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3 years ago

In rectangle ANGL, AN = 16 and AG = 34. Find the perimeter of ANGL.

2 answers:

8 0

In a rectangle, opposite sides are equal so you can multiply the side lengths by 2 and add them so 16(2)+34(2) and yu get 32+68. The perimeter is 100

irina1246 [14]3 years ago

4 0

16 (2)=32

34 (2)=68

32+68=100

The perimeter is 100

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WINSTONCH [101]

<h2>Answer and Explanation to questions 13,14,15</h2>

13) $\mathbf{\overline{XY}\cong\overline{CD}}$ as given in the question.

14) $\mathbf{\overline{XY}\cong\overline{YZ}}$ Since Y is the midpoint of XZ. So, Y will divide XZ in equal halves into XY and YZ.

15) $\mathbf{\overline{CD}\cong\overline{YZ}}$

$\because\overline{\textrm{XY}}\cong\overline{\textrm{CD}}$ and $\overline{\textrm{XY}}\cong\overline{\textrm{YZ}}$ . So, $\overline{\textrm{CD}}\cong\overline{\textrm{YZ}}$

<h2>Answer and Explanation to questions 16,17,18</h2>

∠3 is supplementary to ∠1 means: ∠3 + ∠1 = 180°

And, according to figure ∠1 + ∠2 = 180° as ∠1 and ∠2 form a straight line.

∠3 + ∠1 = 180° .............(i)

∠1 + ∠2 = 180° .............(ii)

subtracting equation (i) and (ii) will give ∠3 = ∠2 ..........(iii)

15) ∠3 is supplementary to ∠1 as given in the question

16) ∠2 is supplementary to ∠1 as shown be equation (ii)

18) ∠3 ≅ ∠2 as shown by equation (iii)

<h2>Answer and Explanation to questions 19</h2>

∠3 and ∠4 form a straight line. Therefore, ∠3 + ∠4 = 180° .......(i)

∠4 and ∠5 form a straight line. Therefore, ∠4 + ∠5 = 180° .......(ii)

subtracting equation (i) and (ii)

∠3 + ∠4 - (∠4 + ∠5) = 180°-(180°)

∠3 + ∠4 - ∠4 - ∠5 = 180°-180°

∠3 - ∠5 = 0

∴ ∠3 = ∠5 (Hence Proved)

4 0

3 years ago

Stacey's text messaging plan charges 20¢ for each message over 450 in addition to a $14 base charge. If she owes $18.00 for text

Sidana [21]

$18 = 14 + 0.20(t)

- 14

4 = 0.20t

Divide 4 by 0.20

t = 20

0.20 * 20 = 4

4 + 14 = 18

Because it only charged her for texts after 450, its 450 + 20.

470. She sent 470 texts that month.

3 0

3 years ago

Gertrude sold 104 cars last year. There are 52 weeks in a year. What was the rate at which she sold cars?

seraphim [82]

104/52= 2. 2 per week

3 0

3 years ago

What is a counterexample of the statement “all square roots are irrational”

skad [1K]

Rather than trying to guess and check, we can actually construct a counterexample to the statement.

So, what is an irrational number? The prefix "ir" means not, so we can say that an irrational number is something that's not a rational number, right? Since we know a rational number is a ratio between two integers, we can conclude an irrational number is a number that's not a ratio of two integers. So, an easy way to show that not all square roots are irrational would be to square a rational number then take the square root of it. Let's use three halves for our example:

$\sqrt{(\frac{3}{2})^2}=\\\sqrt{\frac{9}{4}}=\\\frac{3}{2}$

So clearly 9/4 is a counterexample to the statement. We can also say something stronger: All squared rational numbers are not irrational number when rooted. How would we prove this? Well, let $\frac{a}{b}$ be a rational number. That would mean, $\frac{a^2}{b^2}$ , would be a/b squared. Taking the square root of it yields: