Algebra 1 Math Prep

Maya is designing a triangular garden. She knows the area of the triangle can be calculated using the formula: Area = 0.5 * Base * Height. Given the following dimensions for her garden:
B = 3b²
H = 12p⁷b¹⁹

• 18b²¹p⁷

• 18b⁷p²¹

• 36b²¹p⁷

• 36b³⁸p⁷

Answer explanation

The area of a triangle is given by the formula A = 1/2 * B * H. Substituting B = 3b^2 and H = 12p^7b^19, we get A = 1/2 * 3b^2 * 12p^7b^19 = 18b^(2+19)p^7 = 18b^21p^7. Thus, the correct answer is 18b^21p^7.

Tags

CCSS.HSA.APR.A.1

• -64p²⁰/ 49r⁶

• 64p²⁰/ 49r⁶

• -8p²⁰/ 14r⁶

• -64p¹²/ 49r⁵

Answer explanation

To simplify \left(\frac{-8p^{10}}{7r^3}\right)^{2}, square both the numerator and denominator: (-8)^2 = 64, (p^{10})^2 = p^{20}, and (7r^3)^2 = 49r^6. Thus, the result is \frac{64p^{20}}{49r^{6}}.

Tags

CCSS.HSA.APR.A.1

Answer explanation

To simplify \(\sqrt{100d^6f^4z^2}\), we take the square root of each factor: \(\sqrt{100} = 10\), \(\sqrt{d^6} = d^3\), \(\sqrt{f^4} = f^2\), and \(\sqrt{z^2} = z\). Thus, the result is \(10d^3f^2z\).

Arjun is organizing his book collection. He has 5⁵ books on one shelf and decides to remove 5³ books to donate. How many books are left on the shelf, expressed using exponents?

• 5^-15

• 5⁸

• 5^-8

• 5²

Answer explanation

To simplify 5^5 * 5^-3, use the property of exponents that states a^m * a^n = a^(m+n). Here, 5^(5 + (-3)) = 5^2. Thus, the correct answer is 5^2.

Tags

CCSS.8.EE.A.1

Nora is organizing a math competition and she wants to include a question about exponents. She writes the following expression:

(xyz)⁰ =

• 0

• 1

• xyz

• -1

Answer explanation

Any non-zero number or variable raised to the power of 0 equals 1. Therefore, (xyz)^0 simplifies to 1.

Tags

CCSS.6.EE.A.1

Isla is designing a rectangular garden. If the ratio of the length to the width of the garden is 3:2 and the width is 8 cm, what is the length?

• 10 cm

• 5 cm

• 12 cm

• 15 cm

Answer explanation

The ratio of length to width is 3:2. Given the width is 8 cm, we can set up the equation: length = (3/2) * width = (3/2) * 8 = 12 cm. Thus, the length of the rectangle is 12 cm.

Tags

CCSS.7.G.A.1

Michael scored 19 out of 25 on his math test. What is his score as a percent?

• 19%

• 25%

• 76%

• 50%

Answer explanation

To convert 19/25 to a percent, divide 19 by 25 to get 0.76, then multiply by 100. This gives 76%, which is the correct answer.

Nora is designing a ramp for a skateboard park. She wants the ramp to be parallel to an existing ramp that follows the line
y = 2x + 3. If the new ramp needs to pass through the point (5, -4), what is the equation of the line in slope-intercept form?

• y = -2x + 14

• y = 2x - 14

• y = 2x - 6

• y = -1/2x + 6

Answer explanation

The slope of the given line y = 2x + 3 is 2. A parallel line has the same slope. Using point-slope form with point (5, -4), we find y = 2x - 14, which matches the correct answer.

Aria is planning a road trip and wants to calculate her fuel costs. She knows that her car consumes fuel at a rate that can be represented by a linear equation. If she starts her trip with 4 gallons of fuel and the fuel consumption rate is 1/2 gallon per hour, write the slope-intercept form of the equation that represents the fuel left in the tank after x hours of driving.

• y=1/2x+4

• y=-1/2x+4

• y=4x-1/2

• y=2x+1/2

Answer explanation

To find the slope-intercept form (y = mx + b), use the point (2,5) and slope m = 1/2. Plugging in, 5 = (1/2)(2) + b gives b = 4. Thus, the equation is y = 1/2x + 4, which matches the correct choice.

Tags

CCSS.7.RP.A.2D

Emma is planning a garden and wants to create a path that follows a straight line. What is the equation of this path in slope-intercept form?

• y = 2x + 5

• y = -2x + 5

• y = -2x

• y = 5

Answer explanation

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. The correct equation, y = -2x + 5, has a slope of -2 and a y-intercept of 5, matching the line's characteristics.

Tags

CCSS.7.RP.A.2D