Mathematics High School

simplify into one fraction
7/x-3 + 3/x-5

simplify into one fraction
-5/x-3 - -4.x+2

simplify into one fraction
6/x+7 - 3/x-2

Answers

Answer 1

To simplify the given expressions into one fraction, we find a common denominator for each set of fractions, adjust the numerators accordingly, and then combine the numerators over the common denominator.

To simplify the given expressions into one fraction, we need to find a common denominator and combine the fractions accordingly. Let's go through each expression step by step.

For the expression 7/x-3 + 3/x-5, the common denominator would be (x-3)(x-5). We need to multiply each fraction by the denominator that it's missing to get common denominators, and then sum the numerators over the common denominator.

The expression -5/x-3 - (-4)/(x+2) involves subtracting fractions. To simplify, we again find a common denominator, which is (x-3)(x+2), and proceed similarly to the first expression.

For 6/x+7 - 3/x-2, the common denominator is (x+7)(x-2). We perform the same process of equating denominators and combining.

To illustrate with the first expression:
(7(x-5))/((x-3)(x-5)) + (3(x-3))/((x-3)(x-5)) = (7x - 35 + 3x - 9)/((x-3)(x-5))

Combine the numerators to get a single fraction:

(10x - 44)/((x-3)(x-5))

Apply the same approach to the other two expressions to get them into a single fraction form.

Related Questions

Which number supports the given conjecture?

If a number is divisible by both 3 and 4, then the number is also divisible by 6.


A.
18

B.
42

C.
48

D.
64

Answers

The answer is C.

48/3 = 16
48/4 = 12
48/6 = 8


A school did a survey among 100 students to find their sports preferences. The students were asked about their preferences for soccer or volleyball. Out of the total 80 people who liked soccer, 30 also liked volleyball. There were 45 people who liked volleyball.

Part A: Summarize the data by writing the values that the letters A to I in the table below represent. (5 points)


Like soccer
Do not like soccer
Total
Like volleyball
A
D
G
Do not like volleyball
B
E
H
Total
C
F
I


Part B: What percentage of the survey respondents did not like either soccer or volleyball? (3 points)

Part C: Do the survey results reveal a greater dislike for soccer or volleyball? Justify your answer. (2 points)

Answers

Asked and answered elsewhere.
https://brainly.com/question/9914822

_____
A picture of your table would be most helpful.

ANYONE WHO KNOWS SURFACE AREA!!!

I need help urgently!

Answers

[tex]A_1=\dfrac{1}{2}\cdot6\cdot5.2=15.6\ cm^2\\\\A_2=\dfrac{1}{2}\cdot6\cdot5=15\ cm^2\\\\A=A_1+3A_2\to A=15.6+3\cdot15=15.6+45=\boxed{60.6\ cm^2}[/tex]

"when the population standard deviation is unknown, sample size is less than 30, and the population has a normal or near-normal distribution"

Answers

The population standard deviation is unknown, sample size is less than 30, and the population has a normal or near-normal distribution.

The function f(x) = 12x + 50 gives the amount of money a worker earns for working x hours per week. What is the inverse function?

Answers

12x + 50 = 62 but you have to multiply x by 12. I don't know what x is so maybe subtract 12 and 50 to get x. 50 - 12 = 38/ 38 x 12 = 456, then divide that by 50. 456 / 50 = 9.12, round up or down and get 9. 9 is your answer!!!


                                                               

You buy a new yoga ball. The ball has a diameter of 26 inches. What is the volume of the ball? Use 3.14 for pi. Round your answer to the nearest hundredth.

Answers

the formula for volume of a ball is:

V = 4/3 x PI x r^3
 we are told PI = 3.14

the diameter is 26 inches so r ( radius )= 26 / 2 = 13 inches

 now we have V = 4/3 x 3.14 x 13^3

V = 9198.11 cubic inches

Answer:

The volume of the ball is [tex]9,198.11\ in^{3}[/tex]

Step-by-step explanation:

we know that

The volume of a sphere (yoga ball) is equal to

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

In this problem we have

[tex]r=26/2=13\ in[/tex] -----> the radius is half the diameter

substitute

[tex]V=\frac{4}{3}(3.14)(13^{3})=9,198.11\ in^{3}[/tex]

A recipe for cake calls for 5.25 deciliters of milk. How many liters of milk are needed for the cake?

Answers

To convert the amount of milk from deciliters to liters we proceed as follows:
1 liter = 10 deciliters
therefore the amount of liters used in making the cake will be found as follows:
5.25/10×1=0.525 liters

Answer: 0.525 liters

Write the standard equation for a circle with center (−6, −8), that passes through (0, 0)

Answers

Standard equation:  (x-h)^2 + (y-k)^2 = r^2

Here,                        (0-[-6])^2 + (0-[-8])^2 = r^2
Find r:                           36        +   64         = 100, so r = 10

Then the desired equation is (x+6)^2 + (y+8)^2 = 10^2

the perimeter of this figure is 42.5 cm. Find the area of this figure.

Answers

the picture in the attached figure

let
AB=x

we know that
perimeter of the figure=10*x
perimeter=42.5 cm
so
42.5=10*x
x=42.5/10
x=4.25 cm

area of the figure=area of rectangle +area of square
area of rectangle=4.25*(4.25*3)----> 54.1875 cm²
area of square=4.25²----> 18.0625 cm²

area of the figure=54.1875+18.0625-----> 72.25 cm²

the answer is
72.25 cm²

Answer:

72.25

Step-by-step explanation:

I just took the test and got it correct

What is the y-intercept of the function f(x) = –2/9 + 1/5

Answers

The equation has no X variable so whatever that adds up to becomes the y-intercept. 

- 2/9 + 1/5 >> - 10/45 + 9/45 = - 1/45 


Your y-int is - 1/45 or (0, - 1/45)

What is the sum os the interior angles of the polygon?

Answers

to find the suum the formula is (n - 2) x 180 degrees

1/2g^2 + 7/2 + 3g^2- 4/5g + 1/4

Answers

For this case we have the following expression:
 1 / 2g ^ 2 + 7/2 + 3g ^ 2- 4 / 5g + 1/4
 The first thing we must do is to group terms with the same degree:
 g ^ 2 (1/2 + 3) - 4 / 5g + (7/2 + 1/4)
 Then, rewriting we have:
 (7/2) g ^ 2 - (4/5) g + (15/4)
 Answer:
 (7/2) g ^ 2 - (4/5) g + (15/4)
Final answer:

The expression [tex]1/2g^2 + 7/2 + 3g^2 - 4/5g + 1/4[/tex]5/4 by combining like terms, which include the [tex]g^2[/tex]s and the constants.

Explanation:

The student's question involves combining like terms and simplifying a polynomial expression in mathematics. The expression provided is [tex]1/2g^2 + 7/2 + 3g^2 - 4/5g + 1/4.[/tex]ed to combine like terms, which involves adding or subtracting the coefficients of terms with the same degree.

First, combine the g2 terms (1/2g2 + 3g2) to get 7/2g2. Next, the constant terms (7/2 + 1/4) are combined to yield 15/4. The term with g, which is -4/5g, does not have a like term, so it remains as it is. After combining like terms, the simplified expression is 7/2g2 - 4/5g + 15/4.

Need help to write equations for 5, 6 & 7

Answers

6)
A quadratic function has the form
y = ax^2 + bx + c

Use point (3, 5) in the equation above:

5 = a(3^2) + 3b + c
5 = 9a + 3b + c
9a + 3b + c = 5     Equation 1

Use point (4, 3) in the equation above:

3 = a(4^2) + 4b + c
16a + 4b + c = 3    Equation 2

Use point (5, 3) in the equation above.

5 = a(5^2) + 5b + c
25a + 5b + c = 5       Equation 3.

Now solve the system of equations of equations 1, 2, and 3 to find the coefficients, a, b, and c.

9a + 3b + c = 5
16a + 4b + c = 3
25a + 5b + c = 5

Subtract the first equation from the second equation.
Subtract the second equation from the third equation.
You get
7a + b = -2
9a + b = 2

Subtract the first equation above from the second equation to get.
2a = 4
a = 2

Substitute:
7a + b = -2
7(2) + b = -2
b = -16

9a + 3b + c = 5
9(2) + 3(-16) + c = 5
18 - 48 + c = 5
c - 30 = 5
c = 35

The equation in standard form is

y = 2x^2 - 16x + 35

We can find it in vertex form:

y = 2(x^2 - 8x) + 35

y = 2(x^2 - 8x + 16) + 35 - 32

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

Javier is comparing two checking accounts. One has a monthly fee of $10 and a per-check fee of $0.10, and the other has a monthly fee of $12 and a per-check fee of $0.05. What is the minimum number of checks Javier needs to write for the second bank to be a better option?

Answers

When Javier writes 40 on both accounts they cost him the same amount of money so it should be 41.

Javier needs to write 41 checks for the second bank to beat better

Answer:

41 is the answer for this question. Hope this helps.

Step-by-step explanation:

(apex)

HELPPPPPPPPPPPPP and explain

Answers

Remark
There are a number of ways you could do this. The most straight forward might be to simply multiply the second equation to get the answer.

Step One 
Multiply the second equation by 2
2(2x^2 + 1/y^2 = 12)       Remove the brackets.
4/x^2 + 2/y^2 = 12 * 2 
4/x^2 + 2/y^2 = 24         

Step Two
Add  the new equation and the first original equation
1/x^2 - 2/y^2 = 1
4/x^2 + 2/y^2 = 24

5 / x^2 = 1 + 24
5/x ^2 =   25       Divide both sides by 5
1/x^2 = 5            Reciprocate the x^2 and the 5 (That means turn them upside down.

x^2 = 1/5
Take the square root of both sides.
x = +/- 1/sqrt(5)  Rationalize the denominator.
[tex]{x = } \frac{1}{ \sqrt{5} } * \frac{ \sqrt{5} }{ \sqrt{5} }\\ \\{x = } \frac{ \sqrt{5} }{5} [/tex]

Step 3
Place this answer in for x^2 to get y^2. and then y

1/(1/5) - 2/y^2 = 1

Interlude
You can use your calculator to see what 1/(1/5) is. Change the 1/5 to 0.2
1/0.2 = 5 Just put it in as
1
÷
0.2
=
You should get 5

Continued
5 - 2 / y^2 = 1 Subtract 5 from both sides.
 - 2/y^2 = 1 - 5
-2 / y^2 = - 4 Divide both sides by - 2
1 / y^2 = -4/-2
1 / y^2 = 2    Now reciprocate both sides.
y^2 = 1/2      Take the square root.
y = +/-  1/sqrt(2)  And rationalize the denominator
y = +/-   sqrt(2) / 2 Done the same way as for the x.

There's only 1 there. I'll let you find it.

Need help on this question

Answers

Hello,
Please, see the attached file.
Thanks.

Henry can write 5 pages of his novel in 3 hours. at this rate, how many pages can henry write in 888 hours?

Answers

If he writes 5 pages in 3 hours, you take 888 divide it by 3 and get 296. Then, you write 5 and 3 as a fraction, 5/3. Multiply both by 296 and you get 1480 pages in 888 hours. 

I hope this helps!
Write and solve an equation of ratios:

 5 pages          p
------------- = -------------    Cross multiply.  Solve for p.
  3 hrs            888 hrs

Multiply the binomial and find the coefficients
(X+y)^1=__×+__y

(×+y)^2=__x^2+__xy+__y^2

(X+y)^3=__×^3+__×^2y+__y^3

(×+y)^4=__×^4+__x^3y+__x^2y^2+__xy^3+__y4

Answers

We can use the pascal triangle to solve this problem.
 
 For this case, rewriting each binomial we have:
 (x + y) ^ 1 = 1x + 1y

 (x + y) ^ 2 = 1x ^ 2 + 2xy + 1y ^ 2

 (x + y) ^ 3 = 1x ^ 3 + 3x ^ 2y + 3xy ^ 2 + 1y ^ 3

 (x + y) ^ 4 = 1x ^ 4 + 4x ^ 3y + 6x ^ 2y ^ 2 + 4xy ^ 3 + 1y4

92.4 is 150% of what number?

Answers

1. We assume, that the number 92.4 is 100% - because it's the output value of the task. 
2. We assume, that x is the value we are looking for. 
3. If 92.4 is 100%, so we can write it down as 92.4=100%. 
4. We know, that x is 150% of the output value, so we can write it down as x=150%. 
5. Now we have two simple equations:
1) 92.4=100%
2) x=150%
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
92.4/x=100%/150%
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for what is 150% of 92.4

92.4/x=100/150
(92.4/x)*x=(100/150)*x       - we multiply both sides of the equation by x
92.4=0.666666666667*x       - we divide both sides of the equation by (0.666666666667) to get x
92.4/0.666666666667=x 
138.6=x 
x=138.6

now we have: 
150% of 92.4=138.6

Answer:

Number is 61.6

Step-by-step explanation:

Given  : 92.4 is 150%.

To find : what number.

Solution : We have given 92.4 is 150%.

Let the number  = x

According to question :

150% of x = 92.4

[tex]\frac{150}{100} *x[/tex] = 92.4

On multiplying both sides by 100

150 x = 92.4 * 100.

150 x = 9240

On dividing both sides by 150 .

x = [tex]\frac{9240}{150}[/tex].

x = 61. 6

Therefore, Number is 61.6

A carpenter earns $18 an hour for a regular work week (40) hours. He earns time and a half for overtime. The weekly wage function is W(h)={                  18h                                         040} where h is the number of hours worked for the week. Find the wage if the carpenter worked 42.5 hours in the week

Answers

18×40=720 regular time
18×1.5=27 overtime per hour
27×2.5= 67.5 overtime

$720+$67.50=$787.50

Final answer:

To find the carpenter's weekly wage after working 42.5 hours, we calculate the regular pay for 40 hours at $18 per hour, which is $720, and then add the earnings from 2.5 hours of overtime at time and a half ($27 per hour), which is $67.5. The total weekly wage is $787.5.

Explanation:

To calculate the weekly wage of the carpenter who worked 42.5 hours, with $18 per hour for the first 40 hours and time and a half for overtime, we will use the wage function provided: W(h) = 18h for hours up to 40, and for hours above 40, it's (18 × 1.5) × (h - 40). Let's apply this to the 42.5 hours worked.

The carpenter's earnings for the regular 40 hours are $720 (which is 40 hours × $18). For the 2.5 hours of overtime, he earns time and a half, which is $27 per hour (18 × 1.5). The overtime earnings are $67.5 (2.5 hours × $27). So, the total wage is:

$720 + $67.5 = $787.5

Therefore, the carpenter's weekly wage for working 42.5 hours at the given rate is $787.5.

what is the volume , in cubic units , of a pyramid of height 8 and a square base of length 15?

Answers

pretty sure its 48 cm3

What is the sum or difference 6x^7+8x^7

Answers

Answer: 14x^7

You add the coefficients (numbers to the left of the variable terms) to get 6+8 = 14 which is the coefficient of the final answer. The x^7 stays the same. It's like saying "we have 6 apples added to 8 apples, so there are 14 apples overall". Replace "apples" with "x^7" and it's the same idea.
Final answer:

The sum of the expressions 6x^7 and 8x^7 is 14x^7. This follows the simple rule of addition with similar terms, where the coefficients are added together while the variable remains the same.

Explanation:

The sum of 6x7 and 8x7 follows the usual rules of addition, it treats similar terms in a similar way to ordinary numbers. To combine these expressions, you simply add or subtract the coefficients (the number parts), while keeping the variables (the letter parts) the same. In this case, the variable is x7. Thus, adding the coefficients 6 and 8 gives you 14, and you keep the x7 the same. The sum is therefore 14x7.

Learn more about Adding Polynomials here:

https://brainly.com/question/30136851

#SPJ3

PLEASE HELP!!!!!!!!!!!!!!!!! What is the simplified form of the expression k^3(k^7/5)^-5

A. k^4
B. 1/k^1/4
C. k^1/4
D. 1/k^4

Answers

(k^3)(k^(7/5))^-5
= (k^3)(k^(7/5*-5))
= (k^3)(k^-7)
= k^(-7+3)
= k^-4
= 1/k^4
Which is choice D.

If ΔGET≅ΔMAP, then what corresponding parts are congruent? segment TG and segment AM ∠T and ∠P segment MP and segment ET ∠E and ∠M

Answers

Answer:

2nd Option is correct that is ∠T and ∠P.

Step-by-step explanation:

We are given that ΔGET ≅ ΔMAP

We need to find Congruent part from the given options.

Since, we are given the figure of the congruent triangles with marking not any instruction with which vertex is congruent to which vertex.

So, The Given Name of the Congruent triangle.

We deduce that

G ↔ M

E ↔ A

T ↔ P

Using this we get following congruent parts,

GE ≅ MA , GT ≅ MP and ET ≅ AP

∠G ≅ ∠M ,  ∠E ≅ ∠A and ∠T ≅ ∠P.

Therefore, 2nd Option is correct that is ∠T and ∠P.

Answer:

∠T and ∠P

Step-by-step explanation:

A teacher asked her students to divide a large number by 50.
• Aslan divided the number by 50.
• Lucy divided the number by 5 and then divided the answer she got by 10.
• Jack divided the number by 10 and then divided the answer he got by 40.
Who among these got the correct answer assuming they did NOT make mistakes in division?

Answers

Answer:

c

Step-by-step explanation:

Final answer:

Aslan and Lucy got the correct answer of x/50, while Jack made a mistake in his calculation.

Explanation:

To find out who got the correct answer, we need to evaluate the division calculations of each student. Let's assume the large number is 'x'.

Aslan divided the number by 50, so his answer is x/50.

Lucy divided the number by 5 and then divided the answer by 10, so her answer is (x/5)/10 = x/50.

Jack divided the number by 10 and then divided the answer by 40, so his answer is (x/10)/40 = x/400.

Therefore, both Aslan and Lucy got the correct answer of x/50, while Jack made a mistake in his calculation.

Learn more about Division here:

https://brainly.com/question/37843448

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A jar contains 30 red marbles, 50 blue marbles, and 20 white marbles. you choose one marble from the jar at random. what is the theoretical probability of choosing a white marble?

Answers

30+50+20=100 = altogether marbles
P(white)= 20/100 =1/5
P(white)=1/5
[tex]|\Omega|=100\\ |A|=20\\ P(A)=\dfrac{20}{100}=\dfrac{1}{5}=20\%[/tex]

Write a formula for the sum of the first n terms in this series.

Answers

Let n=1 and evaluate the choices. You will find only one of them gives 1 as a result:
  A) 4n² - 3n

In a certain population, 95% of the people have rh-positive blood. suppose that two people from this population get married. what is the probability that they are both rh-negative, thus making it inevitable that their children will be rh-negative? web assign answer

Answers

P(rh-positive) = 95% = 0.95

Therefore,
P(rh-negative) = 1-P(rh-positive) = 1-0.95 = 0.05

Then,
P(rh-negative) for both parents = 0.05*0.05 = 0.0025

Final answer:

The probability that both partners in a marriage are Rh-negative in a predominantly Rh-positive population is 0.25% or 1 in 400, critical for understanding the risk of hemolytic disease of the newborn in subsequent pregnancies.

Explanation:

The probability that both people in a marriage are Rh-negative in a population where 95% of the people are Rh-positive is calculated using the complement. Assuming that 5% of the population is Rh-negative, we would calculate the probability that both parents are Rh-negative by multiplying the individual probabilities:

P(both Rh-negative) = P(one Rh-negative) × P(other Rh-negative) = 0.05 × 0.05 = 0.0025

Therefore, the probability that both people are Rh-negative, and thus all of their children would also be Rh-negative, is 0.25% or 1 in 400.

Rh factor and blood type compatibility are crucial in reproduction and transfusion medicine. Understanding these concepts can help prevent complications such as hemolytic disease of the newborn, which occurs during second or subsequent pregnancies due to sensitization of the Rh-negative mother's immune system to Rh-positive fetal cells from a previous pregnancy.

Please explain “ write the equation of the perpendicular bisector of rs point r is located at (-1,3) and point s is located at (3,1) “

Answers

Hi there!

First, we'll need to find the midpoint of RS in order to bisect it. Using the midpoint formula, we can determine that the midpoint of RS is (1,2). Then, we'll need to find the slope of RS, then find the opposite reciprocal of the slope of RS to find the slope of our new line because perpendicular lines have opposite reciprocal slopes. The slope of our new line is 2. Next, we can plug our values into point-intercept form to find the equation. 

WORK:
y - 2 = 2(x - 1)
y - 2 = 2x - 2
y = 2x

ANSWER:
D - y = 2x

Hope this helps!! :)
If there's anything else that I can help you with, please let me know!

PLEASE HELP AS SOON AS POSSIBLE!!!!!!!!!!!!!!!!!! |r+3| ≥7 solve the inequality (please show work and steps )

Answers

|r+3| = (r+3) when r ≥ -3 so for r ≥ -3
                        r + 3 ≥ 7
                               r ≥ 4
|r+3| = -(r+3) when r < -3 so for r < -3
                     -(r + 3) ≥ 7
                         r + 3 ≤ -7
                               r ≤ -10
The answer to this question is r ≤ -10, r ≥ 4
So the solution would be:
|r+3| = (r+3)
r + 3 ≥ 7
  r ≥ 4
|r+3| = -(r+3)
  -(r + 3) ≥ 7
   r + 3 ≤ -7
r ≤ -10
So the answer is r ≤ -10, r ≥ 4
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