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3 years ago

What is the solution for the system of equations? 2y=4x-12 and y=-2x+2

1 answer:

6 0

$2y = 4x - 12 \\ y = - 2x + 2 \\ \\ 2( - 2x + 2) = 4x - 12 \\ - 4x + 4 = 4x - 12 \\ 4 = 8x - 12 \\ 16 = 8x \\ 2 = x \\ \\ y = - 2(2) + 2 \\ y = - 4 + 2 \\ y = - 2$
(2,-2)

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3) What is the SURFACE AREA of the solid with the given measurements? Square Pyramid base edge 4 cm, slant height 11 cm

atroni [7]

Answer:

Step-by-step explanation:

height h = 11 cm

slant height s = 11.180339887499 cm

side length a = 4 cm

lateral edge length e = 11.357816691601 cm

1/2 side length r = 2 cm

volume V = 58.666666666667 cm3

lateral surface area L = 89.442719099992 cm2

base surface area B = 16 cm2

total surface area A = 105.44271909999 cm2

4 0

3 years ago

Find f such that the given conditions are satisfiedf’(x)=x-4, f(2)=-1

kicyunya [14]

Given:

$f^{\prime}\left(x\right)=x-4,\text{ and}f\left(2\right)=-1$

To find:

The correct function.

Explanation:

Let us consider the function given in option D.

$f(x)=\frac{x^2}{2}-4x+5$

Differentiating with respect to x we get,

$\begin{gathered} f^{\prime}(x)=\frac{2x}{2}-4 \\ f^{\prime}(x)=x-4 \end{gathered}$

Substituting x = 2 in the function f(x), we get

$\begin{gathered} f(2)=\frac{2^2}{2}-4(2)+5 \\ =2-8+5 \\ =-6+5 \\ f(2)=-1 \end{gathered}$

Therefore, the given conditions are satisfied.

So, the function is,

$f(x)=\frac{x^{2}}{2}-4x+5$

Final answer: Option D

6 0

1 year ago

Chloe wants to cut a 37 in. piece of ribbon into three pieces. The second piece is to be 2 in. longer than the first, and the th

valentinak56 [21]

1st piece = x

2nd piece = x+2

3rd piece = x+2+3 = x+5

37 = x +x+2 + x+5 =

37 = 3x+7

30=3x

x = 30/3 = 10

1st piece = 10 inches

2nd piece = 10+2 = 12 inches

3rd piece = 10+5 = 15 inches

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3 years ago

To be a vertical angle, the angles have to be next to each other. <br> A. True<br> B. False

12345 [234]

False, vertical angles are not next to each other but opposite of each other

3 0

3 years ago

Find the range, median, first and third quartiles, and interquartile range for each data set OF THE NUMBERS 52 72 96 21 58 40 75

Andrej [43]

Answer:

Range: 75 Median: 58 1Q: 40 3Q: 75 Interquartile: 35

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3 years ago