Lesson 4

Evaluate:

1. \(10^0\)
2. \(\frac{10^3}{10^3}\)
3. \(10^2 + 10^1 + 10^0\)

Write each expression as a single power of 10.

1. \(\frac{10^3 \boldcdot 10^4}{10^5}\)
2. \((10^4) \boldcdot \frac{10^{12}}{10^7}\)
3. \(\left(\frac{10^5}{10^3}\right)^4\)
4. \(\frac{10^4 \boldcdot 10^5 \boldcdot 10^6}{10^3 \boldcdot 10^7}\)
5. \(\frac{(10^5)^2}{(10^2)^3}\)

The Sun is roughly \(10^2\) times as wide as Earth. The star KW Sagittarii is roughly \(10^5\) times as wide as Earth. About how many times as wide as the Sun is KW Sagittarii? Explain how you know.

Jada has a scale map of Kansas that fits on a page in her book. The page is 5 inches by 8 inches. Kansas is about 210 miles by 410 miles. Select all scales that could be a scale of the map. (There are 2.54 centimeters in an inch.)

1 in to 1 mi

1 cm to 1 km

1 in to 10 mi

1 ft to 100 mi

1 cm to 200 km

1 in to 100 mi

1 cm to 1000 km

Select all the expressions that are equivalent to \(\text-36x+54y-90\).

\(\text-9(4x-6y-10)\)

\(\text-18(2x-3y+5)\)

\(\text-6(6x+9y-15)\)

\(18(\text-2x+3y-5)\)

\(\text-2(18x-27y+45)\)

\(2(\text-18x+54y-90)\)

Bananas cost $1.50 per pound, and guavas cost $3.00 per pound. Kiran spends $12 on fruit for a breakfast his family is hosting. Let \(b\) be the number of pounds of bananas Kiran buys and \(g\) be the number of pounds of guavas he buys.

1. Write an equation relating the two variables.
2. Rearrange the equation so \(b\) is the independent variable.
3. Rearrange the equation so \(g\) is the independent variable.

Lin’s mom bikes at a constant speed of 12 miles per hour. Lin walks at a constant speed \(\frac13\) of the speed her mom bikes. Sketch a graph of both of these relationships.