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Whitepunk [10]
3 years ago
14

Which expressions are equivalent to 5 (one-third x + 7) minus 3 (one-half x minus 4)? Select three options.

Mathematics
1 answer:
Karo-lina-s [1.5K]3 years ago
8 0

<em><u>The equivalent expressions are:</u></em>

5(\frac{1}{3}x + 7) - 3(\frac{1}{2}x - 4) = \frac{5}{3}x +5(7) - \frac{3}{2}x +3(4)

5(\frac{1}{3}x + 7) - 3(\frac{1}{2}x - 4) = \frac{x}{6} + 47

5(\frac{1}{3}x + 7) - 3(\frac{1}{2}x - 4) = \frac{1}{6}x + 35 + 12

<em><u>Solution:</u></em>

<em><u>Given expression is:</u></em>

5(\frac{1}{3}x + 7) - 3(\frac{1}{2}x - 4)

We have to find the equivalent expression

By distributive property,

a(b + c) = ab + ac

<em><u>Therefore, one of equivalent expression is:</u></em>

5(\frac{1}{3}x + 7) - 3(\frac{1}{2}x - 4) = \frac{5}{3}x +5(7) - \frac{3}{2}x +3(4)

<em><u>The other equivalent expressions are:</u></em>

5(\frac{1}{3}x + 7) - 3(\frac{1}{2}x - 4) = \frac{5}{3}x + 35 - \frac{3}{2}x +12\\\\Combine\ the\ like\ terms\\\\5(\frac{1}{3}x + 7) - 3(\frac{1}{2}x - 4) = \frac{10-9}{6}x + 35 + 12\\\\Simplify\ the\ above\\\\5(\frac{1}{3}x + 7) - 3(\frac{1}{2}x - 4) = \frac{1}{6}x + 35 + 12\\\\5(\frac{1}{3}x + 7) - 3(\frac{1}{2}x - 4) = \frac{x}{6} + 47

Thus equivalent expression is found

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Answer:

88 cm³

Step-by-step explanation:

V=\frac{lwh}{3}

V = (11 × 4 × 6) ÷ 3

88 cm³

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3 years ago
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dimaraw [331]

Answer:

2

Step-by-step explanation:

Simplify the following:

(-(2 + 2/3))/(-(1 + 1/3))

(-(2 + 2/3))/(-(1 + 1/3)) = (-1)/(-1)×(2 + 2/3)/(1 + 1/3) = (2 + 2/3)/(1 + 1/3):

(2 + 2/3)/(1 + 1/3)

Put 1 + 1/3 over the common denominator 3. 1 + 1/3 = 3/3 + 1/3:

(2 + 2/3)/(3/3 + 1/3)

3/3 + 1/3 = (3 + 1)/3:

(2 + 2/3)/((3 + 1)/3)

3 + 1 = 4:

(2 + 2/3)/(4/3)

Put 2 + 2/3 over the common denominator 3. 2 + 2/3 = (3×2)/3 + 2/3:

((3×2)/3 + 2/3)/(4/3)

3×2 = 6:

(6/3 + 2/3)/(4/3)

6/3 + 2/3 = (6 + 2)/3:

((6 + 2)/3)/(4/3)

6 + 2 = 8:

(8/3)/(4/3)

Multiply the numerator by the reciprocal of the denominator, (8/3)/(4/3) = 8/3×3/4:

(8×3)/(3×4)

(8×3)/(3×4) = 3/3×8/4 = 8/4:

8/4

The gcd of 8 and 4 is 4, so 8/4 = (4×2)/(4×1) = 4/4×2 = 2:

Answer: 2

7 0
3 years ago
Read 2 more answers
In Question 1, what do you notice about the x-coordinates before and after a horizontal stretch? What do you notice about the y-
ozzi

Answer:

The value of nx is the ratio of the transformed x-coordinates to the original x-coordinates in each horizontal stretch. The value of ny is the ratio of the transformed y-coordinates to the original y-coordinates in each vertical stretch.

Step-by-step explanation:

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6 0
3 years ago
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Please explain your answer
Irina18 [472]
\text{Distance = } \sqrt{(5 + 8)^2+ (-3 + 3)^2 }=   \sqrt{13^2} = 13

Answer: 13 units
6 0
3 years ago
AB is a diameter of a circle, center O. C is a point on the circumference of the circle, such that
Solnce55 [7]

Given:

AB is the diameter of a circle.

m∠CAB = 26°

To find:

The measure of m∠CBA.

Solution:

Angle formed in the diameter of a circle is always 90°.

⇒ m∠ACB = 90°

In triangle ACB,

Sum of the angles in the triangle = 180°

m∠CAB + m∠ACB + m∠CBA = 180°

26° + 90° + m∠CBA = 180°

116° + m∠CBA = 180°

Subtract 116° from both sides.

116° + m∠CBA - 116° = 180° - 116°

m∠CBA = 64°

The measure of m∠CBA is 64°.

7 0
3 years ago
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