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stealth61 [152]
3 years ago
12

A line through the origin and (10,4) is showin in the standard (x,y) coordinate plane below. The acute angle between the line an

d the positive x-axis has measure θ.

Mathematics
1 answer:
Snowcat [4.5K]3 years ago
5 0

Answer:

\cos\theta=\frac{10}{\sqrt{116}}

Step-by-step explanation:

To solve this, we can imagine a line drawn directly down from the point (10,4) to the x-axis. This would make a right triangle with length 10 and height 4.

\cos\theta is equal to the length of adjacent leg to the angle divided by the length of the hypotenuse of the triangle. From the picture, we can see the adjacent leg is 10.

We can use Pythagorean's Theorem to find the hypotenuse (let c represent the length of the hypotenuse):

10^2+4^2=c^2

100+16=c^2

116=c^2

c=\sqrt{116}

Thus, we know the adjacent is 10, and the hypotenuse is \sqrt{116}. This means \cos\theta=\frac{10}{\sqrt{116}}.

Hope this helps!

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Find the slope please
Katarina [22]

Answer:

slope is -\frac{3}{4}

Step-by-step explanation:

1,-1  -3,2 are two points on the graph

the equation to find slope is \frac{y_{1}- y_{2} }{x_{1}- x_{2} }

so \frac{2--1}{-3-1} = -\frac{3}{4}

or you can count how many places it changed in the equation \frac{rise}{run}

7 0
3 years ago
Todd uses 21 white tiles & some black tiles to make a mosaic.The mosaic has a total area of 144 square centimeters.Each tile
icang [17]

Answer: Todd used 27 black tiles.

Step-by-step explanation:

Let x represent the number of black tiles that Todd used.

Todd uses 21 white tiles & some black tiles to make a mosaic. This means that the total number of white and black tiles that Todd used is 21 + x

Each tile has an area of 3 square centimeters. This means that the total area covered by the white tiles is

21 × 3 = 63 square centimeters

Also, the total area covered by the black tiles is

3 × x = 3x square centimeters

The mosaic has a total area of 144 square centimeters. This means that

3x + 63 = 144

3x = 144 - 63

3x = 81

x = 81/3 = 27

3 0
3 years ago
Okay so m giving a lot of points so here! (My handwriting is bad lol)
lilavasa [31]

11. >

12. >

14. <

15.<


Hopefully this helps :)

8 0
3 years ago
Read 2 more answers
The data below represents the number of essays that students in Mr. Ji's class wrote. 2,3,5,5,6,7,8,8,11 Which box plot correctl
sweet-ann [11.9K]

Answer:

C

Step-by-step explanation:

2,3,5,5,<u>6</u>,7,8,8,11

6 is the middle line, 8 is the end of the box, and 4 is the beginning of the bow.

Hope this helps.

5 0
3 years ago
The mass of substances left in a sample
professor190 [17]

This question tests one's knowledge of states of matter. Kim would have to classify the water as gaseous matter in this case.

<h3>Why should Kim classify the water as gaseous?</h3>

Remember, she boiled all the liquid away. Hence in their evaporated state, the water now assumes a gaseous form.

Matter can exist in various states. They are:

  • Solids;
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Learn more about states of matter at:
brainly.com/question/16982523

6 0
2 years ago
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