Rewrite as equivalent rational expressions with denominator (c- 9) (c+9)(c + 6):
Answers
Answer:
Step-by-step explanation:
as (c + 9)(c - 9) = c² - 81
and (c - 9)(c + 6) = c² - 3c - 54
8(c + 6) = 8c + 48
(c² - 81)(c + 6) (c - 9)(c + 9)(c + 6)
10c(c + 9) = 10c² + 90c
(c² - 3c - 54)(c + 9) (c - 9)(c + 9)(c + 6)
The equivalent rational expressions with denominator (c- 9) (c+9)(c + 6) are;
1. 8 / (c² - 81) = 8 / (c + 9) (c - 9)
2. 10c / (c² - 3c - 54) = 10c / (c + 6) (c - 9)
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expressions are,
1. 8 / (c² - 81)
2. 10c / (c² - 3c - 54)
Now,
Solve the expressions for the denominator (c- 9) (c+9)(c + 6) as;
1. 8 / (c² - 81) = 8 / (c² - 9²)
= 8 / (c + 9) (c - 9)
Thus, 8 / (c² - 81) = 8 / (c + 9) (c - 9)
2. 10c / (c² - 3c - 54) = 10c / (c² - (9- 6)c - 54)
= 10c / (c² - 9c + 6c - 54)
= 10c / [c(c-9) + 6(c - 9)]
= 10c / (c + 6) (c - 9)
Thus, 10c / (c² - 3c - 54) = 10c / (c + 6) (c - 9)
Therefore, The equivalent rational expressions with denominator (c- 9) (c+9)(c + 6) are;
1. 8 / (c² - 81) = 8 / (c + 9) (c - 9)
2. 10c / (c² - 3c - 54) = 10c / (c + 6) (c - 9)
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ2
Related Questions
Lauren received a box of 12 identical-looking truffles for Valentine's Day. 3/4 of them have a fruit filling and 2/3 of the remaining are coffe-flavored. 1/3 of the fruit-filled ones have raspberry filling and 1/6 of the remaining fruit-filled truffles have strawberry flavor. What is the probability that she will draw a flavor she doesn't reconize.
A. 1/3
B. 2/5
C. 1/2
D. 3/4
Answers
C. 1/2
9 of the truffles are fruit-filled. 2 are coffee-flavored. one is unaccounted for.
Of the 9 fruit-filled ones, 3 are raspberry and one is strawberry. 5 are unaccounted for.
Putting together the ones we don't know, we get 6 unknown ones. 6/12, or 1/2, is the answer.
If sin A =P then the value of tan thita + sec thita is
Answers
i guess you have copied the wrong question.. it should be somewhat like if tan theta + sec theta = p then find tge value of sin theta...
secθ+tanθ=P
⇒(secθ+tanθ)² = P²
⇒sec² θ+tan² θ+2tanθsecθ=P²
⇒2tan²θ + 1 + 2 sinθ/cos θ = P²
⇒2 sin²θ+ cos²θ+ 2 sinθ total by cos²θ = P²
Applying componendo and dividendo
=> 2sin²θ+ cos²θ+ 2sinθ- cos²θ/ 2sin²θ+ cos²θ+ 2sinθ- cos²θ = p²-1 / p²+1
⇒2sinθ(sinθ+1)/ 2(sinθ+1) = p²-1 / p²+1
=> sinθ = p²-1/ p²+1
Amanda's parents invested $10,000 into a savings account for her college fund when she was born. The savings plan compounds interest yearly at a rate of 3.75%. How much money will be in Amanda's college fund when she turns 18? Round your answer to the nearest cent.
A. $20,652.19
B. $19,149.68
C. $20,146.75
D. $19,399.29
Answers
Answer:
D. $19,399.29[tex] \: \: \: \: \: \: [/tex]
The graph shows a proportional relationship between the number of workers and weekly cost in dollars for a company. Use the points (6,4800) and (15,12000) to find the weekly cost for the company for each worker. Use pencil and paper. Describe what a unit rate is used for?
Answers
The weekly cost per worker is: $800
Unit rate can be used for calculating expenses, calculating cost of multiple units, or calculating expenses.
