Which equation describes how the parent function, y=x², is vertically stretched by a factor of 4?Oy=x³+4Oy=(x+4)³Oy-4x²Oy=x*

\(\cfrac{40.5}{8.1} ~~ \begin{cases} 40.5\implies \frac{405}{10}\\\\ 8.1\implies \frac{81}{10} \end{cases}\implies \cfrac{ ~~ \frac{405}{10} ~~ }{\frac{81}{10}}\implies \cfrac{405}{10}\cdot \cfrac{10}{81}\implies \cfrac{405}{81}\cdot \cfrac{10}{10} \\\\\\ \cfrac{5\cdot 81}{81}\cdot \cfrac{10}{10}\implies \cfrac{5}{1}\cdot \cfrac{81}{81}\cdot \cfrac{10}{10}\implies \cfrac{5}{1}\cdot 1\cdot 1\implies \cfrac{5}{1}\)

Number of car sold are 98.

Number of trucks sold are 66.

Given,

Dealer 1 sold 164 cars and trucks and dealer 2 sold 229 cars and trucks .

Let number of cars sold are x.

Let number of cars sold of y .

Now,

For dealership 1 equation will be,

x + y = 164  ......(1)

For dealership 2 equation will be,

As the cars are sold twice and trucks are sold half .

2x + y/2 = 229......(2)

Solving 1 and 2,

y = 66

x = 98

Thus number of car sold are 98.

Thus number of trucks sold are 66.

Learn more about linear equation,

https://brainly.com/question/29111179

#SPJ1

The ordered pair that represents the point plotted and labeled A include the following: (−1, 2).

In Mathematics and Geometry, the translation of a graph to the left simply means a digit would be subtracted from the numerical value on the x-coordinate of the pre-image:

g(x) = f(x - N)

Conversely, the translation of a graph upward means a digit would be added to the numerical value on the y-coordinate (y-axis) of the pre-image.

g(x) = f(x) + N

Note: "Point A is one unit left and two units up from the origin. "

Since point A is one unit left and two units up from the origin (0, 0), we can logically deduce the following:

(x, y)                   →           (x - 1, y + 2)

Origin (0, 0)        →           (0 - 1, 0 + 2) = point A (-1, 2).

Read more on function and translation here: brainly.com/question/31559256

#SPJ1

Answer:

A: -2 + 3i

B: -1 + -1i

C: 3 + -4i

D: 4 + 1i

Step-by-step explanation:

These are the answers, Basically just normal graphing. run/rise.

I hope this helps! :)))))

Answer:

the product of 2a+3b-c and2a+3b-c is(2a+3b-c)²

Answer:

\(\huge\boxed{\sf x = 9}\)

Step-by-step explanation:

3(x + 4) - 11 = 28

3(x + 4) = 28 + 11

3(x + 4) = 39

3x + 12 = 39

3x = 39 - 12

3x = 27

x = 27/3

\(\rule[225]{225}{2}\)

Answer: -1 Is the answer.

Answer:

x = 11

Step-by-step explanation:

8x + 5y = 48

8x + 5(-8) = 48  ==> plugin y = -8

8x + (-40) = 48  ==> simplify

8x - 40 = 48

8x = 88  ==> add 40 on both sides to simplify x

x = 11 ==> divide both sides by 8 to isolate x

Answer:

\(8x + 5y = 48 \\ put \: y = - 8 \\ 8x + 5 \times - 8 = 48 \\ 8x + ( - 40) = 48 \\ 8x - 40 = 48 \\ 8x = 48 + 40 \\ 8x = 88 \\ x = \frac{88}{8} \\ x = 11 \: anwer \: \)

Hope it will help you...

Answer:

Step-by-step explanation:

To identify the year in which the population will reach 0, we need to determine the rate at which the population is decreasing, and use that rate to predict when the population will be 0.

We can use the two data points given to find the rate of population decrease. Let P be the population and t be the time in years since 2010. Then we have:

P(0) = 7900 (population in 2010)

P(2) = 7700 (population in 2012)

We can find the rate of population decrease by using the formula for the slope of a line:

slope = (P(2) - P(0)) / (t(2) - t(0)) = (7700 - 7900) / (2 - 0) = -100/year

The negative sign indicates that the population is decreasing, and the magnitude of the slope (-100/year) tells us the rate at which it is decreasing.

