X2 + 7x – 18 x2

Since ABCD is a parallelogram, the two pairs of _________ sides (AB¯ and CD¯, as well as AD¯ and BC¯) are congruent. Then, since

Marysya12 [62]

Answer:

1. Opposite

2. angle-side-angle criterion

Step-by-step explanation:

Since ABCD is a parallelogram, the two pairs of (opposite) sides (AB¯ and CD¯, as well as AD¯ and BC¯) are congruent. Then, since ∠9 and ∠11 are vertical angles, it can be concluded that ∠9≅∠11. Since ABCD is a parallelogram, AB¯∥CD¯. Since ∠2 and ∠5 are alternate interior angles along these parallel lines, the Alternate Interior Angles Theorem allows that ∠2≅∠5. Since two angles of △AEB are congruent to two angles of △CED, the Third Angles Theorem supports that ∠8≅∠3. Therefore, using the (angle-side-angle criterion), it can be stated that △AEB≅△CED. Then, applying the definition of congruent triangles, it can be stated that AE¯≅CE¯, which makes E the midpoint of AC¯. Use a similar argument to prove that △AED≅△CEB; then it can be concluded that E is also the midpoint of BD¯. Since the midpoint of both line segments is the same point, the segments bisect each other by definition. Match each number (1 and 2) with the word or phrase that correctly fills in the corresponding blank in the proof.

A parallelogram posses the following features:

1. The opposite sides are parallel.

2. The opposite sides are congruent.

3. It has supplementary consecutive angles.

4. The diagonals bisect each other.

7 0

3 years ago

Family has an annual income of $23 comma 400. Of this, one fourth

denis23 [38]

Amount spent for food = $5850, housing = $4680, clothing = $2340, savings = $2600, taxes = $5850, expenses = $2080.

Step-by-step explanation:

Step 1:

Given details are Total Income = $23,400

Step 2:

Amount spent for food, F= 1/4th of 23,400 = $1/4 \times 23400$

= $5850

Step 3:

Amount spent for housing, H = 1/5th of 23,400 = $1/5 \times23400$

= $4680

Step 4:

Amount spent for clothing, C = 1/10th of 23,400 = $1/10 \times 23400$ = $2340

Step 5:

Amount spent for savings, S = 1/9th of 13,400 = $1/9\times 23400$ = $2600

Step 6:

Amount spent for taxes, T = 1/4th of 23,400 = $1/4 \times 23400$ =$5850

Step 7:

Find amount spent on other expenses by totaling all expenditures and subtracting from the annual income.

Annual Income = F + H + C + S + T + E

Amount spent on other expenses, E = 23400 - (5850 + 4680 + 2340 + 2600 + 5850)

E = 23400 - 21320

E = $2080

5 0

3 years ago

PLEASE HELP!!! ILL MARK BRAINLIEST

KiRa [710]

Answer:

Beatz on demand

Step-by-step explanation:

Even though it starts at 25 for the fee it has a lower monthly rate cost then itunes. While iTunes charges 8.99 per month Beatz on demand only charges 5.99 a month

8 0

3 years ago

Read 2 more answers

What is the value for x? Enter your answer in the box. x =

BaLLatris [955]

<A = <C = 73
<B = 180 - (<A + C)
6x + 4 = 180 - 2(73)
6x + 4 = 180 - 146
6x + 4 = 34
6x = 30
x = 5

answer
x = 5

6 0

3 years ago

PLZ HELP I SUCK AT MATH :( JUST LIKE MY USERNAME SAYS :(

Citrus2011 [14]

Answer:

Option C and Option D have exactly one solution.

Step-by-step explanation:

The equation will have exactly one solution when it completely solves and we get value of x.

Checking all choices

(Choice A)

-19x + 18 = -19x + 18

-19x+19x=18-18

0=0

(infinite solutions)

(Choice B)

-19x -18 = -19x + 18

-19x+19x=18+18

0≠36

(no solution)

(Choice C)

19x + 18 = -19x + 18

19x+19x=18-18

38x=0

x=0

(One solution)

(Choice D)

19x - 18 = -19x + 18

19x+19x=18+18

38x=36

x=36/38

x=18/19

(One solution)

So, Option C and Option D have exactly one solution.

4 0

3 years ago

X2 + 7x – 18 x2 – 15x + 54