Recall:
Unit rate is calculated using: [tex]\mathbf{\frac{y_2 - y_1}{x_2 - x_1} }[/tex]
Unit rate represents the amount of a quantity compared to its unit of measure.
Unit rate can be used for calculating expenses, calculating cost of multiple units, or calculating expenses.
Since the relationship between number of workers and weekly cost is proportional, we would apply [tex]\mathbf{\frac{y_2 - y_1}{x_2 - x_1} }[/tex] in determining the weekly cost per worker using the points, (6, 4800) and (15, 12000):
SubstituteUnit rate/weekly cost per worker = [tex]\frac{12,000 - 4,800}{15 - 6} = \frac{7,200}{9} = 800[/tex]
Unit rate/weekly cost per worker = $800
In summary, the weekly cost per worker is: $800
Unit rate can be used for calculating expenses, calculating cost of multiple units, or calculating expenses.
Learn more here:
https://brainly.com/question/19154956
n a very large population that has a proportion of a particular disease p, a researcher conducting a study on this disease, is taking samples sequentially until she receives three cases consecutively. Find the mean and the variance of the number of samples she needs to take.
Answers
Answer:
sorry don't speak Spanish
Which of the following correctly shows the re-grouping for 45 x 12? Group of answer choices 40 x 10; 5 x 10; 40 x 2; 5 x 40
40 x 10; 5 x 10; 40 x 5; 5 x 2
40 x 5; 5 x 10; 40 x 2; 5 x 2
40 x 10; 5 x 10; 40 x 2; 5 x 2
Answers
Answer:
40x10;5x10;40x2;5x2
400+50+80+10
=540
There are three compartments for luggage and each compartment has a capacity of 25 pieces of luggage. The first two compartments are full up and the last one contains 8 pieces of luggage. How many pieces of luggage are there?
Answers
Answer:
the first 2 compartments have 25 so 25+25=50, and the last has 8 in it so 50+8=58
Sampling Seventy-two percent of Americans squeeze their toothpaste tube from the top.
This and other not-so-serious findings are included in The First Really Important Survey of
American Habits. Those results are based on 7000 responses from the 25,000 questionnaires
that were mailed.
a. What is wrong with this survey?
b. As stated, the value of 72% refers to all Americans, so is that 72% a statistic or a parameter?
Explain.
c. Does the survey constitute an observational study or an experiment?
Answers
answer this question fast
Answers
Explanation: there is two flavors and three different shapes that each flavor comes in.
1/7 divided by blank equals 14
Answers
Answer:
1/98
Step-by-step explanation:
Step 1: Translate statement into equation.
[tex]\frac{1}{7}/x = 14[/tex] [tex]\frac{1}{7x}=14[/tex]Step 2: Multiply both sides by 7x.
[tex]\frac{1}{7x} * 7x = 14 * 7x[/tex] [tex]1 = 98x[/tex]Step 3: Divide both sides by 98.
[tex]\frac{1}{98} =\frac{98x}{98}[/tex] [tex]x = \frac{1}{98}[/tex]Step 4: Check if solution is correct.
[tex]\frac{1}{7}/\frac{1}{98}[/tex] [tex]\frac{1}{7}*98[/tex] [tex]14[/tex]Therefore, the answer is 1/98.
Which of the following statements describes a positive correlation?
The more I study the lower my test scores
The greater the cost, the better the merchandise
Walnut is more dense than pine
none of the other alternatives are correct
Answers
Answer:
The greater the cost, the better the merchandise
Step-by-step explanation:
It’s giving a positive correlation.
The scale for a map to actual distance is 2 centimeters to 100 miles. The driving distance on the map between Los Angeles and Las Vegas is 5.4 centimeters. What is the actual distance, in miles, between Los Angeles and Las Vegas?
Answers
[tex]\begin{array}{ccll} \stackrel{cm}{map}&\stackrel{mi}{actual}\\ \cline{1-2} 2&100\\ 5.4&x \end{array}\implies \cfrac{2}{5.2}=\cfrac{100}{x}\implies 2x = 520\implies x = \cfrac{520}{2}\implies x = 260[/tex]
Find the general solution of the given differential equation x2 y’ -2xy = x4 + 3
Answers
[tex] \times 2 \: y \: - 2xy = \times 4 + 3 = \times - \frac{3}{4} \: y \: e \: r[/tex]
Which equation reprints a line passing through the point (8,16) with a slope of 3
Answers
Tell me if you want step by step!
Hope this helps. :)
A half circle is joined to an equilateral triangle whose
sides are each 10 units long.
What is the perimeter of this shape?
Please explain too
Answers
We want to find the perimeter of the given figure. We will find that the perimeter of the figure is 35.7 units.
Remember that for a circle of diameter D, the perimeter or circumference is:
p = pi*D
where pi = 3.14
So we have a half-circle and an equilateral triangle, and we know that the equilateral triangle sides measure 10 units each.
Notice that the diameter of the half-circle is equal to the side length of the triangle, then the diameter is D = 10
Then the length of the arc of the half-circle is just given as half the circumference of a circle with a diameter of 10 units, this is:
C = (1/2)*3.14*10 = 15.7
And to this we must add the two sides of the triangle that belong to the perimeter, remember that each one measures 10 units, then the total perimeter is:
Perimeter = 15.7 + 10 + 10 = 35.7
If you want to learn more, you can read:
https://brainly.com/question/9350935
solve pls brainliest
Answers
3. How many 1/8's are in 1 1/4?
Answers
Answer:
10
Step-by-step explanation:
There are two 1/8 in one 1/4. There are eight 1/8 in 1. 8/8 + 1/8 + 1/8 = ten 1/8.
I need answers to all of these and explanation as well. Thank you.
Answers
4) d
let's firstly convert the mixed fractions to improper fractions, and then proceed
[tex]\stackrel{mixed}{4\frac{3}{8}}\implies \cfrac{4\cdot 8+3}{8}\implies \stackrel{improper}{\cfrac{35}{8}}~\hfill \stackrel{mixed}{1\frac{1}{4}}\implies \cfrac{1\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{5}{4}} \\\\[-0.35em] ~\dotfill\\\\ -4\frac{3}{8}-\left( -1\frac{1}{4} \right)\implies -\cfrac{35}{8}-\left( -\cfrac{5}{4} \right)\implies -\cfrac{35}{8}+\cfrac{5}{4}\implies \cfrac{-(1)(35)~~ +~~(2)(5)}{\underset{\textit{using this as LCD}}{8}}[/tex]
[tex]\cfrac{-35+10}{8}\implies -\cfrac{25}{8}\implies -3\frac{1}{8}[/tex]
5)
hmmm we can pick any of those %, hmmm let's use 18%, keeping in mind that the whole amount is really the 100% and that's say "x", hmmm we know the 18% of "x" is $5.87.
[tex]\begin{array}{ccll} \%&amount\\ \cline{1-2} 18&5.87\\ 100&x \end{array}\implies \cfrac{18}{100}=\cfrac{5.87}{x}\implies \cfrac{9}{50}=\cfrac{5.87}{x} \\\\\\ 9x = 293.5\implies x = \cfrac{293.5}{9}\implies x = 32.6\overline{1}\qquad \textit{about 32 bucks and 61 cents}[/tex]
Mr. and Mrs. Bruce took a boat trip which left Cala for Friends’ Island at 11:45 in the morning. The trip lasted for 1 hour and 20 mins. When did they arrive at Friends’ Island?
Answers
A 9 in the thousandths place has 10 times the value of a 9 in the ? Place.
Answers
Answer:
hundredths place
Answer:
ten thousandths place
Step-by-step explanation:
9 in the thousandths place is basically 0.009, and a 9 in the ten thousandths place is basically 0.0009, which multiplied by ten is 0.009
the area of a circle in terms of pi is 4pi m2. find the value of the diameter
Answers
Answer:
4 m
Step-by-step explanation:
The area of a circle is given in terms of diameter by ...
A = (π/4)d²
Then the diameter in terms of area is ...
d = √(4A/π)
For the given area, the diameter is ...
d = √(4·4π/π) = 4 . . . meters
The diameter of the circle is 4 meters.
3 and 1/13 in simplest form.
Answers
Answer:
3 1/3 is already in the simplest form. It can be written as 0.230769 in decimal form (rounded to 6 decimal places).
Have an awesome day! :D
HELP WITH PART C
Lionfish are considered an invasive species, with an annual growth rate of 65%. A scientist estimates there are 7,000 lionfish in a certain bay after the first year.
Part C: If scientists remove 1,300 fish per year from the bay after the first year, what is the recursive equation for f (n)? Show all necessary math work.
So I know that the equation would be
[tex]f(n) = (f_{n-1} )(r)[/tex]
Where f(n) is the number of years but I am confused on how to fill out the rest. Any help would be appreciated. Thank you.
Answers
The recursive equation for f(n) will be f(n) = 4242.42(1.65)ⁿ - 1300n.
What is an exponent?Let Consider the function:
y = a (1 ± r) ˣ
Where x is the number of times this growth/decay occurs,
a = initial amount, and r = fraction which this growth/decay occurs.
Lionfish are considered an invasive species, with an annual growth rate of 65%.
Then the equation will be
f(n) = P(1.65)ⁿ
P = initial population
A scientist estimates there are 7,000 lionfish in a certain bay after the first year.
7000 = P(1.65)
P = 4242.42
Then the equation will be,
f(n) = 4242.42(1.65)ⁿ
If scientists remove 1,300 fish per year from the bay after the first year.
Then the recursive equation for f(n) will be,
f(n) = 4242.42(1.65)ⁿ - 1300n
Learn More about the exponent link is given below.
brainly.com/question/5497425
#SPJ2
escape resort rents snowshoes in the winter the resort changes charges seven dollars per day and a flat fee of three dollars to cover cleaning right in equation that shows how the cost why depends on the length of the rental and days X do not include $in the equation
Answers
Answer:
Y=7x+3
Step-by-step explanation:
Can I get help please....
Sara bought 3/4 of a pound of bananas and 3/5 of a pound of pears. How much fruit did Sara buy?
Answers
Answer:
2 fruits
Step-by-step explanation:
That's because bananas and pears are two different fruits
Answer:
1 7/20 pounds
Step-by-step explanation:
3/4 + 3/5
Use common denominator of 20
15/20 + 12/20
Add numerators
27/20
Reduce
1 7/20 pounds
If 2x + y = 7, what is the value of y when x = 3? A. 1 B. 3 C. 5 D. 7 E. 9
Answers
Answer:
the correct answer is A.1
the result is explained below in the photo
Answer:
y = 1
Step-by-step explanation:
2x + y = 7
x = 3
plug in 3 for x
2(3) + y = 7
Multiply 2 * 3
6 + y = 7
Therefor y = 1
helppp please!!!!!!!!!!!!!!
Answers
Answer:
No
No
Yes
Yes
No
Step-by-step explanation:
In this case we are looking at substitution, so any where you find x put three(3) in replace of it.
And remember the answer should be 36,
I find it difficult to type the answer so I will take a picture instead.
If point S ( 3, 4 ) is reflected across the line y=1, what are the coordinates of its reflections image?
Answers
Answer: C
Step-by-step explanation: If point P(3,10) is reflected across the line y=1, the coordinates of it's reflection image is (3,-8)
Simplify: 7√(1/3) + 2 1/3√(1/3) + 3√(147)
Answers
Step-by-step explanation:
7 √(1/3) - 2 1/3 √(1/3) +3√147
→7(1/√3) - (7/3)(1/√3) +3√(3×7×7)
→ (7/√3) - (7/3√3) +3×7√3
→ (7/√3) - (7/3√3) + 21√3
On Rationalising the denominators then
→ [ 7√3/(√3×√3)]-[7√3/(3×√3×√3) +21√3
The Rationalising factor of√3 =√3
→ (7√3/3)-[7√3/(3×3)]+21√3
→ (7√3/3)-(7√3/9)+21√3
LCM of 3 and 9 = 9
→ [(3×7√3)-(7√3)+(9×21√3)]/9
→ (21√3-7√3+189√3)/9
→[(21-7+189)√3]/9
→ [(210-7)√3]/9
→ 203√3/9 Ans.
Hope this helps.
What is 34 ÷ 14?A) 1B) 3C) 4D) 316
Answers
Answer:
2.42
Step-by-step explanation:
Answer: 2.4
Step-by-step explanation: It is 2.4 because it is 2 remainder 6