Figure this out please

Mathematics

2 answers:

rusak2 [61]3 years ago

7 0

Answer:

570 cm³

Step-by-step explanation:

Check the rule in your picture about Calculating the volume of a prism:

Volume = (2×15)×19

= 570

irina [24]3 years ago

6 0

<h3>Answer: 380 cubic cm</h3>

Explanation:

The front and back faces are trapezoids. Focus on one of the trapezoids.

I'll focus on the front face. It has parallel sides of b1 = 15 and b2 = 5. The height is h = 2.

The area of this trapezoid is

A = h*(b1+b2)/2

A = 2*(15+5)/2

A = 2*20/2

A = 40/2

A = 20

So any vertical cross sectional area is 20 square cm.

Multiply this by the depth of the prism, which is 19, to get the volume of the prism

Volume = (area of cross section)*(depth)

Volume = (20)*(19)

Volume = 380 cubic cm

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Which is the approximate solution to the system y = 0.5x + 3.5 and y = − 2/3 x + 1/3 shown on the graph? (–2.7, 2.1) (–2.1, 2.7)

AlekseyPX

Answer:

The approximate solution to the system is $(-2.7, 2.1)$ .

Step-by-step explanation:

To solve the system of equations $\begin{bmatrix}y=0.5x+3.5\\ y=-\frac{2}{3}x+\frac{1}{3}\end{bmatrix}$ you must:

$\mathrm{Rationalize\:equations}\\\\\begin{bmatrix}y=\left(\frac{1}{2}\right)x+\left(\frac{7}{2}\right)\\ y=-\frac{2}{3}x+\frac{1}{3}\end{bmatrix}$

$\mathrm{Subsititute\:}y=-\frac{2}{3}x+\frac{1}{3}\\\\\begin{bmatrix}-\frac{2}{3}x+\frac{1}{3}=\frac{1}{2}x+\frac{7}{2}\end{bmatrix}$

$\mathrm{Isolate}\:x\:\mathrm{for}\:-\frac{2}{3}x+\frac{1}{3}=\frac{1}{2}x+\frac{7}{2}\\\\-\frac{2}{3}x=\frac{19}{6}+\frac{1}{2}x\\\\-\frac{7}{6}x=\frac{19}{6}\\\\6\left(-\frac{7}{6}x\right)=\frac{19\cdot \:6}{6}\\\\-7x=19\\\\x=-\frac{19}{7}\approx-2.7$

$\mathrm{For\:}y=-\frac{2}{3}x+\frac{1}{3}\\\\\mathrm{Subsititute\:}x=-\frac{19}{7}\\\\y=-\frac{2}{3}\left(-\frac{19}{7}\right)+\frac{1}{3}\\\\y=\frac{15}{7}\approx 2.1$