Math midterm

Which expression is equivalent to (1/8)^-6 • (1/8)^3

(1/8)^-3

The system of equations is shown by the graph. y = 25x + 200 y = 50x + 75 Two lines graphed on a coordinate plane. The first line has a Y intercept of 200 and a slope of 25, and the second has a Y intercept of 75 and a slope of 50. The lines intersect at the point, 5, 325.

(5,325)

Select all the algebraic expressions equivalent to m5/n5

-(mn^-1)^5 -(mn)^5 -m^5n^-5

Use the properties of operations to multiply the expression. (x − 1.2)(−0.2x)

-0.2x^2+0.24x

Which number is a rational number? 1. √2 2. Pi 3. 0.7777777777........ 4. √5

0.77777... is rational

A silicon chip is 14 nanometers thick. A nanometer is equal to 0.000000001 meter. Express the thickness of the chip in cm using scientific notation.

1.4 × 10-8 cm

Factor 39x^3y^2 − 52x^2y^2 completely.

13x^2y^3(3x-4)

Solve for x in the equation shown (x - 2) = -1/4 (x - 8)

3 and 1/5

Solve the equation x^3=64 for x

4

What is the value of the expression (-1/4)^2+ the square root of 2^2+12?

65/16

Select the value of each exponential number as a fraction 7^-4/7^-2 (1/3^6)•(1/3)^-2 9^-2•9^2 11^-1 ~~~~~~~~~~~~~~~~~~ 1/11 1/49 1 1/81

7^-4/7^-2 —————> 1/49 (1/3^6)•(1/3)^-2—————-> 1/81 9^-2•9^2 —————-> 1 11^-1 —————-> 1/11

Find 6.3•10^-5\(9 • 10^-3) in scientific notation

7x10^-3

Which number line represents the solution set of the inequality 0.8 − 4x ≥ 4.8?

A number line with a closed circle at negative 1, shaded to the left.

Consider the equation shown 0.5x + 1.5x + 8.5 + x + 4.5 = 2.5x + 3.5x - 2 Part a: which equation shows how to combine like terms A. 3x+13=6x-2 B. 2x + 12 = 5x - 2 C. 3x + 4 = 7x - 2 D. 2x - 3 = x - 2 Part b: Solve the equation for x

A- 3x+13=6x-2 B- 5

Sita rented a canoe. The equation y = 15x + 25 represents the cost in dollars, y, of renting the canoe for x hours. Select all of the true statements. Choices: The slope is 25, it means the total cost of renting the canoe increases $25 each hour. The y-intercept is 25, it means the initial cost of renting the canoe is $25. The slope is 15, it means the cost of renting the canoe increases $15 each hour. The y-intercept is 15, it means the initial total cost of renting the canoe is $15.

Correct: The y-intercept is 25, it means the initial cost of renting the canoe is $25. The slope is 15, it means the cost of renting the canoe increases $15 each hour.

Select all of the solutions to the equation x2 = 169. Answer choices: x = −84.5 x = −16 x = −13 x = 13 x = 16 x = 84.5

Correct: x = −13 x = 13

Select the correct symbol to compare 3√125 and 4.8.

Cube root of 125 > 4.8

What is the slope of the line? A line on a coordinate plane that passes through the points A negative 2 comma 4 and B 3 comma negative 2.

Equation: y = -1.2x + 1.6.

Complete the table below Exponent Form Simplified Form 6^−1 6^3•6^-3 (6^-6)/(6^-3) (1/6)^6•(1/6)^-2

Exponent Form Simplified Form 6^−1 ———> 1/6 6^3•6^-3 -——> 1 (6^-6)/(6^-3) ——> 1/216 (1/6)^6•(1/6)^-2 -> 1/1296

How many solutions does the system of equations below have? A coordinate plane with a single line graphed on it. (Technically two but they are overlapping so only one is visible.)

IMS/ infinitely many solutions

Mercury is the closet planet to the Sun at a distance of 36 million miles. The closest star to the Sun is Proxima Centauri, which is 4.24 light years away. A light year is 5.9 × 1012 miles. Part A Which is the distance in miles from Mercury to the Sun in scientific notation? Part B How many miles from the Sun is Proxima Centauri? Express your answer in scientific notation. Part C About how many times greater is the distance from the Sun to Proxima Centauri compared to the distance from the Sun to Mercury?

Part A: 3.6x10^7 Part b: 2.36 * 10^13 miles Part c: 7x10^5

China has a population of approximately 1,382,323,332 people. The population of the United States is about 324,118,787 people. Part A Approximate each population using scientific notation. Part B About how many more people live in China than in the United States?

Part a: china= 1.4x10^9 Usa: = 3.2 x 10^8 Part b: China has 1.08x10^9 than the USA

Compare the square root of ten and 3.46

Part a: number line: the square root of ten should come before 3.46 <—3—the square root of ten——3.46———-—4-> Part b: select the correct answer choices ~~The square root of ten is less than 3.46 ~~3.46 is greater than the square root of ten

Dante's soccer team sells T-shirts to raise money for new equipment. For each T-shirt sold, the team raises $8. Parents also make a group donation of $100 toward the equipment. Graph a linear equation that represents this situation.

The first quadrant of a coordinate plane. The horizontal axis is labeled number of t-shirts and the vertical axis is labeled amount raised in dollars. A ray begins at the point (0, 100) and passes through the point (10, 180).

When do use an open circle

When it is ONLY a greater/less than sign

When do use a closed circle?

When it is a greater/less than or equal to sign

Solve the equation 8/3x + 1 = 2/3x for x

X=-1/2

Solve the equation 750 + 0.05x = 1,100 + 0.025x for x.

X=14,000

Solve the equation 750 + 37.5x = 850 + 102.75x − 70.25x for x.

X=20

What is the value of n in the equation 2.3 × 109 = (1 × 103)(2.3 × 10n)?

n = 0.105825

What is the equation of the linear relationship in slope-intercept form? A coordinate plane with a line graphed. The Y-intercept of a line is 20 and the line passes through the points, 1, 30, 2, 40, and 3, 50.

y = 10x + 20

Select all the irrational numbers Possible choices: (select all that apply) —pi —315/8 — -0.25 — the square root of seven — 17/36

—pi —the square root of seven