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3 years ago

In order for RECT to be a rectangle, what must the value of x be?

Mathematics

1 answer:

Readme [11.4K]3 years ago

6 0

Answer:

x = 21

Step-by-step explanation:

If RECT is a rectangle, each of its interior angles are right angles, 90°. Since ∠RTC is split into two angles, the sum of the two angles must be 90°. (Angles that add to 90° are called complementary angles).

∠RTC = ∠RTE + ∠ETC Formula for complementary angles

90 = 2x + 6 + 42 Substitute the angles

90 = 2x + 48 Combined like terms to simplify

Now isolate "x" to solve

90 - 48 = 2x + 48 - 48 Subtract 48 from both sides

42 = 2x

42/2 = 2x/2 Divide both sides by 2

x = 21

Therefore x is 21.

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The arena at the Berry Center holds 9,500 people. During one of the graduation ceremonies, 95% of the seats were occupied. How m

motikmotik

Answer:

9,025

Step-by-step explanation:

9,500 multiplied by 0.95

3 0

3 years ago

Select all expressions that are equivalent to 4x+2(2x-5)-(3-5x)

Arada [10]

For this case we have the following expression:

$4x + 2 (2x-5) - (3-5x)$

Applying distributive property to the terms within parentheses taking into account that:

$- * + = -\\- * - = +$

We have:

$4x + 4x-10-3 + 5x =$

We add similar terms taking into account that:

Equal signs are added and the same sign is placed.

$4x + 4x + 5x-10-3 =\\13x-13$

Thus, an equivalent expression is:

$13x-13$

Answer:

$13x-13$

4 0

2 years ago

What is the value of 4p-2, when p=8

ohaa [14]

4p - 2 when p=8

(4 x 8) - 2
32 - 2
30

answer: 30
hope it helped :)

7 0

3 years ago

Read 2 more answers

The distance between City A and City B is 250 miles. A length of 2.3 feet represents this distance on a certain wall map. City C

masya89 [10]

The distance between city C and city D is 450 miles.

<u>Solution:</u>

Given, The distance between City A and City B is 250 miles.

A length of 2.3 feet represents this distance on a certain wall map.

City C and City D are 4.14 feet apart on this map.

We have to find what is the actual distance between City C and City D?

Now, distance between a and b is 250 miles ⇒ 2.3 feet on map

Then, distance between c and d be n miles ⇒ 4.14 feet on map.

Now, by chris cross method.

250 x 4.14 = 2.3 x n miles.

2.3n = 1035

n = 450

Hence, the distance between city C and city D is 450 miles.

8 0

3 years ago

Suppose the speeds of vehicles traveling on a highway are normally distributed and have a known population standard deviation of

erik [133]

Answer:

2.88

Step-by-step explanation:

Data provided in the question

$\sigma$ = Population standard deviation = 7 miles per hour

Random sample = n = 32 vehicles

Sample mean = $\bar X$ = 64 miles per hour

98% confidence level

Now based on the above information, the alpha is

= 1 - confidence level

= 1 - 0.98

= 0.02

For $\alpha_1_2$ = 0.01

$Z \alpha_1_2$ = 2.326

Now the margin of error is

$= Z \alpha_1_2 \times \frac{\sigma}{\sqrt{n}}$

$= 2.326 \times \frac{7}{\sqrt{32}}$

= 2.88

hence, the margin of error is 2.88

5 0

3 years ago