A. find the value of a. B. Find the value of the marked angles.

Mathematics

2 answers:

Marat540 [252]3 years ago

8 0

The marked angles are opposite angles, and as such they have the same measure. So, we have

$6a+11 = 2a+83$

Subtract 2a and 11 from both sides to get

$4a = 72$

Divide both sides by 4 to get

$a = \dfrac{72}{4} = 18$

Now that we know the value of a, we can compute the measure of the angles. We can also verify that the solution we found is correct by verifying that both expressions actually give the same result:

$6a+11 = 6\cdot 18 + 11 = 119$

$2a+83 = 2\cdot 18 + 83 = 119$

Tatiana [17]3 years ago

6 0

i hope it can help you

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Solve the system by substitution. y = -4x 23 - 5y = 44

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<h3>Explanation</h3>

Given the system of equations.

$\begin{cases} y = - 4x \\ 23 - 5y = 44 \end{cases}$

Substitute y = -4x in the second equation.

$23 - 5( - 4x) = 44 \\ 23 + 20x = 44 \\ 20x = 44 - 23 \\ 20x = 21 \\ x = \frac{21}{20}$

Substitute the value of x in any given equations. I will substitute the value of x in the first equation.

$y = - 4x \Longrightarrow y = - 4( \frac{21}{20} ) \\ y = \cancel{ - 4}( \frac{21}{ \cancel{20}} ) \Longrightarrow y = - \frac{21}{5} \\ y = - \frac{21}{5}$

Answer Check by substituting both values in two equations.

First Equation

$y = - 4x \Longrightarrow - \frac{21}{5} = - 4( \frac{21}{20} ) \\ - \frac{21}{5} = \cancel{ - 4}( \frac{21}{ \cancel{20}} ) \\ - \frac{21}{5} = - \frac{21}{5} \: \: \: \checkmark$