 course. The department chair selects every tenth student's final grade from a list of all students enrolled in the course and calculates the average final grade.
The sampling technique used in the given scenario is Systematic sampling technique.
Systematic sampling technique
Systematic sampling is a probability sampling technique in which researchers randomly choose individuals of a population at regular intervals. The sampling interval, or fixed periodic interval, is calculated by dividing the population size by the required sample size.
Types of Systematic sampling technique
A systematic sample can be generated in three ways:
Systematic random sampling: The most common type of systematic sampling in which the subject is chosen at a predefined interval.
Linear systematic sampling: Instead of picking the sample interval at random, a skip pattern is constructed by following a linear path.
Circular systematic sampling: It occurs when a sample begins from the same spot where it ends.
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5) Simplify the expression and identify any restrictions on x.
Answer:
attached in the file
I need help with 9 10 and 11
Which relation is a function?
Select all that apply.
Responses
{(2, 1), (2,3), (3, 4), (4,5)} {(2, 1), (2,3), (3, 4), (4,5)}
{(2, 1), (−2,1), (3, 2), (4,2)} {(2, 1), (−2,1), (3, 2), (4,2)}
{(−1, 2), (−2,2), (−3, 2), (−4,2)} {(−1, 2), (−2,2), (−3, 2), (−4,2)}
{(2, 1), (2,3), (−2, 5), (−2,7)} {(2, 1), (2,3), (−2, 5), (−2,7)}
{(2, 2), (3,3), (4, 4), (5,5)}
The relations which are functions as required to be identified in the task content are;
{(2, 1), (−2,1), (3, 2), (4,2)} {(−1, 2), (−2,2), (−3, 2), (−4,2)}{(2, 2), (3,3), (4, 4), (5,5)}Which relations are functions among the given answer choices?It follows from the task content that the relations which are functions among the given answer choices are to be identified.
Since the definition of a function is such that; a function is a special kind of relation in which case only one output value is assigned to each input values.
Put simply, a function has only one output value for each input value.
Therefore, it follows from the definition above that the relations which are functions among the given answer choices are as listed above.
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Line l Intersects line m. Find the value of a,b, x. Give reasons
The angles in the intersected lines are as follows:
a = 80 degreesb = 80 degreesx = 92 degreesHow to find angles when lines intersect?When lines intersect angle relationships are formed such as vertically opposite angles, linear angles etc.
Angle a is vertically opposite to angle b.
Vertically opposite angles are congruent.
Therefore,
∠a ≅ ∠b
Hence,
x + 8 = 100(vertically opposite angles)
x = 100 - 8
x = 92
b + x + 8 = 180(sum of angles on a straight line)
b + 92 + 8 = 180
b = 180 - 100
b = 80 degrees.
Hence,
a = 80 degrees
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What is the domain of the function
f(x) = 2x + 3
when the range is {3, 5, 9}?
Answer:
Domain: {9, 13, 21}
Step-by-step explanation:
BRAINLIEST PLEASE!!!Answer:
(0,1,3)Step-by-step explanation:
f(x)=2x+3let y= f(x)y=2x+3interchanging x and y in the expression x=2y+3making y the subject in the equation y=(x-3)/2f(x)-¹=(x-3)/2when x= 3 =(3-3)/2 =0when x=5 =(5-3)/2 = 1when x= 9 =(9-3)/2 = 3If you vertically stretch the exponential function f(x) = 2x by a factor of 4, what is the equation of the new function?
The equation of the new function is g(x) = 4(2ˣ)
How to determine the equation of the new function?The exponential equation is given as
f(x) = 2ˣ
Then, we have the transformation to be:
Vertically stretch by a scale factor of 4
The scale factor can be represented as k
So, we have
k = 4
The rule of vertical stretch by a scale factor of k is represented a
g(x) = kf(x)
So, we have
g(x) = 4 * 2ˣ
This gives
g(x) = 4(2ˣ)
Hence, the equation is g(x) = 4(2ˣ)
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Determine if the table how a proportional relationhip. X 25. 6 72. 8 77. 2 y 6. 4 18. 2 19. 3 Ye, it i proportional becaue all y over x ratio are equivalent to one fourth. Ye, it i proportional becaue all y over x ratio are equivalent to one third. No, it i not proportional becaue 25. 6 over 6. 4 doe not equal 18. 2 over 72. 8. No, it i not proportional becaue 18. 2 over 72. 8 doe not equal 77. 2 over 19. 3
Proportional relationship for the given table is true and is define as
Yes, it is proportional because all y over x ratio are equivalent to one fourth.
