2 years ago

Use substitution to solve this system of equations. 4x-5y=19 y=8x-11

1 answer:

3 0

$4x-5y=19 \\
y=8x-11 \\ \\
\hbox{substitute 8x-11 for y in the 1st equation and solve for x:} \\
4x-5(8x-11)=19 \\
4x-40x+55=19 \\
4x-40x=19-55 \\
-36x=-36 \\
x=\frac{-36}{-36} \\
x=1 \\ \\
\hbox{substitute 1 for x in one of the equations and solve for y:} \\
y=8 \times 1-11 \\
y=8-11 \\
y=-3 \\ \\
(x,y)=(1,-3)$

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2 years ago

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Dmitry [639]

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First option

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3 years ago

In triangle abc, a is a right angle, and ab = 16√3, and the measure of b=30 degrees. What is the length of ac.

salantis [7]

Answer:

the length of ac is 16.

Step-by-step explanation:

Given;

A is right angle, = 90⁰

B is 30⁰

ab = 16√3

↓

↑

A → ← B

If this right angle triangle is considered, length bc is the hypotenuse and length ac is the opposite side of angle B.

The length of ac is calculated as follows;

$tan \ B = \frac{opposite \ side}{adjacent \ side} \\\\tan \ B = \frac{ac}{ab} \\\\ac = ab \ \times \ tan \ B\\\\ac = 16\sqrt{3} \ \times \frac{\sqrt{3} }{3} \\\\ac = \frac{16 \sqrt{9} }{3} \\\\ac = \frac{16 \times 3}{3} \\\\ac = 16$