All categories

3 years ago

The product of $7d^2-3d+g$ and $3d^2+hd-8$ is $21d^4-44d^3-35d^2+14d-16$. What is $g+h$?

Mathematics

1 answer:

galina1969 [7]3 years ago

3 0

<h2>Answer:</h2><h2>g = 2 and h = -5</h2>

Step-by-step explanation:

To find the product with unknown values of variables, multiply the terms and equate the value to the given product.

$(7d^{2} - 3d + g)(3d^{2} + hd - 8)$ = $21d^{4} + 7hd^{3} - 56d^{2} - 9d^{3} - 3hd^{2} + 24d + 3gd^{2} + ghd - 8g$

$(7d^{2} - 3d + g)(3d^{2} + hd - 8)$ = $21d^{4} + (7h-9) d^{3} + (3g-56-3h)d^{2} + (24+gh)d -8g$ ... (1)

Comparing eq(1) to the product given in question,

-8g = -1

g = 2

24 + gh = 14, sub g =2,

24 + 2h = 14

h = -5

You might be interested in

In this hanger, the weight of the triangle is x and the weight of the square is y.

Sedbober [7]

Answer:

y = 4

Step-by-step explanation:

4y 1x

3x 1y

1x=6

6+16 =22

18+4= 22

4 0

3 years ago

A city has current population of 55,000, and it is growing at a rate of 2% each year. What is the approximate predicted populati

PtichkaEL [24]

The correct answer is C

8 0

3 years ago

Find the area of the shaded regions. Give your answer as a completely simplified exact value in terms of π (no approximations).

Lapatulllka [165]

Hello!

The formula for the area of a sector can be written as follows:

Area = $\frac{1}{2}$ $r^{2}$ (R)

In the above formula, “r” represents the radius while “R” represents the radian measure of a sector. The radius is given to us in the image above as 10 inches. However, we still need the radian measure of the two sectors. To find this measure, we can use the following conversion:

1 degree = $\frac{pi}{180}$ radians

Because the two sectors have a given measure of 72 degrees, we need to multiply both sides of the above conversion by 72:

72 degrees = $\frac{72pi}{180}$

Reduce the fraction on the right side of the equation:

72 degrees = $\frac{2pi}{5}$

We now have the radian measure of both sectors. Now simply insert this and any other known values into the “area of a sector” formula above:

Area = $\frac{1}{2}$ $10^{2}$ ( $\frac{2pi}{5}$ )

Simplify the right side of the equation to get the following answer:

Area = 20 pi

We have now proven that the area of one sector is equal to 20 pi.

If, however, you need the combined area of the two identical sectors, simply multiply the proven area by 2 to get a total area of 40 pi.

I hope this helps!

3 0

3 years ago

Suppose that in a casino game the payout is a random variable X . If X is positive, you gain money, if negative, you lose.

Vanyuwa [196]

Answer:

the conditional probability that X = 1 , X = 2 and X = 3 is 0.7333 (73.33%) , 0.25 (25%) and 0.0167 (1.67%) respectively

Step-by-step explanation:

a player wins money when i>0 then defining event W= gain money , then

P(W) = p(i>0) = p(1)+p(2)+p(3)

then the conditional probability can be calculated through the theorem of Bayes

P(X=1/W)= P(X=1 ∩ W)/P(W)

where

P(X=1 ∩ W)= probability that the payout is 1 and earns money

P(X=1 / W)= probability that the payout is 1 given money was earned

then

P(X=1/W)= P(X=1 ∩ W)/P(W) = P(X=1) / P(W) = p(1) /[p(1)+p(2)+p(3)] = 11/40 /(11/40+3/32+1/160 ) = 0.7333 (73.33%)

similarly

P(X=2/W)=p(2) /[p(1)+p(2)+p(3)] = 3/32 /(11/40+3/32+1/160 ) = 0.25 (25%)

P(X=3/W)=p(2) /[p(1)+p(2)+p(3)] = 1/160 /(11/40+3/32+1/160 ) = 0.0167 (1.67%)

8 0

3 years ago

How would you describe the difference between the graphs of f(x) = x2 +4 and<br> G(y) = y2 +4 ?

ivann1987 [24]

Answer:

They're the exact same, except for the variables.

Step-by-step explanation:

Since the variable can be any letter, it is the exact same equation but with different letters as x. Although the equation of G(y) has a y instead of x, you know y is the x and g(y) is the y because the y inside of the parentheses tells us that y is the independent variable.

5 0

3 years ago