which is a factored form of 216p^3 + 125q^3?
The factored form of [tex]\( 216p^3 + 125q^3 \) is \( (6p + 5q)(36p^2 - 30pq + 25q^2) \).[/tex]
To find the factored form of the expression [tex]\(216p^3 + 125q^3\)[/tex], we can use the sum of cubes formula:
[tex]\[ a^3 + b^3 = (a + b)(a^2 - ab + b^2) \][/tex]
Where a = 6p and b = 5q.
Substituting these values into the formula, we get:
[tex]\[ 216p^3 + 125q^3 = (6p)^3 + (5q)^3 \][/tex]
[tex]\[ = (6p + 5q)((6p)^2 - (6p)(5q) + (5q)^2) \][/tex]
[tex]\[ = (6p + 5q)(36p^2 - 30pq + 25q^2) \][/tex]
Therefore, the factored form of [tex]\( 216p^3 + 125q^3 \) is \( (6p + 5q)(36p^2 - 30pq + 25q^2) \).[/tex]
Complete question:
What is the factored form of 216p³+125q³?
Solve the equation below for y.
8x - 2y = 24
A. y= 4x - 12
B. y= 12 - 4x
C. y = 8x - 24
D.y = 4x - 8
The given equation, when solved for y gives y = 4x - 12.
Hence, option A is correct.
Given is an equation 8x - 2y = 24, we need to solve for y.
To solve the equation for y, you need to isolate y on one side of the equation.
Let's do that step by step:
Start with the original equation:
8x - 2y = 24
Get rid of the constant term on the left side by subtracting 8x from both sides:
-2y = -8x + 24
Now, we want to solve for y, so we need to get rid of the coefficient of y (-2).
To do that, divide both sides by -2:
y = (-8x + 24) / -2
Simplify the right side of the equation:
y = -8x / -2 + 24 / -2
Simplify further:
y = 4x - 12
So, the solution for y is:
A. y = 4x - 12
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A baseball that usually cost $65 is on sale for $55.25. what is the percent off?
5 lollipops and 12 toffees have a mass of 61 grams and 10 lollipops and 13 toffees have a mass of 89 grams . Calculate the mass of one lollipop and one toffee
How many years will it take for 2000 to double at a simple interest rate of 8%? explain how you found your answer
The table below shows the temperature (in °F) t hours after midnight in Phoenix on March 15. The table shows values of this function recorded every two hours.
Estimate the value of T′(8). Give units in your answer.
What is the meaning of T′(8)?
t 0 2 4 6 8 10 12 14
T 73 73 70 68 73 80 86 89
We need to estimate the value of T'(8) and then we need to give the meaning of this value. Since we have a table and not an expression of a function our goal is to find the Average Rate of Change between two points.
For a nonlinear graph whose slope changes at each point, the average rate of change between any two points [tex](x_{1},f(x_{1}) \ and \ (x_{2},f(x_{2})[/tex] is the slope of the line through the two points. So:
[tex]ARC=\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}} =\frac{Change \ in \ y}{Change \ in \ x}=m_{sec}[/tex]
1. Estimated value of T′(8).
T'(8) means the derivative of the function T(t) when t = 8 hours. So, we can estimate this value using the average rate of change:
[tex]ARC=\frac{T(8)-T(6)}{8-6} =\frac{73-68}{8-6}=\frac{5}{2} \ degrees \ per \ hours[/tex]
2. The meaning of T′(8)
This means the average temperature after midnight in Phoenix on March 15, from t = 6 to t = 8 hours, that is, for each hour the temperature rises 5/2 degrees on the Fahrenheit scale. The points have been plotted in the Figure bellow.
The rate of change of the temperature is 3 degrees Celsius per hour. This response means that temperature has an instantaneous increase rate of 3 degrees Celsius per hour at [tex]t = 8\,h[/tex].
We can estimate the rate of change of the temperature, in degrees Celsius per hour, by calculating the average of two consecutive secant lines, whose expression is presented below:
[tex]T'(t) \approx \frac{1}{2}\cdot \left[\frac{T(t+\Delta t)-T(t)}{\Delta t} + \frac{T(t)-T(t-\Delta t)}{\Delta t} \right][/tex] (1)
If we know that [tex]\Delta t = 2[/tex], [tex]T(6) = 68[/tex], [tex]T(8) = 73[/tex] and [tex]T(10) = 80[/tex], then the estimated value of the rate of change of the temperature is:
[tex]T'(8) = \frac{1}{2}\cdot \left[\frac{80-73}{2}+\frac{73-68}{2} \right][/tex]
[tex]T'(8) \approx 3\,\frac{^{\circ}C}{h}[/tex]
The rate of change of the temperature is 3 degrees Celsius per hour. This response means that temperature has an instantaneous increase rate of 3 degrees Celsius per hour at [tex]t = 8\,h[/tex].
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Which graph shows the axis of symmetry for the function f(x) = (x – 2)2 + 1?
Answer:
B
Step-by-step explanation:
Does it matter if you add azero when you divide a dcimal.
Answer:
no it does not matter
Step-by-step explanation:
What is the side length of a cube with a volume of 4913 m3? m
Is 69 a prime or composite number
Answer:
composite
divisible by 3,1,69,23
Have a nice day!
Step-by-step explanation:
A group of men and women were asked what their favorite pet was, and the results of the survey were tabulated. find p(b/not
a.
The slope of a line is -, and the y-intercept is . What is the equation of the line written in general form?
A) 10x + 3y - 1 = 0
B)x + 3y + 10 = 0
C) x + 3y - 10 = 0
to express the polynomial d^2+d^3-d+3 in standard form, which term should be written first?
*the quartic term
*the constant term
*the cubic term
*the quadratic term ...?
Answer:
Option 3- the cubic term
Step-by-step explanation:
Given : Polynomial [tex]d^2+d^3-d+3[/tex]
To find : To express the polynomial in standard form, which term should be written first?
Solution :
The given polynomial [tex]d^2+d^3-d+3[/tex]
The standard form of polynomial is arranged according to the higher degree to the lowest degree.
The degree is the power, first the higher degree then the lower and last the constant term.
In our given polynomial the highest degree is 3 so it is the first term of the polynomial.
The standard form is [tex]d^3+d^2-d+3[/tex]
Therefore, The required result is the cubic term is written first.
The ordered pair below is a solution to which equation? (2, 12) A. y = 6x B. y=1/2x C. y = 2x D. y=1/6x
If the principal is $350 and the interest rate is 3 percent, what is the simple interest earned in one year? simple interest = P × r × t Select one of the options below as your answer: A. $10.50 B. $30.25 C. $105
Answer:
The option A. $10.50 is correct
Step-by-step explanation:
Principal = $350
Rate = 3%
⇒ Rate = 0.03
Time = 1 year
Now, Simple Interest is given by the formula : Principal × Rate × Time
Therefore, Simple Interest = 350 × 0.03 × 1
⇒ Simple Interest = $10.50
Hence, The option A. $10.50 is correct
14 inches of snow fell in 4 hours how much snow fell each hour
being timed help
What is the common ratio for the geometric sequence?
43,4,12,36,...
Determine the volume of the right circular cone generated by rotating the line y = 1/3x about the y-axis between y = 0 and y = 3.
A) V = 81pi cu.units
B) V = 84pi cu.units
C) V = 82pi cu.units
D) V = 85pi cu.units
E) V = 83pi cu.units
In this exercise we want to calculate the volume of a circular cone in this way we have that the rotation will be given by:
Letter A
First let's write the rotation in favor of the X, this will be equal to:
[tex]y = x/3\\x = 3y[/tex]
So substituting this value in the function we find that:
[tex]x^2 =(3y)^2= 9y^2\\\int\limits^3_0 {9y^2} \, dx =81 \pi[/tex]
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This table represents an exponential function.
What is the ratio of outputs for any two inputs that are 2 apart?
Divide the larger output by the smaller output.
Enter your answer in the box as a decimal to the nearest hundredth.
This is how the table looks
Number of Years from Now Value of a Scooter ($)
0|45
1|48.24
2|51.71
3|55.44
4|59.43
Answer:
it is 1.15 the dude on top is right it is 1.15 i took the test and it 1.15
Step-by-step explanation:
The output of the defined number operation indicates the operations involved in the function.
The ratio of outputs for any two inputs that are 2 apart is approximately 1.149.
Reasons:
The table is presented as follows;
[tex]\begin{array}{|cc|c|}Number \ of \ years \ from \ Now&&Value \ of \ a \ Scooter\\0&&45\\1&&48.24\\2&&51.71\\3&&55.44\\4&&59.43\end{array}\right][/tex]
The ratio of the outputs for two inputs that are 2 apart, with the larger output divided by the smaller output are;
[tex]Between \ 0 \ and \ 2; \dfrac{51.71}{45} = 1.149 \overline 1[/tex]
[tex]Between \ 1 \ and \ 3; \dfrac{55.44}{48.24} \approx1.1493[/tex]
[tex]Between \ 2 \ and \ 4; \dfrac{59.43}{51.71} \approx 1.149294140[/tex]
Therefore;
The ratio of outputs for any two inputs that are 2 apart is approximately 1.149.
