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3 years ago

Please help me factor this!! Thanks!

Mathematics

1 answer:

Goryan [66]3 years ago

5 0

We need to find two numbers that multiply to 24 (last coefficient) and add to 10 (middle coefficient). Through trial and error, the two values are 6 and 4

6 + 4 = 10
6*4 = 24

So we can break up the 10ab into 6ab+4ab and then use factor by grouping

a^2 + 10ab + 24b^2
a^2 + 6ab + 4ab + 24b^2
(a^2+6ab) + (4ab+24b^2)
a(a+6b) + 4b(a+6b)
(a+4b)(a+6b)

Therefore, the original expression factors completely to (a+4b)(a+6b)

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find the x-intercepts of the parabola with vertex (1,20) and y-intercept (0,16) write your answer in this form

bagirrra123 [75]

Hello here is a solution :

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3 years ago

A filter filled with liquid is in the shape of a vertex-down cone with a height of 9 inches and a diameter of 6 inches at its op

Alina [70]

Answer: Level of the liquid dropping at 28.28 inch/second when the liquid is 2 inches deep.

Step-by-step explanation:

Since we have given that

Height = 9 inches

Diameter = 6 inches

Radius = 3 inches

So, $\dfrac{r}{h}=\dfrac{3}{9}=\dfrac{1}{3}\\\\r=\dfrac{1}{3}h$

Volume of cone is given by

$V=\dfrac{1}{3}\pi r^2h\\\\V=\dfrac{1}{3}\pi \dfrac{1}{9}h^2\times h\\\\V=\dfrac{1}{27}\pi h^3$

By differentiating with respect to time t, we get that

$\dfrac{dv}{dt}=\dfrac{1}{27}\pi \times 3\times h^2\dfrac{dh}{dt}=\dfrac{1}{9}\pi h^2\dfrac{dh}{dt}$

Now, the liquid drips out the bottom of the filter at the constant rate of 4 cubic inches per second, ie $\dfrac{dv}{dt}=-4\ in^3$

and h = 2 inches deep.

$-4=\dfrac{1}{9}\times \pi\times (2)^2\dfrac{dh}{dt}\\\\-9\pi =\dfrac{dh}{dt}\\\\-28.28=\dfrac{dh}{dt}$

Hence, level of the liquid dropping at 28.28 inch/second when the liquid is 2 inches deep.

7 0

3 years ago

What is the solution set of the equation x^2 - 7x - 18 = 0

photoshop1234 [79]

(x-9)(x+2)=0
x=9 or x=-2

3 0

3 years ago

Read 2 more answers

I have 18 ones,15 hundreds,15 tens,and 8 thousands.what number am i?

antoniya [11.8K]

15818 ?? This is making me get a headache

3 0

3 years ago

Here is the question: Jamey purchased a new boat for 61014.00. She read that the value of the new boats change by -2/19 in the f

olga55 [171]

The value of Jamey's boat after the first year of purchase is <u>$54,591.47</u>.

<h3>What is a reduction in value?</h3>

The change in the value of the new boat can be described as a reduction in value, which is akin to the depreciation of the initial value.

The reduction means that the value of the boat fell after the first year of use.

The reduction or change in value and the new value after the first year can be computed as follows:

<h3>Data and Calculations:</h3>

Purchase price = $61,014

Change in value after first year = -2/19

Change in value (dollars) = $6,422.53 ($61,014 x 2/19)

Value after the first year = $54,591.47 ($61,014 - $6,422.53)

Thus, the value of Jamey's boat after the first year of purchase is <u>$54,591.47</u>.

Learn more about reduction in the value of an asset at brainly.com/question/25806993

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6 0

2 years ago