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3 years ago

Find the values of the variables and please give the reasons

Mathematics

1 answer:

nikklg [1K]3 years ago

8 0

180 ÷3 = 60 ° (angles on a straight line equals to 180 ° )

a+b+60 =180°

a+ b= 180 ° - 60° = 120°

(a+b) are 2 variables

so 120 ÷2 =60 °

therefore a and b =60 °

c +b+ 60° = 180° ( co - interior angles are supplementary angles )

c+60° +60° =180°

c +120° =180°

c =180°-120°

c=60 °

d=60° (alternate angles are equal )

c+b+d=180°

60° +60° + d = 180°

d=180°-120°

d=60°

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3 years ago

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inysia [295]

<h3>Answer: 14x - 8</h3>

=======================================================

Explanation:

I'll use the quadratic formula to find the roots or x intercepts. This slight detour allows us to factor without having to use guess-and-check methods.

The equation is of the form ax^2+bx+c = 0

a = 12
b = -11
c = -5

This leads to...

$x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-11)\pm\sqrt{(-11)^2-4(12)(-5)}}{2(12)}\\\\x = \frac{11\pm\sqrt{361}}{24}\\\\x = \frac{11\pm19}{24}\\\\x = \frac{11+19}{24} \ \text{ or } \ x = \frac{11-19}{24}\\\\x = \frac{30}{24} \ \text{ or } \ x = \frac{-8}{24}\\\\x = \frac{5}{4} \ \text{ or } \ x = -\frac{1}{3}$

Now use those roots to form these steps

$x = \frac{5}{4} \ \text{ or } \ x = -\frac{1}{3}\\\\4x = 5 \ \text{ or } \ 3x = -1\\\\4x - 5 =0 \ \text{ or } \ 3x+1 = 0\\\\(4x-5)(3x+1) = 0$

Refer to the zero product property for more info.

Therefore, the original expression factors fully to (4x-5)(3x+1)

Use the FOIL rule to expand it out and you should get 12x^2-11x-5 again.

----------------------------------------------

We did that factoring so we could find the side lengths of the rectangle.

I'm using the fact that area = length*width

L = length = 4x-5
W = width = 3x+1

The order of length and width doesn't matter.

From here, we can then compute the perimeter of the rectangle

P = 2(L+W)

P = 2(4x-5+3x+1)

P = 2(7x-4)

P = 14x - 8

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2 years ago

at a particular school 50% of students travel by bus. if this represents 600 children how many children attend the school

hichkok12 [17]

Answer:

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Find the values of the variables and please give the reasons​

Find the values of the variables and please give the reasons