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zimovet [89]
3 years ago
9

Choose the graph which represents the solution to the inequality. 12x + 4 ≤ -8

Mathematics
1 answer:
user100 [1]3 years ago
3 0

Answer:

<h2>x\leq -1</h2>

Step-by-step explanation:

Steps:

12x+4-4\leq -8

Subtract 4 from both sides:

12x+4-4\leq -8-4

Simplify:

12x\leq \frac{-12}{12}

Divide both sides by 12:

\frac{12x}{12} \leq \frac{-12}{12}

Simplify:

x\leq -1

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Step-by-step explanation:

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Step-by-step explanation:

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3 years ago
While standing on top of a hill at a ski resort, Alexa Latour spots the ski lodge below. If the vertical height of the hill is 1
alexira [117]

Answer: The distance to the lodge is 1514 ft

Step-by-step explanation: Please refer to the diagram attached.

The point where Alexa is standing at the top of the hill is marked as point A. The vertical height of the hill is from point A to point B which has been given as 1209 ft. Also, when Alexa looks down, she does that at an angle of depression measuring 53 degrees. Therefore while looking at the lodge, she forms an angle between her line of sight and the height of the hill. That angle is calculated as 90 degrees minus 53 degrees and that equals 37 degrees (as shown in the diagram). Note that her line of sight is AC since the ski lodge is at point C. Therefore the distance she must ski in order to get to point C (which shall be represented by X) shall be calculated using trigonometric ratios.

Note that we have a reference angle which is 37. We also have an adjacent which is 1209 (the side that lies between the reference angle and the right angle). And then we want to calculate the hypotenuse, yet unknown, (which is the side facing right angle). Since we have an adjacent, a hypotenuse and the reference angle, X can be calculated as

Cos A = Adjacent/Hypotenuse

Cos A = AB/AC

Cos 37 = 1209/X

By cross multiplication we now have X = 1209/Cos 37

By using our calculator or checking the table of values, Cos 37 = 0.7986

X = 1209/0.7986

X = 1513.899

Approximated to the nearest feet,

X = 1514 ft

8 0
3 years ago
Mrs. Curtis wants to buy online tickets for a concert. Two options are given here.
pshichka [43]
Option 1- y= 53x+10
Option 2- y= 55x 
55x+10=53x
-53x     -53x
2x=10
x=5 
6 0
3 years ago
WHOEVER GETS THIS RIGHT IN 3 MINUTES GETS THE BRAINLIEST!! Four times the sum of a number and 15 is at least 120. Let x represen
larisa [96]

Hey there!

Let's call this "number" x. We want four times the sum of this number and 15 to equal at least 120.

Therefore, we want this number times four plus fifteen to be greater than or equal to 120. We have:

4(x+15)\geq 120

Distribute:

4x + 60 \geq 120

Subtract:

4x\geq 60

Divide:

x\geq 15

Your answer is C.

Hope this helps!

7 0
3 years ago
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