Which polynomial does the model represent?
A white square, two white rods, one black rod, one white unit block and three black unit blocks are shown.
A. –x³ + 2x² – 3x + 2
B. x² + x – 2
C. –x² – x + 2
D. –x² + x – 2
It is impossible to determine which polynomial the model represents without further information or context.
For questions 2 and 3, simplify each polynomial.
3x2 + 6 – 2x + 5x – 4x2 + 9
A. –x2 + 3x + 15
B. 7x2 + 3x + 3
C. x2 – 3x + 15
D. –x2 + 7x + 15
3x^2 - 4x^2 + 5x + (-2x) + (6 + 9) simplifies to:
-x^2 + 3x + 15
Therefore, the answer is A. -x^2 + 3x + 15.
For questions 2 and 3, simplify each polynomial.
3x^2 + 6 – 2x + 5x – 4x^2 + 9
A. –x2 + 3x + 15
B. 7x2 + 3x + 3
C. x2 – 3x + 15
D. –x2 + 7x + 15
3x^2 - 4x^2 + 5x - 2x + 6 + 9 can be simplified by combining like terms:
=x^2 + 3x + 15
Therefore, the answer is C. x^2 - 3x + 15.
4x^2 + 8x – 11x + 6 – 5x^2 + 2
A. –x^2 – 3x + 8
B. –x^2 + 3x + 8
C. x^2 – 3x + 8
D. x^2 + 3x + 8
Starting with 4x^2 - 5x^2 + 8x - 11x + 6 + 2:
=-x^2 - 3x + 8
Therefore, the answer is A. -x^2 - 3x + 8.
What are the coefficients in the polynomial 4x² + 3x – 3?
A. 4, –3, –3
B. 4, 3
C. 4, 3, 3
D. –4, –3
The coefficients in the polynomial 4x² + 3x - 3 are 4, 3, and -3.
Therefore, the answer is A. 4, -3, -3.
Add or subtract.
(m^2 – m + 3) + (m – 1)
A. m^2– m – 2
B. m^2 + 2
C. m^2 – 2
D. m^2 + m + 2
Starting with (m^2 - m + 3) + (m - 1):
= m^2 - m + 3 + m - 1
= m^2 + 2
Therefore, the answer is B. m^2 + 2.
(5x^2 + x – 3) – (–2x^3 + 4)
A. –2x^3 + 5x^2 + x – 7
B. –2x^3 + 5x^2 + x + 1
C. 2x^3 + 5x^2 + x – 7
D. 2x^3 + 5x^2 + x + 1
Starting with (5x^2 + x - 3) - (-2x^3 + 4):
= 5x^2 + x - 3 + 2x^3 - 4
= 2x^3 + 5x^2 + x - 7
Therefore, the answer is A. -2x^3 + 5x^2 + x - 7.
Suppose you earned 8t – 3 dollars on Monday and 6t + 5 dollars on Tuesday. What were your total earnings? Simplify your answer.
A. 2t + 2
B. 2t – 8
C. 14t + 2
D. 14t – 8
Your total earnings, obtained by adding 8t - 3 and 6t + 5, are:
= 14t + 2
Therefore, the answer is C. 14t + 2.
f^2 ∙ f ^3
A. f^5
B. f^6
C. (2f)^5
D. (2f)^6
When multiplying two powers with the same base, you add the exponents. In this case, f^2 multiplied by f^3 is:
f^(2+3) = f^5
Therefore, the answer is A. f^5.
Start Fraction 64 superscript 10 baseline over 64 superscript 5 baseline End Fraction
A. 64 superscript Start Fraction 10 over 5 End Fraction baseline
B. 64^50
C. 64^15
D. 64^5
Start Fraction 64^10 / 64^5 End Fraction can be simplified as:
= 64^(10-5)
= 64^5
Therefore, the answer is D. 64^5.
Start Fraction x superscript 16 baseline over x superscript 3 baseline End Fraction
A. Lower x superscript Start Fraction 16 over 3 End Fraction baseline
B. x^48
C. x^19
D. x^13
Start Fraction x^16 / x^3 End Fraction can be simplified using exponent rules:
= x^(16-3)
= x^13
Therefore, the answer is D. x^13.
Which of the following expressions is true?