As given in the question,
Value of x and y in the given table are :
x : 25. 6, 72. 8, 77. 2
y : 6. 4, 18. 2, 19. 3
To check the proportional relationship there should exist constant of proportionality that ratio of corresponding y/x should be constant.
y / x for all the values of x and y:
First values:
y /x = 6.4 / 25.6
= 0.25
Second values:
y/x = 18.2/ 72.8
= 0.25
Third values :
y /x = 19.3/ 77.2
= 0.25
0.25 is equivalent to One fourth ( 1/4).
Constant of proportionality exist = 0.25 or One fourth.
Therefore, in the table first option: yes, it is proportional because all y over x ratio are equivalent to one fourth is correct.
The complete question is:
Determine if the table how a proportional relationship.
x : 25. 6, 72. 8, 77. 2
y : 6. 4, 18. 2, 19. 3
Yes, it is proportional because all y over x ratio are equivalent to one fourth.
Yes, it is proportional because all y over x ratio are equivalent to one third.
No, it is not proportional because 25. 6 over 6. 4 doe not equal 18. 2 over 72. 8.
No, it is not proportional because 18. 2 over 72. 8 doe not equal 77. 2 over 19. 3
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The graphs of functions f(x) and g(x) = f(x) + k are shown: Graph of line f of x going through ordered pairs 0, 1 and 2, 6. Graph of line g of x going through ordered pairs 0, negative 1 and 2, 4. What is the value of k? a k = 2 b k = −2 c k = 1 d k = −1
Based on the graphs of functions f(x) and g(x) = f(x) + k, the value of k is: B. k = -2.
What is y-intercept?In Mathematics, the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).
Since the graph of the line for function f(x) passes through the ordered pairs (0, 1) and (2, 6), its y-intercept is given by:
y = f(0) = 1.
Since the graph of the line for function g(x) passes through the ordered pairs (0, -1) and (2, 4), its y-intercept is given by:
y = g(0) = -1.
From the information provided above, we have the following function:
g(x) = f(x) + k
g(0) = f(0) + k
Making k the subject of formula, we have:
k = g(0) - f(0)
k = -1 - 1
k = -2.
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if the mean and mode are 15 and 10, respectively, then determine the potential range of the median for a positively skewed distribution
The median will be greater than 10 and less than 15.
Given,
The mean of the skewed distribution = 15
The mode of the skewed distribution = 10
We have to find the potential range of the median for a positively skewed distribution;
Here,
The empirical relationship between mean, median, and mode for a frequency distribution that is positively skewed is mean > median > mode. Based on this, the range of the median is 15 > median > 10 if the mean is 15 and the mode is 10.
Therefore,
The median will be higher than 10 and lower than 15.
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Let the random variable b represent the number of books a student buys at the next book fair. What is the expected value of b ?.
The expected value of the random variable b is given as follows:
2.404 books.
How to obtain the expected value of a discrete probability distribution?The expected value of a discrete probability distribution is given by the sum of each outcome of the distribution multiplied by it's respective probability.
From the histogram given by the image at the end of the answer, the distribution is given as follows:
P(X = 1) = 0.285.P(X = 2) = 0.333.P(X = 3) = 0.168.P(X = 4) = 0.136.P(X = 5) = 0.063.P(X = 6) = 0.015.Then the expected value of the random variable b is obtained as follows:
E(X) = 1 x 0.285 + 2 x 0.333 + 3 x 0.168 + 4 x 0.136 + 5 x 0.063 + 6 x 0.015 = 2.404 books.
Missing InformationThe histogram is given by the image at the end of the answer.
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The table shows the ingredients for one batch of barbecue sauce. Anne has 9 cups of ketchup and makes the greatest number of whole batches of barbecue sauce possible. How much ketchup remains?
Answer:
hi do you mind making the question a bit clear? where is the table?
Step-by-step explanation:
help meeeeeeeeeeeeeeeeeee pleaseee!!!!help meeeeeeeeeeeeeeeeeee pleaseee!!!!help meeeeeeeeeeeeeeeeeee pleaseee!!!!help meeeeeeeeeeeeeeeeeee pleaseee!!!!
a. [tex]123.1(1.069)^3 \approx 150.4[/tex]
b. [tex]123.1(1.069)^{20} \approx 467.5[/tex]
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeehelp meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeehelp meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Step-by-step explanation:
b.) 8/7≈ 1.1
Final.) and then using the exponential decay formula, 18.1 will be left after
Given f(x)=3x+4f(x)=3x+4, find f(4)f(4).
Answer:
f(x) = 3x + 4
f(4) = 3(4) + 4 = 12 + 4 = 16
prove: if the bisector of an exterior angle of a triangle is parallel to a side of the triangle, the triangle is isosceles
The proof that if bisector of an exterior angle of a triangle is parallel to a side of triangle, triangle is isosceles is shown below .
