Solve the following system of equations.

Mathematics

1 answer:

V125BC [204]3 years ago

7 0

Answer:

x = 3 and y = -6

Step-by-step explanation:

Use the elimination method to get rid of one of the variables.

Find the value of one variable.

Find the value of the remaining variables using substitution.

Clearly state the final answer.

Check your answer by substituting both values into either of the original equations.

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Please help ! only G-J 15 points for this.

kogti [31]

Answers: G) ∠BCS = 57.5°

H) ∠FHI = 72°

I) ∠ACB and also ∠DCH

J) ∠CHD (which can also be named ∠BHE)

<u>Step-by-step explanation:</u>

First of all, I checked your answers for A-F and they are all correct. YAY!

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G) Draw a point halfway between B and D and label it S. Then draw a ray from C passing through S.

∠ACB and ∠BCD are supplementary so

65° + ∠BCD = 180°

⇒ ∠BCD = 115°

Since ray CS bisects ∠BCD, then ∠BCS is half of ∠BCD.

$\angle BCS=\dfrac{1}{2} (\angle BCD)\\\\. \quad \quad=\dfrac{1}{2}(115^o)\\\\. \quad \quad =\large\boxed{57.5^o}$

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H) The instructions state to draw a line from H to F. This divides ∠DHI into two angles: ∠FHD and ∠FHI. Since lines BI and EG are perpendicular, then ∠DHI = 90°. It is given that ∠FHI is 4 times larger than ∠FHD so we can use substitution...

∠FHD + ∠FHI = ∠DHI

∠FHD + 4(∠FHD) = 90°

5(∠FHD) = 90°

∠FHD = 18°

∠FHI = 4(∠FHD)

= 4 (18°)

= $\large\boxed{72^o}$

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I) adjacent means they share a side and supplementary means they form a straight angle. There are two angles that are adjacent and supplementary to ∠ACH.