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3 years ago

Graph the systems of equations.

Mathematics

1 answer:

Pepsi [2]3 years ago

3 0

Using a graphical tool we obtain that the solution of this system
(intersection between the lines)

is given by the point (x,y) = (2,4)

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Find the volume of this square based pyramid. 10 cm 8 cm 8 cm V = [?] cm3

oksano4ka [1.4K]

Answer:

213.3

Step-by-step explanation:

The volume of a pyramid is 1/3 base times height.

Using this formula, our square base is 8*8, or 64 square units.

Multiplying that by the height, 10. We get 64*10, 640.

Finally dividing by 3, we have 213.3333333333...

Rounding that to the nearest tenth, 213.3.

3 0

3 years ago

A pound of grapes costs $2.49. Lucas bought two pounds of grapes. He gave the clerk a $10.00 bill. How much change did Lucas get

GaryK [48]

Answer:

$5.02

Step-by-step explanation:

$2.49 × 2 = $4.98

$10 - $4.98 = $5.02

7 0

2 years ago

from a window 24 feet above the ground, the angle of elevation to the top of another building is 38 degrees. The distance betwee

Snowcat [4.5K]

Answer:

The height of the building is $73.2\ ft$

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

In the right triangle ABC

$tan(38\°)=\frac{BC}{AB}$

we have

$AB=63\ ft$

substitute and solve for BC

$tan(38\°)=\frac{BC}{63}$

$BC=(63)tan(38\°)=49.2\ ft$

Find the height of the building

The height of the building (h) is equal to

$h=BC+24=49.2+24=73.2\ ft$

8 0

3 years ago

The math department of a college has 20 faculty members, of whom 5 are women and 15 are men. A curriculum committee of 4 faculty

Furkat [3]

Answer:

155 ways are there to select the committee that has more women than men.

Step-by-step explanation:

The order is not important.

For examle, a committee of John, Elisa, Josh and Rose is the same committee as Elisa, John, Josh and Rose. So we use the combinations formula to solve this problem.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

How many ways are there to select the committee that has more women than men?

It can either be 3 women and a men, or 4 women.

3 women and a men

1 men from a set of 15

3 women from a set of 5

$C_{5,3}*C_{15,1} = \frac{5!}{3!(2)!}*\frac{15!}{1!(14)!} = 150$

4 women

4 women from a set of 5

$C_{5,4} = \frac{5!}{4!1!} = 5$

Total

150 + 5 = 155

155 ways are there to select the committee that has more women than men.

3 0

3 years ago

Could anyone give me the answer to this question?

love history [14]

Answer:

Step-by-step explanation:

$\angle AOC$ is made up of s + r, and since r is $\frac{3}{5}$ of $\angle AOC$ we know r must be the remaining $\frac{2}{5}$ of $\angle AOC$ .

We can solve for $\angle AOC$ by using this equation:

$\frac{2}{5}\angle AOC = 24\\(\frac{2}{5}\angle AOC)\frac{5}{2} = (24)\frac{5}{2}\\ \boxed{\angle AOC = 60}$

1. 2 fifths of $\angle AOC$ is 24

2. multiply both sides by $\frac{5}{2}$ to isolate $\angle AOC$

3. $\angle AOC$ is 60°

We can now solve for r

$r = \frac{3}{5}\angle AOC\\r = \frac{3}{5}(60)\\\boxed{r = 36}$

1. the equation the problem gave us

2. substitute $\angle AOC$ for 60 (we solved for it before)

3. $r$ is 36°

4 0

2 years ago