Rewrite as equivalent rational expressions with denominator (5c+9)(c−3)(c−8): 8/5c^2-6c-27, 2c/5c^2-31c-72
The equivalent rational expression with the same denominator as given will be 8(c - 8)/[(c - 3)(5c - 9)(c - 8)] and 2c(c - 3)/[(c - 3)(5c - 9)(c - 8)].
What is an expression?A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.
An expression is a mathematical proof of the equality of two mathematical expressions.
As per the given expression,
8/(5c² - 6c - 27) , 2c/(5c² - 31c - 72)
Now, take the first denominator,
5c² - 6c - 27 = 5c² - 15c + 9c - 27
⇒ 5c(c - 3) - 9(c - 3)
⇒ (c - 3)(5c - 9)
Take the second denominator
5c² - 31c - 72 = 5c² - 40c + 9c - 72
⇒ 5c(c - 8) + 9(c - 8)
⇒ (c - 8)(5c + 9)
Therefore, the expression converts as,
8/[(c - 3)(5c - 9)] , 2c/[(c - 8)(5c + 9)]
8/[(c - 3)(5c - 9)] = 8(c - 8)/[(c - 3)(5c - 9)(c - 8)]
2c/[(c - 8)(5c + 9)] = 2c(c - 3)/[(c - 3)(5c - 9)(c - 8)]
The denomiantor of both expression are same.
Hence "The equivalent rational expression with the same denominator as given will be 8(c - 8)/[(c - 3)(5c - 9)(c - 8)] and 2c(c - 3)/[(c - 3)(5c - 9)(c - 8)]".
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The structured question below,
To become a member at Anytime Fitness you must pay
an initiation fee of $49.99 when you sign up, $33.99 per
month for the membership.
How many months would you have been with Anytime
Fitness if you paid a total of $321.91 ?
It would take 8 months of membership for the total money paid of $321.91.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. A variable can either be dependent or independent. A dependent variable depend on other variable while an independent variable does not depend on other variables.
Let x be the number of months subscribed. Hence,
For Fitness :
Total payment = 33.99 x + 49.99
if you paid a total of $321.91 then the number of months subscribed will be;
321.91 = 33.99 x + 49.99
33.99 x = 321.91 - 49.99
33.99 x = 271.92
x = 271.92/33.99
x = 8
It would take 8 months of membership for the total money paid of $321.91.
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A harbour seal dives 35 metres below the ocean's surface. Then it dives down an additional 12 metres Determine the seal's new position relative to the surface of the ocean?
The seal's new position relative to the surface of the ocean is 47 meters below.
How to calculate the value?It is important to note that that question has to do with elevation which is the change in position with regards to the sea or ocean level.
In this case, the harbour seal dives 35 metres below the ocean's surface and then it dives down an additional 12 metres
The new position will be;
= -35 - 12
= -47
This implies that it's 47 meters below the ocean surface.
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Note one gallon of water equals 231 cubic inches. If Anna is going to clean the fish tank which measures 48 inches long by 11 inches wide by 35 inches high, how many gallons of water will it take to fill the fish tank?
If any one sees this question please help me answer it because I am having a lot of trouble.
It will take 80 gallons of water to fill the fish tank.
What is volume?The amount of space occupied by a three-dimensional object or region of space.
Given that, Anna is going to clean the fish tank, which measures 48 inches long by 11 inches wide by 35 inches high
The fish tank is cuboidal,
Volume of cuboid = length*width*height
Therefore, volume of fish tank = 48*11*35 = 18,480 in³
1 gallon = 231 in³
So, 18,480 in³ = 18,480/231 gallons = 80 gallons
Hence, Volume of tank = 80 gallons
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How you find interest rates
HELP!! which expression is equivalent to the given expression 2X^2 -11 X -6
Answer: C.
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Fabian has $700 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax. He buys a new bicycle for $387.10. He buys 3 bicycle reflectors for $4.43 each and a pair of bike gloves for $12.36. He plans to spend some or all of the money he has left to buy new biking outfits for $45.81 each. What is the greatest number of outfits Fabian can buy with the money that's left over?
kind of suck help please ? brianslest
Answer:
[tex]d=7[/tex]
[tex]a_9=59[/tex]
Step-by-step explanation:
If the first term of a sequence is [tex]3[/tex] and the second term is [tex]10[/tex], then each successive term in the sequence is [tex]7[/tex] more than the previous term. The common difference is [tex]7[/tex] ( [tex]d=7[/tex] ).
