Which reason best explains the motivation for American expansionism?
A. It would be important to maintain political influence in developing countries.
B. A U.S. naval presence around the world would decrease the chance of future wars.
C. American goods would stimulate local economies throughout the world.
D. New markets for American goods would strengthen the U.S. economy.
it
D
D
B
C
100% i promise
barry Allen aka aka the flash is correct
@barry allen aka the flash is 100% percent correct, thank you :)
Simplify the expression.
(2k + 1) (k – 4)
A. 2k2 – 7k + 4
B. 2k2 –3k + 4
C. 2k2 + 9k + 4
D. 2k2 – 7k – 4
Expanding using FOIL method, we get:
(2k + 1) (k – 4) = 2k(k – 4) + 1(k – 4) = 2k² – 8k + k – 4
Simplifying the expression, we get:
2k² – 7k – 4
Therefore, the answer is D. 2k² – 7k – 4.
Simplify the expression.
(–y + 4)(2y – 1)
A. 2y2 + 7y + 3
B. 2y2 + 5y – 4
C. –2y2 + 9y – 4
D. –2y2 + 6y + 3
Using FOIL method, we get:
(–y + 4)(2y – 1) = –2y² + y + 8y – 4
Simplifying the expression, we get:
–2y² + 9y – 4
Therefore, the answer is C. –2y² + 9y – 4.
Short Answer
Note: For questions 22–23, your teacher will grade your response to ensure you receive proper credit for your answer.
Look at the given triangles.
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 the sum of its three sides:
Perimeter = vertical leg + horizontal leg + hypotenuse
Perimeter = (4x + 2) + (5x - 4) + (7x + 7)
Simplifying, we get: Perimeter = 16x + 5
The perimeter of the red triangle is the sum of its three sides:
Perimeter = vertical leg + horizontal leg + hypotenuse
Perimeter = (x + 3) + (x + 7) + (2x - 5)
Simplifying, we get: Perimeter = 4x + 5
b. The difference between the perimeter of the larger triangle and the perimeter of the smaller triangle can be found by subtracting the smaller perimeter from the larger perimeter:
Difference = Perimeter of larger triangle - Perimeter of smaller triangle
Difference = (16x + 5) - (4x + 5)
Simplifying, we get: Difference = 12x
c. Substituting x = 3 in the expressions for the perimeters, we get:
Perimeter of blue triangle = 16(3) + 5 = 53
Perimeter of red triangle = 4(3) + 5 = 17
Therefore, the perimeter of the blue triangle when x = 3 is 53 units and the perimeter of the red triangle when x = 3 is 17 units.
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 incorrectly added the exponents instead of multiplying them. Eden accidentally wrote the wrong exponent for 6 on the right side of the equation.
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
First, we need to determine the value of x that corresponds to each block. Let's assign x to the value of a white unit block, so we know that:
- The white square represents x².
- The two white rods represent 2x.
- The black rod represents -x.
- The one white unit block represents 1.
- The three black unit blocks represent -3.
Adding all of these values together, we get:
x² + 2x - x + 1 - 3 = x² + x - 2
Therefore, the polynomial that the model represents is B. x² + x - 2.
Which polynomial does the model represent?
A black 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
Similar to the previous problem, let's assign x to the value of a white unit block. However, this time we also need to determine the value of a black unit block. Let's assign y to the value of a black unit block, so we know that:
- The black square represents x².
- The two white rods represent 2x.
- The black rod represents -y.
- The one white unit block represents 1.
- The three black unit blocks represent -3y.
Adding all of these values together, we get:
x² + 2x - y + 1 - 3y = x² + 2x - 4y + 1
Therefore, the polynomial that the model represents is D. –x² + x - 2y + 1.
For questions 2 and 3, simplify each polynomial.
4x2 + 4 – 5x + x – 2x2 + 8
A. –2x2 + 4x + 12
B. –2x2 – 4x + 12
C. 2x2 + 4x + 12
D. 2x2 – 4x + 12
Combining like terms, we get:
4x² - 2x² - 5x + x + 8 + 4 = 2x² - 4x + 12
Therefore, the simplified polynomial is D. 2x² - 4x + 12.
For questions 2 and 3, simplify each polynomial.
4x^2 + 4 – 5x + x – 2x^2 + 8
A. –2x2 + 4x + 12
B. –2x2 – 4x + 12
C. 2x2 + 4x + 12
D. 2x2 – 4x + 12
Combining like terms, we get:
4x² - 2x² - 5x + x + 8 + 4 = 2x² - 4x + 12
Therefore, the simplified polynomial is D. 2x² - 4x + 12.
3x2 + 5x – 7x + 3 – 5x2 + 2
A. –2x2 + 2x + 5
B. –2x2 – 2x + 5
C. 2x2 – 2x + 5
D. 2x2 + 2x + 5
Combining like terms, we get:
3x² - 5x² + 5x - 7x + 3 + 2 = -2x² - 2x + 5
Therefore, the simplified polynomial is B. -2x² - 2x + 5.
What are the coefficients in the polynomial 7x² – 4x + 6?
A. –7, 4
B. 7, 4, –6
C. 7, –4, 6
D. 7, –4
The coefficients in the polynomial 7x² - 4x + 6 are 7, -4, and 6.
Therefore, the answer is C. 7, -4, 6.
Add or subtract.
(m2 – m + 3) + (m – 1)
A. m2– m – 2
B. m2 + 2
C. m2 – 2
D. m2 + m + 2
Using the distributive property and combining like terms, we get:
(m² - m + 3) + (m - 1) = m² - m + 3 + m - 1
= m² + 2
Therefore, the answer is B. m² + 2.
Add or subtract.
(7x2 – x – 2) – (–6x3 + 3)
A. 6x3 + 7x2 – x – 5
B. –6x3 + 7x2 – x + 1
C. –x3 – x – 5
D. x2 – x + 1
Distributing the negative sign inside the parentheses, we get:
(7x² - x - 2) - (-6x³ + 3) = 7x² - x - 2 + 6x³ - 3
Combining like terms, we get:
6x³ + 7x² - x - 5
Therefore, the answer is A. 6x³ + 7x² - x - 5.
Start Fraction 100 superscript 12 baseline over 100 superscript 8 baseline End Fraction
A. 100 superscript Start Fraction 12 over 8 End Fraction baseline
B. 10096
C. 1004
D. 10020
Which of the following expressions is true?
A. 43 • 45 < 412
B. 52 • 53 > 55
C. 32 • 34 = 32
D. 52 • 54 = 58
The only answer choice that could be true is C, which simplifies to 9 • 81 = 32. However, this expression is not true, since 9 • 81 = 729, not 32.
Therefore, none of the given expressions are true.
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
We can simplify the expressions using the properties of exponents:
A. 4^3 • 4^5 = 4^8, which is less than 4^12. Therefore, this expression is true.
B. 5^2 • 5^3 = 5^5, which is equal to 5^5. Therefore, this expression is not true.
C. 3^2 • 3^4 = 3^6, which is not equal to 3^2. Therefore, this expression is not true.
D. 5^2 • 5^4 = 5^6, which is not equal to 5^8. Therefore, this expression is not true.
Therefore, the answer is A. 4^3 • 4^5 < 4^12
Which of the following expressions is true?
A. 2^4 • 2^3 = 2^12
B. 3^3 • 3^6 > 3^8
C. 4^2 • 4^2 > 4^4
D. 5^5 • 5^2 = 5^10
We can simplify the expressions using the properties of exponents:
A. 2^4 • 2^3 = 2^7, which is not equal to 2^12. Therefore, this expression is not true.
B. 3^3 • 3^6 = 3^9, which is greater than 3^8. Therefore, this expression is true.
C. 4^2 • 4^2 = 4^4, which is equal to 4^4. Therefore, this expression is not true.
D. 5^5 • 5^2 = 5^7, which is not equal to 5^10. Therefore, this expression is not true.
Therefore, the answer is B. 3^3 • 3^6 > 3^8.