If T is the midpoint of SU, then ST ≅ TU.
Therefore we have the equation:
6x = 2x + 32 <em>subtract 2x from both sides</em>
4x = 32 <em>divide both sides by 4</em>
x = 8
ST = 6x → ST = 6(8) = 48
TU = ST, therefore ST = 48
SU = ST + TU = 2ST, therefore SU = 2(48) = 96
<h3>Answer: ST = 48, TU = 48, SU = 96</h3>
Answer:
Option B k > 0
Step-by-step explanation:
we know that
Observing the graph
The slope of the line is positive
The y-intercept is negative
we have
![3y-2x=k(5x-4)+6\\ \\3y=5kx-4k+6+2x\\ \\3y=[5k+2]x+(6-4k)\\ \\y=\frac{1}{3}[5k+2]x+(2-\frac{4}{3}k)](https://tex.z-dn.net/?f=3y-2x%3Dk%285x-4%29%2B6%5C%5C%20%5C%5C3y%3D5kx-4k%2B6%2B2x%5C%5C%20%5C%5C3y%3D%5B5k%2B2%5Dx%2B%286-4k%29%5C%5C%20%5C%5Cy%3D%5Cfrac%7B1%7D%7B3%7D%5B5k%2B2%5Dx%2B%282-%5Cfrac%7B4%7D%7B3%7Dk%29)
The slope of the line is equal to
![m=\frac{1}{3}[5k+2]](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B1%7D%7B3%7D%5B5k%2B2%5D)
Remember that the slope must be positive
so

The value of k is greater than -2/5
Analyze the y-intercept

1.5 is greater than zero
so
the solution for k is the interval ------> (1.5,∞)
therefore
must be true
k > 0
Option C: (0,125) is the y - intercept.
Explanation:
The given function is 
We need to determine the y - intercept.
<u>The value of y - intercept:</u>
The y - intercept is the value of y when x = 0
The y - intercept of the function can be determined by substituting x = 0 in the function.
Hence, let us substitute x = 0 in the function
, we have,

Simplifying the terms, we get;



Thus, the value of y is 125.
Hence, the y - intercept is 125.
Therefore, the coordinates of the y - intercept are (0,125)
Hence, Option C is the correct answer.
Answer:
d (w) = 0.1w² – w+ 5
Step-by-step explanation:
d(w) = c(w) - a(w)
= -0.3w²+2w+13 -(-0.4w²+3w+8)
= -0.3w²+0.4w²+2w-3w+13-8
= 0.1w²-w+5
Step-by-step explanation:
