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Aleksandr [31]
3 years ago
10

P=-30h+74 The variable h represents the number of hours he has spent reading, the variable p represents the number of pages left

to read. How many hours of reading will Ethan have to do in order to have 14 pages left to read?
Mathematics
1 answer:
olchik [2.2K]3 years ago
6 0

Answer: Ethan will have to spend 2 hours reading if 14 pages are left to read

Step-by-step explanation:

Given the equation

P=-30h+74

where p =number of pages left to read and

h= the number of hours he has spent reading

Therefore , if Ethan has 14 pages left to read, then the number of hours Ethan will have to read will be

P=-30h+74

14= -30h + 74

30h= 74-14

30h= 60

h = 60/30

h =2 hours

Ethan will have to spend 2 hours reading if 14 pages are left to read

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Y/7=4 I need help on this one
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Which type of triangle is formed by joining the vertices A(-3, 6), B(2, 1), and C(9, 5)?
muminat

Answer:

An obtuse scalene triangle

Step-by-step explanation:

First, we calculate the length of the sides:

Side a – the distance between points B and C – is:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\d=\sqrt{(9-2)^2+(5-1)^2}\\d=\sqrt{(7)^2+(4)^2}\\d=\sqrt{49+16}\\d=\sqrt{65}\\d\approx{8.06}

Side b – the distance between points C and A – is:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\d=\sqrt{(-3-9)^2+(6-5)^2}\\d=\sqrt{(-12)^2+(1)^2}\\d=\sqrt{144+1}\\d=\sqrt{145}\\d\approx{12.04}

Side c – the distance between points A and B – is:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\d=\sqrt{(2-(-3))^2+(1-6)^2}\\d=\sqrt{(5)^2+(-5)^2}\\d=\sqrt{25+25}\\d=\sqrt{50}\\d\approx{7.07}

Then, we calculate the measure of the angles:

\angle{A}=\textrm{arccos}(\frac{b^2+c^2-a^2}{2bc})=\textrm{arccos}(\frac{12.04^2+7.07^2-8.06^2}{2(12.04)(7.07)})\approx{40.23^{\circ}}

\angle{B}=\textrm{arccos}(\frac{a^2+c^2-b^2}{2ac})=\textrm{arccos}(\frac{8.06^2+7.07^2-12.04^2}{2(8.06)(7.07)})\approx{105.27^{\circ}}

\angle{C}=180^{\circ}-40.23^{\circ}-105.27^{\circ}=34.50^{\circ}

None of the sides are equal, so the triangle is not equilateral nor isosceles. None of the angles are 90°, so the triangle is not right. One of the angles is greater than 90°, so the triangle must be obtuse scalene.

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