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 errorThe 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]
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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?
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.
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?
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.
3.2x + 7.9 + 8.2 + 6.7x
Simplify the expressions. (not equations!)
Please help ASAP.
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?
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
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
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.
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
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]?
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.
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?
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.
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?
Answer:
x=1.5
Step-by-step explanation:
d) x + y = 42 X-6 = 5 (-6)
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.
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:
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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
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.
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.
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!!!!
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.
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:
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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?
Answer:
I believe the answer is $27.32
Find the value of x.
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.
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
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:
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
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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.
Sides given by
10x+2x+52x+3Opposite 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=7inOne 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 in2)
x + 5 with 2x - 3
It makes:
2x - 3 = x + 52x - x = 5 + 3x = 8The sides are:
8 + 5 = 13 and2*8 - 5 = 13 inCorrect answer choice is 1)
Which expression is equivalent to (7x+9y)2
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?
Please help me solve this problem ASAP
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.