A. 4^3 • 4^5 < 4^12
B. 5^2 • 5^3 > 5^5
C. 3^2 • 3^4 = 3^2
D. 5^2 • 5^4 = 5^8
Starting with the first expression, 4^3 • 4^5 < 4^12 can be simplified as:
4^8 < 4^12
This statement is true, since 4^8 is smaller than 4^12.
Therefore, the answer is A. 4^3 • 4^5 < 4^12.
Which of the following expressions is true?
A. 8^3 • 8^2 < 8^4
B. 4^4 • 4^4 = 4^16
C. 2^2 • 2^6 < 2^8
D. 3^3 • 3^3 > 3^5
Starting with the first expression, 8^3 • 8^2 < 8^4 can be simplified as:
8^5 < 8^4
This statement is not true, since 8^5 is greater than 8^4.
Therefore, the correct answer must be one of the other options.
Looking at option B, 4^4 • 4^4 = 4^16, we can simplify as:
4^8 = 4^16
This statement is also not true, since 4^8 is not equal to 4^16.
Similarly, looking at option D, 3^3 • 3^3 > 3^5, we can simplify as:
3^6 > 3^5
This statement is true, since 3^6 is greater than 3^5.
Therefore, the answer is D. 3^3 • 3^3 > 3^5.
Write the value of the expression.
Start Fraction 4 superscript 5 baseline over 4 superscript 5 baseline End Fraction
A. 1
B. 4
C. 5
D. 0
Start Fraction 4^5 / 4^5 End Fraction can be simplified using the exponent rule:
= 1
Therefore, the answer is A. 1.
Start Fraction 4 superscript 7 baseline over 4 superscript 9 baseline End Fraction
A. –16
B. Start Fraction 1 over 16 End Fraction
C. one-eighth
D. 8
Start Fraction 4^7 / 4^9 can be simplified by subtracting the exponent in the denominator from the numerator:
= 4^(7-9)
= 1/16
Therefore, the answer is B. Start Fraction 1 over 16 End Fraction.
Multiply. Write the result in scientific notation.
(1.4 • 10^1)(8 • 10^4)
A. 9.4 • 10^4
B. 9.4 • 10^5
C. 1.12 • 10^5
D. 1.12 • 10^6
To multiply numbers in scientific notation, you multiply their coefficients and add their exponents.
(1.4 • 10^1)(8 • 10^4) can be simplified as:
= (1.4 * 8) * 10^(1+4)
= 11.2 * 10^5
Since 11.2 is greater than 1 and less than 10, we can write the result in scientific notation as:
= 1.12 * 10^6
Therefore, the answer is D. 1.12 • 10^6.
(1.1 ∙ 10^–5)(3 ∙ 10^–2)
A. 4.1 ∙ 10^–7
B. 4.1 ∙ 10^10
C. 3.3 ∙ 10^–7
D. 3.3 ∙ 10^10
To multiply numbers in scientific notation, you multiply their coefficients and add their exponents.
(1.1 • 10^-5)(3 • 10^-2) can be simplified as:
= (1.1 * 3) * 10^(-5-2)
= 3.3 * 10^(-7)
Therefore, the answer is C. 3.3 ∙ 10^-7.
7t^4 ∙ 7t^4
A. 49t^8
B. 14t^4
C. 49t^16
D. 14t^8
When multiplying two powers with the same base, you add the exponents. In this case, 7t^4 times 7t^4 is:
7^2 * (t^4 * t^4) = 49 * t^(4+4) = 49t^8
Therefore, the answer is A. 49t^8.
–x(7x – 8)
A. 6x^2 – 9x
B. –7x – 8x
C. –7x^2 + 8x
D. 7x + 8x
–x(7x – 8) can be simplified using the distributive property:
= -7x^2 + 8x
Therefore, the answer is C. -7x^2 + 8x.
5k^2(–6k^2 – 2k + 6)
A. –30k^3 + 3k^2 + 30k
B. 30k^4 – 10k^3 + 11k^2
C. –k^4 + 3k^3 + 11k^2
D. –30k^4 – 10k^3 + 30k^2
5k^2(-6k^2 - 2k + 6) can be simplified using the distributive property:
= -30k^4 - 10k^3 + 30k^2
Therefore, the answer is D. -30k^4 - 10k^3 + 30k^2.
