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3 years ago

The three steps are shown below were used to find an expression equivalent to 2/5( 15x- 30y)+10x

Mathematics

1 answer:

Tresset [83]3 years ago

8 0

step 1 is to distribute the bracket by $\frac{2}{5}$

= $\frac{2}{5}$ × 15x - $\frac{2}{5}$ × 30y + 10x

= 6x - 12y + 10x ← step 1

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Step-by-step explanation: The theoretical probability that Margaret, when choosing first, will choose a jack, is 1/13.

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4 years ago

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morpeh [17]

Answer:

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3 years ago

What is the sum of 12 – 5i and –3 4i? –16 63i 9 – i 9 – 9i 15 – 9i

Anarel [89]

The sum of the complex number 12 – 5i and –3 + 4i is 9 - i

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2 years ago

What is the measure of the angle of intersection when AB is the

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3 years ago

A cone with height h and radius r has volume V = 1/3πr2h. If the cone has a height of 6 in. and volume V = 8πx2 + 24πx + 18π, wh

Bingel [31]

Answer:

Step-by-step explanation:

The volume for a cone is given by:

$\displaystyle V=\frac{1}{3}\pi r^2h$

For a given cone with a height of 6 inches, the volume is represented by:

$\displaystyle V=8\pi x^2+24\pi x+18\pi$

We want to find the radius r in terms of x.

Since the height is 6, this means that:

$\displaystyle V=\frac{1}{3}\pi r^2(6)=2\pi r^2$

By substitution:

$2\pi r^2=8\pi x^2+24\pi x+18\pi$

Divide both sides by 2π:

$\displaystyle r^2=\frac{8\pi x^2+24\pi x+18\pi}{2\pi}=4x^2+12x+9$

Factor the right. Notice that we have a perfect square trinomial*:

$4x^2+12x+9=(2x)^2+2(2x)(3)+(3)^2$

Factor:

$4x^2+12x+9=(2x+3)^2$

Therefore:

$r^2=(2x+3)^2$

Take the square root of both sides. The radius should be positive, so we only need to consider the positive case:

$r=\sqrt{(2x+3)^2}=2x+3$

And our answer is C!

*Note:

$a^2+2ab+b^2=(a+b)^2\\\\\text{In this case } a = 2x\text{ and } b =3$

5 0

3 years ago