MATHEMATICS HIGH SCHOOL

Which value of x satisfies both -9x + 4y = 8 and -3x - y = 4 given the same value of y?ОА
1
7
ОВ.
7
9
Ос.
8
7
D. -9
OE.
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Answers

Answer 1
Answer:

Answer:

-(8)/(7)

Step-by-step explanation:

-9x+4y=8

-3x-y=4

Multiple the entire second equation by 4

-12x-4y=16

-9x+4y=8

__________

-21x=24

divide each side by -21 and simplify

x= -(8)/(7)

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If csc theta =sqrt5/15 find sin theta

Answers

The cosecant is the reciprocal of the sine, so

\sin \theta = (15)/(√(5)) = 3 √(5)

That's not the sine of a real angle because it's out of the range -1 to 1.

a family has five children The probability of having a gil is 1/2 What is the probability of having exactly 2 girls out of five children

Answers

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Find the area of sector AOB. Enter your answer in terms of a fraction of π and rounded to the nearest tenth.The area of sector AOB is _____ π ≈ _____ mm2.

Answers

40/360 = 1/9

Sector AOB is 1/9 of the total circle.

A = pi x 3^2

A = 9pi

9pi / 9 = 1pi

The area of sector AOB is 1pi = approximately 3.1 mm^2.

Hope this helps!! :)

What is the fraction equivalent of 40% in simplest form? 2/5 4/10 40/100 4/100 pan​

Answers

Answer:

2/5

Step-by-step explanation:

Answer:

2/5

Step-by-step explanation:

good luck you got this

Johnny B's rectangular garden is 5 feet long and 10 feet wide. He wants to make the area of his garden 6 times as large by increasing the length and width by the same amount. Find the number of feet by which each dimension must be increased.

Answers

Answer:

The length is 15 and the width is 20

Step-by-step explanation: 10 times 5 is 50 and 6 times is 300 which is the area you are looking for. 15 times 20 is 300 and you add 5 to each numbers so it works.

PLEASE HELP!!! needs to be answered in sentaces(01.07 HC)

Michael and Derrick each completed a separate proof to show that corresponding angles AKG and ELK are congruent. Who completed the proof incorrectly? Explain.

Line AB is parallel to EF, transversal GJ crosses line AB at K and crosses line EF at L.

Michael's Proof


Statement Justification
1. line AB ∥ line EF with transversal segment GJ 1. Given
2. angle AKG is congruent to angle AKL 2. Vertical Angles Theorem
3. angle BKL is congruent to angle ELK 3. Alternate Interior Angles Theorem
4. angle AKG is congruent to angle ELK 4. Transitive Property


Derrick's Proof

Statement Justification
1. line AB ∥ line EF with transversal segment GJ 1. Given
2. angle AKG is congruent to angle BKL 2. Vertical Angles Theorem
3. angle BKL is congruent to angle ELK 3. Alternate Interior Angles Theorem
4. angle AKG is congruent to angle ELK 4. Transitive Property

Answers

The proof that is completed incorrectly is Michael's proof of the statement "corresponding angles AKG and ELK are congruent."

Both proofs start with the same given information – lines AB and EF are parallel, and transversal segment GJ crosses line AB at point K and crosses line EF at point L. Both proofs also rely on the same theorems – the vertical angles theorem and the alternate interior angles theorem. However, the difference is in the way the two proofs make the jump from the first three statements to the fourth statement.

In Michael's proof, statement number 3 is incorrect. Statement 3 in Michael's proof states that "angle BKL is congruent to angle ELK" based on the alternate interior angles theorem. However, this statement is not true because the interior angle BKL is not formed by the intersection of two straight lines from a point on the line AB and a point on the line EF, which is required for the alternate interior angles theorem to apply.

In contrast, Derrick's proof uses the vertical angles theorem before applying the transitive property in statement 4. The statement "angle AKG is congruent to angle ELK" in Derrick's proof is a result of applying the transitive property to the statement that "angle AKG is congruent to angle BKL" in statement 3 and the statement that "angle BKL is congruent to angle ELK" in statement 2, which are both results of applying the vertical angles theorem. This is a valid proof.

Therefore, Michael's proof is incorrect because of an incorrect application of the alternate interior angles theorem, while Derrick's proof is correct because it uses the vertical angles theorem and applies the transitive property correctly.
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