(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
21 answers
The product is equal to (2.2 x 4) times (10^-3 x 10^-2) which simplifies to 8.8 x 10^-5. Therefore, the answer is D. 8.8 ∙ 10–5.
Simplify the expression.
8t5 ∙ 8t5
A. 64t25
B. 64t10
C. 16t10
D. 16t5
8t5 ∙ 8t5
A. 64t25
B. 64t10
C. 16t10
D. 16t5
When multiplying two terms with the same base (in this case, both terms are 8t5), we add the exponents. So, 8t5 x 8t5 simplifies to (8 x 8) times (t5 x t5), which is 64t10. Therefore, the answer is B. 64t10.
Simplify the expression.
–x(7x – 8)
A. 6x2 – 9x
B. –7x – 8x
C. –7x2 + 8x
D. 7x + 8x
–x(7x – 8)
A. 6x2 – 9x
B. –7x – 8x
C. –7x2 + 8x
D. 7x + 8x
To simplify this expression, we need to distribute the -x to both terms inside the parenthesis:
-x(7x - 8) = -x(7x) + (-x)(-8)
= -7x^2 + 8x
Therefore, the answer is C. -7x^2 + 8x.
-x(7x - 8) = -x(7x) + (-x)(-8)
= -7x^2 + 8x
Therefore, the answer is C. -7x^2 + 8x.
Simplify the expression.
3k2(–2k2 – 4k + 7)
A. –6k3 – k + 10k
B. –6k4 – 12k3 + 21k2
C. k4 – k3 + 10k2
D. 6k4 – 12k3 + 10k2
3k2(–2k2 – 4k + 7)
A. –6k3 – k + 10k
B. –6k4 – 12k3 + 21k2
C. k4 – k3 + 10k2
D. 6k4 – 12k3 + 10k2
To simplify this expression, we need to distribute the 3k2 to all three terms inside the parenthesis:
3k2(-2k2 - 4k + 7) = -6k^4 - 12k^3 + 21k^2
Therefore, the answer is B. -6k4 - 12k3 + 21k2.
3k2(-2k2 - 4k + 7) = -6k^4 - 12k^3 + 21k^2
Therefore, the answer is B. -6k4 - 12k3 + 21k2.
Simplify the expression.
(3k + 2)(k – 3)
A. 3k2 – 7k – 5
B. 3k2 – 7k – 6
C. 3k2 – 4k – 6
D. 3k2 – 4k – 5
(3k + 2)(k – 3)
A. 3k2 – 7k – 5
B. 3k2 – 7k – 6
C. 3k2 – 4k – 6
D. 3k2 – 4k – 5
To simplify the expression, we use the FOIL method, which stands for First, Outer, Inner, Last.
(3k + 2)(k - 3) = (3k)(k) + (3k)(-3) + (2)(k) + (2)(-3)
= 3k^2 - 9k + 2k - 6
= 3k^2 - 7k - 6
Therefore, the answer is B. 3k2 – 7k – 6.
(3k + 2)(k - 3) = (3k)(k) + (3k)(-3) + (2)(k) + (2)(-3)
= 3k^2 - 9k + 2k - 6
= 3k^2 - 7k - 6
Therefore, the answer is B. 3k2 – 7k – 6.
Simplify the expression.
(–2y + 5)(y + 3)
A. –2y2 + 8y + 15
B. –2y2 – y + 15
C. 2y2 + 8y + 8
D. 2y2 – y + 8
(–2y + 5)(y + 3)
A. –2y2 + 8y + 15
B. –2y2 – y + 15
C. 2y2 + 8y + 8
D. 2y2 – y + 8
Using the FOIL method:
(-2y + 5)(y + 3) = (-2y)(y) + (-2y)(3) + (5)(y) + (5)(3)
= -2y^2 - 6y + 5y + 15
= -2y^2 - y + 15
Therefore, the answer is B. -2y2 - y + 15.
(-2y + 5)(y + 3) = (-2y)(y) + (-2y)(3) + (5)(y) + (5)(3)
= -2y^2 - 6y + 5y + 15
= -2y^2 - y + 15
Therefore, the answer is B. -2y2 - y + 15.
