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]
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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]
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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
, Ohio in 1990, the number of residents has decreased by 5% every 5 years. In 1990, there were 182,000 residents in Dayton, Ohio. Estimate the population in 2020 to the nearest whole number.
Answers
Answer:
133,787 residents
Step-by-step explanation:
First thing we need to do here is calculate the number of 5 years between 2020 and 1990
That would be 2020-1990 = 30/5 = 6
Now to estimate the present population, we will be needing an exponential equation
P = I(1-r)^n
where P is the present population at 2020
I is the population at 1990 which is 182,000
r is the percentage decrease every 5 years which is 5% or simply 5/100 = 0.05
n is the number of 5 years between 1990 and 2020 which is 6
Plugging all these values we have;
P = 182000(1-0.05)^6
P = 182000(0.95)^6
P = 133,786.724
To the nearest whole number, P = 133,787 residents
Simplify, and then write in exponential form. Do not evaluate.
(7^2)^4
Answers
Answer:
7^8
Step-by-step explanation:
(7^2)^4
We know a^b^c = a^(b*c)
(7^2)^4 = 7^(2*4)
= 7^(8)
Body Mass Index (BMI) is given by the formula BMI=705W/H2 , where W is the weight of a person in pounds, and H is their height, measured in inches. If a person is 6 feet 3 inches tall, and weighs 209 pounds, what is their BMI? Round your answer to the nearest tenth.
Answers
Answer:
BMI = 26.1
Step-by-step explanation:
The body mass index is given by the below formula as :
[tex]BMI=\dfrac{705\times W}{H^2}[/tex]
Here,
W is the weight of a person in pounds and H is height measured in inches.
If height of a person is 6 feet 3 inches, it means its height is 75 inches. Its weight is 209 pound.
So, plugging all values we get ,
[tex]BMI=\dfrac{705\times 209}{(75)^2}\\\\BMI=26.1[/tex]
So, the body mass index is 26.1.
A population of rabbits doubles every 60 days according to the formula P=10(2)^t/60, where P is the population of rabbis on day t. What is the value of t when the population is 320
Answers
Answer:
[tex] 320 = 10 (2)^{t/60}[/tex]
If we divide both sides by 10 we got:
[tex] 32 = 2^{t/60}[/tex]
We can apply natural log on both sides and we got:
[tex] ln (32) = \frac{t}{60} ln(2) [/tex]
And solving the value of t we got:
[tex] t = 60 \frac{ln(32)}{ln(2)}= 300[/tex]
So then we can conclude that after t = 300 days we will have approximately 320 rabbits
Step-by-step explanation:
For this case we have the following function:
[tex] P(t) = 10 (2)^{t/60}[/tex]
Where P is the population of rabbis on day t. And for this case we want to find the value of t when P =320 so we can set up the following equation:
[tex] 320 = 10 (2)^{t/60}[/tex]
If we divide both sides by 10 we got:
[tex] 32 = 2^{t/60}[/tex]
We can apply natural log on both sides and we got:
[tex] ln (32) = \frac{t}{60} ln(2) [/tex]
And solving the value of t we got:
[tex] t = 60 \frac{ln(32)}{ln(2)}= 300[/tex]
So then we can conclude that after t = 300 days we will have approximately 320 rabbits
You pick one card from each set and find the sum. How many different sums are possible?
Answers
Answer:
24 possibilities
Step-by-step explanation:
2*2*6=24
24 possibilities
The number of different sums possible is 24 possibilities.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
We have been given that pick one card from each set and find the sum.
Therefore, we need to find the number of different sums that are possible;
2 x 2 x 6=24
24 possibilities
Hence, the number of different sums possible is 24 possibilities.
Learn more about probability here;
https://brainly.com/question/9326835
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is -8 rational or irrational
Answers
Answer:
rational
Step-by-step explanation:
All numbers that are not rational are considered irrational. An irrational number can be written as a decimal, but not as a fraction. An irrational number has endless non-repeating digits to the right of the decimal point. The number 22/7 is a irrational number
Kono Dio Da!!!
Answer:
I'm pretty sure it is rational
Step-by-step explanation:
:)
if the sides of a triangle and area is given. How to find perimeter
Answers
Answer:
add it up to see if it's 180
Answer:
Well since you have the sides you would add up all of the sides to find the perimeter.
Step-by-step explanation:
What is the measure of the unknown angle?
50°
Answers
If you want to find the energy quantum of light, you multiply the frequency of the radiation (v) by "h". What is "h"?
Answers
Answer:
H is E
Step-by-step explanation:
In the formula of the energy of photons "h" signifies Planck's constant.
What is Planck's constant?The Planck constant, often known as Planck's constant, is a crucial physical constant in quantum physics. The mass-energy equivalency establishes the relationship between mass and frequency, and the constant establishes the relationship between a photon's energy and frequency.
In the equation energy E = h X v. The "h" there signifies Planck's constant
Planck's constant is a value, that shows the rate at which the energy of a photon increases/decreases, as the frequency of its electromagnetic wave changes.
Therefore, in the formula of the energy of photons "h" signifies Planck's constant.
To know more about Planck's constant follow
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An item is regularly priced at $85. It is on sale for 15% off the regular price.
Someone help
Answers
Answer:72.25
Step-by-step explanation:
Answer:
$72.25 is the price of the $85 item on sale for 15% off the regular price.
Step-by-step explanation:
First you need to find out how much 15% off the original price is:
85 x .15 (change percent to a decimal by moving the decimal point to the left two times, so if it was 25%, the decimal form is .25)
85 x .15= 12.75, so there is $12.75 off the original price of $85.
$85 - $12.75= $72.25!
Yw!
6x - 2y = 10
2x + 3y = 51
Solving the first equation above for y gives:
y =
X-5
DO NE
Answers
Answer:
y = 3x -5
Step-by-step explanation:
6x - 2y = 10
-6x. -6x
Inverse Operations
-2y = -6x + 10
÷-2. ÷-2. ÷-2
y = 3x - 5
Answer:
6x – 2y = 10
2x + 3y = 51
Solving the first equation above for y gives:
y = (3) x – 5
Which choice shows the result of substituting
3x – 5 into the second equation for y?
2(3x – 5) + 3x = 51
----------2x + 3(3x – 5) = 51 its B
2(3x – 5) + 3y = 51
Solving the equation 2x + 3(3x – 5) = 51
for x gives x =
---6.
The complete solution to the system is:
----(6, 13)
Step-by-step explanation:
27 = z/0.3 as a salution
pleeeeaaaaasssseee i need help
Answers
Answer:
z = 81/10 = 8.100
Step-by-step explanation:
A pilot is flying a plane 20000 ft above the ground.The pilot begins a 2 descent to an airport runway.How far is the airplane from the start of the runway(in ground distance)
Answers
Answer:
381623 ft
Step-by-step explanation:
Since the airport altitude is 20000 ft and the pilot needs a 2° descent, to calculate the distance of the airplane at the start of this approach, first this is represented in the diagram attached. The distance from the runway at the start is x.
[tex]tan(3) = \frac{20000}{x} \\x=\frac{20000}{tan(3)} \\x=381623ft[/tex]
The airplane is at a distance of 381623 ft away from the airplane runaway at the start of the descent.
The city limits of Las Pythagoras form a perfect shape of an isosceles right triangle whose legs are both 25 2525 kilometers long. The population in Las Pythagoras is 100 , 000 100,000100, comma, 000 people. What is the population density of Las Pythagoras?
Answers
320
Step-by-step explanation:
a shoreline is changing -3 centimeters each year due to erosion. what is the change in shoreline over 6 years?
Answers
Answer:
-18
Step-by-step explanation:
Martin charges $10 for every 5 bags of leaves he rakes. Last weekend, he raked 27 bags of leaves. How much money did he earn?
Answers
Answer:
$54 : 27 bags
Step-by-step explanation:
its to much to explain
i got my math wrong
Kati has of a bag of frozen fruit. She used of the fruit to make smoothies. Which equation represents the amount of fruit Kati used to make smoothies?
Answers
Answer:
The amount of frozen fruit used to make smoothies is equal to the total number of frozen fruits minus the remainder of fruits after making smoothies.
Step-by-step explanation:
Let
Total number of frozen fruits = F
Let the amount of frozen fruits used for making smoothies = S
The remaining frozen fruits = R
Then
F - S = R
To get the amount of frozen fruits used to make smoothies, we make S the subject of the formula.
-S = R - F
S = F - R
That is, the amount of frozen fruit used to make smoothies is equal to the total number of frozen fruits minus the remainder of fruits after making smoothies.
Which solution set is graphed on the number line?
Answers
Answer:
An inequality, such as x>2 can be graphed on the number line.
Step-by-step explanation:
An inequality, such as x>2 can be graphed on the number line. An open circle as a stating point, indicates the number is NOT included in the solution. Where as a closed circle or "dot" indicates the number IS included in the solution.
Answer:
An inequality, such as x>2 can be graphed on the number line.
Step-by-step explanation:
Oliver has lots of bags. There are
three types of bags that he collects.
travel bags, hand bags and school bags.
If the probability of getting a travel
bag is 5/10 and the probability of getting hand
bag is 4/10: what is the relative
frequency probability of getting a school bag?
Answers
Answer:
1/10
Step-by-step explanation:
if you add all of it it becomes 10/10
Which size is the best buy?
Lemonade
Size. Price
12 ounces. $.89
18 ounces. $1.69
24 ounces. $2.09
pls help me
Answers
Answer:
A) 12 ounces for $0.89
Explanation:
$0.89 ÷ 12 = $0.07
$1.69 ÷ 18 = $0.09
$2.09 ÷ 24 = 0.087
Now we know the different prices for each ounce, as you can see the 12 ounces is definitely the best buy.
I hope this helps!
can someone help? 25 points
Answers
Answer:
Triangle A: acute
Triangle B: acute
Triangle C: obtuse
Triangle D: right
Step-by-step explanation:
acute= less than 90 degrees each angle
obtuse=more than 90 degrees for one angle
right=equal exactly 90 degrees for one angle
Answer:
A=Acute
B. Acute
C.Obtuse
D.Right
Step-by-step explanation:
a,and b, and are acute becuase there angles are less than 90 degrees.
d is obtuse beucase the angleismore than 90 degrees
D is right beucase the angle is 90 degrees and it hasthat square in the corner.
A circle has a radius of square root 131 units and is centered at (0,-4.3).
Whats the equation of this circle?
Answers
Answer:
x^2 + (y + 4.3)^2 = 131
Step-by-step explanation:
The basic equation of a circle with center at (h, k) and radius r is
(x - h)^2 + (y - k)^2 = r^2. Here the center is (0, -4.3) and the radius is √131. Substituting as indicated, we get:
(x - 0)^2 + (y + 4.3)^2 = 131, or
x^2 + (y + 4.3)^2 = 131
AWARDING BRAINLIEST! PLEASE HELP!!!
Answers
Answer:
Right triangle
Step-by-step explanation:
we are given three sides as 14 ft, 48 ft, and 50 ft
Firstly, we will verify for right angle
We know that any triangle is right angled when it satisfies Pythagoras theorem
We know that hypotenuse side value is always largest
so, hypotenuse=c=50
Let's assume other two sides as
a=14
b=48
now, we can use Pythagoras theorem formula
C²=a²+b²
we can plug values and we check whether left side is equal to right side
50²=14²+48²
2500=196+2304
2500=2500
we can see that left side is equal to right side
Since, it satisfies Pythagoras theorem
Therefore, Right triangle is the answer
Answer:
I believe, obtuse.
Step-by-step explanation:
You have one extremely small side, two long sides. If you put your hands together and logically measure the 14 length side, you'd realize it is obtuse. I have no mathematical evidence.
What does angle B equal?
Answers
NO. IM SORRY. I DID NOT MEANT THAT. DONT TRUST MY ANSWER.
Delete my answer due to my stupidity
The arc length
shown below is 15 feet.
State the equation that relates arc length to central angle.
Find the angle
in radians.
Convert your answer from Part II to degrees and write it to the nearest hundredth of a degree.
Answers
Answer:
s = rθ2.5 radians143.24°Step-by-step explanation:
The applicable formula is ...
s = rθ
where s is the arc length, r is the circle's radius, and θ is the central angle in radians.
Filling in the given values, we find ...
15 = 6θ
θ = 15/6 = 2.5 . . . radians
Pi (π) radians is 180°, so the angle in degrees is ...
2.5(180°/π) ≈ 143.24°
Siobhan has two babysitting job offers for the same weekend.The snachez family would like her to babysit from Friday at 6:00 pm through Saturday at 9:30 am.They will pay her $150.The martins would like her to babysit friday night from 5:00 pm to 11:00 pm and will pay her $15 per hour.Wich family is offering to pay her more per hour?Wich is offering to pay her more overall?
Answers
Answer:
The Martin family pays $5.33 more per hour
The Sanchez family pays $60 more in total
Step-by-step explanation:
The Sanchez family want her to babysit for 15.5 hours for a total of $150.
To find out the hourly rate you do $150/15.5 which is $9.67 per hour.
The Martin family wants her to babysit for a total of 6 hours for $15 an hour.
To find out the total you do $15 x 6 which is $90.
Which product has 4 zeros after the digit 3? 0.03 times 10 with the power of 5. 0.3 times 10 with the power of 4 0.03 times 10 with the power of 4. 0.03 times 10 with the power of 5
Answers
Answer:
[tex]0.3 * 10^5[/tex]
Step-by-step explanation:
0.3
^ You need to move the three before the decimal place and leave 4 empty digits (0) between
0.3
3.0
30.0
300.0
3000.0
30000.0
A total of 5 moves.
Each move is equivalent to x, the preceding value, times 10. x * 10
Repeated multiplication times the same factor equates to exponentiation, so for a total of 5 moves, it is notated as [tex]10^5[/tex], giving you an expression of:
[tex]0.3 * 10^5[/tex]
GO TO MY LATEST QUESTION IT IS EASY BUT IDK THE ANSWERRRRR
here it is: Which of the following numbers can be expressed as a decimal that terminates? seven over four, five over nine, three over eight, two over three
Answers
Answer:7/4= 1.75 and 3/8=0.375
Step-by-step explanation:
5/9= 0.555555.......
3/8=0.375
2/3=0.666666......
How do you terminate stuff?
In a capture-recapture study, 97 grizzly bears were tagged and released back into the wild. A month later, 200 bears were captured of which 36 were tagged. About how many grizzly bears are in the population?
Answers
Answer:
539
Step-by-step explanation:
Let the total population of grizzly bears=x
In the first capture, 97 were tagged.
Therefore, ratio of the total population to the tagged=x:97
A month later, when 200 bears were captured, 36 were tagged.
Ratio of the sample to the tagged=200:36
Since a sample is representative of the population, the ratios are the same. We therefore have:
x:97=200:36
[tex]\dfrac{x}{97} =\dfrac{200}{36}\\ $Cross multiply\\36x=200 X 97\\x=200 X 97 \div 36\\x=538.9 \approx 539[/tex]
There are about 539 grizzly bears in the population
Fenyang got 666 rabbits to raise on his farm. From the following month forward, the rabbit population doubled every month.
Answers
Answer:
geometric sequence
Step-by-step explanation:
