Error Analysis A student added the rational
expressions as follows:
5x 7 5x 7(7) 5x + 49
+
+
x
x + 7
Describe and correct the error the student
12
x+7
Х
x+7
x+7

Answers

Answer 1

Rational expressions are expressions that can be represented as fractions

The solution to the sum of the rational expressions is [tex]\frac{5x^2 + 7x + 49}{x^2 + 7x}[/tex]

How to determine the error

The student operation is given as:

[tex]\frac { 5 x } { x + 7 } + \frac { 7} { x } = \frac { 5 x } { x + 7 } + \frac { 7 ( 7 ) } { x + 7 } = \frac{5x + 49}{x + 7}[/tex]

The student's error is that, he multiplied the numerator of 7/x by 7, and he added 7 to the denominator

The correction is as follows:

[tex]\frac { 5 x } { x + 7 } + \frac { 7} { x }[/tex]

Take the LCM

[tex]\frac { 5 x } { x + 7 } + \frac { 7} { x } = \frac{5x^2 + 7(x + 7)}{(x + 7)x}[/tex]

Open the brackets

[tex]\frac { 5 x } { x + 7 } + \frac { 7} { x } = \frac{5x^2 + 7x + 49}{x^2 + 7x}[/tex]

Hence, the solution to the sum of the rational expressions is [tex]\frac{5x^2 + 7x + 49}{x^2 + 7x}[/tex]

Read more about rational expressions at:

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Related Questions

An app brought in $2 million in revenue before giving 10% of its revenue to pay for the reward prizes. How much revenue did the app earn the store after paying for the reward prizes?

Answers

0.10x2000000=200000 so then 2000000-200000=1800000

Answer:

$1,800,000 dollars

Step-by-step explanation:

Given the following question:

10% of 2,000,000

An app brought in $2 million in revenue before giving 10% of that revenue to pay for prizes. We need to find how much revenue did the app earn AFTER the store paid for the reward prizes.

[tex]\frac{10\times2000000}{100} =10\times2000000=20000000\div100=200000[/tex]
10% of 2 million is 200,000.
[tex]2000000-200000=1800000[/tex]

The app earned "$1.8 million" after paying for the reward prizes.

Hope this helps.

In a certain clothing store, 3 shirts and 5 ties cost $60, and 2 shirts and 3 ties cost $39. What is the cost of each shirt? If s = the cost of a shirt and t = the cost of a tie, which system of equations represents the problem? 3s 5t = 60 and 2s 3t = 39 s t = 60 and 5s 8t = 99 3t 5s = 60 and 2t 3s = 39.

Answers

Answer:

ties cost $3

shirts cost $15

Step-by-step explanation:

s=shirts

t = ties

3 shirts and 5 ties cost $60:

3s+5t=60

2 shirts and 3 ties cost $39:

2s+3t=39

−2(3s+5t=60)

3(2s+3t=39)

−6s−10t=−120

6s+9t=117

add equations together:

−t = −3

t = 3

so ties cost $3, use either of the original equations to solve the price of shirts:

2s+3⋅(3)=392

s+9=392s=30

s=15

so shirts cost $15

Answer:

3s + 5t = 60 and 2s + 3t = 39

Step-by-step explanation:

How many ounces are in 2 1/4 pounds?

Answers

Answer:

36 ounces

Step-by-step explanation:

1 lb = 16oz

So just multiply 2 lb by 16 to get 32.

Then you can multiply 16 by 0.25 (a.k.a 1/4) OR divide 16 by 4

You get 4 ounces

Finally, add 32 and 4 to get your total of 36 ounces.

36 ounces.
1 pound= 16 ounces
1/4 pound= 4 ounces
16+16=32
32+4=36
36

3.2x + 7.9 + 8.2 + 6.7x
Simplify the expressions. (not equations!)
Please help ASAP.

Answers

Answer:

9.9x + 16.1

Step-by-step explanation:

SImplify using like terms

Simplify:

3.2x + 7.9 + 8.2 + 6.7x3.2x + 6.7x + 7.9 + 8.29.9x + 16.1

-Chetan K

Is square root of 0.49 a rational number?

Answers

Answer:

yes it is a rational number because the square root of 0.49 is 0.7

Step-by-step explanation:

Hope that helps!

A garden is going to be built in the city park in the shape of a parallelogram, with a rectangular walkway
running through it. The garden region is shown in the following figure. Find the area of the garden region by
finding the areas of the individual shapes shown in the figure.
78 ft
72 ft
30 ft
20 ft
Answer

Answers

Answer:

7,456 im only 9 but i think it's right.

Step-by-step explanation:

Answer:  The answer is 7,456!

Step-by-step explanation: 78 x 78 + 30 x 30 + 20 times 20 + 72 equals to 7456!

acks father drives to work in 30 min when driving at his usual speed. When traffic is bad, he drives 30mph slower and the trip takes one hour longer. How far is Jacks Fathers work from home in miles


me give brainliest

Answers

Answer:

Jack's fathers work is 1350 miles away from home

Step-by-step explanation:

Equation for trip 1:

Usual speed=x

Time=30 minutes

Formula for distance: d=st

d=30x

Equation for trip 2:

Speed= x-30

Time=90 minutes

d=90(x-30)

Now we solve for x using simultaneous equations:

30x=90(x-30)

x=45

Now to find d we sub in our new found value into one of the two equations (it doesn't matter which one)

d=30(45)

d=1350 miles

I NEED HELP PLZ ASAP , I AM SO STUCK ON THIS.

Answers

Function

d. 4f(t)

=4(t²+9)

=4t²+36

e. (f(t))²+8

=(t²+9)² + 8

= t⁴+18t²+81+8

= t⁴+18t²+89

Can anyone help please

Answers

Answer:

7

Step-by-step explanation:

love is = 4, because love + love = 8 meaning its 4+4

heart is = 5, because heart - 4(love) = 1

bird is = 3, because bear is = 9 since 5(heart) + 4(love) is bear, and 3 birds make  a bear.

Answer:

17

8 ÷ 2 = 4. love = 4.

heart - 4 = 1. heart = 5.

love 4 + heart 5 =9. bear =9

9÷3=3. birds = 3.

what is [tex]4\sqrt{16}[/tex]?

Answers

The square root of 16 is 4, so 4 times 4 equals 16

Your answer is 16 :)

The climate in which Jonah lives is mild all year long except during the hotter summer months. For 3 months out of the year, Jonah needs to use 4 portable fans to cool his home. If the electricity to use one fan costs 1 cent per hour and each fan is on for about 96 hours per month, what is his total electricity cost for the fans during one year? a. $6. 72 b. $3. 84 c. $11. 52 d. $2. 88 Please select the best answer from the choices provided A B C D.

Answers

Using proportions, it is found that his total electricity cost for the fans during one year is given by:

b. $3.84

What is a proportion?

A proportion is a fraction of a total amount.

In this problem, for 3 months, he uses 4 portable fans, and each fan is on for about 96 hours per month, hence the total number of hours he uses it is:

4 x 96 = 384 hours.

The cost is one one cent per hour, hence:

$0.01 x 384 = $3.84.

Which means that the total cost is of $3.84, and option b is correct.

More can be learned about proportions at https://brainly.com/question/24372153

Tom the painter is painting window frames on a house. He knows that the angle his ladder should make with the ground should be between 55° and 35° in order to be safe. Tom's ladder is 8m and he wishes to paint a window frame 6.3m above the ground.

Is Tom's ladder safe to use?

Answers

Answer:

Tom should use a ladder that is smaller or at the the same height of the window frame. Here it says that he is using a ladder that is taller than the window frame, and this can be very uncomfortable for the person who is using the ladder, so it would be recommendable for Tom to use a smaller ladder, probably a ladder that is only a few inches smaller or taller than the window frame. Using a ladder that is like this should be safe to use.

Step-by-step explanation:

Hope this helps =)

A farmer keeps a record of the weekly milk yield of his herd of seven cows over a period of six months. He finds that the mean yield is 24 litres. He buys another cow that he is told will produce 28 litres of milk a week. Work out the effect this will have on the mean milk yield of his cows.​

Answers

Answer:

A farmer keeps a record of the weekly milk yield of his herd of seven cows over a period of six months. He finds that the mean yield is 24 liters. He buys another cow that he is told will produce 28 liters of milk a week. Work out the effect this will have on the mean milk yield of his cows.​

Step-by-step explanation:

Hope it helps<3

Answer:

24.5 liters/week

Step-by-step explanation:

24 liters/week for 7 cows is 168 liters/week

Add 1 cow that produces 28 liters/week

The new total is 196 liters/week for 8 cows

(196 liters/week for 8 cows)/(8 cows) = 24.5 liters/week is the new mean.

Brett's fish tank can hold up to 10.5 gallons of water before it overflows. Brett has poured 9 gallons of water into his fish tank so far.

Let x represent how many more gallons of water Brett can pour into his fish tank. Which inequality describes the problem?

Answers

Answer:

x=1.5

Step-by-step explanation:

d) x + y = 42 X-6 = 5 (-6)​

Answers

Answer: X = -24 Y = 66

Step-by-step explanation:

5(-6) = -30

X = 6 - 30 = -24

Y = 42 + 24 = 66

Hello there, Today we will solve your math problem

[tex]{\huge{\boxed{\mathfrak{{Question}}}}[/tex]

[tex]x+y=42\\x-6=5(-6)[/tex]

________________

First off let's isolate [tex]x[/tex]

after doing that we can substitute [tex]x[/tex] for [tex]-12[/tex]

Here is our equation

[tex]-12+y=4[/tex]

solve for [tex]y[/tex] and we get that [tex]y=16[/tex]

________________

[tex]{\huge{\boxed{\mathfrak{{Answer}}}}[/tex]

[tex]{\boxed{x=-12}}[/tex][tex]{\boxed{y=16}}[/tex]Have a good day!