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
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. For the blue triangle, the perimeter is given by:
perimeter = (vertical leg) + (horizontal leg) + (hypotenuse)
perimeter = (4x + 2) + (5x - 4) + (7x + 7)
perimeter = 16x + 5
For the red triangle, the perimeter is given by:
perimeter = (vertical leg) + (horizontal leg) + (hypotenuse)
perimeter = (x + 3) + (x + 7) + (2x - 5)
perimeter = 4x + 5
b. The difference between the perimeter of the larger (blue) triangle and the perimeter of the smaller (red) triangle is:
(16x + 5) - (4x + 5) = 12x
So the expression for the difference in perimeters is 12x.
c. To find the perimeters of each triangle when x = 3, we substitute x = 3 into the expressions we found for the perimeter:
For the blue triangle: perimeter = 16(3) + 5 = 53
For the red triangle: perimeter = 4(3) + 5 = 17
So when x = 3, the perimeter of the blue triangle is 53 and the perimeter of the red triangle is 17.
perimeter = (vertical leg) + (horizontal leg) + (hypotenuse)
perimeter = (4x + 2) + (5x - 4) + (7x + 7)
perimeter = 16x + 5
For the red triangle, the perimeter is given by:
perimeter = (vertical leg) + (horizontal leg) + (hypotenuse)
perimeter = (x + 3) + (x + 7) + (2x - 5)
perimeter = 4x + 5
b. The difference between the perimeter of the larger (blue) triangle and the perimeter of the smaller (red) triangle is:
(16x + 5) - (4x + 5) = 12x
So the expression for the difference in perimeters is 12x.
c. To find the perimeters of each triangle when x = 3, we substitute x = 3 into the expressions we found for the perimeter:
For the blue triangle: perimeter = 16(3) + 5 = 53
For the red triangle: perimeter = 4(3) + 5 = 17
So when x = 3, the perimeter of the blue triangle is 53 and the perimeter of the red triangle is 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?
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. 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 wrote the incorrect product where instead of adding the exponents, she multiplied them. Eden also wrote the incorrect product, where it seems she only added the exponents for 6 and did not square 6. Emma added the exponents correctly and multiplied 6^2 and 6^5 to get 6^7.
b. Erin wrote the incorrect product where instead of adding the exponents, she multiplied them. Eden also wrote the incorrect product, where it seems she only added the exponents for 6 and did not square 6. Emma added the exponents correctly and multiplied 6^2 and 6^5 to get 6^7.
: 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.
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 start by using the formula:
distance = rate × time
Since we want to find the time it takes for the signal to travel from the satellite to the surface of the Earth, we can rearrange the formula as:
time = distance / rate
The distance the signal needs to travel is the height of the satellite above the Earth's surface, which is given as 3.54 × 10^7 meters. The rate of the radio signal is given as 3.00 × 10^8 meters per second. Substituting these values into the formula, we get:
time = (3.54 × 10^7 meters) / (3.00 × 10^8 meters per second)
time = 0.118 seconds
Therefore, it will take 0.118 seconds for a radio signal to travel from a satellite to the surface of the Earth.
distance = rate × time
Since we want to find the time it takes for the signal to travel from the satellite to the surface of the Earth, we can rearrange the formula as:
time = distance / rate
The distance the signal needs to travel is the height of the satellite above the Earth's surface, which is given as 3.54 × 10^7 meters. The rate of the radio signal is given as 3.00 × 10^8 meters per second. Substituting these values into the formula, we get:
time = (3.54 × 10^7 meters) / (3.00 × 10^8 meters per second)
time = 0.118 seconds
Therefore, it will take 0.118 seconds for a radio signal to travel from a satellite to the surface of the Earth.
-x(5x - 4)
4x^2 - 5x
-5x - 4x
5x + 4x
-5x^2 + 4x
4x^2 - 5x
-5x - 4x
5x + 4x
-5x^2 + 4x
Simplification of -x(5x - 4):
-x(5x - 4) = -x(5x) + (-x)(-4)
= -5x^2 + 4x
Therefore, the answer is -5x^2 + 4x.
-x(5x - 4) = -x(5x) + (-x)(-4)
= -5x^2 + 4x
Therefore, the answer is -5x^2 + 4x.
4k^2 (-3k^2 - 4k + 5)
-12k^4-16k^3+20k^2
12k^4 - 16k^3 + 9k^2
-12k^3 + 20k
k^4 + 9k^2
-12k^4-16k^3+20k^2
12k^4 - 16k^3 + 9k^2
-12k^3 + 20k
k^4 + 9k^2
Simplification of 4k^2 (-3k^2 - 4k + 5):
We can distribute 4k^2 to each of the terms inside the parenthesis and get:
4k^2 (-3k^2 - 4k + 5) = -12k^4 - 16k^3 + 20k^2
Therefore, the answer is -12k^4 - 16k^3 + 20k^2.
We can distribute 4k^2 to each of the terms inside the parenthesis and get:
4k^2 (-3k^2 - 4k + 5) = -12k^4 - 16k^3 + 20k^2
Therefore, the answer is -12k^4 - 16k^3 + 20k^2.