Find the product of all real values of r for which 1/2x=r-x/7

Answers

Answer 1

Answer:

[tex]r = \±\sqrt{14[/tex]

[tex]Product = -14[/tex]

Step-by-step explanation:

Given

[tex]\frac{1}{2x} = \frac{r - x}{7}[/tex]

Required

Find all product of real values that satisfy the equation

[tex]\frac{1}{2x} = \frac{r - x}{7}[/tex]

Cross multiply:

[tex]2x(r - x) = 7 * 1[/tex]

[tex]2xr - 2x^2 = 7[/tex]

Subtract 7 from both sides

[tex]2xr - 2x^2 -7= 7 -7[/tex]

[tex]2xr - 2x^2 -7= 0[/tex]

Reorder

[tex]- 2x^2+ 2xr -7= 0[/tex]

Multiply through by -1

[tex]2x^2 - 2xr +7= 0[/tex]

The above represents a quadratic equation and as such could take either of the following conditions.

(1) No real roots:

This possibility does not apply in this case as such, would not be considered.

(2) One real root

This is true if

[tex]b^2 - 4ac = 0[/tex]

For a quadratic equation

[tex]ax^2 + bx + c = 0[/tex]

By comparison with [tex]2x^2 - 2xr +7= 0[/tex]

[tex]a = 2[/tex]

[tex]b = -2r[/tex]

[tex]c =7[/tex]

Substitute these values in [tex]b^2 - 4ac = 0[/tex]

[tex](-2r)^2 - 4 * 2 * 7 = 0[/tex]

[tex]4r^2 - 56 = 0[/tex]

Add 56 to both sides

[tex]4r^2 - 56 + 56= 0 + 56[/tex]

[tex]4r^2 = 56[/tex]

Divide through by 4

[tex]r^2 = 14[/tex]

Take square roots

[tex]\sqrt{r^2} = \±\sqrt{14[/tex]

[tex]r = \±\sqrt{14[/tex]

Hence, the possible values of r are:

[tex]\sqrt{14[/tex] or [tex]-\sqrt{14[/tex]

and the product is:

[tex]Product = \sqrt{14} * -\sqrt{14}[/tex]

[tex]Product = -14[/tex]


Related Questions

Linda had breakfast in a café. It cost $12.40. She paid with a $20 bill.

How much change did Linda get? Estimate first, then calculate the exact amount.

Answers

Around 8$ back. The exact amount would be 7.60$
estimate $8.00
calculate $7.60

Given that a senior citizen suffers from anxiety, what is the probability that he or she also suffers from sleep disorder

Answers

Answer:

Probability [also suffers from sleep disorder] = 0.5555 (Approx)

Step-by-step explanation:

Note:

Missing

Sleep disorders =  92%

Suffer from anxiety = 9%

Both sleep disorders and anxiety = 5%

Computation:

Probability [also suffers from sleep disorder] = 5% / 9%

Probability [also suffers from sleep disorder] = 0.5555 (Approx)

Find the value of x so that L is parallel to M. State the converse used!


50 Points! please help and show work!

Answers

Answer:

6 degrees

Step-by-step explanation

Find the diagram attached. In Line geometry, there is a theorem that states that the sum of the adjacent interior angles is 180 degrees. According to the diagram, the adjacent interior angles are 7x- 15 and 24x + 9.

The sum of this angles must give 180 degrees as shown;

7x-15 + 24x + 9 = 180

7x+24x-15+9 = 180

31x-6 = 180

31x = 180+6

31x = 186

x = 186/31

x = 6

Hence the value of x is 6 degrees

The students in Mrs. Plumas two classes wrote a total of 200 letters to their pen pals. Every student wrote 4 letters. How many students are in each class, if the classes are equal in size?

Answers

Answer:

50

Step-by-step explanation:

200/4=50

There are 25 students in each class.

What is an expression?

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

Let's assume that there are x students in each class.

Since there are two classes, the total number of students is 2x.

Now,

Since every student wrote 4 letters.

The total number of letters written = 4 x the number of students.

200 = 4 x (2x)

200 = 8x

x = 200/8

x = 25

Therefore,

There are 25 students in each class.

Learn more about expressions here:

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The area of a regular hexagon inscribed in a circle with radius 5 is what . Round your answer to the nearest whole number.

Answers

Answer:

Area of regular hexagon inscribed in circle = 64.95

Step-by-step explanation:

Given:

Radius = 5 unit

Find:

Area of regular hexagon inscribed in circle

Computation:

Area of regular hexagon inscribed in circle = 6[1/2][r²sin60]

Area of regular hexagon inscribed in circle = 6[1/2][5²(0.866)]

Area of regular hexagon inscribed in circle = 64.95

What is 3.5 x 4.95? need help on this

Answers

Answer:

3.5 x 4.95 = 17.325

Step-by-step explanation:

May I have brainliest please? :)

Answer:

17.325

we know this is correct because five times three and a half is near this so we know its correct

-3/8 - 7/8 =
explicar el procedimiento por favor ​

Answers

Answer:

-1/4

Step-by-step explanation:

-3/8 - 7/8= 4/8=1/2

A summer camp wants to hire counselors aides to fill its staffing needs at minimum cost

Answers

Answer:

8 counselors and 12 aids

Step-by-step explanation:

minimum number of staff to run camp = 20

Ratio of counselors to aids to work together = 2:3

To get the multiply factor = 20 / (2 counselors + 3 aids) = 20 / 5 =4

minimum number of counselors needed = 4 x 2 = 8 counselors

minimum number of aids needed = 4 x 3 = 12 aids

Find QS
7
22
19
6
none are correct

Answers

Answer:

-10

Step-by-step explanation:

None of the above

Answer:

QS = 19

Step-by-step explanation:

4x - 5 = 2x - 5 + 12

2x = 12

x = 6

QS = 19  

*NEED ANSWER ASAP* *GIVING AWAY 10 POINTS*

A horseshoe weighs 8.2 ounces. The nails make up 0.2 of that weight. What is the weight of the horseshoe without the nails?

A. 1.64 oz
B. 6.56 oz
C. 9.84 oz
D. 16.4 oz

Answers

Answer: A horseshoe weighs 8.2 ounces The nails in the horseshoe weigh 0.12 ounces.

Step-by-step explanation: B should be your answer have a great day :)

Answer:

B

Step-by-step explanation:

i did 8.2 divided by 20 percent ( .2)

then subtracted

equal 6.56

The perimeter of a kite is 50 mm. The length of one of its sides is 1 mm more than twice the length of another. Find the length of the LONGEST side of the kite. Only type the number of the longest side. *

Answers

Answer:

17 mm

Step-by-step explanation:

P = 50 mm

2x + 1 + x = 25

x = 8

2(8) + 1 = 17 mm

The length of the longest side is 17 mm

If Toni is trying to calculate her net worth, which of the following items would go on the liabilities list? *
A. Original sale price of her car
B.Her Mortgage
C.Savings account balance
D. Value of her 401(k) plan​

Answers

Answer:

B

Step-by-step explanation:

The only item that will serve as a liability is Her Mortgage. Option B is correct

Liabilities can be termed as money owned by a person or an amount of money borrowed with the intention to pay back after a period of time.

If Tony is trying to calculate her net worth, then we need to select a property that will serve as a debit for him instead of credit.

From the listed option, the only item that will serve as a liability is Her Mortgage

Learn more here: https://brainly.com/question/14921529

Karen made $288 for 18 hours of work,
At the same rate, how much would she make for 13 hours of work?

Answers

Answer:

She would make 500,000 or else she will speak to the manager.

Step-by-step explanation: Karen will speak to her manager and torture her manager until the manager gives her the money.

Answer: 208

Step-by-step explanation:

$288 ÷ 18 = 16 < 16 would be the amount she gets in 1 hour.

The question asks how much she would make for 13 hours

All you do is 16 x 13 and your answer is 208 :D

I hope this helped ill simplify it for you

You divide 288 by 18 then you take your answer of 16 and multiply it with 13 which you get 208

Hope it helped :D

WILL MARK BRAINLIEST
Heyyy no funny buisness i need answes ASAP

Max ran 5 miles on Thursday. One mile is equal to 5,280 feet. Which proportion can be used to determine how many feet, x, Max ran on Thursday?

Answers

5 miles on Thursday, with one mile=5,280 ft. You do 5 multipled by 5,289 which you get 26,499

Please help I will brainliest!! Really urgent!!

and tell you me how you go it, not just the answer please!❤️

Answers

Answer:

11x + 5

Step-by-step explanation:

Hope this helps!!!

Here is the answer its an attachment below!
I hope this helps!

10x +7 = -3х – 3 help guys

Answers

Answer:

x = -10/13

Step-by-step explanation:

10x + 7 = -3x - 3

Add 3x to both sides

10x + 3x + 7 = -3x + 3x - 3

13x + 7 = 0x - 3

13x + 7 = -3

Subtract 7 from both sides

13x + 7 - 7 = -3 - 7

13x + 0 = -10

13x = -10

Divide both sides by 13

13x ÷ 13 = -10 ÷ 13

1x = -10/13

x = -10/13

What is the slope of the line whose equation is 2y=3x+4

Answers

Answer:

3/2

Step-by-step explanation:

use the slope-intercept formula y=mx+b to find the slope

hope this helped♥

Answer:

3/2

Step-by-step explanation:

If you divide both sides by 2 to convert to y=mx+b, you get y=3/2x+2. M is the slope, which means that the slope is 3/2.

16) Mrs. Mamie wants to travel 390 miles on a highway. She drives 130 miles in 2 hours. If she has 7 hours to travel at that rate, will she arrive at her destination on time? Explain.







17) You can buy 5 cans of green beans at the Village Market for $2.60. You can buy 10 of the same cans of beans at Sam’s Club for $7.70. Which place is the better buy? Explain.







Page 33

5) Benjamin wants to buy a video game that costs $24, but he only wants to spend 40% of his savings. How much must Benjamin save in order to buy the game?





There are 60 members in a music club. 25% of them like jazz, 15% of them like pop music, 20% of them like rock music and 50% of the rest like classical music. How many members enjoyed classical music?






A total of 48 students sat for a mathematics examination. Only 75% of them passed. How many students passed the examination?





During an election, Albert received 60% of the 30 votes cast. Anthony received the remaining votes. How many more votes did Albert receive?






Six people can pack 1500 boxes in 4 days. At the same rate, how many boxes can eight people pack in 6 days?







If 5 workers complete one task in 7 days, then how many days will 7 workers take to complete the same task?

Answers

Answer:

Mrs Mamie will arrive at her destination on time !

Step-by-step explanation:

Mrs Mamie drives 130miles in 2 hours that means 65 miles/h

During 7 hours she travels 65*7=455 miles that definetely is more than 390 miles as necessary.

SO YES, Mrs Mamie will arrive at her destination on time !

What is the answer i just put something can you’ll plz help mhee fast❤️

Answers

Answer:

This is for sure B. Non-proportional

Step-by-step explanation:

The numbers on the left side go down every time, the way you can tell instantly that this is non-linear and hence non-proportional is because the numbers on the left start, then go down, then go up,

May I have brainliest please? :)

Suppose A stock is worth $40. It goes up 10%. how much is it worth now?

Answers

Answer:

$44

Step-by-step explanation:

10% of 40 is 4

40+4=44

hope this helps :3

if it did pls mark brainliest

The table of values models the quadratic function y = x2 + 7x – 9. What are the missing y-values in the table for the x-values?

Answers

The answer is letter B.

y = x² +7x-9

y= (-2)²+7(-2)-9

y=4+-14-9

y=-19

y=(-1)²+7(-1)-9

y=1+-7-9

y=-6+-9

y= -15

y=(0)²+7(0)-9

y=0+0-9

y=-9

y=(1)²+7(1)-9

y=1+7-9

y=8-9

y= -1

y=(2)²+7(2)-9

y=4+14-9

y=18-9

y=9

The missing values of the given quadratic function are option (b)-19,-15,-9,-1,9

What is a quadratic function?

Quadratic function is an function which contains one unknown variable and the highest power of this unknown variable is 2. Let x be the unknown variable then the quadratic function y in x is given by

y = ax²+bx+c, where a, b, c are constants and a≠0

Given that  a quadratic function y is:

y = x² +7x -9

Value of y  when x = -2

y(-2) =  (-2)² +7(-2) -9 = -19

Value of y  when x = -1

y(-1) =  (-1)² +7(-1) -9 = -15

Value of y  when x = 0

y(0) =  (0)² +7(0) -9 = -9

Value of y  when x = 1

y(1) =  (1)² +7(1) -9 = -1

Value of y  when x = 2

y(2) =  (2)² +7(2) -9 = 9

The missing values in the table are -19,-15,-9,-1,9

Therefore, option b is correct option.

