MATHEMATICS HIGH SCHOOL

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Answer 1

Answer:

The value of x is 8 and the value of y is 21.

The given lines $l$ and $m$ are parallel to each other. Thus,

Angles, $(7x+12)^o$ and $(12x-28)^o$ are equal due to absolutely none angles.

$7x+12=12x-28\n5x=40\nx=8$

The sum of the angles $(12x-28)^o$ and $(9y-77)^o$ is equal to $180^o$ .

$(12x-28+9y-77)=180\n12*8-28+9y-77=180\ny =21$

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Which of the following is the equation of a line that passes through the points (0,6) and (2,10)?A. y = -2x + 6
B. y = 2x - 6
C. y = 2x + 6
D. y = -2x - 6

Answers

Given:
(0,6) and (2,10)

a) y = -2x + 6 ; y = -2(2) + 6
y = -2(0) + 6 ; y = -4 + 6
y = 6 ; y = 2

b) y = 2x - 6
y = 2(0) - 6
y = -6

c) y = 2x + 6 ; y = 2(2) + 6
y = 2(0) + 6 ; y = 4 + 6
y = 6 ; y = 10 Choice C. is the correct equation.

Answer: option c!

Step-by-step explanation:

Line KL has an equation of a line y = 4x + 5. Which of the following could be an equation for a line that is perpendicular to line AB? (6 points)y = 4x − 8

y = 1 over 4x − 8

y = −4x − 8

y = −1 over 4x − 8

Answers

To find a perpendicular slope (or line), the slope (in this case 4x) must be the opposite sign and its reciprocal, which is basically the fraction flipped upside down. Since 4 is technically 4/1, that fraction flipped is 1/4. And since you need to flip the sign too, instead of it being a positive number, it's negative. Your answer is -1/4x-8

y = -1 over 4x - 8 is the answer I think

Explain which theorems, definitions, or combinations of both can be used to prove that alternate exterior angles are congruent.

Answers

1. The first theorem used is that vertical angles are congruent.
2. The next theorem used is that adjacent angles in a parallelogram are supplementary.
3. The definition of supplementary angles is then used for angle formed by intersecting lines.
4. The theorem on vertical angles is used again.
5. Finally, the definition of the transitivity property is used to prove that alternate exterior angles are congruent.

Using the Corresponding Angles Theorem, Vertical Angles Theorem, and the Transitive Property of Congruence, we can prove that alternate exterior angles (e.g, <4 and <5) are congruent by the alternate exterior angles theorem.

Recall:

Alternate exterior angles are angles that lie outside the two lines that is cut across by a transversal but on opposite sides along the transversal.
Examples of alternate exterior angles are <2 and <7; <4 and <5 as shown in the figure attached below.

If we are given that $m \parallel n$ in the diagram attached below, the following are theorems and definitions we can use to prove that $\angle 4 \cong \angle 5$ (alternate exterior angles).

Statement 1: $\angle 4 \cong \angle 8$

Reason: Corresponding Angles Theorem

The corresponding angles theorem states that when two parallel lines (lines m and n) are intersected by a transversal line (line w), the two corresponding angles formed (e.g. <4 and <8) are congruent.

Statement 2: $\angle 8 \cong \angle 5$

Reason: Vertical Angles Theorem

The Vertical Angles Theorem states that the opposite vertical angles (e.g. <8 and <5) formed when two lines (lines n and w) intersect are congruent to each other.

Statement 3: $\angle 4 \cong \angle 5$

Reason: Transitive Property of Congruence

The Transitive Property of Congruence states that if a = b; and b = c; then a = c.

Therefore, using the Corresponding Angles Theorem, Vertical Angles Theorem, and the Transitive Property of Congruence, we can prove that alternate exterior angles (e.g, <4 and <5) are congruent by the alternate exterior angles theorem.

Learn more here:

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What is the value of x?
O 78
0 84
o 96
O 102

Answers

Answer:

96°

Explanation

Given problem:

Find the value of x in the diagram;

Given that lines a and b are parallel lines and transversal c cuts through them;

the two given angles are said to be equal and alternate angles;

So;

99 = x + 3

x = 99 - 3 = 96°

The value of x is 96°

Please help!!!!!!!!!!!!!!!!!!!!

Answers

$\left \{ {{6a+11b=36} \atop {4a-2b=-32}} \right. \n \left \{ {{6a+11b=36} \atop { (-(3)/(2)) *(4a-2b=-32)}} \right.$
$(6a+11b=36)+ (-6a+3b=48)= 6a-6a+11b+3b=36+48 \n 14b=84 \n b=6$
$4a-2(6)=-32 \n 4a=-32+12=-20 \n a=-5$

Solve the problem.If a lawn sprinkler sprays 15 feet in every direction, what is the area of the yard that gets watered?