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3 years ago

5

Which expression is equivalent to (5z^2+3z+2)^2

2 answers:

ZanzabumX [31]3 years ago

5 0

Answer:

$25z^{4} +30z^{3} +29z^{2} +12z+4$

Step-by-step explanation:

The trinomial is squared, so it can be solved with the following notable product

$(a+b+c)^{2} = a^{2} +b^{2} +c^{2} +2ab+2ac+2bc$

If we substitute the indicated values

$a=5z^{2} ; b=3z; c=2$

Tendremos lo siguiente

$(5z^{2} +3z+2)^{2} = (5z^{2} )^{2} +(3z)^{2} +2^{2} +2(5z^{2} )(3z)+2(5z^{2} )(2)+2(3z)(2)$

performing indicated operations

$25z^{4} +9z^{2} +4+30z^{3} +20z^{2} +12z$

accommodating terms

$25z^{4} +30z^{3} +9z^{2} +20z^{2} +12z+4$

reducing terms

$25z^{4} +30z^{3} +29z^{2} +12z+4$

zmey [24]3 years ago

3 0

<span>Which expression is equivalent to (5z^2+3z+2)^2</span>

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For her presentation on the Wonders of the World, Mary baked a square pyramid-shaped cake as pictured below. The slant height of

mihalych1998 [28]

Answer:

$V=196in^3$

Step-by-step explanation:

The volume of a pyramid is:

$V=\frac{A_{b}h}{3}$

where $A_{b}$ is the area of the base and $h$ is the height (the perpendicular measurement between base and highest point, not the slant height)

Since the base is a square, the area is given by:

$A_{b}=l^2$

where $l$ is the length of the side: $l=8in$ , thus:

$A_{b}=(8in)^2\\A_{b}=64in^2$

Now we need to find the height, for this we use the right triangle that forms with half of a square side (8in/2 = 4in), the slant height (10in), and the height.

In this right triangle, the slant height is the hypotenuse, the leg 1 is the unknown height, and leg 2 is half of the square side.

Using pythagoras:

$hypotenuse^2=leg1^2+leg2^2$

substituting our values, and indicating that leg 1 is height h:

$(10in)^2=h^2+(4in)^2$

$100in^2=h^2+16in^2$

and solving for the height:

$h^2=100in^2-16in^2\\h^2=84in^2\\h=\sqrt{84in^2}\\ h=9.165in$

and finally we calculate the volume using this height and the area of the base:

$V=\frac{A_{b}h}{3}$

$V=\frac{(64in^2)(9.165in)}{3} \\V=195.5in^3$

rounding to the nearest cubic inch: $V=196in^3$

4 0

4 years ago

How to write an algebraic expression for (r+1) /14

Fittoniya [83]

I'm not so good but I think thatmeans r is a different number and its half of 14 so figure out an equation

8 0

3 years ago

Find the volume of the triangular prism in the picture shown. Round your answer to the

Olenka [21]

Given:

A figure of a triangular prism.

Height of triangular base = $9\dfrac{2}{3}$ yd

Base of triangular base = 4 yd

Height of prism = 4 yd.

To find:

The volume of the triangular prism.

Solution:

Volume of a triangular prism is:

$V=Bh$ ...(i)

Where, B is the area of triangular base and h is the height of the prism.

Area of triangular base is:

$B=\dfrac{1}{2}\times base\times height$

$B=\dfrac{1}{2}\times 4\times 9\dfrac{2}{3}$

$B=2\times \dfrac{29}{3}$

$B=\dfrac{58}{3}$

Putting $B=\dfrac{58}{3}$ and h=4 in (i), we get

$V=\dfrac{58}{3}\times 4$

$V=\dfrac{232}{3}$

$V=77.33...$

$V\approx 77.3$

The volume of the triangular prism is 77.3 cubic yards. Therefore, the correct option is 2.

4 0

3 years ago

Simplify the equation -4(2x-4)

marin [14]

Answer:

-8x + 16

Step-by-step explanation:

This is called expanding brackets in algebra

1. you need to multiply the numeral on outside of the brackets with each of thosse on the inside

-4 x 2x = 8x

-4 x -4 = 16

4 0

3 years ago

Can someone pls help me with this. I’ll give brainliest

allochka39001 [22]

Answer:

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Step-by-step explanation:

4 0

3 years ago

Read 2 more answers