Also, Learn more about the quadratic functions from  the link below:

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Find the value of r so the line that passes through each pair of points has the given slope.
Point 1:(-7,2)
Point 2:(-8,r)
m = -5

Answers

Answer:

7

Step-by-step explanation:

[tex]\frac{r - 2}{-8+7} = -5[/tex]

r - 2 = - 5(- 1) ⇒ r = 7

There are (36)2 ⋅ 30 candies in a store. What is the total number of candies in the store? (5 points)


A. 3 to the power of 3

B. 3 to the power of 4

C. 3 to the power of 8

D. 3 to the power of 12

Answers

Answer:

i thibbnk

Step-by-step explanation:

For what value of a is the volume of the tetrahedron formed by the coordinate planes and the plane (x/a) (y/10) (z/6)

Answers

This question is incomplete, the complete question is;

For what value of a is the volume of the tetrahedron formed by the coordinate planes and the plane (x/a) + (y/10) + (z/6) = 1 equal to 10?

Answer: the value of a is 1

Step-by-step explanation:

Given that;

Volume of tetrahedron bounded by plane (x/a) + (y/10) + (z/6) = 1

and coordinate plane is; V = 1/6|abc|

(x/a) + (y/10) + (z/6) = 1

volume = 10

so

10 = 1/6 | a × 10 × 6 |

60 = a × 10 × 6

60 = 60a

a = 60 / 60

a = 1

Therefore the value of a is 1

If (92)P = 98, what is the value of p? (5 points) 2 03 04 O 6​

Answers

Answer: 1.065

Step-by-step explanation:

(92)P = 98

98/92= 1.0652

Therefore 92(1.0652) = 97.9984

If we round it up it’s about 98

what percentage of 25kg is 15kg​

Answers

Answer:

1.6 repeating

Step-by-step explanation:

25 divided by 15 is 1.6666... and to check your math you could multiply that answer by 15, and that would give you 25

15kg is 60 percent of 25kg, which means that if we take 25kg and divide it into 100 parts, 60 of those parts will be 15kg.

To calculate the percentage of 25kg that is 15kg, we can use the following formula:

percentage = (part / whole) * 100

In this case, the part is 15kg and the whole is 25kg. So, the percentage is:

percentage = (15kg / 25kg) * 100

= 60%

Therefore, 15kg is 60% of 25kg.

To understand this in more detail, let's break down the formula. The first part, (part / whole), is simply the fraction of the whole that is the part. In this case, the part is 15kg and the whole is 25kg, so the fraction is 15/25.

The second part, * 100, simply converts the fraction to a percentage. So, 15/25 * 100 = 60%.

In other words, 60% of 25kg is 15kg. This means that if we take 25kg and divide it into 100 parts, 60 of those parts will be 15kg.

To learn more about percent here:

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hi I want help . what is the prime factorization of 17.?​

Answers

Well, the prime factorization would be 17 itself! This happens because 17 is a prime number.

If we take another example, like 13 or any other prime number, this will occur. Since 1 isn't a prime number, nor composite number, we won't include 1. Therefore, the prime factorization of 13 would also be 13 itself.

What is the value of x.

Answers

Step-by-step explanation:

If TR=SR=ST

SO,

all angles are equal

one angle =180/3=60°

but,here,

In angle S =60°

7x+4=60

7x=60-4

7x=56

x=56/7

x=8°

Answer:

The RST[tex]\huge{\triangle}[/tex]  is same in all side,

it is equilateral triangle.

so each angel =180/3=60°

But,

According to the question,

7x+4=607x=60-47x=56x=56/7x=8

1. a. Anita hadoſ a bag of fertilizer left. She used

of what was left. What question about Anitas

fertilizer can be answered by calculating !!!

Answers

Answer:

hello your question is incomplete below is the complete question

answer : what part of the bag of fertilizer left was used by Anita

Step-by-step explanation:

Anita had 1/2 bag of fertilizer left

and she used (3/4  of the fertilizer

that means she used ( 3/4 * 1/2 ) bag of fertilizer

hence the question about  Anita's fertilizer that can be answered is ; what part of the bag of fertilizer left was used by Anita

A cost regular sells for 59.00 it is on sale 20% what is the sale price of the coat

Answers

Answer:

ll.8 dollars

Step-by-step explanation:

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