Answer:2.19 monthd
Step-by-step explanation:
Cris borrowed money from her brother 6 months ago. She now owes him 56.50
Let x= original money borrowed from her brother 6 months ago
She has not borrowed and she is paying 15.75 on her debt each month for the last 6 months. This means in the past 6 months,she has paid 15.75×6= 94.5
She now owes him 56.50. This means original money,x-56.50 =94.5
x = 94.5+56.50=151
If she now increases her monthly payment to 25.75, let the number of months be y, she will pay 25.75y in y months
25.75y =56.50
y =2.19 months
Answer:
Given
Number of stacks = 2
Stack 1 = 6 cups; h1 = 15cm
Stack 2 = 12 cups; h2 = 23cm
Let's first find the average:
With an average of 4/3, to obtain the number of cups needed to obtain a height of 50m, we have:
50 / (4/3)
= 50 * 3/4
= 150/4
= 37.5
From the answer, we can see that the number of cups is not really proportional to the height of the stack, because the average of stack one and stack 2 are different.
Step-by-step explanation:
For this problem, we are going to use the <em>law of sines</em>, which states:
![\dfrac{\sin{A}}{a} = \dfrac{\sin{B}}{b} = \dfrac{\sin{C}}{c}](https://tex.z-dn.net/?f=%20%5Cdfrac%7B%5Csin%7BA%7D%7D%7Ba%7D%20%3D%20%5Cdfrac%7B%5Csin%7BB%7D%7D%7Bb%7D%20%3D%20%5Cdfrac%7B%5Csin%7BC%7D%7D%7Bc%7D%20)
In this case, we have an angle and two sides, and we are trying to look for the third side. First, we have to find the angle which corresponds with the second side,
. Then, we can find the third side. Using the law of sines, we can find:
![\dfrac{\sin{39^{\circ}}}{11} = \dfrac{\sin{B}}{13}](https://tex.z-dn.net/?f=%20%5Cdfrac%7B%5Csin%7B39%5E%7B%5Ccirc%7D%7D%7D%7B11%7D%20%3D%20%5Cdfrac%7B%5Csin%7BB%7D%7D%7B13%7D%20)
We can use this to solve for
:
![13 \cdot \dfrac{\sin{39^{\circ}}}{11} = \sin{B}](https://tex.z-dn.net/?f=%2013%20%5Ccdot%20%5Cdfrac%7B%5Csin%7B39%5E%7B%5Ccirc%7D%7D%7D%7B11%7D%20%3D%20%5Csin%7BB%7D%20)
![B = \sin^{-1}{\Big(13 \cdot \dfrac{\sin{39^{\circ}}}{11}\Big)} \approx 48.1](https://tex.z-dn.net/?f=%20B%20%3D%20%5Csin%5E%7B-1%7D%7B%5CBig%2813%20%5Ccdot%20%5Cdfrac%7B%5Csin%7B39%5E%7B%5Ccirc%7D%7D%7D%7B11%7D%5CBig%29%7D%20%5Capprox%2048.1%20)
Now, we can find
:
![C = 180^{\circ} - 48.1^{\circ} - 39^{\circ} = 92.9^{\circ}](https://tex.z-dn.net/?f=%20C%20%3D%20180%5E%7B%5Ccirc%7D%20-%2048.1%5E%7B%5Ccirc%7D%20-%2039%5E%7B%5Ccirc%7D%20%3D%2092.9%5E%7B%5Ccirc%7D%20)
Using this, we can find
:
![\dfrac{\sin{39^{\circ}}}{11} = \dfrac{\sin{92.9^{\circ}}}{c}](https://tex.z-dn.net/?f=%20%5Cdfrac%7B%5Csin%7B39%5E%7B%5Ccirc%7D%7D%7D%7B11%7D%20%3D%20%5Cdfrac%7B%5Csin%7B92.9%5E%7B%5Ccirc%7D%7D%7D%7Bc%7D%20)
![c = \dfrac{11\sin{92.9^{\circ}}}{\sin{39^{\circ}}} \approx \boxed{17.5}](https://tex.z-dn.net/?f=%20c%20%3D%20%5Cdfrac%7B11%5Csin%7B92.9%5E%7B%5Ccirc%7D%7D%7D%7B%5Csin%7B39%5E%7B%5Ccirc%7D%7D%7D%20%5Capprox%20%5Cboxed%7B17.5%7D%20)
c is approximately 17.5.
Complete Question
The complete question is shown on the first uploaded image
Answer:
The line is ![y = -4 x](https://tex.z-dn.net/?f=y%20%20%3D%20%20-4%20x)
Step-by-step explanation:
From the question we are told that
The line is ![y = \frac{1}{4} x + 8](https://tex.z-dn.net/?f=y%20%20%3D%20%20%5Cfrac%7B1%7D%7B4%7D%20x%20%20%2B%208)
The point is P(0,0 )
Generally the equation for a line is ![yn = mx + c](https://tex.z-dn.net/?f=yn%20%3D%20%20mx%20%20%2B%20c)
Now comparing this with the given equation we see that
![m =\frac{1}{4} = slope](https://tex.z-dn.net/?f=m%20%20%3D%5Cfrac%7B1%7D%7B4%7D%20%3D%20%20slope)
![C =8 = intercept](https://tex.z-dn.net/?f=C%20%20%3D8%20%20%3D%20%20intercept%20)
Generally the slope of the perpendicular to the given line is mathematically evaluated as
![m_1 = - \frac{1}{m}](https://tex.z-dn.net/?f=m_1%20%20%3D%20-%20%20%5Cfrac%7B1%7D%7Bm%7D)
=>
=>
Generally from the univesal equation of a line and the given point we have that
y = mx + c at p(0,0) and
is
0 = -4 (0 ) + c
=> c = 0
Hence the equation perpendicular to the line given at the point given is
![y = -4 x](https://tex.z-dn.net/?f=y%20%20%3D%20%20-4%20x)
Answer: Mural height: 22ft and the Mural width is 10ft
Step-by-step explanation: I took the test and got it wrong, but they told me the correct answers after I took the test. (I got to K-12) Proof: