Answers
Answer: This took me a long time to type, hope you read it and find it helpful and easy to understand...
1. [tex]x=1[/tex]
2. [tex]x=\frac{3}{2}[/tex]
3. [tex]x=1[/tex]
4. [tex]x=\frac{6}{5}[/tex]
Step-by-step explanation:
1.
[tex]\frac{1}{x}-\frac{x-2}{3x}=\frac{4}{3x}[/tex]
To make it easier to add / subtract fractions, we are looking for common denominators. I can see that if I move the fraction on the left with a denominator 3x to the right, I'll be able to add two equations with like denominator.
Let's add [tex]\frac{x-2}{3x}[/tex]
[tex]\frac{1}{x}=\frac{4}{3x}+\frac{x-2}{3x}[/tex]
Add the numerators and keep the same denominator.
[tex]\frac{1}{x}=\frac{4+x-2}{3x}[/tex]
[tex]\frac{1}{x}=\frac{2+x}{3x}[/tex]
To get rid of the denominator x on the left side, we can multiply by x.
[tex](x)\frac{1}{x}=\frac{2+x}{3x}(x)[/tex]
[tex]1=\frac{2+x}{3}[/tex]
Now multiply by 3.
[tex](3)1=\frac{2+x}{3}(3)[/tex]
[tex]3=2+x[/tex]
Subtract 2.
[tex]3-2=x\\1=x[/tex]
The value of x is 1.
Proof.
[tex]\frac{1}{x}-\frac{x-2}{3x}=\frac{4}{3x}[/tex]
[tex]\frac{1}{1}-\frac{1-2}{3(1)}=\frac{4}{3(1)}[/tex]
[tex]1-\frac{-1}{3}=\frac{4}{3}[/tex]
[tex]1+\frac{1}{3}=\frac{4}{3}[/tex]
[tex]\frac{1*3+1}{3} =\frac{4}{3}\\\frac{4}{3}=\frac{4}{3}[/tex]
I can't show the proof to the following problems because I have a 5000 character limit.
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2.
[tex]\frac{5x-5}{x^2-4x} -\frac{5}{x^2-4x}=\frac{1}{x}[/tex]
Again, we have like denominators, therefore, we can simply subtract the numerators and keep the same denominator.
[tex]\frac{5x-5-5}{x^2-4x}=\frac{1}{x}[/tex]
[tex]\frac{5x-10}{x^2-4x}=\frac{1}{x}[/tex]
Again, we can multiply by x to get rid of the x in the denominator.
[tex](x)\frac{5x-10}{x^2-4x}=\frac{1}{x}(x)[/tex]
Do not distribute the x in the numerator yet because we're gonna eliminate it later.
[tex]\frac{(x)(5x-10)}{x^2-4x}=1[/tex]
Factor the denominator.
[tex]\frac{(x)(5x-10)}{(x)(x-4)}=1[/tex]
Simplify x's.
[tex]\frac{5x-10}{x-4} =1[/tex]
Multiply by x-4 to get rid of the denominator.
[tex](x-4)\frac{5x-10}{x-4} =1(x-4)[/tex]
[tex]5x-10=x-4[/tex]
Add 10
[tex]5x=x-4+10[/tex]
Subtract x
[tex]5x-x=-4+10[/tex]
Combine like terms;
[tex]4x=6[/tex]
Divide by 4.
[tex]\frac{4x}{4}=\frac{6}{4}[/tex]
[tex]x=\frac{6}{4}[/tex]
Simplify by 2.
6/2 = 3
4/2 = 2
[tex]x=\frac{3}{2}[/tex]
-----------------------------------------------------------------------
3.
[tex]\frac{x^2-7x+10}{x}+\frac{1}{x}=x+4[/tex]
Same denominator, add numerators.
[tex]\frac{x^2-7x+10+1}{x}=x+4[/tex]
[tex]\frac{x^2-7x+11}{x}=x+4[/tex]
Multiply by x to get rid of the x.
[tex](x)\frac{x^2-7x+11}{x}=(x+4)(x)[/tex]
[tex]x^2-7x+11=x^2+4x[/tex]
Subtract [tex]-x^2-4x[/tex]
[tex]x^2-7x+11-x^2-4x=0[/tex]
Combine like terms;
[tex]-11x+11=0[/tex]
Subtract 11.
[tex]-11x=-11[/tex]
Divide by -11
[tex]x=\frac{-11}{-11} \\x=1[/tex]
-------------------------------------------------------------------------
4.
[tex]\frac{x^2+7x+10}{5x-30}+\frac{x}{x-6}=\frac{x^2-13x+40}{5x-30}[/tex]
It's easier if you move the operation with denominator x+6 to the right side with negative sign and bring the operation on the right side to the left side with negative sign as well.
[tex]\frac{x^2+7x+10}{5x-30}-\frac{x^2-13x+40}{5x-30}=-\frac{x}{x-6}[/tex]
Now, since we have the same denominators, we can simply subtract numerators.
[tex]\frac{x^2+7x+10-(x^2-13x+40)}{5x-30} =-\frac{x}{x-6}[/tex]
Distribute the negative sign.
[tex]\frac{x^2+7x+10-x^2+13x-40}{5x-30} =-\frac{x}{x-6}[/tex]
Combine like terms;
[tex]\frac{20x-30}{5x-30}=-\frac{x}{x-6}[/tex]
Factor.
I can see that I can factor a 5 on both numerator and numerator. This will allow me to simplify them.
[tex]\frac{(5)(4x-6)}{(5)(x-6)} =-\frac{x}{x-6}[/tex]
Simplify.
[tex]\frac{4x-6}{x-6}=-\frac{x}{x-6}[/tex]
Multiply by x-6
[tex](x-6)\frac{4x-6}{x-6}=-\frac{x}{x-6}(x-6)[/tex]
This will simplify the denominators.
[tex]4x-6=-x[/tex]
Add x and 6.
[tex]4x+x=6\\[/tex]
Combine like terms;
[tex]5x=6[/tex]
Divide by 5.
[tex]x=\frac{6}{5}[/tex]
Related Questions
How can you determine if a point is a solution to a system of linear equations?
Please Help!
Answers
Answer:
You can substitute the x value of coordinate (x,y) in the equation. If the outcome = the y value in the coordinate (x,y), then you have determined it to be on the system of linear equations.
Step-by-step explanation:
Point P has a coordinates: ( Px , Py ).
You can choose which value is easy to substitute. Eighter start with the Py or you could start with the Px. It could save you time if you pick the right one for the job.
If you want to verify if any point is valid in any (linear) equation(s), you can:
a) substitute the x value of coordinate (x,y) in the equation, and if the outcome has the same value as y in the coordinate (x,y), then that point is a valid solution of the (linear) equation.
b) substitute the y value of coordinate (x,y) in the equation, and if the outcome has the same value as x in the coordinate (x,y), then that point is a valid solution of the (linear) equation.
Answer:
You can substitute the x value into the equation if the answer for y is the same for the y coordinate you will have your answer.
Step-by-step explanation:
what is the slope of the line passing through (2,9) and (2,-14)
Answers
Answer:
The slope is undefined
Step-by-step explanation:
When graphed, the two points form a vertical line, since we can't divide the slope by zero thw slope is considered as undefined
A rectangular playground is 10m longer than it is wide.The area of the playground is 1400m² Calculate the width and length of the playground. solve using quadratic formula please?
Answers
Answer:
[tex] 1400 = x(x+10)= x^2 +10x[/tex]
We can rewrite this expression like this:
[tex] x^2 +10 x -1400 =0[/tex]
And we can use the quadratic formula given by:
[tex] x = \frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
Where [tex] a =1 , b=10 , c= -1400[/tex]
And replacing we got:
[tex] x = \frac{-10 \pm \sqrt{10^2 -4(10)(-1400)}}{2*1}[/tex]
And solving we got:
[tex] x_1 =32.75 , x_2 = -42.75[/tex]
And since the value can't be negative the answer would be x = 32.75 and the value of y = 32.75+10 =42.75
Step-by-step explanation:
For this case we know that we have a rectangular playground and the area can be founded with this formula:
[tex] A = xy[/tex]
Where x represent the width and y the length. From the problem we know that A =1400 m^2 and the heigth is 10m longer than the wide so we can write this condition as:
[tex] y = 10 +x [/tex]
And replacing this formula into the area we got:
[tex] 1400 = x(x+10)= x^2 +10x[/tex]
We can rewrite this expression like this:
[tex] x^2 +10 x -1400 =0[/tex]
And we can use the quadratic formula given by:
[tex] x = \frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
Where [tex] a =1 , b=10 , c= -1400[/tex]
And replacing we got:
[tex] x = \frac{-10 \pm \sqrt{10^2 -4(10)(-1400)}}{2*1}[/tex]
And solving we got:
[tex] x_1 =32.75 , x_2 = -42.75[/tex]
And since the value can't be negative the answer would be x = 32.75 and the value of y = 32.75+10 =42.75
Answer:
Step-by-step explanation:
Given Data:
Area = 1400m²
L = 4+w
W= w
Area = L * W
1400 = ( 4+W) W ²
1400 = 4w + w ²
w ² + 4w - 1400 = 0
- b ± √ b ² - 4ac / 2a
Where;
a = 1
b = 4
c = -1400
- 4 ± √4² - 4(1)(-1400) / 2(1)
= - 4 ± 74.94 /2
= - 4 + 74.94 / 2 or - 4 - 74.94 / 2
= 35.47 or - 39.47
Find the volume of a pyramid with a square base, where the area of the base is
8.7 m and the height of the pyramid is 10 m. Round your answer to the nearest
tenth of a cubic meter.
Answers
Answer: 29.0
Step-by-step explanation:
The volume of a pyramid is equal to l*w*h/ 3 and we know that the length times the width is the same as the base.
so we will multiply 8.7 * 10= 87 /3= 29
Volume = 87 m³
You need to multiply the area and the height to find the volume. If you have the length, width, and height, then you need to multiply and 3 and divide it by 3. Hope I helped :)
Which expression represents finding the volume of the entire solid? Be careful
Answers
Answer:
Option 6
Step-by-step explanation:
To find the volume of a cone you use the formula 1/3*pi*r^2*h which would be pi*9^2*7. Then the volume of a cylinder is pi*9^2*50, so option 6 is right I believe.
thomas has a square swimming pool at home. Each side is 18 m long. What is the area of the swimming pool
Answers
Answer:
324 m^2
Step-by-step explanation:
since it is a square, each side is 18 meters. to find the area, you multiply the length by the width. the answer is 324 m^2
concrete is poured to create a slab in the shape of a rectangular prisim the slab is 50 yards long 1.5 yards wide and 0.25 yard stick how many cubic squares of concrete are needed to create slab
Answers
Answer:
18.75 cubic yards
Step-by-step explanation:
Multiply the length width and height by each other.
50 x 1.5 x 0.25 = 18.75
Answer:
18.75 yards³
Step-by-step explanation:
To solve this, we can solve for the volume of the rectangular prism by using the formula: [tex]V= l*w*h[/tex]
We can plug in the values, giving us:
V= 50×1.5×0.25= 18.75 yards³
I NEED HELP WITH THIS
Answers
Answer:
(i think it is for q6 so) $6
Step-by-step explanation:
4.50÷3=1.50 (that's for 1 pound of fudge)
1.50×4=6
Simplify the expression to a polynomial in standard form:
(x – 3)(x2 – 7x - 2)
Answers
Answer: x to the third power minus 10x to the second power plus 19x plus 6 .
Order each set of numbers from LEAST to GREATEST.
-4 , -5/4 , 0 , -5, -1.5
Answers
Answer:
-5, -4, -1.5, (-5/4) -1.25, 0
Step-by-step explanation:
The higher the negative the lower the number (least).
~Anna
Need help? Contact me for tutoring!
Ernesto wants to buy a snack from the vending machine. The vending machine has 5 different kinds of chips, 8 different candy bars, and 2 different kinds of cookies. If he chooses one at random, what is the probability that it is a cookie?
Answers
Answer:
The probability that it is a cookie is [tex]\frac{2}{15}[/tex]
Step-by-step explanation:
To find the probability that it is a cookie if he chooses one at random;
probability = required outcome / all possible outcome
The all possible outcome will be gotten by adding up all the snacks. that is;
required outcome = 5 + 8 + 2 = 15
The required outcome is the snack he chooses, that is; required outcome = 2
Probability (of choosing a cookie) =required outcome / all possible outcome
=[tex]\frac{2}{15}[/tex]
Therefore, the probability that it is a cookie is [tex]\frac{2}{15}[/tex]
A survey of 539 adults aged 18-24 year olds was conducted in which they were asked what they did last Friday night. It found:
189 watched TV
163 hung out with friends
29 watched TV and ate pizza, but did not hang out with friends
49 watched TV and hung out with friends, but did not eat pizza
36 hung out with friends and ate pizza, but did not watch TV
30 watched TV, hung out with friends, and ate pizza
60 did not do any of these three activities
How may 18-24 year olds (of these three activities) only ate pizza last Friday night?
Your Answer:
Answers
Answer:
95 people ate pizza
Step-by-step explanation:
Add the ones highlighted
The _________ of a matrix is usually written as "m x n", where m is the number of rows and n is the number of columns.
Answers
Answer:
size
Step-by-step explanation:
Example: (1 0 2) has 1 row and 3 columns, so m = 1 & n = 3 and the size is 1 x 3.
Keith makes 8 dollars for each hour of work. Write an equation to represent his total pay p after working h hours.
Answers
Answer:
P=8h
Step-by-step explanation:
P is the total amount of dollars that Keith will make, while h is the number of hours he will work for. If you multiply the number of hours he works for and how much he makes in an hour which is 8. You will get the total amount.
What is the value of x in the equation below?
3(12x- 24) = 16
O 2
6
08
10
Answers
Answer:
x = 2,444
Step-by-step explanation:
3(12x - 24) = 16
36x - 72 = 16
36x = 16 + 72
36x = 88
x = 88/36
x = 2,444
what is between 1/6 and 2/6 on a number line
Answers
Answer:
3/12 or 1/4
Step-by-step explanation:
To find what is between, we have to use the formula:
x + y= z
z/2 = midpoint!
So, we can do that with this number.
1/6 + 2/6 = 3/6. We could simplify it, but let’s keep it at 3/6
3/6 divided by 2 = 3/6 · 1/2 = 3/12
So, the midpoint would be 3/12.
Raheem found a worm that was 6 centimeters long what is the length of the worm in in millimeters
Answers
Answer:
60 millimeters
Step-by-step explanation:
1 centimeter is 10 milimeters. So, 6 centimeters is 60 millimeters.
*please mark brainliest*
What is the mean of the data set below? Round to the nearest tenth when necessary. 10, 30, 53 *
Answers
A quadratic function y = f(x) is plotted on a graph and the vertex of the resulting
parabola is (-6, -3). What is the vertex of the function defined as
g(x) = -f(x) + 3?
Answers
Answer:
Step-by-step explanation:
You revived 1/4 pound of candy from your grandmother, 1/2 pound of candy from your sister, and 1/8 pound of candy from your best friend. How many pounds of candy did you receive?
Answers
Answer:
⅞ pound
Step-by-step explanation:
You received 1/4 pound of candy from your grandmother.
You received 1/2 pound of candy from your sister.
You received 1/8 pound of candy from your best friend.
The total amount of candy you received is given as the sum of all the candy that he received from your grandmother sister and best friend.
The total amount of candy is therefore:
¼ + ½ + ⅛ = ⅞ pound
You received ⅞ pound of candy in total.
Simplify:
2(xy - 7) = [?]
x = -1 and y = 3
Answers
Answer:2(xy-7)= -20
Step-by-step explanation:
Plug in -1 for x and 3 for 3, as the question says that x and y represent those values.
2(xy-7) = ?
2((-1)(3) - 7) = ?
2(-3-7)=?
2(-10)
-20
2(xy - 7) = -20
The expresssion 2(xy - 7) = -20 , when x = -1 & y = 3
What is expression ?
In mathematics, if two or more numbers or variables present with one or more mathematical operations, then the statement is called expression.
Example : 4x-3y+4, where x,y are variables, 3 & 4 are numbers and they are operated with addition and subtraction, so this is an expression.
What is the value of given expression ?Here, in the problem, x = -1 & y = 3
The given expression is 2(xy - 7) .....(1)
Now, we have to put the values of x & y in (1),
So, 2(xy - 7)
= 2{(-1)(3)-7}
= 2{-3-7}
= 2×(-10)
= -20
So, the value of the expression is -20
Learn more about expression here :
https://brainly.com/question/723406
#SPJ2
Solve if u r genius
11*11=4
22*22=16
33*33=?
Answers
Answer:
36
Step-by-step explanation:
bc 11*11=2*2=4
22*22=4*4=16
33*33=6*6=36
u add 1 and 1 together
then u add 2 and 2 together and then u add the 3 and 3 together to get 2, 4 and 6
Answer:
The answer is 36.
Step-by-step explanation:
This is a brain-solving question :
(1+1)×(1+1)
= 2×2
= 4
(2+2) × (2+2)
= 4×4
= 16
(3+3) × (3+3)
= 6×6
= 36
You are going to the grocery to buy the candies for you and your sisters/brothers. You want to buy
chocolates and gums. Each chocolate costs 1.50 AED and each gum costs 0.50 AED. At the end you spent a total
of 78.50 AED. You bought a total of 87 chocolates and gums combined. You must report the number of
chocolates bought and the number of gums bought. How many chocolates were bought and how many gums
were bought?
Answers
Answer: 35 chocolates were bought and 52 gums were bought.
Step-by-step explanation:
c + g = 87 where c is the number of chocolate and g is the number og gums
1.50c + 0.50g = 78.50 solve both equations by elimination.
-1.50c - 1.50g = -130.5
1.50 + 0.50g = 78.50
-1g = -52
g= 52
1.50c + 0.50(52) = 78.50
1.50c + 26 = 78.50
-26 -26
1.50c = 52.5
c = 35
Please help with this
Answers
Answer:
C
Step-by-step explanation:
A quadratic function can be defined as a function where the highest degree or exponent is 2. Since option B has a zero in front of the x squared, it is not a quadratic function because 0 times anything is zero. Therefore, the only other option with an exponent of 2 is C.
Hope this helped! :D
Colin, Sara and Gordon share some sweets in the ratio 5:2:1. Colin gets 36 more sweets than Gordon. How many sweets are there altogether?
Answers
c=36+g
c:g:s=5:2:1
The ratio gives us two equations so that's three equations in three unknowns. Actually we're after the total t; let's put that in to solve for directly.
c:g:s:t = 5 : 2 : 1 : 5+2+1
We turn the ratio to fraction equations. s has the one; let's write everything in terms of s.
c/s = 5/1, g/s = 2/1, t/s = 8/1
Clearing the fractions,
c = 5s, g = 2s, t = 8s
Our other equation is
c = 36 + g
Substituting in for c and g,
5s = 36 + 2s
Solving,
3s = 36
s = 12
That's right; let's just get the total t.
t = 8s = 72
Answer: 72
78% of what number is 22?
Answers
Answer: 22 is 78% of 28
Step-by-step explanation:
22÷28×100=78
78 is the percentage
Answer:
28. 21 or 28.2 or 28
Step-by-step explanation:
Since 22 is equal to 78% percent, then x is equal to 100%
78% = 22
100% = x
Cross múltiply
100(22) = 78x
2200 = 78x
÷ 78. ÷78
28.205 = x
Depending on what your rounding off to, nearest tenth, hundreths, or whole number
tenth = 28.2
whole number= 28
hundreth= 28. 21
neli has 3 partically full cans of of white paint.They contain 1/3 gallon,1/5 gallon, and 1/2 gallon of paint.about how much paint does neli have in all
options
^^^^^^^^
Less than 1 1/2 gallons.
More than 2 gallons.
Between 1 1/2 gallons and 2 gallons
(which one?)
(help pls)
Answers
Answer:
less than 1 and 1/2
Step-by-step explanation:
1/3 + 1/5 + 1/2 = 31/30 which is also equal to 1 1/30
Answer:so wut the answer?
Step-by-step explanation:im dum i dont know
pls help me figure this out thanks
Answers
Answer:
7√3
Step-by-step explanation:
tan 60 = v/7
√3 = v/7
v=7√3
Answer:
[tex]4 \sqrt{5 \\ } [/tex]
what is 2/3 ÷ 4/5 = ?
Answers
Answer:
this is the answer:5/6.
Answer:
= 5/6
Step-by-step explanation:
2/6 ÷ 4/5
= 2/6 × 5/4
= 10/24
= 5/6
Thanks for all the help
Answers
Answer:
<FBE
Step-by-step explanation:
supplementary just mean 180
Answer:
∠CBG or ∠FBG
Step-by-step explanation:
Supplementary angles add up to 180°.
