What is the value of a? What is the value of b?

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions for the questions in the image:

6. Simplify $2(1\frac{1}{2} + \frac{1}{4})$

Convert the mixed number to an improper fraction.
$1\frac{1}{2} = \frac{1 \times 2 + 1}{2} = \frac{3}{2}$
Add the fractions inside the parenthesis.
Find a common denominator, which is 4.
$\frac{3}{2} + \frac{1}{4} = \frac{3 \times 2}{2 \times 2} + \frac{1}{4} = \frac{6}{4} + \frac{1}{4} = \frac{7}{4}$
Multiply the result by 2.
$2 \times \frac{7}{4} = \frac{14}{4}$
Simplify the fraction.
$\frac{14}{4} = \frac{7}{2}$
The final answer is $\boxed{\frac{7}{2}}$ .

7. Remove the brackets: $a - 2(b - 3c)$
Distribute the $-2$ to each term inside the parenthesis.
$a - 2(b - 3c) = a - (2 \times b) - (2 \times -3c)$
Perform the multiplication.
$= a - 2b - (-6c)$
Simplify the expression.
$= a - 2b + 6c$
The correct option is c).
The final answer is $\boxed{\text{c) } a - 2b + 6c}$ .

8. The area of a square is $49 \text{cm}^2$ . Find the perimeter of the square.
Find the side length ( $s$ ) of the square using the area formula ( $A = s^2$ ).
$s^2 = 49 \text{ cm}^2$ $s = \sqrt{49} \text{ cm} = 7 \text{ cm}$
Calculate the perimeter ( $P$ ) of the square using the formula ( $P = 4s$ ).
$P = 4 \times 7 \text{ cm} = 28 \text{ cm}$
The correct option is c).
The final answer is $\boxed{\text{c) } 28 \text{cm}}$ .

9. Express $\frac{3}{8}$ as a percentage.
Multiply the fraction by 100%.
$\frac{3}{8} \times 100\%$
Perform the multiplication.
$= \frac{300}{8}\%$
Simplify the fraction.
$= \frac{75}{2}\% = 37.5\%$
The correct option is d).
The final answer is $\boxed{\text{d) } 37\frac{1}{2}\%}$ .

10. Use the mapping below to answer the question 10 and 11. $2^0 \longrightarrow a$ . What is the value of a?
Evaluate the expression $2^0$ .
Any non-zero number raised to the power of 0 is 1.
$2^0 = 1$
From the mapping, $2^0 = a$ .
Therefore, $a = 1$ .
The final answer is $\boxed{1}$ .

11. What is the value of b?
From the mapping: $2^{-2} \longrightarrow b$ .
Evaluate the expression $2^{-2}$ .
Use the rule $x^{-n} = \frac{1}{x^n}$ .
$2^{-2} = \frac{1}{2^2}$
Calculate the value.
$= \frac{1}{4}$
From the mapping, $2^{-2} = b$ .
Therefore, $b = \frac{1}{4}$ .
The final answer is $\boxed{\frac{1}{4}}$ .

What is the value of a? What is the value of b?

Answer

Step-by-step solution

Convert the mixed number to an improper fraction.

Add the fractions inside the parenthesis.

Multiply the result by 2.

Simplify the fraction.

Distribute the $-2$ to each term inside the parenthesis.

Perform the multiplication.

Simplify the expression.

Find the side length ( $s$ ) of the square using the area formula ( $A = s^2$ ).

Calculate the perimeter ( $P$ ) of the square using the formula ( $P = 4s$ ).

Multiply the fraction by 100%.

Perform the multiplication.

Simplify the fraction.

Evaluate the expression $2^0$ .

From the mapping, $2^0 = a$ .

Evaluate the expression $2^{-2}$ .

Calculate the value.

From the mapping, $2^{-2} = b$ .

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More Mathematics Questions

What is the value of a? What is the value of b?

Answer

Step-by-step solution

Convert the mixed number to an improper fraction.

Add the fractions inside the parenthesis.

Multiply the result by 2.

Simplify the fraction.

Distribute the −2-2−2 to each term inside the parenthesis.

Perform the multiplication.

Simplify the expression.

Find the side length (sss) of the square using the area formula (A=s2A = s^2A=s2).

Calculate the perimeter (PPP) of the square using the formula (P=4sP = 4sP=4s).

Multiply the fraction by 100%.

Perform the multiplication.

Simplify the fraction.

Evaluate the expression 202^020.

From the mapping, 20=a2^0 = a20=a.

Evaluate the expression 2−22^{-2}2−2.

Calculate the value.

From the mapping, 2−2=b2^{-2} = b2−2=b.

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More Mathematics Questions

Distribute the $-2$ to each term inside the parenthesis.

Find the side length ( $s$ ) of the square using the area formula ( $A = s^2$ ).

Calculate the perimeter ( $P$ ) of the square using the formula ( $P = 4s$ ).

Evaluate the expression $2^0$ .

From the mapping, $2^0 = a$ .

Evaluate the expression $2^{-2}$ .

From the mapping, $2^{-2} = b$ .