The formula representing the arithmetic sequence is:
[tex]a_n=7n-4[/tex]
Therefore, the ninth term in the sequence is:
[tex]a_9=7(9)-4[/tex]
[tex]a_9=63-4[/tex]
[tex]a_9=59[/tex]
HELP PLEASE ASAP 30 POINTS PLUS BRAINLEST Find the sum of (8.7 x 10^6) and (5.5 x 10^5). Write the final answer in scientific notation.
14.2 x 10^11
1.42 x 10^10
9.25 x 10^6
9.25 x 10^5
Make Sense and Persevere
There are 5 players on a basketball team. In a game 4 players
scored 6 points each. The team scored a total of 34 points.
How many points did the other player score?
1. Tell how to make sense of the problem.
2. Tell the quantities you know. Then explain what you need
to find first to solve the problem.
3. Tell which operations you will use. Then solve the problem.
help plss? i dont know what this means so answer would be great.
Answer:
(e) b h a k
Step-by-step explanation:
You want the order of operations involved in the transformation ...
g(x) = a(bx -h) +k
Order of operationsThe Order of Operations tells you that multiplication takes precedence over addition, and expressions inside parentheses are evaluated first.
EvaluationWe note there is an expression in parentheses here: (bx -h). In that expression is a multiplication operation (bx) and an addition operation (_-h).
The multiplication is done first, so evaluating this expression in parentheses, we ...
multiply by bsubtract hOnce the parenthetical expression is evaluated, we proceed to the main event. Again, multiplication and addition are required. That means the next two steps are ...
multiply (the value of the parentheses) by aadd kIn summary, the operations we perform during evaluation of the transformation successively apply the parameters ...
b h a k
What’s the the anwser?
The solution to the compound inequality is x < 3 and x >6. The graph of the solution is shown.
What is inequality?The relation between two unequal expressions is defined as inequality.
The given inequalities are 3x + 6 < 15 and 2x - 5 >7.
Solve the first inequality:
3x + 6 <15
3x < 15 -6
3x < 9
x < 3
Solve the second inequality:
2x - 5 > 7
2x > 7 + 5
2x > 12
x > 6
Hence, the solution to the compound inequality is x < 3 and x >6.
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394.6/ 9 but use compatible numbers to estimate the quotient
The quotient estimated value of 394.6/9 is 43.84
What is quotient?A quotient is the number which is generated when we perform division operations on two numbers. Basically, it is the result of the division method. There are four main terminologies used in the arithmetic division such as divisor, dividend, quotient and remainder. For example, 15/3= 5 .The number that is being divided ( 15) is called the dividend, and the number that it is being divided by (3) is called the divisor. The result of the division(5) is the quotient.
Therefore the quotient of 394.6/9= 43.84
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PLS HELP WILL MARK BRAINLYIST
Step-by-step explanation:
the solution to a system of functions (lines or any other form of curve) is the point (or points), where they intersect.
in this case : the point (2, 0)
FYI : if there is no intersection, then there is no solution at all (like with parallel lines).
if the curves fully overlap for at least some distance, then we have infinitely many solutions (at least for real numbers). like for identical lines.
Question 5 (1 point)
What is the area of the figure?
5 cm
11.0 cm
20.0 cm
1 cm
2cm
3 cm
The area of the given figure is 25cm².
Area of rectangle
Area = length x width
Perimeter of rectangle
Perimeter = length + length + width + width
Hence, we have
length = 5cm
width = 5cm
then, by applying the Area of the rectangle, we get
Area = length x width
Area = 5 x 5
= 25cm²
Hence, The area of the given figure is 25cm².
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Exercises 12 -15, decide whether the statement is correct or incorrect. Explain your reasoning in words or by drawing pictures. 12. 1/3 equal to 4/12 13. 4/6 equal to 2/3 14. 2/5 equal to 1/3 15. 2/5 equal to 5/10.
The correct statement:
1/3 equal to 4/12; 4/6 equal to 2/3; 2/5 equal to 5/10
incorrect statement: 2/5 equal to 1/3
What is Fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
a) 4/12
Writing into Simplest form
4/12 = 1/3
b) 4/6
Writing into Simplest form
4/6 = 2/3
c) 2/5 cannot be simplified to 1/5
d) 5/10
Writing into Simplest form
5/10= 1/2
Hence, The correct statement: 1/3 equal to 4/12; 4/6 equal to 2/3; 2/5 equal to 5/10 and incorrect statement: 2/5 equal to 1/3.
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what are her monthly payments
The interest she is pay total is $2340.822 when Angela's bank granted her a 6380 loan with a 3 year add-on interest period. 12.23% is the interest rate per year.
Given that,
For the purpose of buying new equipment for her business of antique restoration, Angela's bank granted her a 6380 loan with a 3 year add-on interest period. 12.23% is the interest rate per year.
We have to find will she pay interest at all.
We know that,
i=p×r×t
Here,
i is interest.
p is principal amount.
r is rate of interest
t is time.
So, p is $6380
r is 12.23%
t is 3 years
So,
i= 6380×0.1223×3
i= $2340.822
Therefore, the interest she is pay total is $2340.822 when Angela's bank granted her a 6380 loan with a 3 year add-on interest period. 12.23% is the interest rate per year.
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"What are the coordinates of your reflected triangle A’B’C’?"
Please help! Thank you!
A' - (-1,4)
B' - (-1,8)
C' - (-5,4)
hope this helps
In a study of helicopter usage and patient survival, among the 49,401 patients transported by helicopter, 244 of them left the treatment center against medical advice, and the other
49,157 did not leave against medical advice. If 40 of the subjects transported by helicopter are randomly selected without replacement, what is the probability that none of them left
the treatment center against medical advice?
The probability is
(Round to three decimal places as needed)
Answer:
40%
Step-by-step explanation:
Simplify to one trigonometric expression.
4 sin
()2 cos()
Answer:
Step-by-step explanation:
the answer is 4
AM median CM=5x-2 MB = 3x +12 Find CB
The length of the segment CB in triangle ABC where [tex]\overline{AM}[/tex] is a median line and CM = 5·x - 2, MB = 3·x + 12, CM = MB, is 66 units
What is a median line of a triangle?A median line is a line that is drawn from a vertex of a triangle to the middle of the opposite side such that the it bisects the opposite side.
The parameters are; [tex]\overline{AM}[/tex] = A median line
Length of segment CM = 5·x - 2
Length of segment MB = 3·x + 12
Required; The length of segment CB
The median line [tex]\overline{AM}[/tex] bisects the segment CB
Therefore; CM = MB
CB = CM + MB (Angle addition postulate)
Which gives; 5·x - 2 = 3·x + 12 (substitution property of equality)
5·x - 3·x = 2 + 12 = 142·x = 14
x = 14 ÷ 2 = 7
x = 7CB = CM + MB
CB = (5·x - 2) + (3·x + 12)
Which gives; CB = 8·x + 10
x = 7
CB = 8×7 + 10 = 66
The length of segment CB = 66
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Question 1 (Multiple Choice Worth 5 points) (Graphing Proportional Relationships MC) The table shows a proportional relationship between x and y. x 4.3 9.2 3.4 y 17.2 36.8 13.6 Which of the following correctly describes the graph of the relationship? a.A line that goes through (0, 0) and (17.2, 4.3). b.A line that goes through (4.3, 17.2) and (36.8, 9.2). c.A line that goes through (17.2, 4.3) and (9.2, 36.8). d.A line that goes through (0, 0) and (4.3, 17.2).
The statement that correctly describes the graph of the relationship is (d) A line that goes through (0, 0) and (4.3, 17.2).
How to describe the graph?The table of values is given as
x 4.3 9.2 3.4
y 17.2 36.8 13.6
The table shows a proportional relationship
This means that the line of the graph must pass through the origin i.e. (0, 0)
From the table of values, we have the following point
(4.3, 17.2)
This means that the line of the graph goes through (0, 0) and (4.3, 17.2).
Hence, the true statement is (d)
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Answer:
No, it is not proportional because 9.2 over 18.4 does not equal 17.6 over 52.8.
