The formula 2x/(x-7) - (x+7)/x therefore equals (x² + 49) / (x × (x-7)).
What does an arithmetic the expression mean?Mathematical expressions consist of at least two integers or factors, a minimum of one math procedure, and a sentence. It's possible to multiply, divide, add, or remove with this mathematical procedure.
To simplify the expression 2x/(x-7) - (x+7)/x, we need to find a common denominator.
First, we can rewrite the second term as (x+7)/(x × 1), so the expression becomes:
2x/(x-7) - (x+7)/(x × 1)
To find a common denominator, we need to multiply the first term by x/x and the second term by (x-7)/(x-7):
2x × x / (x × (x-7)) - (x+7) × (x-7) / (x × (x-7))
Simplifying the expression further, we get:
(2x² - (x² - 49)) / (x × (x-7))
Simplifying the numerator, we get:
(2x² - x² + 49) / (x × (x-7))
And finally, we can simplify the expression to:
(x² + 49) / (x × (x-7))
Therefore, the expression 2x/(x-7) - (x+7)/x is equivalent to (x² + 49) / (x × (x-7)).
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Answer:
\(\frac{x^{2}+49 }{x(x-7)}\)
Step-by-step explanation:
Choose the graph of y < –x2 + 4x + 5.
Answer:
can you show me the graph so I can't answer the question
Answer:
A
Step-by-step explanation:
Edge 2022
For f(x) =2x+1 and g(x)=- squt -7 find (g/f)(x)
Answer:
C
Step-by-step explanation:
If you have any questions about the way I solved it, don't hesitate to ask me in the comments below
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A cyclist rode 3.75 miles in 0.3 hours.
How fast was she going in miles per hour?
Round your answer to the tenths (first) decimal place.
Do not include units (miles per hour) in your answer.
Answer:
Distance covered by cyclist=3.75 miles.
Time =0.3 hours.
Speed= Distance ÷Time
Speed =3.75÷0.3=12.5 miles per hour.
2) Speed = 12.5 miles per hour, Distance = 4.5 miles .
Time = Distance ÷Speed.
Time = 4.5÷12.5=0.36 hours.
Time taken to cover 4.5 miles is 0.36 hours.
Step-by-step explanation:
What is the distance between point A(-9, 15) and B(26, -2)?
A. 38.91
B. 52
C. 39
D. 30.59
Answer:
A 38.91
Step-by-step explanation:
distance formula = d= √((x2-x1)²+(y2-y1)²)
Indicate the answer choice that best completes the statement or answers the question.
Answer:
C
Step-by-step explanation:
m<2:
180 - 60 - 48 = 72
Vertical angle thm:
m<1 = 48
m<3:
180 - 62 - 48 = 70
PLEASE HELPPP URGENT!!!!!!!
Answer:
tienesde qu
Step-by-step explanation:
Answer:
\(5\sqrt{5}\)
Step-by-step explanation:
If you apply the Pythagoras theorem you get that
\(6^{2} +8^2=x^2\\\\36+64=x^2\\\\x^2=100\\\\x=10\)
with x= A D
and get apply it again
\(10^2+5^2=y^2\\\\100+25=y^2\\\\125=y^2\\\\5\sqrt{5} =y\)
with y = A F
and that's our answer
Option D
a car travels 120120 miles from aa to bb at 3030 miles per hour but returns the same distance at 4040 miles per hour. the average speed for the round trip is closest to:
The Average Speed of car for the round trip is 346.28 km/ hr.
Average Speed is calculated by dividing the total distance that something has travelled by the total amount of time it took it to travel that distance.
If a car travels a distance d at rate r₁ and return the same distance at rate r₂, then,
Average Speed = total distance ÷ total time
= 2d ÷ d/r₁ + d/r₂
= 2d ÷ r₂d + r₁d / r₁r₂
= 2r₁r₂ / r₁ +r₂
∴ x = 2× 3030×4040/ 3030 +4040
= 2448240 ÷ 707
= 346.28 km/hr
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You are designing a container in the shape of a cylinder. The radius is 6 inches. You want the container to hold at least 324π cubic inches. What is the least possible height of the container?
The least possible height of the container is ___ inches.
Find the area inside the loop of the following limacon: r=7−14sinθ
The area inside the loop of the limacon given by the polar equation r = 7 - 14sin(θ) is 294π square units.
To find the area inside the loop of the limacon given by the polar equation r = 7 - 14sin(θ), we need to evaluate the integral for half of the area and then double the result.
The curve of the limacon has a loop when 0 ≤ θ ≤ π, so we integrate from 0 to π. The area can be calculated as follows:
A = 2 ∫₀^π 1/2 r² dθ
Using the equation for r given, we can substitute and simplify:
A = 2 ∫₀^π 1/2 (7 - 14sin(θ))² dθ
A = 2 ∫₀^π 1/2 (49 - 196sin(θ) + 196sin²(θ)) dθ
A = ∫₀^π (98 - 392sin(θ) + 392sin²(θ)) dθ
Using the trigonometric identity 1 - cos(2θ) = 2sin²(θ), we can simplify further:
A = ∫₀^π (98 - 392sin(θ) + 196 - 196cos(2θ)) dθ
A = ∫₀^π (294 - 392sin(θ) - 196cos(2θ)) dθ
Integrating with respect to θ:
A = [294θ + 392cos(θ)sin(θ) + 98sin(θ)]₀^π
Evaluating at the limits of integration, we get:
A = [294π + 0 + 0] - [0 + 392cos(0)sin(0) + 98sin(0)]
A = 294π - 0 - 0 = 294π
Therefore, the area inside the loop of the limacon r = 7 - 14sin(θ) is 294π square units.
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? what is the ans of the question
Answer:
a. 12x+22, b. x = 9
Step-by-step explanation:
a. The perimiter in terms of x is 2((4x+8)+(2x+3)) = 12x+22
b. 12x+22=136, 12x=108, x=9
a. 12x+22, b. x = 9
Step-by-step explanation:
a. The perimiter in terms of x is 2((4x+8)+(2x+3)) = 12x+22
b. 12x+22=136, 12x=108, x=9
Calculate the derivative of the following function. y=cos3(sin(8x)) dy/dx = ___
The derivative of y=cos3(sin(8x)) is dy/dx=-24cos2(sin(8x))sin(8x). This can be found using the chain rule, which states that the derivative of a composite function is the product of the derivative of the outer function and the derivative of the inner function. In this case, the outer function is cos3(x) and the inner function is sin(8x).
The chain rule states that the derivative of a composite function f(g(x)) is:
f'(g(x)) * g'(x)
In this case, the composite function is cos3(sin(8x)). The outer function is cos3(x) and the inner function is sin(8x). Therefore, the derivative of the composite function is:
(3cos2(x)) * (cos(sin(8x))) * (8)
Simplifying the expression, we get:
-24cos2(sin(8x))sin(8x)
This is the derivative of y=cos3(sin(8x)).
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ILL GIVE BRAINLY THING
Answer:
the slope is -4/3
Step-by-step explanation:
you can either use the graph or algebra to find the slope.
to use the graph, simply count how many spaces up/down and to the left/right that you go.
to use algebra, take the coordinates of your two points and do (y2-y1)/(x2-x1).
The segment shown is half of AB, where B(-5, 1) is one endpoint of the segment and M(-3, 3) is the midpoint of the segment. What are the coordinates of point A?
I would really appreciate help because I’m super confused, thank you:))
Answer:
(-1,5)
Step-by-step explanation:
For point (x1,y1) and (x2,y2) on coordinate plane if m is the midpoint of these points, then coordinate of mid point is given by
(x1+x2)/2, (y1+y2)/ 2
________________________________
Given point
B= (-5,1)
M = (-3,3)
we have to find point A, let it be (x,y
using the above formula , midpoint m is
-3= (-5+x)/ 2 3= (1+y)/ 2
-3*2= -5+x 6= 1 +y
-6 +5 = x 6-1 =y
x = -1 y = 5
Thus, the coordinates of point A is(-1,5).
