Factor the following:<br><br> −5x2−20x

I can’t figure out, can someone please explain how to get the correct answer?

Karolina [17]

Answer:

a) CD = 9

b) AB = 20

Step-by-step explanation:

In this geometry, all of the right triangles are similar. This means The ratio of short side to long side is the same for all of the triangles.

You are given the short and long sides of ΔADB, and the long side of ΔCDA. You are asked for the short side of ΔCDA, so you can write the proportion ...

CD/AD = AD/BD

CD/12 = 12/16

CD = 12(12/16)

CD = 9

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There are a couple of options for finding AD. One you may be familiar with is the Pythagorean theorem.

AB² = AD² +DB²

AB² = 12² +16² = 144 +256 = 400 . . . . fill in known values

AB = √400 = 20 . . . . . take the square root

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Alternatively, you can use the same proportional relationship that is described above. Here, we make use of the ratio of the hypotenuse to the long side.

AB/BD = CB/AB

AB² = BD·CB = 16·(16+9) = 16·25 . . . . cross multiply; fill in known values

AB = √(16·25) = 4·5 . . . . . take the square root

AB = 20

_____

<em>Additional comment</em>

This geometry, where the altitude of a right triangle is drawn, has some interesting properties. We have hinted at them above.

You can write three sets of proportions for this geometry: the ratios of short side and long side; the ratios of short side and hypotenuse; and the ratios of long side and hypotenuse. When you look at the way the sides touching the longest hypotenuse relate to that hypotenuse, you see three similar relations:

AC = √(CD·CB)

AD = √(DC·DB)

AB = √(BD·BC) . . . . . . . . the relation used in part (b) above

This "square root of a product" is called the <em>geometric mean</em>. In effect, the length of a side touching the longest hypotenuse is the geometric mean of the two segments of that hypotenuse that it touches.

7 0

2 years ago

Pls help, (20 pts, will mark u the brainliest when your correct, PLS ANSWER ASAP)

tester [92]

Answer:

-7

Step-by-step explanation:

7.

step-by-step explanation:

the coefficient multiplies the variable.

it is -7.

4 0

3 years ago

Read 2 more answers

Daniel wants to buy cookies for her friends. The area of a cookie is 113.04 in2. What is the circumference of the cookie?

prisoha [69]

Answer:

The circumference of the cookie is 37.68 inches.

Step-by-step explanation:

We have,

The area of a cookie is 113.04 square inches.

It is circular in shape. The area of circle is given by :

$A=\pi r^2$

r is radius of circle

$r=\sqrt{\dfrac{A}{\pi}} \\\\r=\sqrt{\dfrac{113.04}{3.14}} \\\\r=6\ \text{inch}$

The circumference of circular shaped object is given by :

$C=2\pi r\\\\C=2\times 3.14\times 6\\\\C=37.68\ \text{inch}$

So, the circumference of the cookie is 37.68 inches.

7 0

2 years ago

Please help me, I'm doing a test.

Tju [1.3M]

Answer:

(3,4)

Step-by-step explanation:

first you're going to solve the equation -2x

your equation should now be: $\left \{ {{-2x+3y\\=6} \atop {-2x=2-2y}} \right.$

next you're going to substitute the given value of -2x into the equation $-2x+3y=6$

so your equation should now be: $2-2y+3y=6$

next you're going to solve the equation for y

equation should now be: y=4

than you're going to substitute the given value of y into the equation $-2x=2-2$ × $4$

then you're going to solve the equation for x

your equation should now be: x=3

then the possible solution of the system is the order pair: (x,y)=(3,4)

4 0

2 years ago

A circle has a center of (5,-5) and goes through (6,-2). What is the radius?

Fittoniya [83]

Start with the equation of a circle whose center is at (h,k) and whose radius is r:

(x-h)^2 + (y-k)^2 = r^2

Substituting the given coordinates of the center:

(x-5)^2 + (y-[-5])^2 = r^2, or (x-5)^2 + (y+5)^2 = r^2

Substituding the given coordinates of a point (6,-2) on the circle:

(6-5)^2 + (-2+5)^2 = r^2

Simplifying:

1^2 + 3^2 = r^2, or 1 + 9 = r^2, or 10= r^2. Then r = sqrt(10).

6 0

3 years ago

Factor the following: −5x2−20x