To find the year in which the population will reach 0, we can use the point-slope form of a line:

P - P(0) = slope * (t - t(0))

where P is the population, t is the time in years since 2010, P(0) is the population in 2010, and t(0) is 0 (the year 2010).

Substituting the known values, we get:

P - 7900 = -100 * (t - 0)

Simplifying, we get:

P = -100t + 7900

To find the year in which the population will reach 0, we set P = 0 and solve for t:

0 = -100t + 7900

100t = 7900

t = 79

Therefore, the population will reach 0 in the year 2010 + 79 = 2089.

The solution is, the population will reach 0 in the year 2089.

Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

here, we have,

To identify the year in which the population will reach 0, we need to determine the rate at which the population is decreasing, and use that rate to predict when the population will be 0.

We can use the two data points given to find the rate of population decrease. Let P be the population and t be the time in years since 2010. Then we have:

P(0) = 7900 (population in 2010)

P(2) = 7700 (population in 2012)

We can find the rate of population decrease by using the formula for the slope of a line:

slope = (P(2) - P(0)) / (t(2) - t(0))

         = (7700 - 7900) / (2 - 0)

         = -100/year

The negative sign indicates that the population is decreasing, and the magnitude of the slope (-100/year) tells us the rate at which it is decreasing.

To find the year in which the population will reach 0, we can use the point-slope form of a line:

P - P(0) = slope * (t - t(0))

where P is the population, t is the time in years since 2010, P(0) is the population in 2010, and t(0) is 0 (the year 2010).

Substituting the known values, we get:

P - 7900 = -100 * (t - 0)

Simplifying, we get:

P = -100t + 7900

To find the year in which the population will reach 0, we set P = 0 and solve for t:

0 = -100t + 7900

100t = 7900

t = 79

Therefore, the population will reach 0 in the year 2010 + 79 = 2089.

To learn more on simplification click:

brainly.com/question/28996879

#SPJ2

Answer:

   Title: Height of 11 Children (cm)         Key: 8|5 means 85

                          7 | 9

                          8 | 1 3 5 6 8 8

                          9 | 0 1 3 7

Step-by-step explanation:

Sorry I couldn't upload an image hope this helps : )                    

The value of x in the chord of the circle using the chord-chord power theorem is 0.

The chord-chord power theorem simply state that "If two chords of a circle intersect, then the product of the measures of the parts of one chord is equal or the same as the product of the measures of the parts of the other chord".

From the figure:

The first chord has consist of 2 segments:

Line segment 1 = 27

Line segment 2 = ( x + 16 )

The second chord also consist of 2 sgements:

Line segment 1 = 24

Line segment 2 = ( x + 18 )

Now, usig the Chord-chord power theorem:

27( x + 16 ) = 24( x + 18 )

Solve for x:

27x + 432 = 24x + 432

27x - 24x = 432 - 432

3x = 0

x = 0

Therefore, the value of x is 0.

Option D) 0 is the correct answer.

Learn more about the Chord-chord power theorem here: brainly.com/question/15298662

#SPJ1

Answer:

Step-by-step explanation:

As the slope between (1,0) and (2,2) is 2 and the slope between (2,2) and (4,4) is 1, we can tell that the parabola must be downward opening and have a vertex in the first quadrant

Possibly best to use the vertex form to make 3 equations with 3 unknowns

y = a(x - h)² + k

0 = a(1 - h)² + k  (i)

2 = a(2- h)² + k  (ii)

4 = a(4 - h)² + k  (iii)

subtract i from ii

2 = a((2 - h)² - (1 - h)²)

2 = a(4 - 4h + h² - (1 - 2h + h²))

2 = a(3 - 2h)

a = 2/(3 - 2h)

subtract i  from iii

4 = a((4 - h)² - (1 - h)²)

4 = a(16 - 8h + h² - (1 - 2h + h²))

4 = a(15 - 6h)

substitute for a

4 = (2/(3 - 2h))(15 - 6h)

4(3 - 2h) = 2(15 - 6h)

12 - 8h = 30 - 12h

4h = 18

h = 9/2

a = 2/(3 - 2(9/2))

a = - 1/3

0 = -1/3(1 - 9/2)² + k

k = 49/12

y = (-1/3)(x - 9/2)² + 49/12

expand to get y = ax² + bx + c form

y = (-1/3)(x² - 9x + 81/4) + 49/12

y = (-1/3)x² + 3x - 27/4) + 49/12

y = (-1/3)x² + 3x - 8/3

Answer:

100

Step-by-step explanation:

blue = 1

red = 2

(blue) 100

(red) 200

The inequalities are :

x + 31 < 1 ⇒ x < - 30 ⇒ x + 3 < -27

|x - 6| ≥ 2  ⇒x- 6 ≥ 2 and 6 - x ≤ 2

An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The most frequent application is to size-compare two integers on a number line.

