Question

1. solve the following equation for y

2x +7y = 14

1. evaluate the expression for x = 2

and y = 4.
16x⁰ + 2x²·y⁻¹

1. fill in the blanks with the provided

expressions to match each
expression with its equivalent.
x x⁹ x⁴ x⁻²

\\(\frac{1}{x^2}\\) :

x⁴ ÷ x³ :

(x²)² :

x³·x³·x³ :

1. which expression is equivalent to

\\(\frac{4 \times 10^{-6}}{8 \times 10^3}\\)
a. 5 × 10⁻⁷
b. 5 × 10⁻¹
c. 5 × 10⁻¹⁰
d. 5 × 10⁷

1. rewrite 5⁻¹⁵ using a positive

exponent.

1. in 1902, the yearly attendance at a

major league baseball park was
3.4 × 10⁵ people. one hundred
years later, the yearly attendance
was 1.7 × 10⁶ fans. how many
times greater was the attendance in
2002 than in 1902?

1. find (9.3 × 10⁶) · (1.8 × 10⁴).

express your answer in scientific
notation.

Explanation:

Step1: Isolate the y-term

Subtract $2x$ from both sides.
$7y = 14 - 2x$

Step2: Solve for y

Divide both sides by 7.
$y = \frac{14 - 2x}{7} = 2 - \frac{2x}{7}$

Step1: Substitute x=2, y=4

Replace variables in the expression.
$16(2)^0 + 2(2)^2 \cdot (4)^{-1}$

Step2: Simplify exponents

Calculate $a^0=1$, $a^{-1}=\frac{1}{a}$.
$16(1) + 2(4) \cdot \frac{1}{4}$

Step3: Compute multiplications

Calculate each term.
$16 + 8 \cdot \frac{1}{4} = 16 + 2$

Step4: Sum the terms

Add the resulting values.
$16 + 2 = 18$

Step1: Match $\frac{1}{x^2}$

Use negative exponent rule: $\frac{1}{a^n}=a^{-n}$.
$\frac{1}{x^2} = x^{-2}$

Step2: Match $x^4 \div x^3$

Use quotient rule: $a^m \div a^n=a^{m-n}$.
$x^4 \div x^3 = x^{4-3}=x$

Step3: Match $(x^2)^2$

Use power rule: $(a^m)^n=a^{mn}$.
$(x^2)^2 = x^{2 \times 2}=x^4$

Step4: Match $x^3 \cdot x^3 \cdot x^3$

Use product rule: $a^m \cdot a^n=a^{m+n}$.
$x^3 \cdot x^3 \cdot x^3 = x^{3+3+3}=x^9$

Step1: Split into coefficient and power

Separate the constants and powers of 10.
$\frac{4}{8} \times \frac{10^{-6}}{10^{3}}$

Step2: Simplify coefficient and exponent

Calculate $\frac{4}{8}=0.5$, use quotient rule for exponents.
$0.5 \times 10^{-6-3} = 0.5 \times 10^{-9}$

Step3: Convert to proper scientific notation

Rewrite $0.5$ as $5 \times 10^{-1}$.
$5 \times 10^{-1} \times 10^{-9} = 5 \times 10^{-10}$

Answer:

$y = 2 - \frac{2x}{7}$

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