write the rational expressions as equivalent rational expressions with the lowest common denominator
Answers
1. The equivalent rational expression with the lowest common denominator of [tex]\frac{2}{3d^{2} + 14d^{2} - 5 }[/tex] is [tex]\frac{2}{(d+5)(3d-1)}[/tex]
2. The equivalent rational expression with the lowest common denominator of [tex]\frac{3d}{3d^{2} - 22d + 7}[/tex] is [tex]\frac{3d}{(d-7)(3d-1)}[/tex]
1.
[tex]\frac{2}{3d^{2} + 14d^{2} - 5 }[/tex]
Let factorise the denominator below
3d² + 14d - 5
-15 and 14
Two numbers we can multiply to get -15 and add to get 14 are 15 and -1.
Therefore,
3d²- d + 15d - 5
d(3d - 1) + 5(3d - 1)
(d+5)(3d-1)
Therefore, the equivalent rational expression with the lowest common denominator will be
[tex]\frac{2}{(d+5)(3d-1)}[/tex]
2.
[tex]\frac{3d}{3d^{2} - 22d + 7}[/tex]
Factorise the denominator
3d²- 22d+7
3d²- d - 21d + 7
d(3d - 1) - 7(3d - 1)
(d - 7)(3d - 1)
Therefore, the equivalent rational expression with the lowest common denominator will be
[tex]\frac{3d}{(d-7)(3d-1)}[/tex]
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Related Questions
Aashi buys
2 packets of bread rolls costing £1.40 for each packet
1 bottle of ketchup costing £1.80
3 packets of sausages
Aashi pays with a £10 note.
She gets 45p change.
Work out the price in pounds (£) of one pack of sausages.
(you will get brainliest) !! :D
Answers
Ketchup = K
Sausages = S
2BR +1K + 3S = £10 - 45p
2BR + 1K + 3S = £9.55
2BR = 1.40 x 2 = £2.80
1K = £1.80
£2.80 + £1.80 + 3S = £9.55
3S = £9.55 - £2.80 - £1.80
3S = £4.95
£4.95 / 3 = BR
S = £1.65
The answer is £1.65 for one pack of sausages
Price of one unit Sausage = 1.65
Sum ( Price x Quantity) = Total Expenditure
Price of Bread x Quantity of Bread + Price of Ketchup x Quantity of Ketchup + Price of Sausage x Quantity of Sausage
Total Expenditure Value = 10 - 0.45 = 9.55
Let price of sausage = P
Therefore, 2 (1.40) + 1 (1.80) + 3 P = 9.55
2.80 + 1.80 + 3 Ps = 9.55
4.6 + 3 P = 9.55
3P = 9.55 - 4.60 = 4.95
P = 4.95 / 3 = 1.65
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Write the equation in function form:
8x + 4y = 20
Answers
Function form means just replace y with f(x).
So given 8x + 4y = 20:
Subtract 8x
4y = 20 - 8x
Divide both sides by 4
y = 5 - 2x
__% of 4 is 7
Please answer its due today
Answers
Answer:
175%
hope that helps. :)
Find the sum of A.5 B.3 C.4 D.1
Answers
Answer:
D. Maybe? brainliest suggested
Step-by-step explanation:
Please help I’m timed thank you!!!
Answers
Answer:
BAP=12
ABP=32.5
BCP=45.5
I’m a little lost on this
Answers
Question 7 of 10
Which statement best describes an example of a short-term investment
strategy?
A. Mariam buys an IRA that she can't withdraw from without penalty
until she's 59.5.
B. Mariam invests $4,000 in a mutual fund to create a new income
stream.
O C. Mariam buys a certificate of deposit to set aside money for a
down payment on a car.
D. Mariam buys 100 shares of stock in a proven company known for
solid, dependable performance over time.
SUBMIT
Answers
Answer:
C
Step-by-step explanation:
Its not A because she can't withdraw it for however many years.
Its not B because creating a new income stream is a long term investment.
Its not D because it says she buys stock of a long-term performing company
PLZ HELP. SEE PICTURE FOR DETAILS ON THE PROBLEM
Answers
Answer:
[tex] \frac{1}{3} x + \frac{1}{2} [/tex]
This is the answer after simplifying
PLEASE HELP ME ITS ALGEBRA THANK YOUUUU
Answers
unit rate = 45
so $45 per person
85 guests x 45 = 3825
I hope this helps!
An academy requires there to be 3 teachers for every 72 students and 5 tutors for every 60 students. How many students does the academy have per teacher? Per tutor? How many tutors does the academy need if it has 132 students?