Step-by-step explanation:
due tomorrow help please :)
Answer:
68°
Step-by-step explanation:
The angles are equal to each other. Set them equal and solve for x
5x + 18 = 8x - 12 Subtract 5x from both sides of the equation
18 = 3x - 12 Add 12 to both sides of the equation
30 = 3x Divide both sides by 3
10 = x
Now that you have found x plug is back into 5x + 18
5(10) + 18
50 + 18 = 68
Answer:
∠ FLJ = 68°
Step-by-step explanation:
∠ EKG and ∠ FLJ are alternate exterior angles and are congruent , then
8x - 12 = 5x + 18 ( subtract 5x from both sides )
3x - 12 = 18 ( add 12 to both sides )
3x = 30 ( divide both sides by 3 )
x = 10
Then
∠ FLJ = 5x + 18 = 5(10) + 18 = 50 + 18 = 68°
Abigail Henderson has $3400.00 budgeted for spending money on an upcoming trip to Country A and Country B. Country A's currency is trading at $1.30 per currency A, and Country B's currency is trading at $1.60 per currency B. She plans to spend more time in Country A, so she wants to have four times as much of currency A as currency B. Set up and solve a system of equations to model this problem, and explain what the answer means in practical terms.
If Abigail Henderson has $3400.00 budgeted for spending money on an upcoming trip .The currency needed is 200 euro and 500 pounds.
How to find the currency needed?Formulate an equation
1.30x + 1.60y = 3400
Hence,
x =4y Equation 1
1.30x + 1.60y = 3400 Equation 2
Substitute eq1 into eq2
1.30(4y) + 1.60y = 3400
5.2y +1.60y =3400
6.8y =3400
Divide both side by 6.8y
y =3400/6.8
y = 500
Number of euro
4y where y = 500
4(500)
=2000
Therefore the answer in practical terms is : 2000 euro of European currency and 500 pounds of Britain currency are needed.
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A notebook computer has a mass of 2.25 kilograms . about how many pounds does the notebook weigh
Answer:
5 pounds
Step-by-step explanation:
1 kg = 2.205 lbs.
2.25×2.205
⇒4.96125
Each of 7 students reported the number of movies they saw in the past year. Here is what they reported. 14,10,16,15,7,15,18
Find the number of movies that the students saw. If necessary, round your answer to the nearest tenth
The total number of movies that the students saw is 105.
I got the answer by adding all of the values that the students saw. So I add 14,10,16,15...etc. which gives me the total of 105.
Use point-slope form to write the equation of a line that passes through the
point (20,-10) with slope 13/8.
Answer:
[tex]y+10=\frac{13}{8}(x-20)[/tex]
Step-by-step explanation:
The equation of the line passing through the point [tex](x_1, y_1)[/tex] and slope [tex]m[/tex] is [tex]y-y_1=m(x-x_1)[/tex].
If FG = 10x − 10, GH = x + 4, and FH = 16, what is FG?
If FG = 10x − 10, GH = x + 4, and FH = 16, FG is 10
How to determine FGinformation given in the question include
FG = 10x − 10
GH = x + 4
FH = 16
The problem is solved using substitution. this involves replacement of a variable with another that are same.
An instance of this a line FH having points FG and GH
FH contains FG and GH, hence adding both FG and GH gives FH
FH = FG + GH
plugging in the values
16 = 10x - 10 + x + 4
collecting like terms
16 = 11x - 6
16 + 6 = 11x
22 = 11x
rearranging the equation
11x = 22
x = 2
FG = 10x − 10
substituting the value of x
FG = 10 * 2 − 10
FG = 20 - 10
FG = 10
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Find the ordered pair (s,t) that satisfies the system
s/2 + 5t = 3 + 5t
3t - 6s = 9 + 3t
Answer:
There isn't one. There is no solution.
Step-by-step explanation:
There are multiple ways to solve this system, but here's what I did:
Solve the both equations for s:
s/2 + 5t = 3 + 5t ⇒ s = 6
3t - 6s = 9 + 3t ⇒ s = -3/2
Since s cannot equal both 6 and -3/2 at the same time, there is no real solution to this system.
7 candy bars cost $6.65. At this rate, how much do 9 candy bars cost?
Answer: $8.55
because 6.65 divided by 7 is 0.95 and 0.95 multiplied by 9 is 8.55
so the answer is $8.55