[tex]x+\frac{8x}{x-7} =\frac{56}{x-7}[/tex]

Answers

Answer 1

The equation has two solutions, on is extraneous and x = 7, and the real solution is x = -8.

How to solve the equation?

Here we have the following equation:

x + 8x/(x - 7) = 56/(x - 7)

This is the original equation, notice that if x = 7, we will have a zero on the denominators, and we can't divide by zero, thus, x can't be equal to 7.

Now let's multiply all the equation by (x - 7)

(x - 7)*x + 8x = 56

Now we have a quadratic equation:

x^2 - 7x + 8x - 56 = 0

x^2 + x - 65 = 0

Using the quadratic formula we will get the two solutions:

[tex]x = \frac{-1 \pm \sqrt{1^2 - 4*1*-56} }{2*1} \\\\x = \frac{-1 \pm15}{2*1}[/tex]

Then the two solutions are:

x = (-1 + 15)/2 = 7 (this one is an extraneous solution, we can discard this one)

x = (-1 - 15)/2 = -8

This is our solution.

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Related Questions

Each morning Tess chooses either red ribbon or blue ribbon at random to wear in her hair what is the probability that Tess will choose a red ribbon on both Monday and Tuesday

Answers

The probability of choosing red ribbon on both Monday and Tuesday is 1/4.

What is the probability?

The Probability in mathematics is possibility of an event in time. In simple words how many times that incident is happening in any given time interval.

Given that each morning Tess chooses either red ribbon or blue ribbon at random to wear in her hair.

That means probability of choosing between blue or red is 1/2 in one morning.

Now the probability of choosing red ribbon on both Monday and Tuesday,

1/2 × 1/2

= 1/4

Therefore, the probability of choosing red ribbon on both Monday and Tuesday is 1/4.

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6x + 3y = 3 3x - y = 4

Answers

Answer:

x = 1

y = -1

Step-by-step explanation:

Given equations:

6x + 3y = 3 -------------(1)

3x - y = 4 ----------------(2)

Multiply Eq. (2) by 2

2(3x - y) = 4 × 2

6x - 2y = 8 -------------(3)

Subtract Eq. (3) from Eq. (1)

6x + 3y - (6x - 2y) = 3 - 8

6x + 3y - 6x + 2y = -5

3y + 2y = -5

5y = -5

Divide 5 to both sides

y = -5/5

y = -1

Put y = -1 in Eq. (1)

6x + 3(-1) = 3

6x - 3 = 3

Add 3 to both sides

6x = 3 + 3

6x = 6

Divide 6 to both sides

x = 1

[tex]\rule[225]{225}{2}[/tex]

If you make $31.65 in 8 hours, how much in total?

Answers

Answer:

$253.20

Step-by-step explanation:

The following are rules for repeating patterns. For which rule will the 12th shape be a circle?

A.
triangle, circle, square

B.
circle, square

C.
rectangle, circle

D.
circle, circle, triangle

Answers

Answer:

A Square

B Square

C Circle

D Triangle

Let f(x)=\sqrt(3x-9) and g(x)=3x^(2)-9
A) what is the inverse of function f?
b) is f an inverse of g? Please show all work

Answers

A) The inverse of f(x) is f⁻¹(x) = (x² + 9)/3 and B) f is not an inverse of g.

What is an inverse function?

First to be an inverse function that function needs to one to one function, meaning every different preimage must correspond to a different image.

We can obtain the inverse of a function by switching the variables x and y with their respective positions and solving for y in terms of x.

Given, f(x) = [tex]\sqrt{3x - 9}[/tex].

y = [tex]\sqrt{3x - 9}[/tex].

y² = 3x - 9.

3x = y² + 9.

x = (y² + 9)/3.

y = (x² + 9)/3.

f⁻¹(x) = (x² + 9)/3 and g(x) = 3x² - 9, so f is not an inverse of g.

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Use the Special Integration Formulas (Theorem 8.2) to find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) squareroot of (9 + 49^x2) dx

Answers

The indefinite integral of given integral ∫√(9+49x^2)dx is ∫√(9+49x^2)dx = [tex]\int\sqrt{(9+49x^2)}dx = 1/98[98x\sqrt{9+49x^2}+9In|7x+\sqrt{9+49x^2}}|]+C[/tex].

In the given question we have to find the indefinite integral.

The given integral is

∫√(9+49x^2)dx

Now finding the indefinite integral using the C for the constant of integration.