Answers
help #2 #4 #6 #8 #10 #12
Answers
A landowner recently sold a large plot of land. The sale decreased his total acreage by 12%. Let v be the original acreage.
a. Write two equivalent expressions that represent the new acreage.
Answers
Answer:
.88v or [tex]\frac{22}{50}[/tex]v
Step-by-step explanation:
Answer:
Step-by-step explanation:
Link is needed
A ping pong ball has a 75% rebound ratio. When you drop it from a height of k feet, it bounces and bounces endlessly. If the height of the bounce follows geometric progression, find the general term that represent the situation in term of k. [2 marks] Hence, if the ball dropped from a height of 235ft, determine i. the highest height achieved by the ball after six bounces ii. the total distance travelled by the ball when it strikes the ground for 12th time [2 marks] [3 marks b) The number of cell double after each process of cell division every 2 hours. If there are 120 bacteria initially, how many bacteria will be there after one and half day? [4 marks]
Answers
The movement of the ping pong ball follows a exponential progression.
The expression for the k-th bounce is: [tex]\mathbf{T_k = 235 \times (0.75)^k}[/tex]The height after the 6th bounce is 41.82 ftThe total distance after the 12th bounce is 1584.84ft.There will be 31457280 bacteria after a day and a half.1. Ping pong ball
The given parameters are:
[tex]\mathbf{a = 235}[/tex] --- the initial height
[tex]\mathbf{r = 75\%}[/tex] --- the common ratio
(a) The expression after bouncing k times
To do this, we make use of
[tex]\mathbf{T_n = a \times r^n}[/tex]
So, we have:
[tex]\mathbf{T_n = 235 \times (0.75)^n}[/tex]
In this case; k = n.
So, the equation becomes
[tex]\mathbf{T_k = 235 \times (0.75)^k}[/tex]
Hence, the expression for the k-th bounce is: [tex]\mathbf{T_k = 235 \times (0.75)^k}[/tex]
(b) The height after bouncing 6 times
This means that k = 6.
So, we have:
[tex]\mathbf{T_k = 235 \times (0.75)^k}[/tex]
[tex]\mathbf{T_6 = 235 \times (0.75)^6}[/tex]
[tex]\mathbf{T_6 = 41.82}[/tex]
Hence, the height after the 6th bounce is 41.82 ft
(c) The total distance after the 12th bounce
First, we calculate the total height after the 12th bounce using:
[tex]\mathbf{S_k = \frac{a(1 - r^k)}{1 - r}}[/tex]
So, we have:
[tex]\mathbf{S_k = \frac{235 \times (1 - 0.75^{12})}{1 - 0.75}}[/tex]
[tex]\mathbf{S_k = \frac{235 \times (0.968)}{0.25}}[/tex]
[tex]\mathbf{S_k = 909.92}[/tex]
So, the total distance is:
[tex]\mathbf{Distance = 2 \times S_k - a}[/tex]
[tex]\mathbf{Distance = 2 \times 909.92 - 235}[/tex]
[tex]\mathbf{Distance = 1584.84}[/tex]
Hence, the total distance after the 12th bounce is 1584.84ft.
(2) Cell division
The given parameters are:
[tex]\mathbf{r = 2/2hr}[/tex] --- rate
[tex]\mathbf{a = 120}[/tex] --- initial number of cells
[tex]\mathbf{t = 18}[/tex] --- number of 2 hours is a day and a half
So, the number of bacteria is:
[tex]\mathbf{T_t = ar^t}[/tex]
This gives
[tex]\mathbf{T_t = 120 \times 2^{18}}[/tex]
[tex]\mathbf{T_t = 31457280}[/tex]
Hence, there will be 31457280 bacteria after a day and a half.
Read more about exponential functions at:
https://brainly.com/question/11487261
evaluate f(m-5) and simplify if f(x)=5x-9
Answers
Answer:
f(m-5) = 5m-34
Step-by-step explanation:
f(x)=5x-9
Replace x with m-5
f(m-5) = 5(m-5) -9
Distribute
= 5m-25 -9
= 5m-34
Answer:
answer is 5m - 34
Step-by-step explanation:
!!!!!!!!!!!!!!!!!!!!!!!!
Please help me with number 8
Answers
Answer:
jjejejkwkwkqkkqkqkqkkqkqkq
A cyclist rides her bike at a rate of 10 kilometers per hour what is this rate in miles per hour? How many miles will the cyclist travel in 3 hours? In your computations, assume that 1 mile is equal to 1.6 kilometers l. Do not round your answers
Answers
Answer:
cyclist will travel 64 kilometres in 4 hours
Step-by-step explanation:
speed of cyclist = 10 miles per hour
given 1 mile is equal to 1.6 kilometres.
1*10 miles will be equal to 1.6*10 kilometres
thus , 10 mile is equal to 16 kilometres
using 16 km in place of 10 miles in 10 miles per hour
we have
speed of cyclist = 16 kilometres per hour
we know that distance = speed * time
speed is 16 kilometres per hour
time 4 hours
thus , distance = 16*4 kilometres= 64 kilometres.
cyclist will travel 64 kilometres in 4 hours.
(Hope this helps can I pls have brainlist (crown)☺️)
Simplify.
- 2x - } – 5x + i + x
-
х
-
17/3
-
3
+
10
х
Enter your answer in the box.
Do not use decimals in your answer.
Answers
Answer:
I'dont think it's 77 or not right
Given info:-
Evaluate:
[(1⅕ - 2/5).(-3/5)³]÷(-9)
⇛[6/5 - 2/5).(3³/5³)]÷(-9)
Take the LCM 5 & 5 is 5.
⇛[(6-2 /5). (3*3*3/5*5*5)]÷(-9)
⇛[(4/5).(27/125)]÷(-9)
⇛[4/5 × 27/125)]÷(-9)
⇛[(4*27)/(5*125)]÷(-9)
⇛[20/625] ÷ (-9)
⇛[20/625] ÷ 1/9
⇛20/625 × 9/1
⇛(20*9)/(625*1)
⇛180/625
Now, reduce the fraction by extracting and cancaling out with 5.
⇛36/125 or 0.228 Ans.
Hope this helps!
please ans very easy question
Answers
Answer:
what is the question please tell me on comment
Evaluate the expression 6^2-(8–4^2+7
Answers
Answer
11
you can confirm from by yourself or tell
please mark this answer as brainlist
help with 14 please!!! please also explain!!
Answers
Answer:
f = ab/(a + b)Step-by-step explanation:
#14Given:
1/f = 1/a + 1/bSolving for f:
1/f = b/ab + a/ab1/f = (a + b)/ab cross - multiplyf(a + b) = ab divide by (a + b)f = ab/(a + b)X-6y=6 find an ordered pair
Answers
Answer:
(6,0) or (0,-1)
Step-by-step explanation:
X-6y=6
X=6+6y
X/6=1+y
X/6-1=y
y=X/6-1
We'll use substitution to solve the ordered pair. Let's say Y = 0. We'll insert it back into our equation.
0=X/6-1
1=X/6
6=X
(6,0)
We can also start with X being = 0.
y=0/6 -1
y=-1
(0,-1)
I've attached what that would look like as a graph.
Find the volume of the composite solid.
Answers
Answer:
volume________
7 ft 8 ft 7.5 ft 7 ftCan someone help me please
Answers
Answer:
The financial aid covers $ 1,875
Student needs to pay out-of-pocket $635
Step-by-step explanation:
(2,500) * (3/4) = 7500/4 = 1,875
2,500 - 1,875 = 635
Vocabulary How does a percent relate to a proportion? Drag the words to complete the explanation Each word may be used once or not at all
Answers
Answer:
A percent is a constant of proportionality describing the part of the whole
Step-by-step explanation:
A bag of M&M’s has 7 red, 2 green, 3 blue, and 8 yellow M&M’s. What is the probability of randomly picking: (Round to 4 decimal places)
Answers
Answer:
Y = 40%
R or G = 25%
O = 0%
Step-by-step explanation:
Total M&M's = 7+2+3+8 = 20
PY = 8/20 = .4 or 40%
P(R or G) = (2+3)/20 = 5/20 = .25 = 25%
PO = 0/20 = 0%
If the sales tax rate is 8.9%, how much tax will be paid on a $457 tv?
State your answer in terms of dollars, rounded to the nearest cent (hundredth).
Do not include a $ sign with your response.
Answers
if y varies inversely as x, when y=20 and x=2 find the equation for y. then, find y when x=4
Answers
Answer:
the equation for y=20=1/2
Step-by-step explanation:
y=1/4
y=0.25
What is 449,650 rounded to the nearest ten thousand?
400,000
440,000
449,000
450,000
Answers
Answer:
450,000
Step-by-step explanation:
The ten thousand digit is 4 and if we compare it to 9, it is bigger then 5 therefore it is rounded up and you get the answer of 450,000
x^2-6x+13 step by step to vertex form
Answers
Same value as 40% of 84
Answers
Answer:
33.6
you are welcome :)
Step-by-step explanation: