Answer:
See below in bold.
Step-by-step explanation:
a. |x| = 6
x = 6, -6.
b. |x − 5| = 4
x - 5 = 4
x = 9.
x - 5 = -4
x = 1.
c. 2|x + 3| = −10
No solution because |x + 3| is an absolute value so is always positive.
Answer:
1. Opposite
2. angle-side-angle criterion
Step-by-step explanation:
Since ABCD is a parallelogram, the two pairs of <u>(opposite)</u> 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 <u>(angle-side-angle criterion)</u>, 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.
Answer:
$1200
Step-by-step explanation:
$4000 x .06 = $240 x 5 years = $1200
Answer:
Step-by-step explanation:
Answer:
- 819
Step-by-step explanation:
The sum to n terms of a geometric series is
= 
where a is the first term and r the common ratio
Here a = 1 and r = - 4 ÷ 1 = - 4, thus
= 
= 
= 
= - 819
