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Margaret [11]
3 years ago
10

BRAINLIEST!!! 11. Solve the inequality and graph the solution on a number line.

Mathematics
2 answers:
pshichka [43]3 years ago
8 0

-3(5y - 4) ≥ 17

-15y + 12 ≥ 17

-15y ≥ 5

y ≤ -1/3

To graph this inequality, place a closed circle at the line one to the left of 0. Then, draw a line above or on the number line with an arrow that points to the left.

Hope this helps!! :)

PilotLPTM [1.2K]3 years ago
7 0

Answer:

y≤-1/3 (fraction)

And on the number line it will start from -1/3 (-0.333) and go less than -1/3 ( to the left, and it will be shaded

Step-by-step explanation:

First we expand the brackets, making it -15y+12≥17

Then we move 12 to the other side, making it negative, -15y≥17-12

Simplify, -15y≥5

Then we divide on both sides to isolate y, flipping the greater than sign to less than because when you divide or multiply by a negative number, the sign flips. y≤5/-15

Then we simplify by dividing the fraction by 5, making it -1/3. y≤-1/3

If you have any doubts, inform me

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Check the picture below.

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Complete the two-column proof using the answers in the bank. Given: DF ≅ EF FG bisects ∠DFE Prove: ∆DFG ≅∆EFG
iragen [17]

Answer:

Reasons:

1. Given

2. Given

3. Definition of bisector

4. Reflexive property

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Step-by-step explanation:

This is quite easy to solve. All that you're expected to do is to complete the reason that justifies each statement given in the two-column proof.

Let's complete the proof as follows:

1. Statement: DF \cong EF

1. Reason: Given

We know this statement is true because we are given in the question.

2. Statement: FG bisects <DFE

2. Reason: Given

We also know this because we are told so in the question, as shown in the diagram given.

3. Statement: \angle 1 \cong \angle 2

3. Reason: Definition of bisector

We know this because an angle bisector divides an angle into two equal halves. Therefore, the definition of bisector justifies why it was stated that \angle 1 \cong \angle 2

4. Statement: \overline{FG} \cong \overline{FG}

Reason: Reflexive property.

5. Statement: ∆DFG \cong EFG

5. Reason: SAS Congruence

Two sides (DF and FG) and an included angle (angle 1) of ∆DFG is congruent two corresponding sides (EF and FG) and an included angle (angle 2) of ∆EFG. Therefore, ∆DFG \cong EFG by the Side-Angle-Side (SAS) Congruence Theorem.

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Find the area of the larger rectangle. 
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Answer:

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Step-by-step explanation:

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