A)
The slope-intercept form:
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
m - slope
b - y-intercept
The formula of a slope:
![m=\dfrac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
We have the points (2, 5.1) and (-1, -0.5). Substitute:
![m=\dfrac{-0.5-5.1}{-1-2}=\dfrac{-5.6}{-3}=\dfrac{5.6}{3}=\dfrac{56}{30}=\dfrac{28}{15}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7B-0.5-5.1%7D%7B-1-2%7D%3D%5Cdfrac%7B-5.6%7D%7B-3%7D%3D%5Cdfrac%7B5.6%7D%7B3%7D%3D%5Cdfrac%7B56%7D%7B30%7D%3D%5Cdfrac%7B28%7D%7B15%7D)
Therefore we have:
![y=\dfrac{28}{15}x+b](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7B28%7D%7B15%7Dx%2Bb)
Put the coordinates of the point (-1, -0.5) ot the equation:
![-0.5=\dfrac{28}{15}(-1)+b](https://tex.z-dn.net/?f=-0.5%3D%5Cdfrac%7B28%7D%7B15%7D%28-1%29%2Bb)
<em>multiply both sides by 2</em>
<em>add
to both sides</em>
<em>divide both sides by 2</em>
![b=\dfrac{41}{30}](https://tex.z-dn.net/?f=b%3D%5Cdfrac%7B41%7D%7B30%7D)
Answer: ![\boxed{y=\dfrac{28}{15}x+\dfrac{41}{30}}](https://tex.z-dn.net/?f=%5Cboxed%7By%3D%5Cdfrac%7B28%7D%7B15%7Dx%2B%5Cdfrac%7B41%7D%7B30%7D%7D)
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B)
We have the points (-2, 3) and (3, -4).
Calculate the slope:
![m=\dfrac{-4-3}{3-(-2)}=\dfrac{-7}{5}=-\dfrac{7}{5}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7B-4-3%7D%7B3-%28-2%29%7D%3D%5Cdfrac%7B-7%7D%7B5%7D%3D-%5Cdfrac%7B7%7D%7B5%7D)
Therefore we have:
![y=-\dfrac{7}{5}x+b](https://tex.z-dn.net/?f=y%3D-%5Cdfrac%7B7%7D%7B5%7Dx%2Bb)
Put the coordinates of the point (-2, 3) to the equation of a line:
![3=-\dfrac{7}{5}(-2)+b](https://tex.z-dn.net/?f=3%3D-%5Cdfrac%7B7%7D%7B5%7D%28-2%29%2Bb)
<em>subtract
from both sides</em>
![\dfrac{1}{5}=b\to b=\dfrac{1}{5}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B5%7D%3Db%5Cto%20b%3D%5Cdfrac%7B1%7D%7B5%7D)
Answer: ![\boxed{y=-\dfrac{7}{5}x+\dfrac{1}{5}}](https://tex.z-dn.net/?f=%5Cboxed%7By%3D-%5Cdfrac%7B7%7D%7B5%7Dx%2B%5Cdfrac%7B1%7D%7B5%7D%7D)
Answer:
![y=15(\frac{2}{3})^x](https://tex.z-dn.net/?f=y%3D15%28%5Cfrac%7B2%7D%7B3%7D%29%5Ex)
Step-by-step explanation:
we know that
The equation of a exponential function is of the form
![y=a(b^x)](https://tex.z-dn.net/?f=y%3Da%28b%5Ex%29)
where
a is the initial value or y-intercept
b is the base of the exponential function
In this problem we have
----> the y-intercept is given
substitute
![y=15(b^x)](https://tex.z-dn.net/?f=y%3D15%28b%5Ex%29)
we have the other ordered pair (1,10)
substitute the value of x and the value of y and solve for b
![10=15(b^1)\\10=15b](https://tex.z-dn.net/?f=10%3D15%28b%5E1%29%5C%5C10%3D15b)
