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Vera_Pavlovna [14]
3 years ago
10

Solve: 2x ≤ -2/3 (4x + 4)

Mathematics
2 answers:
Sidana [21]3 years ago
6 0
Answer: x ≤ 1

reason:

first, multiply 4x and 4 by -2/3, which leaves you with the equation 2x ≤ -8/3x + 8/3
then, you add 8/3x to both sides, making it 4 2/3x ≤ 8/3
divide both sides by 4 2/3 and you get x ≤ 1
klio [65]3 years ago
4 0

Answer:

x ≤ 4/7

Step-by-step explanation:

Simplify the given 2x ≤ -2/3 (4x + 4) by multiplying both sides by (3/2):

(3/2)(2x) ≤ (3/2)(-2/3)(4x + 4)

We get 3x ≤ -4x - 4

Solve for x by combining like terms.  Add 4x to both sides, obtaining

7x ≤ 4

and so the solution is the set

x ≤ 4/7

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What is the area of the triangle?<br> 16<br> 8<br> 10
sertanlavr [38]

Answer:

64

Step-by-step explanation:

Find the area of both triangles inside the bigger triangle and add them together.

Use the Pythagorean theorem to find the missing length of the leg in the smallest triangle:

a² + b² = c²

8² + b² = 10²

64 + b² = 100

36 = b²

6 = b

Calculate the area of the smaller triangle:

1/2(<em>b</em>x<em>h</em>)

1/2(6 x 8)

1/2(48)

24

Calculate the area of the bigger triangle:

<em>We know that the longer leg is 10 units because we were able to subtract the length of the smaller triangle's leg from 16.</em>

1/2(<em>b</em>x<em>h</em>)

1/2(10 x 8)

1/2(80)

40

Add both areas to find the area of the largest triangle:

40 + 24 = 64

3 0
3 years ago
If you were to use the substitution method to solve the following system, choose the new
mestny [16]

Answer:

23x = -115

Step-by-step explanation:

In the substitution method, you must solve for 1 variable in 1 equation to replace it in the other equation. For the system:

2x - 7y = 4

3x + y = -17

Solving for y in the second equation:

y = -17 - 3x

Replacing y in the first equation:

2x - 7(-17 - 3x) = 4

2x + 119 + 21x = 4

23x = -115

This is the new equation after use the substitution method.

5 0
3 years ago
What constant term is necessary to complete the perfect square trinomial pictured in the algebra tiles?
gayaneshka [121]
The algebra tiles show two equal factors. They are (x + 4).


Then, the perfect square is the product of the two equal factors, (x + 4) * (x +4).


That is (x + 4)^2.


Then develop that perfect square to find the constant term.


(x + 4)^2 = x^2 + 8x + 16.


That means that the constant term needed to complete the trinomial is 16.


Answer: 16    
3 0
3 years ago
Read 2 more answers
Simplify and solve for x. ​ ​ 5(x+20)= 7x+30
hodyreva [135]

Answer:

x = 35

Step-by-step explanation:

Solve for x:

5 (x + 20) = 7 x + 30

Expand out terms of the left hand side:

5 x + 100 = 7 x + 30

Subtract 7 x from both sides:

(5 x - 7 x) + 100 = (7 x - 7 x) + 30

5 x - 7 x = -2 x:

-2 x + 100 = (7 x - 7 x) + 30

7 x - 7 x = 0:

100 - 2 x = 30

Subtract 100 from both sides:

(100 - 100) - 2 x = 30 - 100

100 - 100 = 0:

-2 x = 30 - 100

30 - 100 = -70:

-2 x = -70

Divide both sides of -2 x = -70 by -2:

(-2 x)/(-2) = (-70)/(-2)

(-2)/(-2) = 1:

x = (-70)/(-2)

The gcd of -70 and -2 is -2, so (-70)/(-2) = (-2×35)/(-2×1) = (-2)/(-2)×35 = 35:

Answer: x = 35

6 0
3 years ago
Read 2 more answers
Peter has four horses.Each one eats 4 pounds of oats,twice a day.How many pounds of oats does he need to feed his horses for 3 d
Kobotan [32]
4 pound of oats twice a day= 8 pounds of oats each day per horse. He has 4 horses so 4 horses times 8 pounds of oats is 32. You multiply 32 pounds times the three days he has to feed which is 96 pounds.
8 0
3 years ago
Read 2 more answers
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