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Which polynomial expression represents the area of the outermost square tile, shown below?
A square shaped tile with length x plus three is shown
x2 + 6x + 6
x2 + 9x + 6
x2 + 6x + 9
x2 − 6x + 9
Answer:
The correct answer is C, "x2 + 6x + 9."
Step-by-step explanation:
I just got it correct on the test.
Final answer:
To find the area of a square tile with sides of length x + 3, we square the binomial, resulting in the polynomial expression x² + 6x + 9, which represents the area of the square tile.
Explanation:
The question asks which polynomial expression represents the area of a square tile with sides of length x + 3. To find the area of a square, you multiply the length of one side by itself. In this case, the length of each side of the square is (x + 3), so the area of the square is (x + 3)(x + 3), or (x + 3)².
To expand this expression, we use the formula for squaring a binomial: (a + b)² = a² + 2ab + b². Applying this formula to our expression, we get:
a = x
b = 3
(x + 3)² = x² + 2(3)x + 3²
(x + 3)² = x² + 6x + 9
Therefore, the correct polynomial expression that represents the area of the square tile is x² + 6x + 9.
What is the length of the hypotenuse of a right triangle with leg lengths of 8 inches and 15 inches?
A. 13 inches
B. 17 inches
C. 21 inches
D.25 inches
Answer:
B.17 INCHESStep-by-step explanation:
Answer:
the answer is B
Step-by-step explanation:
just helping the other guy get brainliest.
A video rental company offers a plan that includes a membership fee of $6 and charges $2 for every DVD borrowed. They also offer a second plan, that costs $48 per month for unlimited DVD rentals. If a customer borrows enough DVDs in a month, the two plans cost the same amount. What is that total cost of either plan? How many DVDs is that?
what does the expression 15 - 3[2+6 (-3] simplify to?
15x+1= y solve for x ...?
15x + 1=y subtract 1 from both sides
15x=y-1 divide both sides by 15
x=(y-1)/15
In order to purchase a home, a family borrows $159,000 at 6.5% for 30 years. Use the table to find their monthly payment. Round the answer to the nearest cent.
a.
$954.00 c.
$1,186.14
b.
$1,006.47 d.
$1,276.36
Answer:
B
Step-by-step explanation:
Bianca wrote the steps for her solution to the equation 2.3 + 8(1.3x – 4.75) = 629.9. She left out the description for the last step.
What is the missing step of her solution?
Add 10.4 to both sides.
Add negative 10.4 to both sides.
Multiply both sides of the equation by 10.4.
Divide both sides of the equation by 10.4.
Mark this and return
Answer: Last Option is correct.
Step-by-step explanation:
Since we have given that
[tex]2.3 + 8(1.3x-4.75) = 629.9[/tex]
We need to solve the above equation,
[tex]2.3 + 8(1.3x-4.75) = 629.9\\\\2.3+10.4x-38=629.9\\\\-35.7+10.4x=629.9\\\\10.4x=629.9+35.7\\\\10.4x=665.6\\\\\text{ Dividing 10.4 on both sides}\\\\x=\frac{665.6}{10.4}\\\\x=64[/tex]
Hence, Divide both sides of the equation by 10.4.
Therefore, Last Option is correct.
Answer:
D
Step-by-step explanation:
Write the fraction as a percent. If necessary, round to the nearest tenth of a percent. 18/25
47.3%
48.6%
72%
73.4%
If f(x) = 3x + 10x and g(x) = 4x – 2, find (f + g)(x).
A. 17x – 2
B. 3x – 6x + 2
C. 3x + 14x – 2
D. 3x + 6x + 2
Answer:c
Step-by-step explanation:
Please!!!!!!!!! I need this answers ASAP Pleas !!!!!!!!
Question 1
If y varies directly with x and y = 4 when x = 12, then what is the value of y when x = 60?
Question 2
If y varies directly with x and y = 3 when x = 12, then what is the value of y when x = 40?
Question 3
Suppose p varies directly with d, and p = 7 when d = 3. What is the value of d when p = 28?
Question 4
What is the direct variation equation for the table of ordered pairs?
x y
80 56
90 63
100 70
Question 5
What is the direct variation equation for the table of ordered pairs?
x y
60 48
70 56
80 64
Answer:
1) 20
2) 20
3) 12
4) 0.7
5)0.8
Step-by-step explanation:
when it asks questions like question 1 and 2 and 3 just take what the number is multiplied by
jack has no more than $24 to spend on DVD's for a party. Each DVD rents for $4. Find the maximum number of DVD's jack can rent for his party. answer must be written on a number line
Answer:
Jack can rent a maximum of 6 DVD's
Step-by-step explanation: