Add or subtract. Simplify where possible. 5/a²b - 7a/5b²
Answers
The simplified expression is (5b - 7a²) / (a²b²).
To add or subtract the expressions 5/a²b and -7a/5b², we need to find a common denominator.
The common denominator for a²b and 5b² is a²b².
Let's rewrite the expressions with the common denominator:
5/a²b = (5 * b) / (a² * b²) = 5b / a²b²
-7a/5b² = (-7a * a) / (5 * a² * b²) = -7a² / 5a²b²
Now, we can combine the expressions:
5b / a²b² - 7a² / 5a²b²
To subtract these expressions, we need to have the same denominator, which we already have. Thus, we can combine the numerators:
(5b - 7a²) / (a²b²)
The simplified expression is (5b - 7a²) / (a²b²).
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Related Questions
If the points a,b and c have the coordinates a(5,2) , b(2,-3) and c(-8,3) show that the triangle abc is a right angled triangle
Answers
Points a,b and c satisfied the Pythagoras theorem. Thus, the triangle abc is a right angled triangle.
Define about the right angled triangle:Every triangle has inner angles that add up to 180 degrees. A right angle and a right triangle are both formed when one of their internal angles is 90 degrees.
The internal 90° angle of right triangles is denoted by a little square in the vertex. The complimentary angles of the other two sides of a right triangle sum up to 90 degrees.The triangle's legs, which are typically denoted by the letters a and b, are the sides that face the complimentary angles.Given coordinates :
a(5,2) , b(2,-3) and c(-8,3).
Find the distance between the points using the distance formula:
d = √[(x2 - x1)² + (y2 - y1)²]
ab = √[(2 - 5)² + (- 3 - 2)²]
ab = √[(-3)² + (- 5)²]
ab = √[9 + 25]
ab = √34
ab² = 34
bc = √[(2 + 8)² + (- 3 - 3)²]
bc = √[(10)² + (- 6)²]
bc = √[100 + 36]
bc = √136
bc² = 136
ac = √[(-8 - 5)² + (3 - 2)²]
ac = √[(-13)² + (1)²]
ac = √[169 + 1]
ac = √170
ac² = 170
Now,
(ac)² = (bc)² + (ab)²
170 = 136 + 24
170 = 170
This, points a,b and c satisfied the Pythagoras theorem. Thus, the triangle abc is a right angled triangle.
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through: (1,-1), Parallel to y = 1/4× - 4
Answers
Answer:
I believe it is y=1/4x.
Question 7 (5 points)
What are the coordinates of the vertices of the image after a 90-degree counter-
clockwise rotation about the origin?
Answers
Answer:
Explanation ↓
Step-by-step explanation:
The origin is the rotation’s set point unless expressed otherwise. In a coordinate plane, when the point (x, y) is revolved in a 90-degree clockwise directive, the projected vision will have a coordinate of (y, -x).
If-4y² − x³ + 4 = 0 then find dy/dx in terms of x and y.
Answers
I’m not sure how to explain this but keep practicing you’ll get it!
Approximately 9% of men have a type of color blindness that prevents them from distinguishing between red and green. suppose that 8 men are selected at random. what is the probability that at least one of them will have this type of red-green color blindness
Answers
Steve went to the concession stand and bought hamburgers and hot dogs for the kids he brought to watch a baseball game. Each child chose either one hamburger or one hotdog. Hot dogs cost $1. 50 each and hamburgers cost $2. 75 each. Steve spent a total of $23. 75 on 10 kids.
(a) Could Steve have bought an equal amount of hamburgers and hot dogs? Justify your answer.
(b) If x represents the number of hotdogs purchased and y represents the number of hamburgers purchased,
write a system of equations that models this situation and determine the number of both items bought
Answers
If Steve spent $23.75 on 10 kids if they each bought either a hotdog or hamburger that cost $1.50 each and $2.75 each respectively, then the number of hotdog he bought is 3 and the number of hamburger he bought is 7.
Let the number of kids who choose hotdog be x and hamburger be y. As there are 10 kids in total
x + y = 10
Cost of one hot dog is $1.50 and the cost of one hamburger is $2.75. Therefore
1.50x + 2.75y = 23.75
Let us assume Steve bought an equal amount of hamburgers and hot dogs, that is x = y. Then
1.50x + 2.75x = 23.75
4.25x = 23.75
x = 95/17
That is x is not a natural number which is not possible as it is the number of kids. So our assumption is wrong. So Steve would not have bought an equal amount of hamburgers and hot dogs.
Solving x + y = 10 and 1.50x + 2.75x = 23.75
y = 7 and x = 3
So the number of hotdog he bought is 3 and the number of hamburger he bought is 7.
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Solve the right triangle given that mZA = 30°, mZC = 90°, and a = 15. Round
your result to one decimal place,
Answers
Answer:23
Step-by-step explanation:
im stuck lol i just need a answer
Answers
Answer:
131 here is the answer and your welcome
find and sketch the domain of the function. f(x, y) = ln(9 − x2 − 9y2)
Answers
To find the domain of the function f(x,y) = ln(9 - x^2 - 9y^2), we need to identify any values of x and y that would make the argument of the natural logarithm negative or equal to zero.
Since the natural logarithm of a non-positive number is undefined, we need to ensure that 9 - x^2 - 9y^2 > 0.
Rearranging this inequality, we get x^2 + 9y^2 < 9, which is the equation of an ellipse centered at the origin with semi-axes of length 3 and 1 in the x and y directions, respectively.
Therefore, the domain of the function is the interior of this ellipse, which we can sketch as follows:
(please imagine an ellipse centered at the origin with semi-axes of length 3 and 1 in the x and y directions, respectively, shaded in)
To find and sketch the domain of the function f(x, y) = ln(9 - x² - 9y²), we need to determine the values of x and y for which the function is defined.
Step 1: Identify the restrictions of the function.
For the natural logarithm function, ln(x), it is defined for x > 0. Therefore, the inside of the logarithm, 9 - x² - 9y², must be greater than 0.
Step 2: Solve for the domain.
9 - x² - 9y² > 0
Rearrange the inequality:
x² + 9y² < 9
Divide by 9:
x²/9 + y² < 1
This inequality represents the interior of an ellipse with semi-major axis a = 3 and semi-minor axis b = 1.
Step 3: Sketch the domain.
To sketch the domain, draw an ellipse centered at the origin (0, 0) with horizontal axis length 6 (from -3 to 3) and vertical axis length 2 (from -1 to 1). The domain includes all points inside the ellipse but does not include the boundary (the ellipse itself).
So, the domain of the function f(x, y) = ln(9 - x² - 9y²) is the interior of the ellipse with equation x²/9 + y² < 1.
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Question 1 of 10
Suppose a triangle has sides 3, 4, and 6. Which of the following must be true?
A. The triangle in question is not a right triangle.
OB. The triangle in question is a right triangle
O C. The triangle in question may or may not be a right triangle.
Answers
c i think because they dont specify
Answer:
Step-by-step explanation:
C because the shape can be manipulated to different angles
Brainliest please
What is ""statistical conclusion validity""? what was the main threat to statistical conclusion validity discussed in class?
Answers
Statistical conclusion validity is the extent to which inferences and conclusions drawn from statistical data are valid.
The main threat to statistical conclusion validity discussed in class is the potential for spurious correlations. This is when two variables appear to be related when in fact they are not.
Statistical conclusion validity is a measure of how valid the conclusions drawn from statistical data are. This is important because it allows us to draw valid inferences from the data. The main threat to statistical conclusion validity discussed in class is the potential for spurious correlations. This is when two variables appear to be related when in fact they are not. For example, a study may show that there is a correlation between ice cream sales and crime rate, when in fact it is merely a coincidence that both variables increase during the summer months. By controlling for other variables and using appropriate statistical tests, it is possible to identify and avoid spurious correlations.
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The sides of a right triangle are 6, 8, and 10.
Find the altitude drawn to the hypotenuse.
(A) 2.4
(B) 4.8
(C) 3.4
(D) 3.5
(E) 4.2
Answers
First find area by taking base 8 = and height = 6 which is equal to 24
Then find area by taking base = 10 and height = altitude, place it equal to 24 by transposing value of altitude will come equal to 4.8
Ruby is visiting San Francisco. From her hotel she walks 4 blocks east and 3 blocks north to a coffee shop. Then she walks 7 blocks west and 6 blocks north to a museum. Where is the museum in relation to her hotel?
Answers
Answer:
Is that from RSM??
Step-by-step explanation:
Express the ratio below in its simplest form. 2:4
Answers
Answer:
1:2
Step-by-step explanation:
we divide both numbers by 2
I believe that the ratio written in its simplest form would be 1:2 in ratio form.
Hope this helps!
Q1. A heavy general purpose truck costs $12,000 has a life of six years with a $2,000 SV. using the
MACRS with a GDS recovery period of five years. What is the BV of the equipment at the end of
(including) year four?
IN EXCEL WITH EXPLANATION PLEASE
Answers
Answer:
Therefore, the book value of the equipment at the end of year four (including year four) is $2,880.
Step-by-step explanation:
To calculate the book value of the equipment at the end of year four using the MACRS method with GDS recovery period of five years, we can use the following steps in Excel:
1. Open a new Excel spreadsheet and create the following headers in row 1: Year, Cost, Depreciation Rate, Annual Depreciation, Cumulative Depreciation, and Book Value.
2. Fill in the Year column with the years 1 through 6 (since the truck has a life of six years).
3. Enter the cost of the truck, $12,000, in cell B2.
4. Use the following formula in cell C2 to calculate the depreciation rate for each year:
=MACRS.VDB(B2, 5, 5, 1, C1)
This formula uses the MACRS.VDB function to calculate the depreciation rate for each year based on the cost of the truck (B2), the GDS recovery period of five years, the useful life of six years, the salvage value of $2,000, and the year (C1).
5. Copy the formula in cell C2 and paste it into cells C3 through C7 to calculate the depreciation rate for each year.
6. Use the following formula in cell D2 to calculate the annual depreciation for each year:
=B2*C2
This formula multiplies the cost of the truck (B2) by the depreciation rate for each year (C2) to get the annual depreciation.
7. Copy the formula in cell D2 and paste it into cells D3 through D7 to calculate the annual depreciation for each year.
8. Use the following formula in cell E2 to calculate the cumulative depreciation for each year:
=SUM(D$2:D2)
This formula adds up the annual depreciation for each year from D2 to the current row to get the cumulative depreciation.
9. Copy the formula in cell E2 and paste it into cells E3 through E7 to calculate the cumulative depreciation for each year.
10. Use the following formula in cell F2 to calculate the book value of the equipment for each year:
=B2-E2
This formula subtracts the cumulative depreciation for each year (E2) from the cost of the truck (B2) to get the book value.
11. Copy the formula in cell F2 and paste it into cells F3 through F7 to calculate the book value for each year.
12. The book value of the equipment at the end of year four (including year four) is the value in cell F5, which should be $2,880.
Please help me solve this asap if possible
Answers
= (y - 5)(y + 5)cm^2
HEY GUYS PLEASE HELP JUST LABEL THEM 1 2 3 and tell me true or false
Answers
2) false
3) true
Please help and show work only do the left side
Answers
bottom was cut off a bit its 4=b
you have six slices of bread, three tomato slices, and two cheese slices. how many tomato-cheese sandwiches can you make? which ingredient(s) limit the number of sandwiches you can make?
Answers
You can make a maximum of two tomato-cheese sandwiches. because you can only make as many tomato-cheese sandwiches as the number of cheese slices you have
To make a tomato-cheese sandwich, you need one tomato slice and one cheese slice. Since you have three tomato slices and two cheese slices, you are limited by the availability of cheese slices.
Therefore, you can only make as many tomato-cheese sandwiches as the number of cheese slices you have, which in this case is two.
The ingredient that limits the number of sandwiches you can make is the cheese slice. You have more tomato slices than cheese slices, so you cannot make more than two tomato-cheese sandwiches.
Even if you have extra tomato slices, you cannot make additional sandwiches because you do not have enough cheese slices to pair with them.
In summary, the number of tomato-cheese sandwiches you can make is determined by the ingredient with the lowest quantity,
which in this case is the cheese slice. Therefore, you can make a maximum of two tomato-cheese sandwiches.
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Which type of sample is selected to reflect the demographic characteristics of the population of interest
Answers
The type of sample that is selected to reflect the demographic characteristics of the population of interest is representative samples. Option b is correct.
Representative samples are selected to reflect the demographic characteristics of the population of interest. This sampling method aims to ensure that the sample closely resembles the larger population in terms of its demographic composition.
By including individuals from various demographic groups in the sample, representative samples allow for more accurate generalizations and conclusions to be drawn about the population as a whole. This sampling approach is commonly used in research studies and surveys to gather data that is representative of the larger population's characteristics and attitudes.
Therefore, b is correct.
Which type of sample is selected to reflect the demographic characteristics of the population of interest?
A. Convenience samples
B. Representative samples
C. Random samples
D. Cumulative samples
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. (a) In the following model for the growth of rabbits, foxes, and hu- mans, R' = R + .3R - 17 - 2H F = F + 4R ..2F .3H H' = H + .IR + 1F + 1H determine the sum and max norms of the coefficient matrix A. (b) If the current vector of population sizes is p = [10, 10, 10], de- termine bounds (in sum and max norms) for the size of p' Ap. Compute p' and see how close it is to the norm bounds. (c) Give a sum norm bound on the size of population vector after four periods, p(4).
