If the slope of a line is-1/3 and two points on the line are (10, 8) and (s,− 3 110), what is the value of s?

Find the unknown length of the right triangle. If necessary approximate the length to the nearest thousandth

WARRIOR [948]

We are given a right triangle and we are asked to determine the hypotenuse given the measure of its sides. To do that we will use the Pythagorean theorem:

$h^2=(10km)^2+(20km)^2$

Now, we solve the square:

$h^2=100km^2+400km^2$

Now, we add the values:

$h^2=500km^2$

Now, we take the square root to both sides:

$h=\sqrt[]{500km^2}$

Solving the operations:

$h=22.361km$

Therefore, the length of the hypotenuse is 22.361 kilometers.

6 0

1 year ago

A building 50 feet high casts a shadow 68 feet long. Find the measure of the angle of elevation of the sun. Round answer to near

Vedmedyk [2.9K]

Answer:

36 °

Step-by-step explanation:

In this case a rectangular triangle is formed so we can use the trigonometric functions to calculate the angle, they give us the value of the two legs, therefore we can apply the tangent function.

Tan A ° = opposite / adjacent

replacing:

Tan A ° = 50/68

Tan A ° = 0.735

A ° = arc tan (0.735)

A ° = 36.32

Which means that the angle of inclination is 36°

4 0

3 years ago

PLZZZ HELP ILL MARK BRAINLIEST Simplify the following expression by combining like terms.Select the most simplified expression 2

meriva

Answer:

c

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Given h (x)= -4x-10, find x when h(x)= -30

Serggg [28]

Step-by-step explanation:

h(x)=-4x-10

but h(x) =-30

-30=-4x-10

-4x=-10+30

-4x=40

-4x/4=40/4

x=10

6 0

3 years ago

Find the volume of each pyramid or come. Round to the nearest tenth if necessary.

Naya [18.7K]

QUESTION 1

The given pyramid has a square base.

The volume of this square pyramid is given by;

$V=\frac{1}{3}\times l^2\times h$

where $l=5ft$ is the length of a side of the square base.

and $h=8ft$ is the height of the pyramid.

We substitute the values into the formula to get;

$V=\frac{1}{3}\times 5^2\times 8 ft^3$

$V=66.7 ft^3$

QUESTION 2

The given pyramid has a rectangular base.

The volume of this rectangular pyramid is given by;

$V=\frac{1}{3}\times l\times b\times h$

where $l=7cm$ and w=4cm are the length and width of a side of the rectangular base.

and $h=8cm$ is the height of the pyramid.

We substitute the values into the formula to get;

$V=\frac{1}{3}\times 7\times 4\times 8cm^3$

QUESTION 3

The given pyramid has a rectangular base.

The volume of this rectangular pyramid is given by;

$V=\frac{1}{3}\times l\times b\times h$

where $l=10in.$ and w=8in are the length and width of a side of the rectangular base respectively.

There is a right triangle created inside this pyramid that can help us find the height of this pyramid.

Notice that the base of this right triangle is half the width of the rectangular base (4in.) and the hypotenuse is 14in.

We need to use Pythagoras Theorem to find the height of this pyramid.

$h^2+4^2=14^2$

$h^2+16=196$

$h^2=196-16$

$h^2=180$

$h=\sqrt{180}$

$h=6\sqrt{5}in.$

We substitute the values into the formula to get;

$V=\frac{1}{3}\times 10\times 8\times6\sqrt{5}in^3$

$V=160\sqrt{5}in^3$

$V=357.8in^3$

QUESTION 4

The radius of the base of the given cone is 12m.

The height of the cone is 25m.

The volume of a cone is calculated using the formula;

$V=\frac{1}{3}\pi r^2h$

We substitute the given values to get;

$V=\frac{1}{3}\pi 12^2\times 25m^3$

$V=3769.9m^3$

QUESTION 5

The given cone has diameter 14yd.

The radius is half the diameter, r=7yd

The radius(7yd), the height (h), and the slant height(25yd being the hypotenuse) form a right triangle.

We apply the Pythagoras Theorem again to get;

$h^2+7^2=25^2$

$h^2+49=625$

$h^2=625-49$

$h^2=576$

$h=\sqrt{576}$

$h=24$

The height of the cone is 24yd.

The volume of a cone is calculated using the formula;

$V=\frac{1}{3}\pi r^2h$

We substitute the given values to get;

$V=\frac{1}{3}\pi 7^2\times 24yd^3$

$V=1231.5yd^3$

QUESTION 6

The height of the given cone is 18mm.

The radius can be calculated using the tangent ratio.

$\tan(66\degree)=\frac{18}{r}$

$r=\frac{18}{\tan(66\degree)}$

$r=8.0141yd$

The volume of a cone is calculated using the formula;

$V=\frac{1}{3}\pi r^2h$

We substitute the given values to obtain;

$V=\frac{1}{3}\pi 8.0141^2\times 18mm^3$

$V=151.1mm^3$

7 0

3 years ago