Gina wilson homework I need help fast it’s due tomorrow
ok so for whatw e do is mulitpy the numbers
A rectangular storage container without a lid is to have a volume of 10 m3. the length of its base is twice the width. material for the base costs $15 per square meter. material for the sides costs $9 per square meter. let w denote the width of the base. Find a function in the variable w giving the cost C in dollars) of constructing the box.
The function in variable w giving the cost C (in dollars) of constructing the box is C(w) = 30w² + 270/w. The result is obtained by using the formula of volume and area of the box.
How to determine the function?We have a rectangular storage container without a lid.
Volume, V = 10 m³Length, l = 2wWidth, w = wBase costs $15/m²Sides costs $9/m²The formula of volume of the box is
V = l × w × h
Where
l = lengthw = widthh = heightSo, the height is
10 = 2w × w × h
10 = 2w² × h
h = 10/2w²
h = 5/w²
To find the total cost, calculate the area of base and sides of the box!
See the picture in the attachment!
The base area is
A₁ = 2w × w = 2w² m²
The sides area is
A₂ = 2(2wh + wh)
A₂ = 2(3wh)
A₂ = 6wh
A₂ = 6w(5/w²)
A₂ = 30/w m²
The total cost is
C = $15(2w²) + $9(30/w)
C = $30w² + $270/w
The function of the total cost is
C(w) = 30w² + 270/w
Hence, the function of constructing the box is C(w) = 30w² + 270/w.
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how many ways can all 24 slices be distributed across all six people (including you)? assume, of course, that people are distinct, but that pizza slices all look the same and are indistinct.
There are 134596 ways to distribute 24 slices between 6 people
Since pizza slices are the same hence order doesn't matter and also people are distinct so it is a case of combination.
Combination in mathematics is a way of choosing or distributing selected items from a list of the total set with distinct values. It is used when there is no repetition and order doesn't matter. It can also be depicted as permutation/r!
combination = nCr =n!/(r!(n-r!)
where n is the total number of objects
r is the number of chosen objects from the total.
Now, 24c6=24!/6!18!
=24x23x22x21x20x19x18!/6!18!
=24x23x22x21x20x19/6x5x4x3x2x1
=134596
Therefore, There are 134596 ways to distribute 24 slices between 6 people
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5x squared + 5x= 745
Answer:
Look in png I attached
Step-by-step explanation:
1. Simplify the quadratic equation into its standard form
2. Solve the equation using the quadratic formula
3. Determine the quadratic equation’s coefficients a, b and c
4. Plug these coefficients into the quadratic formula
5. Simplify square root of 14925
6. Solve the equation for x
- Centar :)
6=2(y+2)
Y= ?
Solve for Y
Answer:
y = 1
Step-by-step explanation:
6= 2(y+2) Multiply 2*y and 2 *2
6 = 2y + 4
6 - 4 = 2y
2 = 2y - Divide 2 and 2
y = 1
Answer:
yeah the person is right it is y=1
Step-by-step explanation:
Explain how to find coordinates for Q
Answer:
Q = (4, - 1)
Step-by-step explanation:
DF is the diameter of the circle with center Q.
So, Q is the midpoint of DF.
By mid point formula.
\(Q = \bigg( \frac{1 + 7}{2}, \: \: \frac{3 - 5}{2} \bigg) \\ \\ Q = \bigg( \frac{8}{2}, \: \: \frac{ - 2}{2} \bigg) \\ \\ Q = (4, \: \: - 1)\)
What other points are on the line of direct variation through (5, 12)? Check all that apply.
(0, 0)
(2. 5, 6)
(3, 10)
(7. 5, 18)
(12. 5, 24)
(15, 36)
To determine which points are on the line of direct variation through (5, 12), we can use the equation of direct variation, which is given by y = kx, where k is the constant of variation.
