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3 years ago

9

What is the surface area of the prism WILL MARK BRAINLEST WORTH 69 POINTS

1 answer:

marshall27 [118]3 years ago

6 0

Answer:

Surface area of the rectangular prism = $234\,mm^2$

Step-by-step explanation:

The surface area of the rectangular prism is:

$=2((Length\times Width)+(Width\times Height)+ (Height\times Length))$

$Length=15\,mm\\ \\Width=3\,mm\\\\Height=4\,mm$

Area is:

$=2((15\times 3)+(3\times 4)+ (4\times 15))\\\\=2(45+12+60)\\\\=2(117)\\\\=234\,mm^2$

Surface area of the rectangular prism is: $234\,mm^2$

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Find the distance between the point (-2, -3) and the line with the equation y=4-2/3x

otez555 [7]

Answer:

$D = \frac{25\sqrt{13}}{13}$

Step-by-step explanation:

Given

$y = 4 - \frac{2}{3}x$

$(x_1,y_1) = (-2,-3)$

Required

Determine the distance

$y = 4 - \frac{2}{3}x$

Write the above equation in standard form:

$Ax + By + C = 0$

So, we have:

$\frac{2}{3}x+y - 4 = 0$

By comparison:

$A = \frac{2}{3}$ $B = 1$ and $C = -4$

The distance is calculated using:

$D = \frac{|Ax_1 + By_1 + C|}{\sqrt{A^2 + B^2}}$

Where:

$(x_1,y_1) = (-2,-3)$

$A = \frac{2}{3}$ $B = 1$ and $C = -4$

This gives:

$D = \frac{|\frac{2}{3} * (-2) + 1 * (-3) - 4|}{\sqrt{(\frac{2}{3})^2 + 1^2}}$

$D = \frac{|-\frac{4}{3} -3 - 4|}{\sqrt{\frac{4}{9} + 1}}$

Take LCM

$D = \frac{|\frac{-4-9-12}{3}|}{\sqrt{\frac{4+9}{9}}}$

$D = \frac{|\frac{-25}{3}|}{\sqrt{\frac{13}{9}}}$

$D = |\frac{-25}{3}|/\sqrt{\frac{13}{9}}$

$D = \frac{25}{3}/\sqrt{\frac{13}{9}}$

Split the square root

$D = \frac{25}{3}/\frac{\sqrt{13}}{\sqrt{9}}$

Change / to *

$D = \frac{25}{3}*\frac{\sqrt{9}}{\sqrt{13}}$

$D = \frac{25}{3}*\frac{3}{\sqrt{13}}$

$D = \frac{25}{\sqrt{13}}$

Rationalize

$D = \frac{25}{\sqrt{13}} * \frac{\sqrt{13}}{\sqrt{13}}$

$D = \frac{25\sqrt{13}}{13}$

Hence, the distance is:

$D = \frac{25\sqrt{13}}{13}$

4 0

2 years ago

7. The points P(2, -3), Q(3, -2) and R(8, z) are

Hatshy [7]

Answer:

z = 3

Step-by-step explanation:

Since the points are collinear then the slopes between the points are equal.

Calculate the slope m using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = P (2, - 3) and (x₂, y₂ ) = Q (3, - 2)

m = $\frac{-2+3}{3-2}$ = 1

Repeat with

(x₁, y₁ ) = Q (3, - 2) and (x₂, y₂ ) = R (8, z )

m = $\frac{z+2}{8-3}$ = $\frac{z+2}{5}$ , then

$\frac{z+2}{5}$ = 1 ( multiply both sides by 5 )

z + 2 = 5 ( subtract 2 from both sides )

z = 3

4 0

2 years ago

Sarah bought a TV for $250. Three years later she sold it for $180. Work out her percentage loss.

Anna71 [15]

70/250 x 100
Answer: 28%

3 0

2 years ago

What is the equation of a line that passes through the point (3, 11) and is parallel to the line y=2x-4

Law Incorporation [45]

Answer:

The answer should be y=2x+5

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2 years ago

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. Find the solution s

irina [24]

Answer:

34.55/6.28=0

Step-by-step explanation:

7 0

3 years ago