In the question ,
it is given that ,
the angle bisector of the exterior angle of a triangle is parallel to a side .
we have to prove that the triangle will be an isosceles triangle .
In the triangle ABC given below , AB is extended to AD ,
SO , the exterior angle will be angle DAC ,
let AE be the bisector of the the angle .
So , the equal angles are angle DAC and angle EAC .
it is given that AE is parallel to BC , where BC is base .
we know that ,
if any line intersects two parallel lines then every pairs of alternative Interior angles are same and also their corresponding angles are equal .
Here AE is parallel to BC and line BD intersects them ,
So , angle ABC = angle DAE ( corresponding angles )
angle ACB = angle EAC ( alternate angles )
Now , as AE is the bisector of angle DAC ,
we have , angle DAC = angle EAC
So , we get , angle ABC = angle ACB .
In triangle triangle ABC two angles are equal so , the sides opposite to angles to angles will also be equal
that means , AB=AC
Hence , the given Triangle is an isosceles triangle .
Therefore , it is proved that the triangle ABC is an isosceles triangle .
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This graph shows the revenue, cost, and profit functions of a company. How can this company become profitable?
A graph shows the Price per Unit on the x-axis and dollars on the y-axis. A downward parabola revenue vertex at (25, 12,000) intercepts the origin and x-axis at (30, 0) linear function costs intercept the y axis at (0, 13,000).
A.
by increasing its production
B.
by increasing its prices
C.
by reducing its costs
D.
by reducing its prices
Based on this graph which shows the revenue, cost, and profit functions of a company, the way in which this company can become profitable is: C. by reducing its costs.
What is a profit?In Mathematics, a profit can be defined as a measure of the amount of money that is generated when the cost price is deducted from the selling price (revenue) of a good or service, which is usually provided by producers.
Mathematically, the profit made by an entrepreneur or business organization can be calculated by using this mathematical expression:
Profit = Revenue - Cost
In this scenario, the most effective and efficient way in which this company can become profitable is simply by reducing (lowering) its costs because it is incurring more cost than the amount of revenue it generates.
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If the lowest price in the past year occurred 35 days ago, find the approximate average change per day since then. a. $2.08 b. $2.64 c. $0.90 d. $2.99
The approximate change per day since the lowest price occurred 35 days ago, is a. $2.08.
How to find the approximate average change?The approximate average change can be found by the formula :
= ( Current price of stock - Lowest price ) / Number of days since lowest price
Current price of Dagofi Radar stock = $ 130. 58 closing price
Lowest price = $ 57. 71
The approximate average change is:
= ( 130. 58 - 57. 71) / 35
= 72. 87 / 35
= $ 2.08
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Missing part of question:
Consider today's stock listing for Dagofi Radar, shown below.
52 wk High
52 wk Low
Symbol
Div.
Close
Net Change
162.22
57.71
DFR
9.75
130.58
-2.64
Michael swam 2,000 yards on each of eighteen days.
The scatterplot above shows his swim time for and
corresponding heart rate after each swim. The line of
best fit for the data is also shown. For the swim that
took 34 minutes, Michael's actual heart rate was
about how many beats per minutes less than the rate
predicted by the line of best fit?
A) 1
B) 2
C) 3
D) 4
Michael's actual heart rate was about 2 beats per minutes less than the rate predicted by the line of best fit. The correct option is B
What is a scatterplot?A scatterplot is a data visualization that depicts the relationship between two numerical variables. Each dataset member is plotted as a point whose x-y coordinates correspond to its values for the two variables.
On each of the eighteen days, Michael swam 2,000 yards. The scatterplot above depicts his swim time and heart rate after each swim. The data's best fit line is also shown.
From the graph the actual heart rate=150
but calculated heart rate from best fit line=148
Difference between actual and calculated=150−148=2
Option B is correct.
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Examine the table, which represents the number of guests visiting a museum during a period of time.
If the relationship between hours and guests is proportional, what is the value of h?
Enter your answer as a number, like this: 42
Answer:
7
Step-by-step explanation:
649-531=118
We know that there are 118 more guests per hour.
Divide 826 by 118 to get 7.
Answer: 7
Step-by-step explanation:
The first line of the table is 2 and 236 if you divide 236 by 2 you get 118
Then after that you times it by any number after 5.5 until you get 826.
7(x-1)=3x+2 in a improper fraction
Answer:x=9/4 nine over 4 for improper fraction I hope this is helpful mark me brainlist if this sounds good
Step-by-step explanation:
7(x-1)=3x+2
Distribute through the parentheses
7x-7=3x+2
Move the variable to the left-hand side and change its sign
7x-7-3x=2
or Move the constant to the right-hand side and change its sign
7x-7-3x=2
Collect like terms
4x=2+7
And then Add the numbers
4x=9
Divide both sides of the equation by 4
x=9/4
Mixed number is 2 1/4
8
Rachel works at 'Best Price Cars' and earns $9 per hour plus 4% commission on every car she sales. She worked 40 hours last week and sold 36,000 in cars. What
was Rachel's total income last week?