If f(1) = 0, what are all the roots of the function f (x) = x cubed 3 x squared minus x minus 3? Use the Remainder Theorem.

Answers

Remainder theorem tells about the remainder of division of a polynomial with x - a. The roots of given function are: 1, -1, -3

What is remainder theorem for polynomials?

If there is a polynomial p(x), and a constant number 'a', then

[tex]\dfrac{p(x)}{(x-a)} = g(x) + p(a)[/tex]

where g(x) is a factor of p(x)

For the given case, we've got:

[tex]f(x) = x^3 + 3x^2 -x - 3[/tex]

and

f(1) = 0

Thus, for a = 1, from remainder theorem, we get:

[tex]\dfrac{p(x)}{(x-a)} = g(x) + p(a)\\\\\dfrac{f(x)}{(x-1)} = g(x) + f(1)\\\\\dfrac{x^3 + 3x^2 - x - 3}{(x-1)} = g(x) + 0\\\\ \dfrac{x^2(x+3) -1(x+3)}{x-1} = \dfrac{(x^2-1)(x+3)}{(x-1)} = g(x)\\\\(x+1)(x+3) = g(x)[/tex]

Thus, the other factor of f(x) is g(x) = (x+1)(x+3)

And we have:

[tex]\dfrac{f(x)}{x-1} = g(x)\\\\f(x) = (x+1)(x+3)(x-1)[/tex]

Putting it equal to 0, we get:

[tex]f(x) = 0\\(x+1)(x+3)(x-1) = 0\\x = 1, -1, -3[/tex]

Thus,

The roots of given function are: 1, -1, -3

Learn more about polynomial remainder theorem here:

https://brainly.com/question/10488065

Answer:

A

Step-by-step explanation:

got it right on Edge 1943 whilst fighting the German Forces in Northern Italy while my friends were on the beaches of Normandy.

What is the constant of proportionality for the relationship shown in this table? PLEAAASE I WILL MAKE U BRAINLIEST​

Answers

Answer: 3

Step-by-step explanation:

Divide the x numbers by 3 to then get the y numbers

Example: 3 divided by 1 is 3, 6 divided by 2 is 3, and it goes on!

once again the final answer is 3

hope this helps!

In triangle RST, TU bisects angle T. If U is a point on RS, RU = 6,
RT = 9, and ST = 12, find RS.

Answers

Answer:

14.

Step-by-step explanation:

1. RS=RU+US, - US is unknown yet;

2. the property of bisector is:

RU/US=RT/ST;

3. according to the property above:

US=RU*ST/RT; US=12*6/9=8;

4. RS=RU+US; ⇒ RS=6+8=14.

Trevor earns $7. 80 an hour take home pay and works 20 hours each week. Trevor wants to buy a new laptop computer to take to college that costs $780. How many weeks will it take for Trevor to achieve his goal? a. 4 weeks b. 5 weeks c. 6 weeks d. 7 weeks Please select the best answer from the choices provided A B C D.

Answers

Answer:

5 weeks

Step-by-step explanation:

[tex]7.8*20x=780[/tex]

[tex]156x=780[/tex]

[tex]\frac{156x}{156}=\frac{780}{156}[/tex]

[tex]x= 5[/tex]

Hence, the correct answer is 5 weeks.

[RevyBreeze]

HELP NEEDED PLEASE!!!!

Answers

Answer:

B√134

Step-by-step explanation:

the answer is B(√134)

hope it helps

Answer:

B

Step-by-step explanation:

PLEASE ANSWER WILL GIVE BRAINLIEST!!!

Find the length of the three missing sides in the rhombus below.

Answers

Answer:

48

Step-by-step explanation:

All of the sides are 48 because a rhombus has equal sides.

The measure of y is 48.

What are Properties of Rhombus?The lengths of all four sides are equal.The two opposite sides are parallel.Angles opposite each other are equal.Diagonals intersect at right angles, or 90 degrees.The diagonals of a rhombus cut through its opposite angles.The total of two neighboring angles, i.e., 180°, is supplementary.

Given:

As, we know that Rhombus resemble property of Square which has all sides Equal.

Then, the four sides of Rhombus are also Equal.

Then, x=z and y= 48.

Hence, the measure of y is 48.

Learn more about Rhombus here:

https://brainly.com/question/27870968

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If Michael and Lmani go out to eat and their food costs 25.30 and there is a 8% meals tax how much is the meal?

Answers

Answer:

I believe the answer is $27.32

Find the value of x.

Answers

Answer:

25

Step-by-step explanation:

(2x+15)+x+90=180

3x=75

x=25

A student has some​ $1 and​ $5 bills in his wallet. He has a total of 11 bills that are worth ​$31. How many of each type of bill does he​ have? The student has enter your response here ​$1 bills and enter your response here ​$5 bills.

Answers

Answer:

6 $1 bills, 5 $5 bills

Step-by-step explanation:

Say the student has x $1 bills.

Then they have 11 - x $5 bills.

31 = 1 * x + (11 - x) * 5 = 55 - 4x

4x = 55 - 31 = 24

x = 6

So, they have 6 $1 bills and 11 - 6 = 5 $5 bills

Answer:

5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1. As you see those are eleven numbers/bills so your answer may be, The student has 5, 5$ bills and 6, 1$ bills. which makes up 31$.

Step-by-step explanation:

solve for me the slop

Answers

Answer: -1

Step-by-step explanation:

Take 2 random coords from the graph to find the slope

(0,4) and (2,2)

(4-2)/(0-2) = -1

Slope

Pick two points on the line

[tex]\tt slope=\dfrac{\Delta Y}{\Delta X}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

point 1: -4,5

point 2: 0,3

[tex]\tt slope=\dfrac{5-3}{-4-0}=\dfrac{2}{-4}=-\dfrac{1}{2}[/tex]

2. Kira's skateboard is 71 centimeters long. What is the length of her skateboard in millimeters? Show your work. Answer:​

Answers

Answer:

710

Step-by-step explanation:

1 centimeter = 0.1 mi millimeter so 71 centimeters= 710 millimeters

i'm in k12 and i just took the test too

hope this helps have a good day ^ω^

The length of Kira's skateboard in millimetres is 710 mm

What is unit conversion?

A unit conversion expresses the same property as a different unit of measurement.

Given that, Kira's skateboard is 71 centimetres long.

1 cm = 10 mm

Converting the units,

71 cm = 10×71 = 710 mm

Hence, the length of Kira's skateboard in millimetres is 710 mm

For more references on unit conversion, click;

https://brainly.com/question/19420601

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A quadrilateral is shown. One pair of opposite sides have lengths of 10 inches and (x + 2) inches. The other pair of opposite sides have lengths (x + 5) inches and (2 x minus 3) inches. Based on the measures shown, could the figure be a parallelogram? 1.Yes, one pair of opposite sides could measure 10 in., and the other pair could measure 13 in. 2.Yes, one pair of opposite sides could measure 10 in., and the other pair could measure 8 in. 3.No, there are three different values for x when each expression is set equal to 10. 4.No, the value of x that makes one pair of sides congruent does not make the other pair of sides congruent.

Answers

Sides given by

10x+2x+52x+3

Opposite sides must be equal

Let's check once

[tex]\\ \tt\hookrightarrow x+5=2x+3\implies x=2[/tex]

Find sides now

10in2+2=4in2+5=7in2(2)+3=4+3=7in

One pair of opposite sides are equal but others not .

It's a trapezium.

Answer:

1. Yes, one pair of opposite sides could measure 10 in., and the other pair could measure 13 in.

Step-by-step explanation:

The opposite pairs are:

1)

10 in with x + 2 inIt makes:x =+2 = 10 ⇒ x = 8 and both sides 10 in

2)

x + 5 with 2x - 3

It makes:

2x - 3 = x + 52x - x = 5 + 3x = 8

The sides are:

8 + 5 = 13 and2*8 - 5 = 13 in

Correct answer choice is 1)

Which expression is equivalent to (7x+9y)2

Answers

Answer:

[tex]49x^2+126xy+81y^2[/tex]

Step-by-step explanation:

Use the square of a binomial theorem

[tex](a+b)^2[/tex]= [tex]a^2+2ab+b^2[/tex]

Now expand the given equation:

[tex](7x+9y)^2=49x^2+126xy+81y^2[/tex]

Hope this helps :)

Have a great day!

4. In one week, Latrina received 18 snickers and 8 butterfingers
What is the ratio of butterfingers to snickers?

Answers

4:9
Butterfingers: 8
Snickers: 18
Create ratio 8:18
Simplify by dividing both by 2

Please help me solve this problem ASAP

Answers

Answer:

Quadrant 2

Step-by-step explanation:

A 90 °counterclockwise rotation, rotates the triangle left one quadrant. Currently the triangle is in quadrant 3.

Answer:

Question 9 right? Well then it would be in quadrant IV

Step-by-step explanation:

Since it is just 90 degrees counterclockwise it would go to the fouth quadrant.

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