Simplify the expression.
(3k + 2)(k – 3)
A. 3k^2 – 7k – 5
B. 3k^2 – 7k – 6
C. 3k^2 – 4k – 6
D. 3k^2 – 4k – 5
Using the distributive property and combining like terms, we can simplify (3k + 2)(k - 3) as:
= 3k^2 - 7k - 6
Therefore, the answer is B. 3k^2 - 7k - 6.
Simplify the expression.
(–y + 4)(2y – 1)
A. 2y^2 + 7y + 3
B. 2y^2 + 5y – 4
C. –2y^2 + 9y – 4
D. –2y^2 + 6y + 3
Using the distributive property and combining like terms, we can simplify (–y + 4)(2y – 1) as:
= -2y^2 + 9y - 4
Therefore, the answer is C. -2y^2 + 9y - 4.
triangles
The blue triangle is a right triangle. The vertical leg is labeled with the expression 4 x plus 2. The horizontal leg is labeled with the expression 5 x minus 4. The hypotenuse is labeled with the expression 7 x plus 7.
The red triangle is a right triangle. The vertical leg is labeled with the expression x plus 3. The horizontal leg is labeled with the expression x plus 7. The hypotenuse is labeled with the expression 2 x minus 5.
a. Write an expression in simplest form for the perimeter of each triangle.
b. Write another expression in simplest form that shows the difference between the perimeter of the larger triangle and the perimeter of the smaller triangle.
c. Find the perimeter for each triangle when x = 3
a. The perimeter of the blue triangle is:
4x + 2 + 5x - 4 + 7x + 7 = 16x + 5
The perimeter of the red triangle is:
x + 3 + x + 7 + 2x - 5 = 4x + 5
b. The difference between the perimeter of the larger triangle (blue) and the perimeter of the smaller triangle (red) is:
(16x + 5) - (4x + 5) = 12x
c. To find the perimeter of each triangle when x = 3, we can substitute 3 for x in the expressions we found in part a.
Perimeter of blue triangle:
16(3) + 5 = 53
Perimeter of red triangle:
4(3) + 5 = 17
Therefore, the perimeter of the blue triangle is 53 and the perimeter of the red triangle is 17 when x = 3.
To find the difference in perimeters:
53 - 17 = 36
Emma, Erin, and Eden completed the problem to the right.
a. Who completed the problem correctly?
b. What did the other two students do wrong in their answers?
Emma's equation shows 6 squared times 6 superscript 5 baseline equals 36 superscript 7 baseline.
Erin's equation shows 6 squared times 6 superscript 5 baseline equals 6 superscript 10 baseline.
Eden's equation shows 6 squared times 6 superscript 5 baseline equals 6 superscript 7 baseline.
a. Emma completed the problem correctly.
b. Erin and Eden both made mistakes in their answers. Erin incorrectly added the exponents when multiplying 6^2 and 6^5, while Eden incorrectly subtracted the exponents.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
A radio signal travels at
3
.
00
⋅
10
8
meters per second. How many seconds will it take for a radio signal to travel from a satellite to the surface of Earth if the satellite is orbiting at a height of
3
.
54
⋅
10
7
meters? Show your work.
We can use the time = distance / speed formula to solve this problem.
The distance is the height of the satellite above Earth's surface, which is 3.54 * 10^7 meters.
The speed is the speed of the radio signal, which is 3.00 * 10^8 meters per second.
Plugging in the values:
time = distance / speed
time = (3.54 * 10^7 meters) / (3.00 * 10^8 meters per second)
Dividing the distance by the speed gives:
time = 0.118 seconds
Therefore, it will take approximately 0.118 seconds for a radio signal to travel from the satellite to the surface of Earth.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
A radio signal travels at
3.00⋅10.8
meters per second. How many seconds will it take for a radio signal to travel from a satellite to the surface of Earth if the satellite is orbiting at a height of
3.54⋅10.7
meters? Show your work.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
A radio signal travels at
3.00⋅10.8
meters per second. How many seconds will it take for a radio signal to travel from a satellite to the surface of Earth if the satellite is orbiting at a height of
3.54⋅10.7
meters? Show your work.