An integral is regarded to be indefinite if it has no lower or upper bounds. In mathematics, the most generic antiderivative of f(x) is known as an indefinite integral and expressed by the expression f(x) dx = F(x) + C.

We can write it as:

[tex]\int\sqrt{(9+49x^2)}dx = \int\sqrt{[(3)^2+(7x)^2]}dx[/tex]

Taking common 7^2

[tex]\int\sqrt{(9+49x^2)}dx = 7\int\sqrt{[(3/7)^2+(x)^2]}dx[/tex]

Using the formula

[tex]\int\sqrt{(a^2+x^2)}dx = \frac{1}{2}\times\sqrt{a^2+x^2} + \frac{1}{2}\cdot a^2In|x+\sqrt{a^2+x^2}|+C[/tex]

[tex]\int\sqrt{(9+49x^2)}dx = 7[x\sqrt{(3/7)^2+x^2}+\frac{1}{2}\cdot(\frac{3}{7})^2In|x+\sqrt{(3/7)^2+x^2}|]+C[/tex]

[tex]\int\sqrt{(9+49x^2)}dx = 7[x\sqrt{9/49+x^2}+1/2\cdot(9/49)In|x+\sqrt{(9/49)+x^2}|]+C[/tex]

[tex]\int\sqrt{(9+49x^2)}dx = 7[x\cdot\frac{\sqrt{9+49x^2}}{7}+1/2\cdot(9/49)In|x+\frac{\sqrt{9+49x^2}}{7}|]+C[/tex]

[tex]\int\sqrt{(9+49x^2)}dx = 7[x\cdot\frac{\sqrt{9+49x^2}}{7}+(9/98)In|\frac{7x+\sqrt{9+49x^2}}{7}|]+C[/tex]

[tex]\int\sqrt{(9+49x^2)}dx = 1/98[98x\sqrt{9+49x^2}+9In|7x+\sqrt{9+49x^2}}|]+C[/tex]

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please help in this grade 7 percentage question im desperate

Answers

Answer:

See below

Step-by-step explanation:

320 x .1 = 32

320 + 32 = 352

352 x .5 = 176

352 + 176 = 528

320 x .65 = 208

320 + 208 = 528

A bag contains five white balls and three black balls. Your goal is to draw two white balls.

(a) You simultaneously draw two balls at random. What is the probability that they are both white?
(b) You simultaneously draw two balls at random. Once you have drawn two balls, you put back any black balls, and redraw so that you again have two drawn balls. What is the probability that you now have two white balls? (Include the probability that you chose two white balls on the first draw.)

Answers

The probability is the first and the second case will be 0.625 and 0.3683, respectively.

What is probability?

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

A pack contains five white balls and three torpedoes. You want to draw two white balls.

Total events = 5 + 3

Total events = 8

You all the while drawing two balls aimlessly. Then the probability that they are both white is given as,

P = 5 / 8

P = 0.625

You all the while drawing two balls aimlessly. Whenever you have drawn two balls, you set back any debases, and redraw with the goal that you again have two drawn balls. Then the probability is given as,

P = [(3/8) x (5/8)] + [(3/8) x (5/8) x (4/7)]

P = (15 / 64) + (60 / 448)

P = 0.3683

The probability is the first and the second case will be 0.625 and 0.3683, respectively.

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a) Work out the minimum number of dogs that could have a mass of more than 24kg}
b) Work out the maximum number of dogs that could have a mass of more than 24kg

Answers

The minimum number of dogs 24kg is 6 and the maximum number of dogs is 18

Maximum and Minimum:

The highest amount or value or number that may be obtained or reached or can be counted is the Maximum value

The least amount or value or number that may be admitted or reached or can be counted is the Minimum value

Here we have a table

Which represents the masses of various dogs

Mass (x) kg frequency

0 ≤ x < 10 2

10 ≤ x < 20 7

20 ≤ x < 30 12

30 ≤ x < 40 6

Here the mass of dogs is represented in class intervals

a) The minimum number of dogs with a mass of more than 24kg.

From the given table,

24 kg will lie in class intervals 20 ≤ x < 30, and 30 ≤ x < 40

In class interval 20 ≤ x < 30, there is a possibility that the mass of dag will be less than 24 kg since it started from 20 kg and is up to 30 kg

In class interval 30 ≤ x < 40, there is no possibility that the mass will be less than 24 kg since it started from 30 kg and is up to 40 kg

So The minimum number of dogs that have a mass of more than 24kg the frequency of class interval 30 ≤ x < 40

Therefore,

The minimum number of dogs with a mass of more than 24kg is 6

b) The maximum number of dogs that have a mass of more than 24kg.

To get the maximum number of dogs we need to take the class interval of 20 ≤ x < 30 as in this the mass could be more than 24 kg.

And in class 30 ≤ x < 40 the mass will be more than 24 kg.

Thus, the Maximum number of dogs with more than 24 kg = 12 + 6 = 18

Therefore,

The maximum number of dogs with a mass of than 24kg is 18

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a plumber cuts 2 3/4 feet from pipe. The pipe is now 13 1/4 feet long. Write and solve an equation of to determine the original length if the pipe

Answers

2=3/4,13=1/4,2-3/4=0,13-1/4=0,2-3/4=0*13,13-1/4=0*2

PLEASE HELPPP!!!

The admission fee at the museum is 8.50 for children and 12.50 for adults on a certain day, a total of 240 people entered the museum and 2400$ was collected.

Use the variable c to represent children and the variable a to represent the adult

Answers

Answer:

Below

Step-by-step explanation:

a + c = 240 re-arrange to c = 240-a

revenue from child tix = 8.50 ( 240-a)

revenue from adult tix = 12.50 a summed, the revenues = 2400

8.5(240-a) + 12.5 a = 2400

2040 - 8.5 a + 12.5 a = 2400

4.5 a = 360

a = 80 tix then c = 240 - a = 160 tix

4 2/3 - 3 3/8 + 4 3/5

Answers

Answer:

18.475?

Step-by-step explanation:

14. A zip wire is shown as the dashed line AC in the diagram.
The zip wire is supported by two vertical posts AB and CD standing on horizontal ground.
CD=2.6 BD=12
The zip wire makes an angle x with the horizontal, as shown in the diagram. The design of the zip wire requires the angle x to be at least 5⁰.
Work out the least possible height of the post $A B$ Give your answer correct to 3 significant figures.

Answers

The least possible height of AB is 3.650 m.

What is a word problem?

A word problem is described as a few phrases outlining a "real-life" situation where a problem needs to be solved using mathematics.

For everything from counting pennies to calculating a tip, we can employ the three primary sorts of word problems: part-part whole, separate and join, and multiply and divide.

Given, CD=2.6 m, BD=12 m

From the figure,

or, tan x = [tex]\frac{AB - 2.6}{12}[/tex]

or, tan 5 [tex]\leq \frac{AB - 2.6}{12}[/tex]

When AB be least, then

[tex]\frac{AB - 2.6}{12}[/tex] = tan 5

or, AB = (12*tan 5) + 2.6

or, AB = 3.650 m

Hence, the least possible height of the AB is 3.650 m.

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write an expression that is equivalent to 2/3 (4x + 9)

Answers

Hello,

I hope you and your family are doing well!

To write an expression that is equivalent to 2/3 (4x + 9), you can simply distribute the 2/3 over the parentheses:

2/3 (4x + 9) = (2/3 * 4x) + (2/3 * 9)

This simplifies to:

2/3 (4x + 9) = (8/3)x + (18/3)

Therefore, an expression that is equivalent to 2/3 (4x + 9) is (8/3)x + (18/3).

Please rate this answer 5 stars and brainliest if you find it helpful.

Happy Holidays & New Year!

Answer: 2 2/3x + 6

Step-by-step explanation: 1 of 3 ways to find how to make the equivalent is to use the distributive property. So, that means we need to multiply or distribute 2/3 to both 4x and 9. So, 2/3 x 4 is roughly 2 2/3. Also, 2/3 x 9 = 6. So, I combined the like terms to get 2 2/3x + 6 as my equivalent expression. I hope this helps.

A unicorn is racing a chinchilla. The chinchilla is one hundred feet a head of the unicorn
and running at a rate of 5.75 feet per second. The unicorn is running at a rate of 30 feet
per second. Write an inequality that shows when the unicorn gets ahead of the
chinchilla.

Answers

The inequality that shows when the unicorn gets ahead of the chinchilla is 30s > 100 + 5.75s.

What is the inequality that shows when the unicorn gets ahead?

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

Let the number of seconds be represented by s.

The chinchilla is one hundred feet a head of the unicorn and running at a rate of 5.75 feet per second. This will be 100 + 5.75s.

The unicorn is running at a rate of 30 feet

per second. This will be 30s

The inequality will be 30s > 100 + 5.75s.

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Please help me. This is my last question and I have no more points left.

The coordinate plane below shows the location of rectangle TUVW.
rectangle TUVW is to be dilated by a factor of 3, with the center of dilation at the point (1,0). drag and drop the the correct answers into each box.

Answers

Step-by-step explanation:

i just answered this question. how often did you post it ?

Write the following as an inequality.
−8 is less than or equal to w, and 3 is greater than or equal to w
Use w only once in your inequality.

Answers

Answer:

Step-by-step explanation:

If -8 is less than or equal to w, and 3 is greater than or equal to w, then we can combine these two inequalities into a single inequality by combining the left and right sides:

-8 ≤ w ≤ 3

This inequality can be read as "w is greater than or equal to -8 and less than or equal to 3." It represents all values of w that are greater than or equal to -8 and less than or equal to 3, including -8 and 3.

I hope this helps! Let me know if you have any questions.

-8w hope this answer helps u a lot!

Kaitlin the trainer has two solo workout plans that she offers her clients: plan A and plan B each client does either one or the other (not both) on Friday there were 3 clients who did plan A and 8 who did plan b on Saturday there were 5 clients who did plan A and 2 who did plan b Kaitlin trained her friday clients for a total of 7 hours and her Saturday clients for a total of 6 hours how long does each of the workout plans last

Answers

To find the length of each workout plan, we can use the total number of hours that Kaitlin spent training her clients on Friday and Saturday and the number of clients who did each plan on those days.

Let A be the length of plan A in hours and B be the length of plan B in hours. We can set up the following system of equations to represent the given information:

3A + 8B = 7
5A + 2B = 6

Solving this system of equations using elimination, we find that A = 0.6 hours and B = 0.4 hours.

Therefore, plan A lasts 0.6 hours and plan B lasts 0.4 hours.

Write an equation in slope-intercept form of the line that passes through (-2,-7) and (-1,6)

Answers

y = 13x + 18
1. Find the slope of the two points. 6-(-7) is 13 and -1 -(-2) is 1, so the slope is 13/1.

2. Write the equation in point slope form.
y - y1 = m(x - x1)
y - 6 = 13(x -(-1)

3. Use distributive property.
y - 6 = 13x + 13

4. Add 6 to both sides.
y = 13x + 18

Hope this helps

A certain vending machine offers 20-ounce bottles of soda for $1.50. The number of bottles X bought from the machine on any day is a random variable with mean 50 and standard deviation 15. Let the random variable Y equal the total revenue from this machine on a given day. Assume that the machine works properly and that no sodas are stolen from the machine. What are the mean and standard deviation of Y?

Answers

The mean and standard deviation of a random variable can be used to describe the distribution of its possible values. In this case, the mean of the random variable X represents the average number of bottles of soda that are bought from the vending machine on a given day, and the standard deviation represents the amount of variation in the number of bottles bought from one day to the next.

To find the mean and standard deviation of the random variable Y, which represents the total revenue from the vending machine on a given day, you will need to use the mean and standard deviation of X and the price per bottle of soda.

The mean of Y can be calculated using the formula:

mean of Y = mean of X * price per bottle

Plugging in the given values, we get:

mean of Y = 50 * $1.50 = $75

So the mean of the random variable Y, which represents the total revenue from the vending machine on a given day, is $75.

The standard deviation of Y can be calculated using the formula:

standard deviation of Y = standard deviation of X * price per bottle

Plugging in the given values, we get:

standard deviation of Y = 15 * $1.50 = $22.50

So the standard deviation of the random variable Y, which represents the total revenue from the vending machine on a given day, is $22.50.

Therefore, the mean and standard deviation of Y, the total revenue from the vending machine on a given day, are $75 and $22.50, respectively.

help please very easy proportional relationship due hurry please than u!

Answers

1) h=1/5 k

(10/2 = 1/5, 20/4 = 1/5... etc)

2) k=5/4 h

(5/4 = 5/4, 10/8=5/4... etc)

3) h=5/1 k

(25/5 = 5/1, 30/6 = 5/1 ... etc)

Hope this helps!

1.6y+y-4/15y+1 1/6y=2 1/3 pls help

Answers

The simplification of the given equation is -630y² + 81y + (+2.6y) * 90y² = 0.

What is the domain of the function?

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

We have,

1.6y+y-4/15y+7/6y=21/3

Move all terms to the left:

1.6y+y-4/15y+7/6y-(21/3)=0

Domain of the equation: 15y!=0

y!=0/15

y!=0

y∈R

Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R