Answer:
![m=0](https://tex.z-dn.net/?f=m%3D0)
Step-by-step explanation:
Given
See attachment
Required
Determine the slope of the line
From the attachment, we have the following points
![(x_1,y_1) = (-4,1)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%20%3D%20%28-4%2C1%29)
and
![(x_2,y_2) = (3,1)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29%20%3D%20%283%2C1%29)
The slope m is then calculated using:
![m = \frac{y_2- y_1}{x_2 - x_1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_2-%20y_1%7D%7Bx_2%20-%20x_1%7D)
Substitute values for the x's and y's
![m = \frac{1-1}{3 - (-4)}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B1-1%7D%7B3%20-%20%28-4%29%7D)
![m = \frac{1-1}{3 +4}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B1-1%7D%7B3%20%2B4%7D)
![m = \frac{0}{7}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B0%7D%7B7%7D)
![m=0](https://tex.z-dn.net/?f=m%3D0)
<em>Hence, the slope is 0</em>
Using relations in a right triangle, it is found that the values of x and y are given by: x = 24, y = 46.4, given by option a.
<h3>What are the relations in a right triangle?</h3>
The relations in a right triangle are given as follows:
- The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.
- The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.
- The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.
First, we start with the vertical line h that divides y, that is <u>opposite to an angle of 30º, with hypotenuse 34</u>, hence:
sin(30º) = h/34
0.5 = h/34
h = 17.
Then, h is opposite to an angle of 45º, while the hypotenuse is x, hence:
![\sin{45^\circ} = \frac{17}{x}](https://tex.z-dn.net/?f=%5Csin%7B45%5E%5Ccirc%7D%20%3D%20%5Cfrac%7B17%7D%7Bx%7D)
![x = \frac{17}{\sin{45^\circ}}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B17%7D%7B%5Csin%7B45%5E%5Ccirc%7D%7D)
x = 24.
y is divided into two segments.
- The first is the adjacent to the angle of 30º, while the hypotenuse is 34.
- The second is adjacent to the angle of 45º, while the hypotenuse is 24.
Then:
![\cos{30^\circ} = \frac{y_1}{34}](https://tex.z-dn.net/?f=%5Ccos%7B30%5E%5Ccirc%7D%20%3D%20%5Cfrac%7By_1%7D%7B34%7D)
![y_1 = 34\cos{30^\circ} = 29.4](https://tex.z-dn.net/?f=y_1%20%3D%2034%5Ccos%7B30%5E%5Ccirc%7D%20%3D%2029.4)
![\cos{45^\circ} = \frac{y_2}{24}](https://tex.z-dn.net/?f=%5Ccos%7B45%5E%5Ccirc%7D%20%3D%20%5Cfrac%7By_2%7D%7B24%7D)
![y_2 = 24\cos{45^\circ} = 17](https://tex.z-dn.net/?f=y_2%20%3D%2024%5Ccos%7B45%5E%5Ccirc%7D%20%3D%2017)
Then, the value of y is given by:
.
More can be learned about relations in a right triangle at brainly.com/question/26396675
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3p + 2n = 8.25 ....multiply by 2
2p + 3n = 8 .........multiply by -3
-------------------
6p + 4n = 16.5 (result of multiplying by 2)
-6p - 9n = - 24 (result of multiplying by -3)
-------------------add
-5n = - 7.5
n = -7.5 / -5
n = 1.50 .............notebooks cost 1.50 each
2p + 3n = 8
2p + 3(1.50) = 8
2p + 4.50 = 8
2p = 8 - 4.50
2p = 3.50
p = 3.50/2
p = 1.75......pens cost 1.75 each
so 2 pens and 2 notebooks cost : 2(1.75) + 2(1.50) = $ 6.50 <==
I believe the answer is 6
(Base * height) divided by 2
In this case the area of the triangle is 1125 cm^2