Answers
In a population growth model for rabbits, foxes, and humans, the sum norm of the coefficient matrix is 4.5 and the max norm is 4.4. Using these norms, we can bound the size of the population vector after one period.
(a) To find the coefficient matrix A, we identify the coefficients of the variables R, F, and H in the given model equations. Once we have A, we can calculate its sum norm by adding up the absolute values of its elements and its max norm by taking the maximum absolute value among its elements. (b) Given the population vector p = [10, 10, 10], we can calculate p'Ap by multiplying p' (transpose of p) with A and then with p. The resulting value will provide the bounds for the size of p'Ap in both sum and max norms. Comparing this value with the norm bounds will indicate how close they are. (c) To determine the sum norm bound for the population vector after four periods, p(4), we need to multiply A by itself four times and calculate the sum of the absolute values of its elements. This sum will give us the desired sum norm bound.
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57 Team one had twice as many workers as team two. Because of increased productivity the number of workers in team one was reduced by 5 and the number of workers in team two was reduced by 2. How many workers are there in each team now if there are 7 more workers in team one?
Answers
Answer:
Team 1 = 15 workers
Team two = 8 workers
Step-by-step explanation:
Let
Number of workers in team 1 = x
Number of workers in team 2 =y
Team one had twice as many workers as team two
x = 2y (1)
number of workers in team one was reduced by 5 and the number of workers in team two was reduced by 2.
x - 5 = y - 2
How many workers are there in each team now if there are 7 more workers in team one?
x - 5 = (y - 2) + 7
x - 5 = y - 2 + 7
x = y - 2 + 7 + 5
x = y + 10
Substitute x = y + 10 into (1)
x = 2y
y + 10 = 2y
10 = 2y - y
10 = y
y = 10
Substitute y = 10 into (1)
x = 2y
= 2(10)
= 20
x = 20
The team now has
Team 1 = x - 5
= 20 - 5
= 15 workers
Team 2 = y - 2
= 10 - 2
= 8 workers
Use the Comparison Test to determine whether the series is convergent or divergent. Σ[infinity]n = 1, n^2/5n^3 - 3. -converges -diverges
Answers
In this case, let's compare it to the series Σ(1/n). We know that the harmonic series Σ(1/n) is divergent. Now, let's see how these two series relate:
n^2/(5n^3 - 3) <= n^2/(5n^3) = 1/(5n)
Since 1/(5n) is smaller term-wise than the original series, and it converges to the known divergent harmonic series Σ(1/n) when multiplied by 1/5, the original series is also divergent. Thus, the answer is: the series diverges.
To use the Comparison Test, we need to find a series that we know the convergence of that is greater than or equal to our given series. We can simplify the given series by canceling out a factor of n in the numerator and denominator:
Σ[infinity]n = 1, n^2/5n^3 - 3 = Σ[infinity]n = 1, 1/5n
We can now compare this to the series Σ[infinity]n = 1, 1/n. Both series have positive terms, so we can compare them as follows:
1/5n ≤ 1/n for all n ≥ 1
Since the series Σ[infinity]n = 1, 1/n is a known divergent series (the harmonic series), we can conclude that our given series Σ[infinity]n = 1, n^2/5n^3 - 3 is also divergent by the Comparison Test.
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What is 150 mm in metres (m)?
A.0.015
B.0.15
C.1.5
D.15
Answers
Answer:
.15 meters
Step-by-step explanation:
answer is B
Step-by-step explanation:
150 mm is 0.15 metres
Jacob is practicing the 100 meter dash. the data show his times in seconds.
14, 13, 13.5, 16, 14, 15.5, 14.5
which box plot shows the distribution of the data?
12
+
12
13
13
14
time (s)
14
time (s)
15
15
16
16
12
12
13
13
14
time (s)
14
time (s)
15
15
16
16
Answers
The set's interquartile range is 2 seconds for the values 14, 13, 13.5, 16, 14, 15.5, and 14.5.
The interquartile range (IQR) represents the second and third quartiles of your data collection (IQR). The spread of the middle half of a data set is provided by the interquartile range, whereas the spread of the complete data set is provided by the range.
Due to it,
Jacob competes in the 100-meter dash.
the information displaying time in seconds,
14, 13, 13.5, 16, 14, 15.5. 14.5
Find the median of the provided set first before calculating the interquartile range.
Data should be arranged from lower to higher values,
13, 13.5, 14, 14, 14.5, 15.5, 16.
The data's median is 14
13, 13.5, and 14 for the set's lower half.