The occurrence of an unfair and/or uneven distribution of opportunities and resources among the people that make up a society is referred to as inequality. To different individuals and in various settings, the word "inequality" may indicate different things.

Inequality is a connection between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance.

The inequalities are :

x + 31 < 1 ⇒ x < - 30 ⇒ x + 3 < -27

|x - 6| ≥ 2  ⇒x- 6 ≥ 2 and 6 - x ≤ 2

To learn more about Inequality refer to :

https://brainly.com/question/13589585

#SPJ1

The inverse of matrix A, if it exists, is:

A^(-1) = [7/43, 2/43; 10/43, 9/43]

To find the inverse of a matrix A, we need to determine if the matrix is invertible by calculating its determinant. If the determinant is non-zero, then the matrix has an inverse.

Given the matrix A = [9, -2; -10, 7], we can calculate its determinant as follows:

det(A) = (9 * 7) - (-2 * -10)

= 63 - 20

= 43

Since the determinant is non-zero (43 ≠ 0), we can proceed to find the inverse of matrix A.

The formula to calculate the inverse of a 2x2 matrix is:

A^(-1) = (1/det(A)) * [d, -b; -c, a]

Plugging in the values from matrix A and the determinant, we have:

A^(-1) = (1/43) * [7, 2; 10, 9]

Simplifying further, we get:

A^(-1) = [7/43, 2/43; 10/43, 9/43].

For more such questions on Inverse of matrix:

https://brainly.com/question/27924478

#SPJ8

A rectangle and two semicircles make up this figure. The perimeter of this figure is 423.52m.

The complete length of a shape's boundary is referred to as the perimeter in geometry. The perimeter of a shape is determined by adding the lengths of all of its edges and sides. Linear measurements like centimeters, meters, inches, and feet are used to express its dimensions. The area around a form's edge is known as its perimeter. The perimeter of a shape is always calculated by summing the lengths of its sides.

Perimeter=2*1/2πd+2a

d=68, a=105

Perimeter = 2*1/2*3.14*68+2*105

423.52m

Learn more about perimeter here

https://brainly.com/question/19819849

#SPJ1

Answer:

Mrs Barnes has the highest

Answer:

Distributive property

Step-by-step explanation:

8 x y = 8y, -8 x -2 = 16

Answer:

Step-by-step explanation:

Select the smaller fraction. 1/10 or 1/2

1/10 = 1 : 10 = 0.1

1/2 = 1 : 2 = 0.5

so your answer is 1/10

Each friend had originally 13 action figures before buying 11 more.

Given that there are 5 friends and each of them has x action figures in his or her collection. When they buy 11 more action figures, the total number of action figures they will have is 120.

a) We need to find an equation that models the problem. Let x be the original number of action figures that each friend had.

Therefore, the total number of action figures that each friend will have after purchasing 11 more is x + 11.

The total number of action figures will be 5(x + 11) = 5x + 55.

Now, according to the problem,5x + 55 = 120

This is our equation that models the problem.

b) We have to solve the equation 5x + 55 = 120 to find the original number of action figures, x, that each friend had before buying 11 more action figures.

5x + 55 = 120

5x = 120 - 55 (subtract 55 from both sides)

5x = 65x = 13

Therefore, each friend had originally 13 action figures before buying 11 more.

For more such questions on figures, click on:

https://brainly.com/question/24491627

#SPJ8

Answer:

2.4 hoped this helped

(let me know if it did) :)

The number of couches manufactured and sold in order to maximise the profit is 1560.

