Find the value of the expression

Values for the area A of the rectangle shown are 12 ≤ A ≤ 36.

Step2247 [10]

A compound inequality is used to combined multiple inequalities.

<em>The compound inequality is: </em> $12 \le 6x \le 36$ <em>.</em>
<em>The solution to the compound inequality is: </em> $2 \le x \le 6$ <em />

We have:

$12 \le A \le 36$

$Length = 2x$

$Width = 3$

The area of the rectangle is:

$A = Length \times Width$

So, we have:

$A =2x \times 3$

$A = 6x$

Substitute 6x for A in $12 \le A \le 36$

$12 \le 6x \le 36$

Divide through by 6

$2 \le x \le 6$

Hence,

The compound inequality is: $12 \le 6x \le 36$ .
The solution to the compound inequality is: $2 \le x \le 6$

Read more about compound inequalities at:

brainly.com/question/17957246

4 0

2 years ago

Liam wants to save $6,265 to purchase a car. if $4,000 is deposited into an account at 7.5% interest, compounded monthly, how ma

timurjin [86]

To solve for time taken we use the compound formula:
A=P(1+r/100*n)^(n*t)
where:
A=future value
P=principle
r=rate
t=time
n=number of terms

6265=4000(1+7.5/(12*100))^(12t)
solving for t we get
1.56625=1.00625^12t
12t=72.0136
t=6.00 years
Answer: 6 years

5 0

3 years ago

During the national day celebrations.Asha decorates her balcony with serial lights of red,green and white colours.The red light

expeople1 [14]

If all three coloured lights blink together at 8:49 pm, they will blink together at 8:50 pm

<u>Solution:</u>

Given that the red light blinks at intervals of 4 seconds, the green at 5 seconds and the white at 6 seconds.

If all three colored lights blink together at 8:49 pm,

We have to find when will they blink together again?

First let us know, at what intervals they all together blink.

For that we have to find the lcm of 4, 5, 6.

L.C.M (4, 5, 6) = 2 x L.C.M(2, 5, 3)

As 2,3,5 are primes, we can’t take common further, so multiply all

= 2 x 2 x 5 x 3

= 4 x 15 = 60

So, after every 60 seconds = 1 minute they will blink.

Then, after 8 : 49 pm, they will blink at 8 : 49 + 1 = 8 : 50 pm.

Hence, they all blink at 8 : 50 pm.

6 0

3 years ago

10 points!!!!! Do 14 and 15 only hurry please.

Aleksandr [31]

Answer:

8. x = 16

9. x = 10

14.

m ∠RSU = 130°

m ∠UST = 50°

15.

m ∠RSU = 124°

m ∠UST = 56°

Step-by-step explanation:

8.

Given ∠DEF is bisected by EG. That is , ∠DEG = ∠GEF

That is , (x + 15)° = 31°

x = 31 - 15 = 16

9.

Given ∠DEF is bisected by EG. That is , ∠DEG = ∠GEF

That is ,

(6x - 4)° = 56°

6x = 56 + 4

6x = 60

x = 10

14.

13x + 5x = 180° [straight line angles ]

18x = 180

x = 10

m ∠RSU = 130°

m ∠UST = 50°

15.

4x + 12 + 2x = 180° [ straight line angles]

6x = 180 - 12

6x = 168

x = 28

m ∠RSU = 4(28) + 12 = 112 + 12 = 124°

m ∠UST = 2(28) = 56°

3 0

3 years ago

Read 2 more answers

URGENT! PLEASE HELP.

Harrizon [31]

The distance BC from Tower 2 to the plane will be 14,065.5 ft and the height of the plane from the ground will be 5,720.9 ft.

<h3>What is a right-angle triangle?</h3>

It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function.

A plane is located at C on the diagram.

There are two towers located at A and B.

The distance between the towers is 7600 feet and angles of elevation are given.

Then in the right-angle triangle ΔADC, we have

$\rm \tan 16 = \dfrac{H}{7600 + X}\\\\\\H = 0.2867(7600 +X)\\\\\\H = 0.2756\ X + 2179.2649$ ...1