Given the point (5, 12), we can substitute these values into the equation and solve for k:
12 = k * 5
k = 12 / 5
k = 2.4
Now, we can check which other points satisfy the equation y = 2.4x:
Checking each point:
(0, 0): 0 = 2.4 * 0 => 0 = 0 (satisfied)
(2.5, 6): 6 ≠ 2.4 * 2.5 => 6 ≠ 6 (not satisfied)
(3, 10): 10 ≠ 2.4 * 3 => 10 ≠ 7.2 (not satisfied)
(7.5, 18): 18 ≠ 2.4 * 7.5 => 18 ≠ 18 (satisfied)
(12.5, 24): 24 ≠ 2.4 * 12.5 => 24 ≠ 30 (not satisfied)
(15, 36): 36 ≠ 2.4 * 15 => 36 ≠ 36 (satisfied)
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Answer:
it is
A, B, D, and, F
Step-by-step explanation:
trust me i just did the asigenment
An airplane flies 1250 km in 1 hour 20 minutes. What is its average speed in kilometers per hour?
Answer:
tiiiuhhhghhjpjjhhjhgghhuuhh
Nate earned $132.50 mowing lawns and $75 as a soccer referee. If he spends $12.75 to see a movie and $6.50 on snacks. How much money does Nate have left?
Answer:
Step-by-step explanation:
jlvkhd.ifkujg,jfu/lor7fulgjv,gluojbuo
a particle moves in a straight line with the given velocity ()=6cos() (in m/s).v(t)=6cos(t) (in m/s). find the displacement and distance traveled over the time interval [0,5].[0,5π].
The displacement and distance traveled depend on the given time interval.
To find the displacement, we need to integrate the velocity function from 0 to 5 or 0 to 5π, depending on the given time interval.
If the time interval is [0,5], we have:
Displacement = ∫[0,5] v(t) dt
Displacement = ∫[0,5] 6cos(t) dt
Displacement = [6sin(t)] from 0 to 5
Displacement = 6sin(5) - 6sin(0)
Displacement ≈ 2.785 meters
If the time interval is [0,5π], we have:
Displacement = ∫[0,5π] v(t) dt
Displacement = ∫[0,5π] 6cos(t) dt
Displacement = [6sin(t)] from 0 to 5π
Displacement = 0 - 6sin(0)
Displacement = 0 meters
To find the distance traveled, we need to integrate the absolute value of the velocity function over the given time interval.
If the time interval is [0,5], we have:
Distance = ∫[0,5] |v(t)| dt
Distance = ∫[0,5] |6cos(t)| dt
Distance = ∫[0,π/2] 6cos(t) dt + ∫[π/2,5] -6cos(t) dt
Distance = [6sin(t)] from 0 to π/2 + [-6sin(t)] from π/2 to 5
Distance = 6 - 6sin(5) ≈ 2.215 meters
If the time interval is [0,5π], we have:
Distance = ∫[0,5π] |v(t)| dt
Distance = ∫[0,5π] |6cos(t)| dt
Distance = ∫[0,π] 6cos(t) dt + ∫[π,2π] -6cos(t) dt + ∫[2π,3π] 6cos(t) dt + ∫[3π,4π] -6cos(t) dt + ∫[4π,5π] 6cos(t) dt
Distance = [6sin(t)] from 0 to π + [-6sin(t)] from π to 2π + [6sin(t)] from 2π to 3π + [-6sin(t)] from 3π to 4π + [6sin(t)] from 4π to 5π
Distance = 0 meters
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Solve the equation -3x²+ 5x + 4=0 . Show your work.
