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Vera_Pavlovna [14]
3 years ago
10

How to solve these two problems ?

Mathematics
1 answer:
puteri [66]3 years ago
4 0

8)  \theta is -0.896 radians

9) length of arc is 41.91 cm

Solution:

8)

Given that,

tan\ \theta = \frac{-5}{4}

\theta is in quadrant 4

To find: \theta

From given,

tan\ \theta = \frac{-5}{4}\\\\\theta = tan^{-1} \frac{-5}{4}\\\\\theta = tan^{-1} (-1.25)\\\\\theta = -51.34

Thus value of \theta is -51.34 degrees

Convert degrees to radians

-51.34\ degree = -51.34 \times \frac{ \pi }{180}\ radian\\\\-51.34\ degree = -0.896\ radian

Thus \theta is -0.896 radians

9)

From given,

radius = 15.4 cm

\theta = \frac{13 \pi }{15}

<em><u>The length of arc when angle in radians is:</u></em>

arc\ length = r \times \theta\\\\arc\ length = 15.4 \times \frac{ 13 \pi }{15}\\\\arc\ length = 15.4 \times 2.721\\\\arc\ length = 41.91

Thus length of arc is 41.91 cm

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kotegsom [21]

Answer: 0; -2

Step-by-step explanation:

Data: y-intercept=x and slope=x

Equation=y=-2

Only step, Point out the y-intercept and slope

-2=y-intercept

0=slope

Reason: Since there is no visible slope, the placeholder would be 0 therefore the slope would be 0, -2 is the only number left so that means the only number that can be y-intercept is -2.

That is why the slope is 0 and the y-intercept is -2

I hope this helps!

5 0
2 years ago
The ratio of students who prefer pineapple to students who prefer kiwi is 12 to 5. Which pair of equivalent ratios could be used
AlexFokin [52]

Answer:

<u> 105</u> students could prefer kiwi if there are 357 total students.

Step-by-step explanation:

Given:

The ratio of students who prefer pineapple to students who prefer kiwi is 12 to 5.

Now, to find number of students prefer kiwi if there are 357 total students.

Let the students prefer pineapple be 12x.

And the students prefer kiwi be 5x.

Total students = 357.

So, we set an equation to get the number of students who prefer kiwi.

According to question:

12x+5x=357

17x=357

<em>Dividing both sides by 17 we get:</em>

x=21.

<em>Thus, students prefer kiwi are:</em>

5x

=5\times 21=105.

Therefore, 105 students could prefer kiwi if there are 357 total students.

3 0
3 years ago
Kyla makes a triangular school pennant. The area of the triangle is 180 square inches. The base of the pennant is z inches long.
kykrilka [37]
We can represent the base as z and the height as 2z+6. We are going to use the formula A=1/2*b*h and solve for z
180=1/2*z*(2z+6)
360=2z^2+6z 
0=2z^2+6z-360
0=2(z^2+3z-180)
0=(z+15)(z-12)
So z=-15 and 12 but it must be positive so then the base is equal to 12

When we plug this into 2z+6 we get 30 for the height
2(12)+6=30

Hope this helps
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3 years ago
If AB is parallel to CD and the slope of CD is-5, what is the slope of AB?
ankoles [38]

Answer:

C. -5

Step-by-step explanation:

If the two lines are parallel, they have the same slope. Therefore the slope of AB is -5.

5 0
3 years ago
-1/2(2x-6)+9=-8 answer
Oxana [17]

Answer:

x= 20 i think sorry if it's wrong⊙﹏⊙

5 0
3 years ago
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