The set's upper half equals 14.5, 15.5, and 16.
Q1 = Lower half's middle period, or 13.5
Q2 = Upper half's middle period, or 15.5
The IQR is 15.5 to 13.5, or 2 seconds.
The set's necessary interquartile range is 2 seconds.
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suppose that the probability is 0.40 that at most two of these individuals purchase an electric oven. what is the probability that at least three purchase the electric oven?\
Answers
Suppose that the probability is 0.40 that at most two of these individuals purchase an electric oven.
What is the probability that at least three purchase the electric oven?The probability that at most two individuals purchase an electric oven is 0.40. Thus, the probability that three or more individuals will purchase an electric oven is 1 - 0.40 = 0.60.In other words, the probability of three or more people purchasing an electric oven is 0.60, given that the probability of at most two people purchasing the electric oven is 0.40.
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Can someone help me ? Please :)
3. A bank offers an annual simple interest
rate of 7% on home improvement loans.
How much would Tony owe if he borrowed
$8,000 for 18 months?
Answers
Answer:
g
Step-by-step explanation:
Suppose the function E(c) represents the earnings of a volleyball team from selling c cupcakes. They are selling each cupcake for $2. They only bought enough supplies to make 100 cupcakes. Describe an appropriate domain and range of this function using interval notation.
Answers
Using domain and range concepts, it is found that:
An appropriate domain for the function is: \(c \in [0,100]\)An appropriate range for the function is \(E \in [0,200]\).------------------------------
The domain of a function are the values that the input can assume.The range of a function are the values that the output can assume.------------------------------
The function E(c) represents the earnings of selling c cupcakes.The input is the number of cupcakes sold c.The output is the earnings E.------------------------------
They have enough supplies to make 100 cupcakes, thus, at most 100 cupcakes can be sold, meaning that an appropriate domain for the function is: \(c \in [0,100]\)If no cupcakes are sold, the earnings will be of $0. If all 100 cupcakes are sold, the earnings will be of $200, as each is sold for $2, meaning that an appropriate range for the function is \(E \in [0,200]\).A similar problem is given at https://brainly.com/question/2145599
Find the value of each variable
Answers
The missing sides of the special right triangles are listed below:
Case 1: y = √2 · 13, x = 13
Case 2: x = y = 15√2
Case 3: x = 6, y = 3√3
Case 4: x = 17√3, y = 17
Case 5: x = y = 10
Case 6: x = 50, y = 25
Case 7: x = y = 4√7
Case 8: x = 16√3, y = 8√3
Case 9: x = 11√3, y = 33
Case 10: x = 3√2, y = 2√6
Case 11: x = √10, y = 2√5
Case 12: x = 4√7, y = 8√21
How to find the length of missing sides
Herein we find twelve cases of special right triangles whose missing sides must be determined by using the following rules:
45 - 90 - 45 Right triangle
r = √2 · x = √2 · y
30 - 60 - 90 Right triangle
x = (1 / 2) · r
y = (√3 / 2) · r = √3 · x
Where:
x - Shortest leg.y - Longest leg. r - Hypotenuse.Case 1
y = √2 · 13
x = 13
Case 2
x = y = 15√2
Case 3
x = 3 / (1 / 2)
x = 6
y = 3√3
Case 4
x = 34 · (√3 / 2)
x = 17√3
y = 34 · (1 / 2)
y = 17
Case 5
x = y = 10
Case 6
x = 25√3 / (√3 / 2)
x = 50
y = 25√3 / √3
y = 25
Case 7
x = y = 2√14 · √2 = 2√28 = 4√7
Case 8
x = 24 / (√3 / 2)
x = 48 / √3
x = 16√3
y = 24 / √3
y = 8√3
Case 9
x = 22√3 · (1 / 2)
x = 11√3
y = 22√3 · (√3 / 2)
y = 33
Case 10
x = √18
x = 3√2
y = √6 / (1 / 2)
y = 2√6
Case 11
x = √10
y = √20
y = 2√5
Case 12
x = 4√21 / √3
x = 4√7
y = 4√21 / (1 / 2)
y = 8√21
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What is 15x+48=120 what is the x value
Answers
So the value of x is 4.8
15x + 48= 120
Now we send the 48 on the right side.
15x= 120-48.
Here we subtract 48 from 120 we get
15x= 72
In the next step we divide the both sides with 15
15x/15= 72/15
x=4.8
So the value of x is 4.8
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first subtract on both sides
15x+48=120
-48 -48
———————
15x=72
then you have 15x=72
divide it by 15 on both sides
15x=72
—— —-
15 15
which gives you x = 4.8