![b=\frac{10}{15}=\frac{2}{3}](https://tex.z-dn.net/?f=b%3D%5Cfrac%7B10%7D%7B15%7D%3D%5Cfrac%7B2%7D%7B3%7D)
substitute
![y=15(\frac{2}{3})^x](https://tex.z-dn.net/?f=y%3D15%28%5Cfrac%7B2%7D%7B3%7D%29%5Ex)
see the attached figure to better understand the problem
Answer:
<h2>
![x1 = - \frac{5}{2}](https://tex.z-dn.net/?f=x1%20%3D%20%20-%20%20%5Cfrac%7B5%7D%7B2%7D%20)
</h2>
![x2 = \frac{4}{3}](https://tex.z-dn.net/?f=x2%20%3D%20%20%5Cfrac%7B4%7D%7B3%7D%20)
Step-by-step explanation:
![18 {x}^{2} + 21x - 60 = 0](https://tex.z-dn.net/?f=18%20%7Bx%7D%5E%7B2%7D%20%20%2B%2021x%20-%2060%20%3D%200)
Divide both sides of the equation by 3
![6 {x}^{2} + 7x - 20 = 0](https://tex.z-dn.net/?f=6%20%7Bx%7D%5E%7B2%7D%20%20%2B%207x%20-%2020%20%3D%200)
Write 7x as a difference
![6 {x}^{2} + 15x - 8x - 20 = 0](https://tex.z-dn.net/?f=6%20%7Bx%7D%5E%7B2%7D%20%20%2B%2015x%20-%208x%20-%2020%20%3D%200)
Factor out 3x from the expression
![3x(2x + 5) - 8x - 20 = 0](https://tex.z-dn.net/?f=3x%282x%20%2B%205%29%20-%208x%20-%2020%20%3D%200)
Factor out -4 from the expression
![3x(2x + 5) - 4(2x + 5) = 0](https://tex.z-dn.net/?f=3x%282x%20%2B%205%29%20-%204%282x%20%2B%205%29%20%3D%200)
Factor out 2x + 5 from the expression
![(2x + 5)(3x - 4) = 0](https://tex.z-dn.net/?f=%282x%20%2B%205%29%283x%20-%204%29%20%3D%200)
When the product of factors equals 0 , at least one factor is 0
![2x + 5 = 0](https://tex.z-dn.net/?f=2x%20%2B%205%20%3D%200)
![3x - 4 = 0](https://tex.z-dn.net/?f=3x%20-%204%20%3D%200)
Solve the equation for X
![2x + 5 = 0](https://tex.z-dn.net/?f=2x%20%2B%205%20%3D%200)
Move constant to R.H.S and change its sign
![2x = 0 - 5](https://tex.z-dn.net/?f=2x%20%3D%200%20-%205)
Calculate the difference
![2x = - 5](https://tex.z-dn.net/?f=2x%20%20%3D%20%20-%205)
Divide both sides of the equation by 2
![\frac{2x}{2} = \frac{ - 5}{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B2x%7D%7B2%7D%20%20%3D%20%20%5Cfrac%7B%20-%205%7D%7B2%7D%20)
Calculate
![x 1= - \frac{5}{2}](https://tex.z-dn.net/?f=x%201%3D%20%20-%20%20%5Cfrac%7B5%7D%7B2%7D%20)
Again,
![3x - 4 = 0](https://tex.z-dn.net/?f=3x%20-%204%20%3D%200)
Move constant to RHS and change its sign
![3x = 0 + 4](https://tex.z-dn.net/?f=3x%20%3D%200%20%2B%204)
Calculate the sum
![3x = 4](https://tex.z-dn.net/?f=3x%20%3D%204)
divide both sides of the equation by 3
![\frac{3x}{3} = \frac{4}{3}](https://tex.z-dn.net/?f=%20%5Cfrac%7B3x%7D%7B3%7D%20%20%3D%20%20%5Cfrac%7B4%7D%7B3%7D%20)
Calculate
![x 2= \frac{4}{3}](https://tex.z-dn.net/?f=x%202%3D%20%20%5Cfrac%7B4%7D%7B3%7D%20)
Hope this helps..
Best regards!!
Answer:
3/5x−3/7
Step-by-step explanation:
Simplify the expression.
3/5x−3/7
-hope it helps