the solutions to the equation -3x² + 5x + 4 = 0 are:
x = (-5 + √73) / (-6)
x = (-5 - √73) / (-6)
To solve the quadratic equation -3x² + 5x + 4 = 0, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax² + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b² - 4ac)) / (2a)
For our equation, a = -3, b = 5, and c = 4. Plugging these values into the quadratic formula, we get:
x = (-5 ± √(5² - 4(-3)(4))) / (2(-3))
Simplifying further:
x = (-5 ± √(25 + 48)) / (-6)
x = (-5 ± √73) / (-6)
So, the solutions to the equation -3x² + 5x + 4 = 0 are:
x = (-5 + √73) / (-6)
x = (-5 - √73) / (-6)
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(9 + 4b) + (-4 +5y) + (1 +2m) =
Answer:
4b+5y+2m+6
Step-by-step explanation:
What does the sign of the correlation correlation coefficient tell you about the relationship between the number of bacteria colonies and the concentration of antibiotics in the dish
answer : variable moves in relation to another
Step-by-step explanation:
solve this equation for x: 3x+4x+x+16
Answer:
x = 2
Step-by-step explanation:
solve this equation for x: 3x+4x+x=16
3x + 4x + x = 16
7x + x = 16
8x = 16
x = 16 : 8
x = 2
----------------------
check3 × 2 + 4 × 2 + 2 = 16 (remember PEMDAS)
6 + 8 + 2 = 16
16 = 16
same value the answer is good
Can u please help me I got a 39 on this assignment and I rly need u to break it down
The scale factor used is 8/3 or 2.67 (rounded to two decimal places).
What is the scale factor?
A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
The scale factor is the ratio of corresponding side lengths. Since the small triangle is the pre-image, its corresponding side length is the base of the large triangle. Therefore, the scale factor is:
scale factor = (corresponding side length of a large triangle) / (corresponding side length of a small triangle)
In this case, the corresponding side lengths are the bases of each triangle. So the scale factor is:
scale factor = (base of large triangle) / (base of small triangle)
The base of the small triangle is 3, and the base of the large triangle is 8. So the scale factor is:
scale factor = 8/3
Therefore, the scale factor used is 8/3 or 2.67 (rounded to two decimal places).
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Maddy and her cousin work during the summer for a landscaping company. Maddy's cousin has been working for the company longer, so her pay is 30% more than Maddy's. Last week, Maddy's cousin worked 27 hours, and Maddy worked 23 hours. Together, they earned $493.85. What is Maddy's hourly pay?
fourth step in the process of coding the responses to survey questions involves assigning a coded value to each response. Which of the following statements is true of this step? It follows the data entry phase of data preparation It is the step where omissions are either coded or left out. It is automated and is the easiest phase of the entire process. It is almost always necessary to avoid problems in the data entry phase. It precedes the data validation phase of data preparation.
The statement that is true of the fourth step in the process of coding the responses to survey questions is that it follows the data entry phase of data preparation.
In the first paragraph, we can summarize the answer as follows: The fourth step in the process of coding survey responses involves assigning a coded value to each response, and it follows the data entry phase of data preparation.
The process of coding survey responses involves converting the qualitative information obtained from the survey into a coded format that can be analyzed and interpreted. After the data entry phase, where the survey responses are typically entered into a database or software system, the fourth step begins. During this step, each response is assigned a specific code or value that represents its meaning or category. This coding process allows for easier analysis and statistical manipulation of the data.
The reason why this step follows the data entry phase is that the data entry phase focuses on accurately capturing the survey responses without any interpretation or coding. Once the responses are entered, the fourth step takes place to assign the appropriate codes. By separating the data entry and coding phases, it ensures that the responses are captured accurately before any coding or interpretation is applied.
While the statement suggests that this step is automated and the easiest phase of the entire process, this may not always be the case. The complexity and ease of this step can vary depending on factors such as the nature of the survey questions, the coding system being used, and the clarity of the response options. Additionally, the statement that it is almost always necessary to avoid problems in the data entry phase is not accurate. The coding step is not directly related to avoiding problems in the data entry phase but rather focuses on transforming the data for subsequent analysis. Furthermore, the statement does not mention anything about omissions; therefore, it is not directly related to the process of coding the responses. Lastly, the statement correctly states that this step precedes the data validation phase, which typically involves checking the accuracy and consistency of the coded data.
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