Simplify: (4/5 ÷ 2/3) × (3/4)
A) 3/5
B) 2/3
C) 6/5
D) 5/6
Solve for x: 3x - 5 = 7
A) 4
B) 2
C) 5
D) 3
The area of a circle with a radius of 7 cm is:
A) 154 cm²
B) 49 cm²
C) 21 cm²
Formula: A = πr²
Answer (2)
The simplified expression results in 10 9 , which is not listed among the choices. For the equation 3 x − 5 = 7 , the solution for x is 4, corresponding to option A. The area of a circle with a radius of 7 cm is approximately 154 cm², matching option A as well.
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Let's solve each part of the question step by step.
4. Simplify: ( 5 4 ÷ 3 2 ) × ( 4 3 )
Division of fractions is the same as multiplying by the reciprocal. So, 5 4 ÷ 3 2 becomes 5 4 × 2 3 .
Multiply the fractions: 5 4 × 2 3 = 5 × 2 4 × 3 = 10 12 .
Simplify 10 12 to 5 6 by dividing both numerator and denominator by 2.
Now, multiply this result by 4 3 : 5 6 × 4 3 = 5 × 4 6 × 3 = 20 18 .
Simplify 20 18 to 10 9 by dividing by 2.
So the answer is 10 9 ; however, since there is no exact match, recheck simplification steps and original choices; the correct answer is missing from the list.
5. Solve for x in the equation: 3 x − 5 = 7
Add 5 to both sides: 3 x − 5 + 5 = 7 + 5 which simplifies to 3 x = 12 .
Divide both sides by 3: 3 3 x = 3 12 , so x = 4 .
The correct answer is A) 4.
6. Find the area of a circle with a radius of 7 cm:
The formula for the area A of a circle is A = π r 2 .
Substitute the radius r = 7 into the formula: A = π × 7 2 .
Calculate 7 2 , which is 49.
So, A = π × 49 .
Approximating π as 3.14, the area is A ≈ 3.14 × 49 , which results in approximately 154 cm².
The correct answer is A) 154 cm².
