Given: Point A is on the bisector of angle P Q R. Prove: Point A is equidistant from the sides of angle P Q R. Art: Three rays Q P, Q A, and Q R point in rightward direction sharing a common endpoint at Q. Ray Q A is horizontal and bisects angle P Q R equally. The perpendicular from point A to ray Q P is made by a dotted line. The perpendicular cuts the ray Q P at X. Angle Q X A is labeled a right angle. The perpendicular from point A to ray Q R is made by another dotted line. The perpendicular cuts ray Q R at Y. Angle Q Y A is labeled a right angle. Drag the answers into the boxes to correctly complete the proof.

Statement Reason
1. QA−→− is the bisector of ∠PQR.
2. Response area Definition of bisector
3.∠QXA and ∠QYA are right angles. Given
4. Response area All right angles are congruent.
5. QA⎯⎯⎯⎯⎯≅QA⎯⎯⎯⎯⎯ Response area
6. Response area AAS Congruence Postulate
7. AX⎯⎯⎯⎯⎯≅AY⎯⎯⎯⎯⎯ Corresponding parts of congruent triangles are congruent.
8. Point A is equidistant from the sides of ∠PQR. Definition of equidistant

step-by-step explanation:

descending order means to order the polynomials from the term with the largest exponent to the term with the smallest exponent.  

therefore, the correct answer is d.  

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .