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2 years ago

Please help thank you

Mathematics

1 answer:

mars1129 [50]2 years ago

3 0

i have no idea about a but

B. LN corresponds to EF

MN corresponds to DF

E corresponds to L

F corresponds to N

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Suppose you know that the volume of the following prism is represent by V(x) = -2x^3 + 14x^2 + 120x.

erastova [34]

Step-by-step explanation:

-2x³ + 14x² + 120x

= -2x(x² - 7x - 60)

= -2x(x - 12)(x + 5).

The other 2 dimensions are -2x and (x + 5).

When using a graphing calculator to maximise the volume of the prism, we get x = 7.378. However this value is not reasonable as it makes -2x and (x - 12) negative, which are the sides of the prism.

8 0

2 years ago

Write in slope-intercept form an equation of the line that passes through the points (−1,12) and (1,2).

zzz [600]

Answer:

$y=-5x+7$

Step-by-step explanation:

step 1

Find the slope

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

the points (−1,12) and (1,2)

substitute

$m=\frac{2-12}{1+1}$

$m=\frac{-10}{2}$

$m=-5$

step 2

we know that

The equation of the line in slope intercept form is equl to

$y=mx+b$

where

m is the slope

b is the y-intercept

we have

$m=-5$

$point\ (1,2)$

substitute in the linear equation and solve for b

$2=-5(1)+b$

$b=2+5=7$

therefore

$y=-5x+7$

4 0

2 years ago

if you want to make a rectangular prism out of cardboard without overlapping cardboard. it has the length of 3 feet the width of

Phantasy [73]

The surface area of a rectangular prism is given by

... S = 2(LW +H(L+W))

For your dimensions, the surface area is

... S = 2(3·1 + 2(3+1)) = 2(3 + 8) = 22 . . . ft²

8 0

3 years ago

Let f(x)=1/2x2+4. The function g(x) is a vertical stretch of f(x) by a factor of 4. What is the equation of g(x)?

andrey2020 [161]

The equation of g(x) is $g(x)=2 x^{2}+16$

Explanation:

Given that the function f(x) is $f(x)=\frac{1}{2} x^{2}+4$

Also, given that the function g(x) is a vertical stretch of f(x) by a factor of 4.

We need to determine the equation of g(x)

<u>Equation of g(x):</u>

The vertical stretch of the function can be determined by multiplying the factor 4 with the function f(x).

Thus, we have,

$g(x)=4 f(x)$

Substituting the values,we have,

$g(x)=4\left(\frac{1}{2} x^{2}+4\right)$

Simplifying the values, we get,

$g(x)=2 x^{2}+16$

Hence, the equation of g(x) is $g(x)=2 x^{2}+16$

6 0

2 years ago

The YTM on a bond is the interest rate you earn on your investment if interest rates don’t change. If you actually sell the bond

AURORKA [14]

Answer / Step-by-step explanation:

(a) The rate of return you expect to earn if you purchase a bond and hold it until maturity is the YTM.

If we recall the bond price equation for this bond is, we have

P0 = $1,060 = $100(PVIFAR%,21) + $1,000(PVIFR%,21)

Using a spreadsheet, financial calculator, or trial and error we find:

R = YTM = 9.42%

b) To find our HPY, we need to find the price of the bond in two years. The price of the bond in two years at the new interest rate, will be:

P2 = $100 (PVIFA 8.42%,17) + $1,000(PVIF 8.42%,17)

Therefore, P2 = $1,139.6

(b2) To calculate the HPY, we need to find the interest rate that equates the price we paid for the bond with the cash flows we received. The cash flows we received were $100 each year for two years and the price of the bond when we sold it. The equation to find our HPY is therefore:

P0 = $1,060 = $100(PVIFAR%, 2) + $1,139.69(PVIFR%, 2)

Solving for R, we get:

R = HPY = 13.52%

Therefore, the realized HPY is greater than the expected YTM when the bond was bought because interest rates dropped by 1 percent; bond prices rise when yields fall.

8 0

2 years ago