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4 years ago

What is the volume of a rectangular prism with the following dimensions

Mathematics

2 answers:

andriy [413]4 years ago

7 0

Answer: 250ft3

Step-by-step explanation:

v=l*w*H

v= 10*5 * 5

v=250

s344n2d4d5 [400]4 years ago

3 0

Answer:

250ft3

Step-by-step explanation:

v=l*w*H

v= 10*5 * 5

v=250

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Solving right triangles

Sav [38]

<h2>1. Answer:</h2>

A right triangles is a triangle having a 90 degree side. According to the figure, the sides of this triangle are expressed in inches. Therefore, we can find the missing sides and angles as follows:

<u>m∠B:</u>

The sum of the three interior angles of any triangle is 180°, therefore:

$m \angle B + 51^{\circ} + 90^{\circ} = 180^{\circ} \\ \\ \boxed{m \angle B = 39^{\circ}}$

We must use the law of sines as follows:

$\frac{CA}{sin39^{\circ}}=\frac{9}{sin51^{\circ}} \\ \\ \therefore CA=\frac{9sin39^{\circ}}{sin51^{\circ}} \\ \\ \therefore \boxed{CA=7.3in}$

$\frac{AB}{sin90^{\circ}}=\frac{9}{sin51^{\circ}} \\ \\ \therefore AB=\frac{9sin90^{\circ}}{sin51^{\circ}} \\ \\ \therefore \boxed{AB=11.6in}$

<h2>2. Answer:</h2>

According to the figure, the sides of this triangle are expressed in meters. Therefore, we can find the missing sides and angles as follows:

<u>m∠A:</u>

The sum of the three interior angles of any triangle is 180°, therefore:

$m \angle A + 53^{\circ} + 90^{\circ} = 180^{\circ} \\ \\ \boxed{m \angle A = 37^{\circ}}$

We must use the law of sines as follows:

$\frac{CA}{sin53^{\circ}}=\frac{5}{sin90^{\circ}} \\ \\ \therefore CA=\frac{5sin53^{\circ}}{sin90^{\circ}} \\ \\ \therefore \boxed{CA=4.0m}$

$\frac{CB}{sin37^{\circ}}=\frac{5}{sin90^{\circ}} \\ \\ \therefore CB=\frac{5sin37^{\circ}}{sin90^{\circ}} \\ \\ \therefore \boxed{CB=3.0m}$

<h2>3. Answer:</h2>

According to the figure, the sides of this triangle are expressed in miles. Therefore, we can find the missing sides and angles as follows:

<u>m∠B:</u>

The sum of the three interior angles of any triangle is 180°, therefore:

$m \angle A + 28^{\circ} + 90^{\circ} = 180^{\circ} \\ \\ \boxed{m \angle B = 62^{\circ}}$

We must use the law of sines as follows:

$\frac{CB}{sin28^{\circ}}=\frac{29.3}{sin62^{\circ}} \\ \\ \therefore CB=\frac{29.3sin28^{\circ}}{sin62^{\circ}} \\ \\ \therefore \boxed{CA=15.6mi}$

$\frac{AB}{sin90^{\circ}}=\frac{29.3}{sin62^{\circ}} \\ \\ \therefore AB=\frac{29.3sin90^{\circ}}{sin62^{\circ}} \\ \\ \therefore \boxed{AB=33.2mi}$

<h2>4. Answer:</h2>

According to the figure, the sides of this triangle are expressed in miles. Therefore, we can find the missing sides and angles as follows:

<u>m∠A:</u>

The sum of the three interior angles of any triangle is 180°, therefore:

$m \angle A + 24^{\circ} + 90^{\circ} = 180^{\circ} \\ \\ \boxed{m \angle A = 66^{\circ}}$

We must use the law of sines as follows:

$\frac{CA}{sin66^{\circ}}=\frac{14}{sin90^{\circ}} \\ \\ \therefore CA=\frac{14sin66^{\circ}}{sin90^{\circ}} \\ \\ \therefore \boxed{CA=12.8mi}$

$\frac{CB}{sin24^{\circ}}=\frac{14}{sin90^{\circ}} \\ \\ \therefore CB=\frac{14sin24^{\circ}}{sin90^{\circ}} \\ \\ \therefore \boxed{CB=5.7mi}$

8 0

3 years ago

Based on the graph, which equation represents the relationship between the height of trees (y) and the amount of rainfall (x)?

slega [8]

<u>Given</u>:

Given that the graph that shows the amount of rainfall( in centimeters) and the height of the trees( in meters)

We need to determine the equation that represents the relationship between the height of trees(y) and the amount of rainfall(x).

<u>Slope of the equation:</u>

The slope can be determined using the formula,

$m=\frac{y_2-y_1}{x_2-x_1}$

Substituting the points (20,10) and (40, 20) in the above formula.

Thus, we get;

$m=\frac{20-10}{40-20}$

$m=\frac{10}{20}$

$m=0.5$

Thus, the slope of the equation is 0.5

<u>y - intercept:</u>

The y - intercept of the equation is the value of y when x = 0.

Thus, from the graph, when x = 0, the value of y is 0.

Hence, the y - intercept is b = 0

<u>Equation of the graph:</u>

The equation of the given graph can be determined using the formula,

$y=mx+b$

Substituting the values, we get;

$y=0.5x+0$

$y=0.5x$

Thus, the equation that represents the relationship between the height of the trees (y) and the amount of rainfall (x) is $y=0.5x$

Hence, Option C is the correct answer.

5 0

3 years ago

Read 2 more answers

Why is 1 not a prime number and why would any negative number not be considered prime?

gregori [183]

<h2>Answer:</h2><h2>The definition of a prime number is a positive integer that has exactly 2 positive divisors.</h2><h2>However 1 has only one positive divisor so it is not prime.</h2><h2>Negative integers can not be prime. Negative numbers are excluded. In fact they are given no though </h2>

8 0

4 years ago

PLEASE HELP

kirza4 [7]

Answer:

- 2/5

Step-by-step explanation:

Answer

Have an nice day and good luck