\(a=3x^3\hspace{5em}b=4x^4 \\\\[-0.35em] ~\dotfill\\\\ c=ab^2\implies c=(\underset{a}{3x^3})(\underset{b}{4x^4})^2\implies c=(3x^3)(4^2x^{4\cdot 2}) \\\\\\ c=3x^3\cdot 16x^8\implies c=(3\cdot 16)x^{3+8}\implies c=48x^{11} \\\\[-0.35em] ~\dotfill\\\\ \boxed{bc}\implies (\underset{b}{4x^4})(\underset{c}{48x^{11}})\implies (4\cdot 48)x^{4+11}\implies \boxed{192x^{15}}\)
Answer:
bc = 192x^15
Step-by-step explanation:
Perform substitution as required, then simplify.
Evaluationbc = b(ab^2) = ab^3 = (3x^3)(4x^4)^3 = (3·4^3)(x^3)(x^(4·3))
= 192x^(3+12)
bc = 192x^15
__
Additional comment
The relevant rules of exponents are ...
(ab)^c = (a^c)(b^c)
(a^b)^c = a^(bc)
(a^b)(a^c) = a^(b+c)
which approximation is closest to the total of students that chose pepperoni
The total number of students is 853.
The number of students who chose pepperoni pizza is 254 + 143 = 397
Divide this by the total of students multiplied by 100 to get the percentage :
\(\frac{397}{853}\times100=46.5\%\)ANSWER :
The closest answer is 47%
Covert 1/4 to seconds
Answer:
a quarter of an hour, or 15 minutes is equal to 15 minutes × 60 = 90 seconds a quarter of an hour, or 15 minutes is equal to 15 minutes × 60 = 90 seconds
Answer:
90 seconds
Step-by-step explanation: We know that,
A quarter of an hour= 60×1/4 =15 mins
15 minutes is equal to 15 minutes × 60 = 90 seconds.
if one jar of jalapeños cost $2, how much will 7 jars cost? can somone help me do this step by step?!:)))
Answer:
14
Step-by-step explanation:
What is the area of the parallelogram?
7
6
square units
WILL MARK BRAINLIEST IF CORRECT (THIS IS KHAN ACADEMY)
Answer:
35 units²
Step-by-step explanation:
area = 7 x 5 = 35 units²
The graph shows how the number of hats in your collection increased since you began collecting 6 months ago. How many hats did you collect during the second month? Hat Collection A graph has time (months) on the x-axis, and total number of hats on the y-axis. Lines connect points (0, 0), (1, 3), (2, 5), (3, 8), (4, 9), (5, 10), (6, 12). hats
Answer:
Step-by-step explanation:
Two hats were collected in the second month (5-3) =2.
Sanda has a summer job that pays time and a half for overtime hours. If she works more than 40 hours per week, her hourly wage for the additional hours is paid at 1.5 times her normal hourly wage of $8. Write a piecewise-defined function that gives Sanda's weekly pay, P, in terms of h, the number of hours worked in a week.
A piecewise-defined function that gives Sanda works 45 hours in a week, her weekly pay would be $380.
To write a piecewise-defined function for Sanda's weekly pay, we need to consider two scenarios: regular hours (up to 40 hours) and overtime hours (more than 40 hours).
Let's define the function as follows:
P(h) = 8h if 0 <= h <= 40
P(h) = (8 * 40) + (1.5 * 8 * (h - 40)) if h > 4
For h (number of hours) between 0 and 40, the pay is simply the hourly wage of $8 multiplied by the number of hours worked. This covers regular hours.
For h greater than 40, we calculate the pay in two parts. The first part is the pay for the first 40 hours, which is calculated as the hourly wage ($8) multiplied by 40. The second part is the pay for the overtime hours, which is calculated by taking the hourly wage ($8), multiplying it by 1.5 to get the time and a half rate, and then multiplying it by the difference between h and 40 (the number of overtime hours).
Let's verify this function with an example:
If Sanda works 45 hours in a week, we can substitute h = 45 into the function:
P(45) = (8 * 40) + (1.5 * 8 * (45 - 40))
= 320 + (1.5 * 8 * 5)
= 320 + (12 * 5)
= 320 + 60
= 380
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16) One autumn morning the temperature went up from -4OC to 5OC a) By how many degrees did the temperature rise? During the afternoon, the temperature then fell by seven degrees from 5OC. b) What was the temperature at the end of the afternoon?
Answer:
Explain it a little more
Step-by-step explanation:
For every 10 apples gathered from trees in an orchard, there are 9 apples that are good to sell. Which equation determines the constant
relationship between g, the number of apples gathered, and s, the number of apples good to sell?
A: s=0.9g
B: s=1.1g
C: g= s - 1
D: g= s + 1
Please answer quick
Answer:
A
Step-by-step explanation:
Answer:
A, 0.9 is 9/10
Determine the number of lines of symmetry for the figure.
Answer:
To find a line of symmetry, look for two halves of the E that are mirror images of each other. The bottom half of E is the mirror image of the top half. So, the horizontal line that passes through the middle of E is a line of symmetry.
Here is another riddle: The sum of two numbers is less than 2. If we subtract the second number from the first, the difference is greater than 1. What are the two numbers? The riddle can be represented by a system of inequalities. Write an inequality for each statement.
Answer:
Let x, y be the two numbers under consideration. Then, x+y<2 and x-y>1.
The system of inequalities represents the given situation are x+y<2 and x-y>1.
Given that, the sum of two numbers is less than 2.
What is a inequality?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Let the first number be x and the second number be y.
x+y<2 -------(1)
If we subtract the second number from the first, the difference is greater than 1.
x-y>1 -------(2)
Therefore, the system of inequalities represents the given situation are x+y<2 and x-y>1.
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Please help me to solve this question.
Answer:
\(314 \frac{2}{7} cm^{2} \)
Step-by-step explanation:
Surface area of sphere= 4πr², where r is the radius of the sphere.
Given that the diameter is 10cm,
2(radius)= 10cm
radius= 10 ÷2
radius= 5cm
Surface area of sphere
\( = 4( \frac{22}{7} )( {5}^{2} ) \\ = 314 \frac{2}{7} cm^{2} \)
What is the equation of the following line written in general form?
Answer:
\( y = \frac{ - 4}{5} x + 7\)
what is p to the power of 2
Answer:
It really depends if there is more work with this, but of it is just p to the power of two. it would be p².
You borrowed ₱15,000.00 from your parents to buy a new video game, and they set an interest rate of 15% per month. How much interest do you owe in one month?
Answer:2250
Step-by-step explanation:
All we need to do is multiply 15,000 by 15% also known as 0.15 as a decimal.
15,000 X 0.15 = 2250
Answer: 2250
What is the constant of proportionality in the table below?
x 5 10 6 9 2
y 15 30 18 27 6
1/3
5
3
15
Answer:
1/3
Step-by-step explanation:
constant proportionality = x/y
x1/y1 , x2/y2 , x3/y3 , ....
5/15 , 10/30 , 6/18 , 9/27 , 2/6
= 1/3 , 1/3 , 1/3 , 1/3 , 1/3
since in all the cases x/y = 1/3 ,
Therefore, the contant proportionality in the given table is 1/3
Hope it's helpful..
40
Why are the solutions to the proportions 8
=
х
and
40
10
8 the same?
10
O because both result in the equation 8X= 400, which simplifies to X = 5
O because both result in the equation 8x=400, which simplifies to x = 50
O because both result in the equation 40x=80, which simplifies to X = 2
O because both result in the equation 40x = 80, which simplifies to X = 20
Answer:
B.
Step-by-step explanation:
They both have the same solution because both end up having
=> 8x = 500
Which is further simplified into
=> x = 50
What is the coefficient of the second term in this expression?
7 + 2n
Answer:
a2 = 11
Step-by-step explanation:
A computer program used one-third of the computers total memory. The computer had a memory of 58 gigabytes. Write an algebraic equation to represent this scenario.
Prove whether the quadrilateral is a parallelogram using the Distance & Slope Formulas D(-5, -6), E(5, 2), F(4, -4), G(-6, -12)
To prove that quadrilateral is a parallelogram using the Distance & Slope Formulas D(-5, -6), E(5, 2), F(4, -4), G(-6, -12), follow these steps
:Step 1: Plot the points in a coordinate plane: (D) (-5,-6), (E) (5,2), (F) (4,-4), (G) (-6,-12)
Step 2: Find the distance of all sides using distance formula.
Distance Formula =sqrt((x2 - x1)² + (y2 - y1)²)DE
= sqrt((5 - (-5))² + (2 - (-6))²)
=sqrt(10²+8²)
=sqrt(164)
= 2 sqrt(41)EF
= sqrt((4 - 5)² + (-4 - 2)²)
=sqrt((-1)²+(-6)²)
=sqrt(37)FG
= sqrt((-6 - 4)² + (-12 - (-4))²)
=sqrt((-10)²+(-8)²)
= 2sqrt(41)DG
= sqrt((-6 - (-5))² + (-12 - (-6))²)
=sqrt((-1)²+(-6)²)
=sqrt(37)
Since the opposite sides are equal, we can say that DE = FG and DG = EF.
Step 3: Find the slope of all sides using slope formula.
Slope Formula = (y2-y1)/(x2-x1)DE
= (2-(-6))/(5-(-5))
=8/10=4/5FG
= (-12-(-4))/(-6-4)=-8/-10=4/5DG = (-6-(-12))/(-5-(-6))=6/1=6EF = (-4-2)/(4-5)=-6/-1=6
Since opposite sides have the same slope, DE // FG and DG // EF. Therefore, we can conclude that the quadrilateral is a parallelogram.In conclusion, the quadrilateral is a parallelogram because opposite sides are parallel.
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simplify:
3/2 x 5/3 ÷ (-2+7)
Answer:
-1/2
Step-by-step explanation:
3/2 x 5/3 ÷ (-2+7)
=> 3/2 x 5/3 ÷ (-5)
=> 3/2 x 5/3 x (-1/5)
=> -1/2
Write the equation of the line through (2,4) with a slope of 2/3 in Point Slope Form
Answer:
y - 4 = 2/3(x - 2)
Step-by-step explanation:
The format for point-slope form is: y - y₁ = m(x - x₁)
where m is the slope, x₁ is the x-coordinate and y₁ is the y-coordinate.
In (2,4), 2 is the x-coordinate and 4 is the y-coordinate.
The slope is 2/3.
When you plug in the values, you get:
y - 4 = 2/3(x - 2)
Hope this helps!
translate into an algebraic expression: x is increased by 50% and decreased by 30% . What is the result?
Answer:
x+4/5x
Step-by-step explanation:
x is increased by 80% 0f it self
80%of x= 4/5x
... x+4/5x
Write y-4=-2(x-(-4)) in standard form.
Correct me if I am wrong I got -2x-y=4
The expression of y - 4 = -2 ( x- (-4) ) in standard form is 2x + y = -4.
Standard form for the equation of a line is Ax + By =C where A is a positive integer and B and C are integers
A standard form is a method of writing mathematical concepts like an equation, expressions, or numbers in standard form. Example: 2.5 billion years is written as 2,500,000,000 years.
Given expression is,
y - 4 = -2(x-(-4))
y - 4 = -2 (x+4)
y - 4 = -2x - 8
Add 2x to each side
2x + y - 4 = 2x - 2x - 8
2x + y - 4 = - 8
Add 4 from each side
2x + y - 4 + 4 = - 8 + 4
2x + y = -4
Therefore,
The expression of y - 4 = -2 ( x- (-4) ) in standard form is 2x + y = -4.
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The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 75, 15, 3 find the 6th term
Answer
0.024
Step-by-step explanation:
1-75
2-15
3-3
4-0.6
5-0.12
6-0.024
Point V lies between points U and W on Line segment U W.
A line has points U, V, W. The length between U V is 2 x minus 4. The length between V W is 4 x + 10.
If UW = 9x – 9, what is UW in units?
5 units
6 units
30 units
36 units
Answer:
The correct answer is (d) 36 units.
Step-by-step explanation:
Just took the test on edge :)
The measure of UW is 36 units
The measure of angles between segmentsFrom the question, a line has points U, V, W. If Point V lies between points U and W on Line segment U W, then;
UV + VW = UW
Given the following
VW = 4 x + 10.
UW = 9x – 9
UV = 2x - 4
Substitute
2x - 4 + 4x + 10 = 9x - 9
6x + 6 = 9x - 9
-3x = -15
x = 5
UW = 9x - 9
UW = 45 - 9
UW = 36 units
Hence the measure of UW is 36 units
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Consider the given pseudo code. Write the function T(n) in terms of the number of operations, and then give the asymptotic (big Oh) complexity of the algorithm, show all the work you do. [ write the summation formula and solve it, or use the "Look for pattern"method. a. Matrix Multiplication
The function T(n) in terms of the number of operations is:
T(n) = 2n^3 + 3n^2 + 2n + 1 and the asymptotic complexity of the matrix multiplication algorithm is O(n^3).
To analyze the provided pseudo code for matrix multiplication and determine the function T(n) in terms of the number of operations, we need to examine the code and count the number of operations performed.
The pseudo code for matrix multiplication may look something like this:
```
MatrixMultiplication(A, B):
n = size of matrix A
C = empty matrix of size n x n
for i = 1 to n do:
for j = 1 to n do:
sum = 0
for k = 1 to n do:
sum = sum + A[i][k] * B[k][j]
C[i][j] = sum
return C
```
Let's break down the number of operations step by step:
1. Assigning the size of matrix A to variable n: 1 operation
2. Initializing an empty matrix C of size n x n: n^2 operations (for creating n x n elements)
3. Outer loop: for i = 1 to n
- Incrementing i: n operations
- Inner loop: for j = 1 to n
- Incrementing j: n^2 operations (since it is nested inside the outer loop)
- Initializing sum to 0: n^2 operations
- Innermost loop: for k = 1 to n
- Incrementing k: n^3 operations (since it is nested inside both the outer and inner loops)
- Performing the multiplication and addition: n^3 operations
- Assigning the result to C[i][j]: n^2 operations
- Assigning the value of sum to C[i][j]: n^2 operations
Total operations:
1 + n^2 + n + n^2 + n^3 + n^3 + n^2 + n^2 = 2n^3 + 3n^2 + 2n + 1
Therefore, the function T(n) in terms of the number of operations is:
T(n) = 2n^3 + 3n^2 + 2n + 1
To determine the asymptotic (big O) complexity of the algorithm, we focus on the dominant term as n approaches infinity.
In this case, the dominant term is 2n^3. Hence, the asymptotic complexity of the matrix multiplication algorithm is O(n^3).
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Determine the domain of the graph shown.
A) [0, 8]
B) [0, 24]
C) [0, 20]
D) [0, 10]
Solve the equation for X. Give an exact solution if possible otherwise give an approximation to 3-decimal places. log,(8x + 2) = 3
The equation log(8x+2) = 3 can be rewritten in exponential form as 10^3 = 8x+2. Simplifying, we get:
1000 = 8x + 2
998 = 8x
x = 124.75
Therefore, the solution to the equation is x = 124.75, which is an approximation to 3-decimal places.
To verify the solution, we can substitute x = 124.75 back into the original equation and check if both sides are equal:
log(8(124.75) + 2) = log(1000)
log(1000) = 3
Since both sides are equal, we can conclude that x = 124.75 is indeed the solution to the equation.
Note that it is important to check the solution obtained from solving the equation as sometimes the solution may not be valid due to the domain of the function involved in the equation.
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In the figure, the slope of mid-segment DE is -0.4. The slope of segment AC is?
A.) 0.4
B.) -0.4
C.) 2
D.) -2
Answer:
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In the figure, the slope of mid-segment DE is -0.4. The slope of segment AC is?
A.) 0.4
B.) -0.4
C.) 2
D.) -2
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Step-by-step explanation:
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# i hope it helps you
# mark me brainliest thank you
To prepare for wrestling season, Tommy wants to eat 24 grams of protein at breakfast. He knows that there are 3 grams of protein in a slice of bacon and 6 grams of protein in an egg. Let x represent the number of slices of bacon he will eat and let y represent the number of eggs he will eat.
b. **Rewrite your equation in slope-intercept form.
a. Write an equation that relates the number of slices of bacon to the number of eggs he will eat, assuming he eats exactly 24 grams of protein.
Answer:
look below for answers for a and b
Step-by-step explanation:
a. 3x=24, x=8
a. 6y=24, y=4
b. 6y=3x+0
y=mx+b is slope intercept form
Answer:b a c
Step-by-step explanation: