The fully factored form is (m-9)(m-12)(m+2) / [2(m+8)(m-8)].
To subtract the rational expressions and find the answer in its fully factored form, we first need to find a common denominator for the two expressions.
The denominators of the two expressions are (m^(2)-64) and (2m^(2)-128). We can factor both of these to find the common denominator.
(m^(2)-64) = (m+8)(m-8)
(2m^(2)-128) = 2(m^(2)-64) = 2(m+8)(m-8)
The common denominator is 2(m+8)(m-8).
Now we can rewrite the two expressions with the common denominator and subtract them:
[(m^(2)+4m-12)(2) - (m^(2)+11m+24)(m+8)(m-8)] / [2(m+8)(m-8)]
= [(2m^(2)+8m-24) - (m^(3)+11m^(2)+24m+8m^(2)+88m+192)] / [2(m+8)(m-8)]
= [m^(3)-17m^(2)-104m-216] / [2(m+8)(m-8)]
= (m-9)(m^(2)-8m-24) / [2(m+8)(m-8)]
= (m-9)(m-12)(m+2) / [2(m+8)(m-8)]
So the answer in its fully factored form is (m-9)(m-12)(m+2) / [2(m+8)(m-8)].
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If you borrow $400 for 5 years at an annual interest rate of 3%, what is the total amount of money you will pay back?
Answer: $460
Step-by-step explanation:
To calculate the total amount of money you will pay back after borrowing $400 for 5 years at an annual interest rate of 3%, you can use the following formula:
Total amount = principal + interest
Principal = the amount you borrowed = $400
Interest = the amount of interest paid over the 5 years period.
To calculate the interest, we can use the formula:
Interest = Principal x Rate x Time
Rate = the annual interest rate expressed as a decimal = 0.03
Time = the time period in years = 5
So, the interest for the 5-year period is:
Interest = $400 x 0.03 x 5 = $60
Therefore, the total amount of money you will pay back is:
Total amount = $400 + $60 = $460
You will pay back $460 over five years if you borrow $400 at an annual interest rate of 3%.
Answer: To calculate the total amount of money to be paid back for borrowing $400 for 5 years at an annual interest rate of 3%, we need to use the formula for simple interest:
Simple interest = Principal x Rate x Time
where:
Principal = $400 (the amount borrowed)
Rate = 3% per year
Time = 5 years
Plugging these values into the formula, we get:
Simple interest = $400 x 0.03 x 5
= $60
Therefore, the total amount of money to be paid back is the sum of the principal and the simple interest:
Total amount = Principal + Simple interest
= $400 + $60
= $460
So, you will need to pay back a total of $460 after 5 years of borrowing $400 at an annual interest rate of 3%.
Step-by-step explanation:
the yearly interest on a sum of money for two consecutive years is is 400 and 440 respectively. calculate rate and principal
The principal is 50 and the rate of interest is 0.4.
The principal (P) and the rate of interest (R) can be calculated using the following equations:
P = (400*2)/(440 - 400)
R = (440 - 400)/(P*2)
Substituting the given values in the equations we get:
P = 2000/40 = 50
R = 40/100 = 0.4
To calculate the rate and principal of the sum of money, we can use the formula for simple interest: I = Prt, where I is the interest, P is the principal, r is the rate, and t is the time in years.
Given that the yearly interest for the first year is 400 and for the second year is 440, we can set up two equations:
400 = Prt
440 = Pr( t + 1)
Since the interest is for two consecutive years, the time in the first equation is t and the time in the second equation is t + 1.
We can rearrange the first equation to solve for P:
P = 400 / rt
Substituting this value of P into the second equation gives us:
440 = (400 / rt)( t + 1)
Simplifying and rearranging gives us:
440rt = 400t + 400
40rt = 400
rt = 10
Since we are looking for the rate and principal, we can substitute the value of rt back into the first equation:
400 = P(10)
P = 40
So the principal is 40 and the rate is 10 / t. To find the rate, we can substitute the value of P back into the first equation and solve for t:
400 = 40(10 / t)
t = 10
So the rate is 10 / 10 = 1.
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Use the function value to find the indicated trigonometric value in the specified quadrant. \[ \mathrm{Fu} \] cc
The function value and the indicated trigonometric value are not specified in the question. Additionally, the specified quadrant is not mentioned. Therefore, it is not possible to provide an accurate answer to this question.
However, generally speaking, to find the indicated trigonometric value in a specified quadrant using a function value, you can use the following steps:
1. Identify the function and the quadrant in which the value is to be found.
2. Use the function value to find the reference angle in the first quadrant.
3. Use the reference angle and the specified quadrant to find the indicated trigonometric value.
For example, if the function value is sin(θ) = 1/2 and the specified quadrant is II, you can use the following steps to find the indicated trigonometric value:
1. Identify the function and the quadrant: sin(θ) and II.
2. Find the reference angle in the first quadrant: θ = 30°.
3. Use the reference angle and the specified quadrant to find the indicated trigonometric value: sin(150°) = 1/2.
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Algebra please help!
Answer:
burrito $3.00 , taco $1.50
Step-by-step explanation:
using the variables b and t for burrito and taco , then
2t + 2b = 9 → (1)
t + 3b = 10.5 → (2)
multiplying (2) by - 2 and adding to (1) will eliminate t
- 2t - 6b = - 21 → (3)
add (1) and (3) term by term to eliminate t
(2t - 2t) + (2b - 6b) = 9 - 21
0 - 4b = - 12
- 4b = - 12 ( divide both sides by - 4 )
b = 3
substitute b = 3 into either of the 2 equations and solve for t
substituting into (1)
2t + 2(3) = 9
2t + 6 = 9 ( subtract 6 from both sides )
2t = 3 ( divide both sides by 2 )
t = 1.5
1 burrito costs $3.00 and 1 taco costs $1.50
In a survey, 195 consumers were asked about their buying preferences concerning a product that is sold in the market under three labels. The results were as follows.
15 buy only those sold under label A.
20 buy only those sold under label B.
28 buy only those sold under label C.
12 buy only those sold under labels A and B.
9 buy only those sold under labels A and C.
12 buy only those sold under labels B and C.
8 buy the product sold under all three labels.
How many of the consumers surveyed buy the product sold under
(a) At least one of the three labels?
consumers
(b) Labels A and B but not C?
consumers
(c) Label A?
consumers
(d) None of these labels?
consumers
104 consumers bought at least one of the three labels, 12 consumers bought labels A and B but not C 44 consumers bought label A and 91 consumers bought none of these labels because of the equations.
To find the number of consumers who buy the product sold under at least one of the three labels, we need to add up the number of consumers who buy the product under each label individually and those who buy the product under multiple labels.
However, we need to be careful not to double count those who buy the product under all three labels. Therefore, the formula for this calculation is:
At least one of the three labels = (A only) + (B only) + (C only) + (A and B only) + (A and C only) + (B and C only) + (A, B, and C)
Plugging in the given values, we get:
At least one of the three labels = 15 + 20 + 28 + 12 + 9 + 12 + 8 = 104 consumers
To find the number of consumers who buy the product sold under labels A and B but not C, we simply use the value given for those who buy only those sold under labels A and B:
Labels A and B but not C = 12 consumers
To find the number of consumers who buy the product sold under label A, we need to add up the number of consumers who buy the product under label A individually and those who buy the product under label A and one or both of the other labels. Therefore, the formula for this calculation is:
Label A = (A only) + (A and B only) + (A and C only) + (A, B, and C)
Plugging in the given values, we get:
Label A = 15 + 12 + 9 + 8 = 44 consumers
Finally, to find the number of consumers who buy the product sold under none of these labels, we subtract the number of consumers who buy the product under at least one of the three labels from the total number of consumers surveyed:
None of these labels = Total consumers - At least one of the three labels = 195 - 104 = 91 consumers
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Arnold bought 19 gallons of milk in gallon and half-gallon jugs. if he bought a total of 24 jugs, how many of each size did he buy?
Answer:
-14 gallon jugs
- 10 half-gallon jugs
Step-by-step explanation:
I'm not an expert at solving these algebraically, so I'm going to do this the old-fashioned way: Guess and Check.
Lets sum up our information:
- He bought 19 gallons
- He bought those 19 gallons with 24 jugs
- There are half-gallon and full gallon jugs
We know that if he bought 24 full gallon jugs, he would have 24 gallons of milk, but he only has 19, so this is not the answer
We know that if he bought 23 full gallons jugs and one half-gallon jug, he would have 23.5 gallons of milk, but he only has 19 gallons of milk, so this is also not the answer.
We keep reducing the number of full gallon jugs and increasing the number of half-gallon jugs until we reach 19 gallons total.
After trying different combinations, we can figure out that he bought
-14 gallon jugs
- 10 half-gallon jugs
Factor 10y-15 Write your answer as a product with a whole number greater than 1.
The answer is 5(2y-3).
Factorization is an easy process wherein you just need to find out the common factors and solve your question as per requirement.
To factor 10y-15, we need to find the greatest common factor (GCF) of the two terms. The greatest common factor (GFC) of 10 and 15 is 5. We can then factor out the GCF from each term to get:
10y-15 = 5(2y-3)
where 5 is a whole number greater than 1.
So the answer as a product with a whole number greater than 1 is 5(2y-3).
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Industry standards suggest that 10 percent of new vehicles require warranty service within the first year. Jones Nissan in Sumter, South Carolina, sold 12 Nissans yesterday. a. What is the probability that none of these vehicles requires warranty service? b. What is the probability exactly one of these vehicles requires warranty service? c. Determine the probability that exactly two of these vehicles require warranty service. d.Compute the mean and standard deviation of this probability distribution.
The answer are mean and standard deviation of this probability distribution are 1.2 and 1.04403065089, respectively
Given that the probability of a new vehicle requiring warranty service within the first year is 10%, we can use the binomial probability formula to answer the questions.
The binomial probability formula is:
P(x) = nCx * p^x * (1-p)^(n-x)
Where:
n = number of trials
x = number of successes
p = probability of success
nCx = number of combinations of n things taken x at a time
a. The probability that none of these vehicles requires warranty service is:
P(0) = 12C0 * 0.1^0 * 0.9^12 = 0.282429536481
b. The probability that exactly one of these vehicles requires warranty service is:
P(1) = 12C1 * 0.1^1 * 0.9^11 = 0.35527136788
c. The probability that exactly two of these vehicles require warranty service is:
P(2) = 12C2 * 0.1^2 * 0.9^10 = 0.23622320128
d. The mean of this probability distribution is:
μ = n * p = 12 * 0.1 = 1.2
The standard deviation of this probability distribution is:
σ = √(n * p * (1-p)) = √(12 * 0.1 * 0.9) = 1.04403065089
Therefore, the mean and standard deviation of this probability distribution are 1.2 and 1.04403065089, respectively.
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Consider the following curve. y= (2 + x^(3))^(1/2). Find y'(x)
y'(x) = 3x^2 / 2(2+x^(3))^(1/2).
Find an equation of the tangent line to the curve at the point
The equation of the tangent line to the curve at the point (1, 3) is y = (3/2)x + 1/2.
To find the equation of the tangent line to the curve at a given point, we first need to find the slope of the tangent line at that point. We can do this by finding the derivative of the curve, which is given by y'(x) = 3x² / 2(2+x³)^(1/2).
Next, we need to find the coordinates of the point at which we want to find the equation of the tangent line. Let's say we want to find the equation of the tangent line at the point (1, 3).
Now, we can use the point-slope form of a line to find the equation of the tangent line. The point-slope form of a line is given by y - y1 = m(x - x1), where m is the slope of the line, and (x1, y1) is a point on the line.
Plugging in the values for the slope and the point, we get:
y - 3 = (3(1)²/ 2(2+(1)³)^(1/2))(x - 1)
Simplifying the equation, we get:
y - 3 = (3/2)(x - 1)
y = (3/2)x + 1/2
So, the equation of the tangent line to the curve at the point (1, 3) is y = (3/2)x + 1/2.
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(In the pic) why do we have to change signs?? I don’t get it pls help
Answer:
x = -2
x = 3
Step-by-step explanation:
Select the correct answer
Answer:
Step-by-step explanation:
A.
Answer:
The answer is C
simplify 2 over 3 (3x - 1) + 4x +3 exponetent 2 - 10x + 5
The simplified expression is -4x + 44/3.
What is an exponetent?An exponent is a numerical value that indicates how many times a number, variable, or expression is to be multiplied by itself. It is usually written as a superscript to the right of the base, such as in the expression 3², where 3 is the base and 2 is the exponent.
The exponent indicates that 3 is to be multiplied by itself 2 times, resulting in a value of 9. Exponents are used in many areas of mathematics, including algebra, calculus, and geometry, and are an important concept for understanding mathematical operations and functions.
To simplify the expression, we need to follow the order of operations and combine like terms where possible:
2/3(3x - 1) + 4x + 3² - 10x + 5
First, simplify the expression inside the parentheses:
2/3(3x - 1) = 2x - 2/3
Next, simplify the squared term:
3² = 9
Now, combine the like terms:
2x - 2/3 + 4x - 10x + 9 + 5 = -4x + 14 + 2/3
Finally, we can rewrite the expression with the fractional coefficient as a mixed number:
-4x + 14 + 2/3 = -4x + 44/3
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I NEED HELP ASAP!!!
1 + 1 = ?
Write the column space C(A) in the vector space A,given that A=[[1,2,0,1],[0,1,2,1],[1,2,1,3],[0,1,2,2]]
Therefore, the column space C(A) in the vector space A is the set of all linear combinations of the columns of A
The column space C(A) in the vector space A can be written as the span of the columns of A. In this case, the columns of A are:
This means that any vector in the column space C(A) can be written as a linear combination of the columns of A. For example, the vector [3,2,4,3] can be written as:
Therefore, the column space C(A) in the vector space A is the set of all linear combinations of the columns of A.
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Can someone please help me? Due today!!
Show work please.
The surface area of a cylinder is approximately 240.33 square inches.
What is the surface area of a cylinder?The formula for the surface area of a cylinder is A = 2πr² + 2πrh, where r is the radius and h is the height of the cylinder.
Given the 24-inch cylindrical tube and its base has a 3-inch diameter.
Here,
Radius r = 3/2 = 1.5 inches
Height h = 24 inches
To determine the surface area of the container, substitute the given values for r = 1.5 and h = 24:
A = 2π(1.5)² + 2π(1.5)(24)
A = 2π(2.25) + 72π
A = 4.5π + 72π
A = 76.5π
We can approximate π as 3.14, then
A ≈ 76.5× 3.14
Apply the multiplication operation, and we get
A = 240.33 square inches
Thus, the surface area of a cylinder is approximately 240.33 square inches.
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A panel in a stained-glass window in the shape of a parallelogram has the dimensions shown. Find the area of the panel.
Based on the given dimensions of the panel, the area of the panel is 39.6 square cm.
What is the area of the panel?The panel is in the shape of a parallelogram.
A parallelogram is a convex quadrilateral in which each pair of opposite edges are parallel and of equal length.
Area of the parallelogram panel is the measure of the extent of a surface usually measured in square units.
Area of the parallelogram panel = base × height
Base = 5.5 cm
Height = 7.2 cm
Area of the parallelogram panel = base × height
= 5.5 cm × 7.2 cm
= 39.6 square cm
Therefore, the area of the parallelogram panel is 39.6 square cm
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Amber receives a $20,000 salary for working as an assistant. If Amber spends 70% of her salary on expenses each year, how much money does Amber spend on expenses? (part = percent x whole)
Answer:
total salary=$20000
spend%=70%
now,
spend no=70% of $20000
=70/100 ×20000
=$14000
now,
total of spend amount of each month=
spend amount×12
=140000×12
=$168000
DUE FRIDAY HELPPPPPP!!!!!!!!!!!!!!!!!!!!!!!!!!!!
1. How many times a day do the minute hand and the hour hand on a clock point in the same direction?
2. At what times do they point in the same direction?
The length of a rectangle is twice its width. Find its area if its perimeter is 7 1/3 cm.
please help ive been stuck on this for a day tyy !!
Answer:
Let's start by using the information given in the problem to write an equation for the perimeter of the rectangle:
Perimeter = 2(length + width)
We know that the length of the rectangle is twice its width, so we can write:
length = 2*width
Substituting this expression into the equation for the perimeter, we get:
Perimeter = 2(2*width + width)
Simplifying this expression, we get:
Perimeter = 6*width
We are given that the perimeter is 7 1/3 cm, which we can convert to a mixed number:
Perimeter = 7 + 1/3 = 22/3
Substituting this value into the equation above, we get:
22/3 = 6*width
Solving for the width, we get:
width = 22/3 ÷ 6 = 11/9
Now that we have the width, we can use the expression for the length to find its value:
length = 2*width = 2(11/9) = 22/9
Finally, we can use the formula for the area of a rectangle, A = length * width, to find the area:
A = (22/9) * (11/9) = 242/81 square cm
Therefore, the area of the rectangle is 242/81 square cm.
Help me. giving brainliest
Answer:
277 milliliters
Step-by-step explanation:
945 - 668 = 277
hope this helpz ya
Answer:
277 milliliters
Step-by-step explanation:
Initial volume of ice tea = 945 milliliters
Final volume of ice tea = 668 milliliters
∴Difference in the volume of ice tea = How much tea Jeffrey drank
= Final volume - Initial volume
= [tex](945 - 668)[/tex] milliliters
= [tex]277[/tex] milliliters
2. For each of the following matrices \( A \in M_{n \times n}(R) \), test \( A \) for diagonalizability, and if \( A \) is diagonalizable, find an invertible matrix \( Q \) and a diagonal matrix \( D
Matrix A is diagonalizable
Yes, it is possible to test a matrix \( A \in M_{n \times n}(R) \) for diagonalizability. If \( A \) is diagonalizable, then there exists an invertible matrix \( Q \) and a diagonal matrix \( D \) such that \( A = Q D Q^{-1}\). To find these matrices, we can use the following steps:
1. Find the characteristic polynomial \( p(\lambda) \) of \( A \).
2. Find the eigenvalues of \( A \) by solving \( p(\lambda) = 0 \).
3. Find the corresponding eigenvectors for each eigenvalue of \( A \).
4. Construct the matrix \( Q \) as a matrix whose columns are composed of the eigenvectors of \( A \).
5. Construct the diagonal matrix \( D \) by placing the eigenvalues of \( A \) along the diagonal entries.
6. Check that \( A = Q D Q^{-1} \).
If these steps all check out, then \( A \) is diagonalizable.
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bro help me find the vol pls
Answer:
volume is L × W x
Step-by-step explanation:
15 x 12 x 6
see attached I wrote down for you.
Answer:
360 ft³
Step-by-step explanation:
Volume of a rectangular pyramid = (lwh)/3 = (12x6x15) / 3 = 1080/3 = 360 ft³
V = (length x width x height) ÷ 3
Sheldon has scored 6/18 of the points in a basketball game. How can you use division to simplify the fraction of the points he scored? What is 6/18 in simplest form?
Answer:
1/3
Step-by-step explanation:
6/18, divide each side by 3 and you get 1/3
find x. 42° 36° 113° x°
Answer:
x=35°
Step-by-step explanation:
please mark as brainliest
Check the picture below.
the formula used to calculate the cost to rent the ford figo is cost (in rand)=R900+R7 x n, (where n is the number of kilometers travelled) write the formulas to calculate the cost of renting the other 2 cars TOYOTA ETIOS-ONLY R15 PER KILOMETER VW POLO VIVO-THE CHEAPEST RATE PER KILOMETER ONLY R1150 BASIC FEE PLUS R3 PER KILOMETER
The formula to calculate the cost to rent Toyota Etios is R15 + R3 n.
The formula to calculate the cost to rent VW Polo Vivo is R11.50 + R3 n.
What is slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
We have the formula used to calculate the cost to rent the Ford Figo is cost (in rand)= R900 + R7 x n.
Now, Toyota Etios cost R15 per Km and per km charge will be R3.
So, the formula to calculate the cost to rent is
= R15 + R3 n
and, VW Polo Vivo cost R11.50 per Km and per km charge will be R3.
So, the formula to calculate the cost to rent is
= R11.50 + R3 n
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Matt is a lawyer who used to charge his clients $330 per hour. Matt recently reconsidered his rates and ultimately decided to charge $231 per hour. What was the percent of decrease in the billing rate?
Answer:
33%
Step-by-step explanation:
Take the original amount and subtract to new amount.
330 -231
99
Divide this by the original amount.
99/300
.33
Change to a percent.
33%
This is the percent decrease.
Big ideas 7.5 (question)
Answer:
Step-by-step explanation:
So when x is translated the + means going right. With y the - means going down. So P is gonna be (-9,-1), Q(-4,0) , and R (-2,-1). See if that helps but I think it is that, but I have another idea what it could be but see if this is right.
Pls help me in this question
The missing numbers in the expressions are:
a. x²
b. 4x²
c. 24x
d. 36x
e. 9x²
f. 1
What are algebraic expressions?Every combination of terms that have undergone operations like addition, subtraction, multiplication, division, etc. is known as an algebraic expression (or variable expression).
Let's use the equation 5x + 7 as an example.
Now here,
We can see that by simplifying the expressions we can see that all of them are in the form of (a+b)².
So, using the same to simplify the equations we get the missing numbers.
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solve for x first answer gets brainliest
Answer:
The answer to your problem is, 9
Step-by-step explanation:
I can conclude that the answer is nine by the following step shown down below.
The bottom triangle the one that it on the " floor ".
It is an equilateral triangle which means that that all sides are the same length ( same with the one on top ).
So if one side is 9, the other side is also 9.
Thus the answer to your problem is, 9
Answer:
[tex]x = 6 \sqrt{3} [/tex]
A business sells items according to the following Cost and
Revenue functions: C(x)=5x+2400 R(x)=−1x^2+370x
(a) Find the profit function:
P(x)= (
b) Find the average profit function:
Pˉ(x)=
(a) The profit function is found by subtracting the cost function from the revenue function. In this case, the profit function P(x) can be found by subtracting C(x) from R(x):
P(x) = R(x) - C(x) = (−1x^2+370x) - (5x+2400)
Simplifying the expression gives:
P(x) = -1x^2 + 370x - 5x - 2400
P(x) = -1x^2 + 365x - 2400
Therefore, the profit function is P(x) = -1x^2 + 365x - 2400.
(b) The average profit function is found by dividing the profit function by the number of items sold, x. In this case, the average profit function Pˉ(x) can be found by dividing P(x) by x:
Pˉ(x) = P(x) / x = (-1x^2 + 365x - 2400) / x
Simplifying the expression gives:
Pˉ(x) = -1x + 365 - 2400/x
Therefore, the average profit function is Pˉ(x) = -1x + 365 - 2400/x.
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