Answer:
66 °F
Step-by-step explanation:
At 4 P.M., the temperature had decreased by 3° from the temperature at 3 P.M., so was ...
4 P.M. temp = 78 °F -3° = 75 °F
This was repeated until 7 P.M.
5 P.M. temp = 75 °F -3° = 72 °F
6 P.M. temp = 72 °F -3° = 69 °F
7 P.M. temp = 69 °F -3° = 66 °F
The temperature at 7 P.M. was 66 °F.
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Of course the repeated subtraction can be simplified using multiplication. The subtraction of 3° four times is equivalent to the subtraction of . . .
(3°)(4) = 12°
That is, the temperature at 7 P.M. is ...
78 °F -3°×4 = 78 °F -12° = 66 °F
Given that the triangles are similar.
When triangles are similar, all three pairs of corresponding sides are in the same ratio.
Similarly in the given triangles, the ratio of the corresponding sides are equal.
Cross multiplying, we get
Dividing both sides of the equation by -4.
So, we get
x = 7.
Slope-intercept form is y=mx+b. our goal is to get y by itself on one side of the equation.
2x-3y+1=0
2x+1=3y
3y=2x+1
y=(2/3)x+1/3
That is the same function but in slope-intercept form.
Answer:
Option D. minimum value at −38
Step-by-step explanation:
we have
Let
Complete the square
------> equation of a vertical parabola in vertex form
The vertex is the point 
The parabola open upward-----> the vertex is a minimum
therefore
minimum value at −38
Answer:
p is approximately equal to 1.125, -1.925
Step-by-step explanation:
We can solve this first by expanding, giving us a quadratic equation in the usual ax² + bx + c format, then solving that for p:
(4p - 4)(13p + 27) = 0
52p² + 108p - 52p - 108 = 0
52p² + 52p - 108 = 0
13p² + 13p - 27 = 0
13p² + 13p = 27
p² + p = 27 / 13
p² + p + 1/4 = 27/13 + 1/4
(p + 1/2)² = 108 / 52 + 13 / 52
(p + 1/2)² = 121 / 52
p + 1/2 = ± √(121 / 52)
p = -1/2 ± 11√(1/13) / 2
At that point we can simply plug those numbers into a calculator and solve it:
p ≈ 1.125, -1.925