The demand function will be

p = 2700 - 0.75x

Here p = price per couch and x = number of couch

Total Fixed cost = $760000

Variable cost per couch = $360

Total cost = Fixed cost + variable cost

T(x) = 760000 + 360x

Revenue function will be

R(x) = Px

(2700 - 0.75x)x

2700x - 0.75x²

Since profit function = Pr(x)

Pr(x) = R(x) - T(x)

= 2700x - 0.75x² -760000 -360x

- 0.75x² + 2700x - 360x - 760000

For maximum profit

\(\frac{d}{dx}(Pr(x)) = 0\)

\(\frac{d}{dx}[-0.75x^{2} + 2340x -760000 ] = 0\)

-1.5x + 2340 = 0

x = 2340/1.5

x = 1560

The couches sold for maximum profit = 1560

Therefore, the number of couches manufactured and sold in order to maximise the profit is 1560.

To learn more about deman function refer here

https://brainly.com/question/15234429

#SPJ1

(x + 6) is the solution for the quadratic equation 5x² + 60x + 187 = 7

Given,

The quadratic equation;

5x² + 60x + 187 = 7

Arrange this in standard form;

5x² + 60x + 187 - 7 = 0

5x² + 60x + 180 = 0

We have to find the solution for this quadratic equation;

Quadratic formula ;

\(\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}\)

Here,

a = 5

b = 60

c = 180

Now,

\(\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}\) = \(\frac{-60(+-)\sqrt{60^{2}-4*5*180 } }{2*5}\) = \(\frac{-60(+-)\sqrt{3600-3600} }{10}\) = -60±0 / 10 = -60/10 = -6 = (x + 6)

That is,

The solution for the quadratic equation 5x² + 60x + 187 = 7 is (x + 6)

Learn more about quadratic equation here;

https://brainly.com/question/17177510

#SPJ4

Answer:

AC = 6

Step-by-step explanation:

x= 6

If you  need work I can send it

The domain of the rational expression (6-x)/(4x+20) is all real numbers except x = -5.

To find the domain of a rational expression, we need to identify any values of x that would result in division by zero. Division by zero is undefined in mathematics
In this case, we need to set the denominator, 4x+20, equal to zero and solve for x:
4x + 20 = 0
Subtract 20 from both sides:
4x = -20
Divide both sides by 4:
x = -5
Therefore, the value x = -5 makes the denominator zero.
Now, we need to consider the values of x for which the denominator is not zero. Since the denominator is a linear expression (a polynomial of degree 1), it is defined for all real numbers except x = -5.
So, the domain of the rational expression (6-x)/(4x+20) is all real numbers except x = -5.

For more such questions on rational

https://brainly.com/question/29270860

#SPJ8

Answer:

6x+0

Step-by-step explanation:

slope intercept form is basically y=mx+b, M is where you put the slope (6) and since your y intercept is 0, you would add it onto the equation. Thus 6x+0., you would also see the line graphed starting at 0, and you rise 6 times (6 up on the y-axis) and run on the x-axis once.

Answer:

Below in bold.

Step-by-step explanation:

3x + y = -1

2x + y=0

Subtract to eliminate y:

3x - 2x + y - y = -1 - 0

x = -1

So, substituting for x in the first equation;

3(-1) + y = -1

y - 3 = -1

y = 2.

The solution is the ordered pair (-1, 2).

The system is a pair of straight lines which intersect at the point (-1, 2).

The value of the determinants are

D=13

Dx =26

Dy =52

Dz =26

The determinant of a matrix is ​​a scalar value calculated for a given square matrix. Linear algebra deals with the determinant, it is calculated using the elements of a square matrix. It can be thought of as a scaling factor for the matrix transformation. Useful for solving a system of linear equations, calculating the inverse of a matrix, and numerical operations.

Given system is

x+ y-z= 4

3x+4y-3z=16

9x- 3y+4z=14

from the system the determinants become,

D=  1   1  -1

      3  4  -3

      9   -3  4

D= 1(16-9)-1(12+27)-1(-9-36)

   =7-39+45

   13

Dx=4   1  -1

      16  4  -3

      14   -3  4

   =26

Dy=1  4  -1

      3  16  -3

      9   14  4

   =52

Dz=1  1  4

      3  4  16

      9   -3  14

 =26

Hence, D=13, Dx=26, Dy=52, Dz=26

To know more about determinants from the given link.

https://brainly.com/question/24254106

#SPJ1

Answer:

2.25

Step-by-step explanation:

9 × 250 m = 2250 mL

1 L = 1000 m

2250 mL × (1 L)/(1000 mL) = 2.25 L

Answer:

thanks

Step-by-step explanation:

:) hahahahahah