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nasty-shy [4]
3 years ago
12

What is the solution to the inequality x + 4 + 2x ≤ 20 + 5x – 32

Mathematics
1 answer:
Illusion [34]3 years ago
5 0

Answer:

x+4+2x = 20+5x-32

Step-by-step explanation:

x+4+2x

= 3x + 4

20+5x-32

= 20-32+5x

= 5x-12

Finding the value of X

3x+4 = 5x-12

= 4+12 = 5x-3x

= 16 = 2x

= 16/2 = X

= 8 = X

By putting the value of X in the equation

(3×8)+4

= 24 +4

= 28

(5×8)-12

= 40-12

28

28 = 28

so the X+4+2x < 20+5x-32 is wrong

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After triangle ACE is dilated by a factor of 6, it has an area of 180 square inches. What was its area before dilation?
Agata [3.3K]

Answer:

The area of triangle ACE before dilation is:  30 square inches

Step-by-step explanation:

We know that when an object is dilated by a scale factor, it gets reduced, stretched, or remains the same, depending upon the value of the scale factor.

  • If the scale factor > 1, the image is enlarged
  • If the scale factor is between 0 and 1, it gets shrunk
  • If the scale factor = 1, the object and the image are congruent

The length of the image can be determined by multiplying the length of the original point by a certain scale factor.

Given that after triangle ACE is dilated by a factor of 6, it has an area of 180 square inches.

Thus, it means the dilated area is 6 times the area before dilation.

Let x be the pre-dilation area

As the dilated area is 6 times the area before dilation, so

6x = 180

divide both sides by 6

6x/6 = 180/6

x = 30 square inches.

Therefore, the area of triangle ACE before dilation is:  30 square inches

4 0
3 years ago
What is the GCF of 24a^3 b and 36ab^2?<br><br> 2ab<br> 4a^3b<br> 12ab<br> 72a^3b^2
Oksi-84 [34.3K]
12ab will be the right answer.

Since 24a^3 = 12ab(2a^2)

And 36ab^2 = 12ab(3b)
6 0
3 years ago
Read 2 more answers
The gravitational force exerted by the planet Earth on a unit mass at a distance r from the center of the planet is:
jolli1 [7]

Answer:

Yes, F is a continuous function of r

Step-by-step explanation:

We are given that

When r<R

F(r)=\frac{GMr}{R^3}

r\geq R

F(r)=\frac{GM}{r^2}

Where M=Mass of the earth

R=Radius of earth

G=Gravitational constant

We have to find the function is continuous of r or not.

LHL

\lim_{r\rightarrow R-}\frac{GMr}{R^3}=\frac{GMR}{R^3}=\frac{GM}{R^2}

RHL

\lim_{r\rightarrow R+}\frac{GM}{R^2}=\frac{GM}{R^2}

F(R)=\frac{GM}{R^2}

When a function is continuous at x=a

Then, LHL=RHL=f(a)

RHL==LHL=F(R)

Hence, the function is continuous of r.

8 0
3 years ago
Mary has used 160 tiles to cover 40% of the back splash in her kitchen how many tiles will it take to cover the entire back spla
dangina [55]

Answer:

400 tiles :)

Step-by-step explanation:

2/5 = 160/x

1/5 = 80/x

80 *5 = 400

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Marla's mom bought a 36-pack of water bottles at the supermarket. Each bottle has 500 mL of water. How many liters of water is t
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Answer:

18 L

Step-by-step explanation:

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18000 mL / 1000 = 18 L

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