Find the real-number root -81

Find the volume of the triangular prism described below.

Luda [366]

The volume of the prism 121.6 cube in.

Step-by-step explanation:

Given,

The base is right angle triangle whose two sides are equal.

So,

Base (b) = 8 in

Another side of right angle triangle (l) = 8 in

Height (h) of the prism = 3.8 in

To find the volume of the prism.

Formula:

V = $\frac{1}{2}$ bhl

Now,

V = $\frac{1}{2}$ ×8×8×3.8 cube in

= 121.6 cube in.

8 0

2 years ago

<img src="https://tex.z-dn.net/?f=%5Csf%202x%2B21%3D3" id="TexFormula1" title="\sf 2x+21=3" alt="\sf 2x+21=3" align="absmiddle"

sergij07 [2.7K]

$\sf \longmapsto \: 2x + 21 = 3$

$\sf \longmapsto2x = 3 - 21$

$\sf \longmapsto2x = - 18$

$\sf \longmapsto \: x = \frac{ - 18}{2}$

$\sf \longmapsto x = - 9$

5 0

2 years ago

Read 2 more answers

Devon made a box with length x+1, width x+3, and height x-3. What is the volume of Devon's box as a function of x?

erica [24]

Answer:

(a)

$V=x^3+x^2-9x-9$

(b)

$x=10$

(c)

$x=\frac{7}{2}$

Step-by-step explanation:

we are given

length is x+1

$L=x+1$

width is x+3

$W=x+3$

height is x-3

$H=x-3$

(a)

we can use volume formula

$V=L\times W\times H$

now, we can plug it

$V=(x+1)\times (x+3)\times (x-3)$

now, we can simplify it

$V=x^3+x^2-9x-9$

(b)

we are given volume =1001

so, we can set V=1001

and then we can solve for x

$V=x^3+x^2-9x-9=1001$

now, we can factor it

$\left(x-10\right)\left(x^2+11x+101\right)=0$

$x-10=0$

$x=10$

(b)

we are given volume

so, we can set

$V=14\frac{5}{8}=\frac{14\times 8+5}{8}$

$V=\frac{117}{8}$

and then we can solve for x

$V=x^3+x^2-9x-9=\frac{117}{8}$

now, we can factor it

$8x^3+8x^2-72x-189=0$

$\left(2x-7\right)\left(4x^2+18x+27\right)=0$

$2x-7=0$

$x=\frac{7}{2}$

8 0

3 years ago

(x^2y^3) = (xy^a)^b

Rainbow [258]

Answer:

C. $\frac{3}{2}$

Step-by-step explanation:

To find the value f b, we need to compare the exponents.

The given exponential equation is:

$( {x}^{2} {y}^{3} )^{3} = ( {x} {y}^{a} )^{b}$

Recall and apply the following rule of exponents.

$( {x}^{m} )^{n} = {x}^{mn}$

We apply this rule on both sides to get:

${x}^{2 \times 3} {y}^{3 \times 3} = {x}^{b} {y}^{ab}$

Simplify the exponents on the left.

${x}^{6} {y}^{9} = {x}^{b} {y}^{ab}$

Comparing exponents of the same variables on both sides,

$b = 6 \: and \:\: ab = 9$

$\implies \: 6b = 9$

Divide both sides by 6.

$b = \frac{9}{6}$

$b = \frac{3}{2}$

4 0

2 years ago

Gabriella and her children went into a grocery store and where they sell apples for $1 each and mangos for $0.50 each. Gabriella

Dafna1 [17]

Answer:

Step-by-step explanation:

Let x represent the number of apples that she wants to buy.

The grocery store sells apples for $1 each and mangos for $0.50 each.

If Gabriella decided to buy 13 mangos, it means that the cost of buying x apples and 13 mangoes is expressed as

x + 13 × 0.5 = x + 6.5

If she buy at least 19 apples, it means that

x + 13 ≥ 19

x ≥ 19 - 13

x ≥ 6

Gabriella has $15 to spend. It means that

x + 6.5 ≤ 15

x ≤ 15 - 6.5

x ≤ 8.5

Therefore, the maximum number of apples that she can buy is 8

5 0

2 years ago