Multiply. Write the result in scientific notation.
(2.3 • 101)(7 • 106)
A. 1.61 • 107
B. 1.61 • 108
C. 9.3 • 106
D. 9.3 • 107
The product of the numbers is:
(2.3 • 101)(7 • 106) = 16.1 • 107
But we want to write this in scientific notation, which means expressing it as a number between 1 and 10 multiplied by a power of 10. We can do this by moving the decimal point to the left one place, and adding 1 to the exponent:
1.61 • 108
Therefore, the answer is B. 1.61 • 108.
(2.2 ∙ 10–3)(4 ∙ 10–2)
A. 2.2 ∙ 106
B. 2.2 ∙ 10–5
C. 8.8 ∙ 106
D. 8.8 ∙ 10–5
When multiplying numbers in scientific notation, we can multiply the coefficients (the non-exponential parts) and add their exponents. Using this rule, we get:
(2.2 ∙ 10–3)(4 ∙ 10–2) = (2.2 * 4) * 10^(-3-2) = 8.8 * 10^-5
Therefore, the answer is D. 8.8 ∙ 10–5.
Simplify the expression.
7t4 ∙ 7t4
A. 49t8
B. 14t4
C. 49t16
D. 14t8
When multiplying two expressions with the same base, we can add their exponents. In this case, both expressions have a base of 7t, so we can add their exponents to get:
7t4 ∙ 7t4 = 7^(1+1) * t^(4+4) = 49t^8
Therefore, the answer is A. 49t8.
Simplify the expression.
–x(7x – 8)
A. 6x2 – 9x
B. –7x – 8x
C. –7x2 + 8x
D. 7x + 8x
When multiplying two terms, we can use the distributive property, which means we multiply each term inside the parentheses by the term outside the parentheses. In this case, we have:
-x(7x – 8) = -x * 7x + (-x) * (-8)
Simplifying, we get:
-x * 7x = -7x^2
-x * (-8) = 8x
Putting it all together, we get:
-x(7x – 8) = -7x^2 + 8x
Therefore, the answer is C. –7x2 + 8x.
Simplify the expression.
5k2(–6k2 – 2k + 6)
A. –30k3 + 3k2 + 30k
B. 30k4 – 10k3 + 11k2
C. –k4 + 3k3 + 11k2
D. –30k4 – 10k3 + 30k2
When using the distributive property to simplify this expression, we will multiply 5k^2 by each term inside the parentheses. We get:
5k^2(-6k^2 - 2k + 6) = (-30k^4 - 10k^3 + 30k^2)
Therefore, the answer is D. –30k^4 – 10k^3 + 30k^2.
Simplify the expression.
(2k + 1) (k – 4)
A. 2k2 – 7k + 4
B. 2k2 –3k + 4
C. 2k2 + 9k + 4
D. 2k2 – 7k – 4
We can simplify this expression by using the distributive property and multiplying each term in the first set of parentheses by each term in the second set of parentheses:
(2k + 1)(k - 4) = 2k * k + 2k * (-4) + 1 * k + 1 * (-4)
Simplifying each term, we get:
= 2k^2 - 8k + k - 4
= 2k^2 - 7k - 4
Therefore, the answer is D. 2k2 – 7k – 4.
Simplify the expression.
(–2y + 5)(y + 3)
A. –2y2 + 8y + 15
B. –2y2 – y + 15
C. 2y2 + 8y + 8
D. 2y2 – y + 8
We can simplify this expression by using the distributive property and multiplying each term in the first set of parentheses by each term in the second set of parentheses:
(-2y + 5)(y + 3) = -2y * y - 2y * 3 + 5 * y + 5 * 3
Simplifying each term, we get:
= -2y^2 - 6y + 5y + 15
= -2y^2 - y + 15
Therefore, the answer is B. –2y2 – y + 15.
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:
P = vertical leg + horizontal leg + hypotenuse = (4x + 2) + (5x - 4) + (7x + 7) = 16x + 5
The perimeter of the red triangle is:
P = vertical leg + horizontal leg + hypotenuse = (x + 3) + (x + 7) + (2x - 5) = 4x + 5
b. The difference between the perimeters of the larger triangle and the smaller triangle is:
(16x + 5) - (4x + 5) = 12x
Another expression that shows the difference is:
2(4x + 2 + 5x - 4 + 7x + 7) - (x + 3 + x + 7 + 2x - 5) = 12x
c. To find the perimeter of each triangle when x = 3, we can substitute x = 3 into the expressions we found in part a. We get:
Perimeter of the blue triangle: P = 16(3) + 5 = 53
Perimeter of the red triangle: P = 4(3) + 5 = 17
Therefore, the perimeter of the blue triangle is 53 when x = 3, and the perimeter of the red triangle is 17 when x = 3.
Can you make it a short awnser
a. Perimeter of blue triangle: 16x + 5; Perimeter of red triangle: 4x + 5
b. Difference in perimeters: 12x or 2(16x + 5) - (4x + 5)
c. Perimeter of blue triangle: 53; Perimeter of red triangle: 17
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?
Unfortunately, there is no problem to the right that you have referenced in the question. Please provide more information or the problem statement so that I can assist you better.
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 got the answer wrong. Erin incorrectly added the exponents instead of multiplying them, while Eden made the same mistake as Erin but also made an error in their arithmetic.