Type your answer...
I need the answers
Rachel's total income is $13320.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Rachel works at 'Best Price Cars' and earns $9 per hour plus 4% commission on every car she sales.
Commission = 9 x 0.04 = $0.36
Commission on 36000 cars = $12960
By working 40 hours he earn = 9 x 40 = $360
Hence, the total income = 360+ 12960 = $13320
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A supply company manufactures copy machines. The unit cost C (the cost in dollars to make each copy machine) depends on the number of machines made. If
x machines are made, then the unit cost is given by the function C(x)=1.2²-600x+82,738. What is the minimum unit cost?
Do not round your answer.
The minimum unit cost is 7738 when the function is C(x)=1.2x²-600x+82,738
What is meant by unit cost?A company's unit cost is the cost of producing, storing, and selling one unit of a specific product. Unit costs encompass all fixed and variable production costs. A cost unit is a quantity measuring unit for a product or service.
A unit cost is the overall cost incurred by a business to manufacture, store, and sell one unit of a specific product or service. Unit costs are the same as cost of goods sold (COGS). This accounting metric incorporates all fixed and variable expenses related with the manufacture of a good or service.
Given,
C(x)=1.2x²-600x+82,738
Minimum value [tex]C_{min}[/tex]=c-(b²/4a)
Where a=1.2, b=-600, c=82738
[tex]C(x)_{min}[/tex]=82738-((-600)²/4(1.2))
=82738-(360000/4.8)
=7738
Therefore, the minimum unit cost is 7738.
Hence, the minimum unit cost is 7738 when the function is C(x)=1.2x²-600x+82,738
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Student are going on a field trip to a play. The play i elling kid ticket and adult ticket. They old a total of 60 ticket. One kid ticket ell for $3 while the adult ticket i $5. They made a profit of $220 that day. How many kid ticket were old?
Number of kids ticket is 40
What do you mean by system of linear equation?
A set of two linear equations with two variables is a system of linear equations. There are infinitely many possible solutions to a linear equation with two variables. There can be a single solution to a system of two linear equations with two variables that satisfies both solutions. It is necessary to combine two equations with two variables into one equation with one variable while solving a system of equations.
Total number of tickets = 60
Cost of 1 kid ticket = $3
Cost of 1 adult ticket = $5
Total profit = $220
Let number of kid tickets = x
number of adult tickets = y
According to question:
x + y = 60 ......(1)
3x + 5y = 220 ........(2)
Substitute the value of x from eq(1) to eq(2)
3(60 - y) + 5y = 220
180 - 3y + 5y = 220
180 + 2y = 220
2y = 220 - 180
2y = 40
y = 40/2
y = 20
Substitute this value of y in eq(1)
x + 20 = 60
x = 60 - 20
x = 40
Therefore, number of kids ticket is 40
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a penny is thrown from the top of a 52.6-meter building and hits the ground 3.31 seconds after it was thrown. the penny reached its maximum height above the ground 0.85 seconds after it was thrown. define a quadratic function, h , that expresses the height of the penny above the ground (measured in meters) as a function of the number of seconds elapsed since the penny was thrown, t.
The quadratic function which models the motion of the penny is
h(t) = -4.9t² -0.327761 t + 52.6
and the maximum height reached is 57.43
h(t) = - 0.5gt² + vt + h
g = 9.8 m/s²
h = 52.6 m
v = ?
For v,
h(t) = -0.5gt² + vt + 52.6
h(t) = - 4.9t² + vt + 52.6
Time when penny hits the ground ; t = 3.31
h(3.31) = 0
0 = -4.9(3.31)² + v(3.31) + 52.6
0 = -53.68489 + 3.31v +52.6
3.31v = -1.08489
v = -1.08489/3.31
v = -0.327761 m/s
Therefore,
h(t) = -4.9t² -0.327761 t + 52.6
2.) Maximum height of the penny above the ground
t = 0.85 seconds
h(0.85) = -4.9(0.85^2)-0.327761 (0.85) + 52.6
Maximum height reached = 57.43 meters
Therefore, the maximum height reached is 57.43 meters.
An object changing its position with regard to time is referred to as motion. Motion is mathematically characterised in terms of displacement, distance, velocity, acceleration, and speed as well as the observer's frame of reference and the measurement of the change in the body's position with respect to that frame over time. Kinematics is the area of physics that studies how motion is affected by forces, whereas dynamics is the area that studies how motion is affected by forces.
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