Rational expressions are expressions that can be represented as a quotient
The equivalent rational expression of [tex]\mathbf{\frac{(5c + 9)(c - 3)}{c - 8}}[/tex] is [tex]\mathbf{\frac{5c^2 -6c-27}{c - 8}}[/tex]
The expression is given as:
[tex]\mathbf{\frac{(5c + 9)(c - 3)}{c - 8}}[/tex]
Expand the numerator as follows
[tex]\mathbf{\frac{(5c + 9)(c - 3)}{c - 8} = \frac{(5c \times c -5c \times 3 + 9\times c -9 \times 3)}{c - 8}}[/tex]
Multiply the factors on the numerator
[tex]\mathbf{\frac{(5c + 9)(c - 3)}{c - 8} = \frac{(5c^2 -15c+ 9c -27)}{c - 8}}[/tex]
Collect and evaluate like terms
[tex]\mathbf{\frac{(5c + 9)(c - 3)}{c - 8} = \frac{(5c^2 -6c-27)}{c - 8}}[/tex]
Remove the brackets
[tex]\mathbf{\frac{(5c + 9)(c - 3)}{c - 8} = \frac{5c^2 -6c-27}{c - 8}}[/tex]
This means that:
[tex]\mathbf{\frac{5c^2 -6c-27}{c - 8}}[/tex] and the given expression [tex]\mathbf{\frac{(5c + 9)(c - 3)}{c - 8}}[/tex] are equivalent
Hence, the equivalent rational expression of [tex]\mathbf{\frac{(5c + 9)(c - 3)}{c - 8}}[/tex] is [tex]\mathbf{\frac{5c^2 -6c-27}{c - 8}}[/tex]
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Yamuna is getting ready to attend Wittenberg University in the fall. She needs 6 notebooks
at $2.19 each and a chromebook at $529.00. If she has $575 to spend, how much does
she have left for lunch?
Answer:
she has $32.86 left for lunch
Step-by-step explanation:
6 books at $2.19 each equals $13.14. plus the chrome book at 529. 529+13.14= $542.14
$575-542.14 equals $32.86
Solve the inequality -3/4(12x+16)<9-5x.
Answer:
x > -21/4
Step-by-step explanation:
Answer:
x > -24/4
Step-by-step explanation:
-3/4 (12x + 16) < 9 - 5x
-3/4 * 12x - 3/4 * 16 < 9-5x
-9x - 3/4 * 16 < 9 - 5x
-9x - 12 < 9 - 5x
-4x - 12 < 9
-4x < 21
A 19 -ft ladder leans against a building so that the angle between the ground and the ladder is 81 ∘. How high does the ladder reach on the building? ft
Answer:
18.77 ft
Step-by-step explanation:
use SOHCAHTOA
The ladder is a side, which is opposite to the angle. The ladder's side is also the hypotenuse of the triangle, so use sin.
sin(81) * 19 = 18.77 ft
Please help me please help please please help me
Answer:
3/2
-4
Step-by-step explanation:
y = mx + c
m = slope = y2 - y1 / x2 - x1
= -4 -2 / 0 - 4
= -6/-4
= 3/2
c = y intercept
y when x = 0
c = -4
Answer:
[tex]y = \frac{2 - ( - 4)}{4 - 0}x - 4 \\ y = \frac{6}{4} x - 4 \\ y = \frac{3}{2} x - 4 \\ [/tex]
Solve for x, please help, thank you
Answer:x=6
Step-by-step explanation:
x+5x=36
Step 1: Simplify both sides of the equation.
x+5x=36
(x+5x)=36(Combine Like Terms)
6x=36
6x=36
Step 2: Divide both sides by 6.
[tex]\frac{6x}{6} =\frac{36}{6}[/tex]
x=6
Answer:
x=6
What is the Scale factor of 35 to 42
QUESTION. What is the Scale factor of 35 to 42
--------------------------------------
[tex]\boxed {\tt 25/35}[/tex]
---------------------------------------
The Scale Factor of 35/42 is the relative difference of one fraction or number (a) to another fraction or number prime (a′). In other words, 35/42 is what you multiply (number a) by to get (number a prime).
In a multiplication problem, we have a multiplier, multiplicand, and a product. You could say that (a) is the multiplier, the Scale Factor of 35/42 is the multiplicand, and (a′) is the product:
multiplier × multiplicand = product
multiplier × scale factor = product
a × 35/42 = a′
In the calculator below, you can enter the multiplier (a) as a fraction. We will then multiply it by the Scale Factor of 35/42 and give you the product (a′) in its simplest form possible.
Simplify the expression w²y³ ÷ wy⁴ please help me thank you for you kindness
Answer:
W/y
Step-by-step explanation:
Simplify the expression using trigonometric identities: sec (–θ) – cos θ.
Answer:
sin θ . tan θ
Step-by-step explanation:
Note : -
sec ( - θ ) = sec θ
Formula / Identity : -
sec θ = 1 / cos θ
sec ( - θ ) - cos θ
= [ 1 / cos θ ] - cos θ
{ LCM = cos θ }
= [ 1 / cos θ ] - [ cos²θ / cos θ ]
= [ 1 - cos²θ ] / cos θ
{ 1 - cos²θ = sin²θ }
= sin²θ / cos θ
{ sin²θ = sin θ . sin θ }
= sin θ . sin θ / cos θ
{ sin θ / cos θ = tan θ }
= sin θ . tan θ
Hence, simplified.
In this problem, I did part a) correctly, but I got 7 points off in part b) but I don’t know why?
Answer: You need to prove that ABCD is a rhombus because it's diagonals are always perpendicular, no matter what.
A rhombus is a quadrilateral and:
- its opposite angles have equal measure.
- The two diagonals of a rhombus are perpendicular; that is, a rhombus is an orthodiagonal quadrilateral.
- Its diagonals bisect opposite angles.
Im so confused- please help
Step-by-step explanation:
a/q
x + x - 3 + 2x - 9 = 36
4x - 12 = 36
4x = 36 + 12 = 48
x = 48/4 = 12
x = 12
so,
x = 12
x - 3 = 12 - 3 = 9
2x - 9 = 2(12) - 9 = 15
we know,
area = 1/2 × base × height
so,
→ 1/2 × 12 × 9
→ 1 × 6 × 9
→ 54 inches.
HOPE THIS ANSWER HELPS YOU DEAR! TAKE CARE
Matthew Bailey, as manager of Designs by Bailey, is upgrading his CAD software. The high-performance (HP) software rents for $3,000 per month per workstation. The standard-performance (SP) software rents for $2,000 per month per workstation. The productivity figures that he has available suggest that the HP software is faster for his kind of design. Therefore, with the HP software he will need five engineers and with the SP software he will need six. This translates into a variable cost of $200 per drawing for the HP system and $240 per drawing for the SP system. At his projected volume of 80 drawings per month, which system should he rent?
Using linear functions, it is found that the high-performance system should be rented.
A linear function has the following format:
[tex]y = ax + b[/tex]
In which:
a is the slope, which is the variable cost.b is the y-intercept, which is the fixed cost.With the high-performance software:
Fixed cost of $3,000 per month, hence [tex]b = 3000[/tex].Cost of $200 per drawing, hence [tex]a = 200[/tex]Then, the model is:
[tex]C_{hp}(d) = 3000 + 200d[/tex]
With the standard-performance software:
Fixed cost of $2,000 per month, hence [tex]b = 2000[/tex].Cost of $240 per drawing, hence [tex]a = 240[/tex]Then, the model is:
[tex]C_{sp}(d) = 2000 + 240d[/tex]
The costs for 80 drawings, that is, [tex]d = 80[/tex] for both cases are given by:
[tex]C_{hp}(80) = 3000 + 200(80) = 19000[/tex]
[tex]C_{sp}(80) = 2000 + 240(80) = 21200[/tex]
Due to the lower cost, the high-performance system should be rented.
A similar problem is given at https://brainly.com/question/20849340
Consider the graph of the of the quadratic function g(x). See below
Answer:
I believe the correct answers would be...
32.) B
33.) C
Step-by-step explanation:
32.)
Since the function is shifted downward 1 unit from the x-axis, "q" would be -1
33.)
If the function is shifted upward 4 units, the "+4" would be on the outside of the parentheses.
Tell whether the fractions are equivalent. Write = or
2/3 ______ 4/6
[tex]\dfrac 23 = \dfrac{2 \times 2 }{3 \times 2} = \dfrac 46[/tex]
Rest of the options
The answer is D, the last one
Help me please! This is so confusing!
Answer:
a) yes, 2, 1/2
b) b = 2t; t = 1/2b
Step-by-step explanation:
a) The number of batteries is twice the number of toys. Using the variables of part B, this relation is ...
b = 2t
This is of the form required for a proportional relation: y = kx, with a value of k=2.
__
If we divide the above equation by 2 on both sides, we get ...
1/2b = t
This is also a proportional relation, with a constant of proportionality of 1/2.
Toys and batteries are in a proportional relationship. The constants of proportionality are 2 or 1/2.
__
b) As we saw above, the equations can be ...
b = 2t
t = 1/2b
i'll mark brainliest, thanks in advance!
Answer:
not enough information.
Step-by-step explanation:
We know one side and the vertical angle. We do not have enough information to determine if the triangles are congruent.
A bag has 2 blue marbles, 3 red marbles, and 5 white marbles. Which events have a probability greater than One-fifth? Select three options. choosing 1 blue marble choosing 1 red marble choosing 1 red marble, not replacing it, and then choosing a blue marble choosing 1 white marble, replacing it, and choosing another white marble choosing 1 white marble
hi i know i'm late but might as well add my answer!
here's your answer: B D E or
B.choosing 1 red marble
D.choosing 1 white marble, replacing it, and choosing another white marble
E.choosing 1 white marble
hope i helped
Answer:
b d and e
Step-by-step explanation:
ya
Which triangles are similar?
Triangle A
34/
A
30
37
12
15
h
53
9
62
16
Triangle C
Triangle B
A. Triangles A and C
B. Triangles A, B, and C
C. Triangles A and B
D. Triangles B and C
Triangle A and C are same because the angles formed by all three sides are same in both triangles.
Hope it helps you....
Please mark as brainlliest!!!
f(3) if f(x) = 2x+2 helpppppppppppppppppp
Answer:
= 8
Step-by-step explanation:
2x = 2 × 3 is 6 because f(3) then + 2 is 8
3 x 2 = 6
6 + 2 = 8
The correct answer is 8
(Hope this helps can I pls have brainlist (crown)☺️)
What is the value of the expression?
(323+1715)−(1135+213)
Enter your answer as a mixed number in simplest form by filling in the boxe
Answer:
690
Step-by-step explanation:
(323+1715)-(1135+213)
(2038)-(1348)
=690
The value of the expression is 690
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is (323+1715)−(1135+213)
We have to find the value of expression
By using PEMDAS rule we solve the expression
Let us find the value in parenthesis
2038 -1348
We get 690
Hence, the value of the expression is 690
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i'll mark brainliest, thanks in advance!
Answer:
SSS
Step-by-step explanation:
are 2 isosceles right triangles congruent, have both sides and angles equal, so the answers are all valid, the simplest is SSS, 2 sides are the same and marked on the drawing, the third is the same accordingly
Please help!!
Choose the definition for the function.
9514 1404 393
Answer:
A. {2x, x<1; (x+5)/2, x≥1}
Step-by-step explanation:
The left side of the graph (x<1) has positive slope and a y-intercept of 0. Only one answer choice matches: choice A.
How many times two odd digits appear in a number when you count from 0 to 999?
The solution is: It occurred 90 times does the digit 5 occur in all the numbers from 100-999 .
What is Arithmetic progression?An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
For instance, the sequence 5, 7, 9, 11, 13, 15.. . is an arithmetic progression with a common difference of 2.
The nth term of AP : a_n = a + (n – 1) × d
here, we have,
Explanation:
Here, we want to know the number of times the digit occurs
We can solve this with arithemetic progression
The first term here is 105, while the last term is 995
However, the difference between each occurrence is 10
Thus, applying the formula:
T_n = a + (n-1) d
T_n is the last term which is 995
a is the first term which is 105
d is the common difference which is 10
n is the number of terms which we want to calculate
Substituting these values, we have it that:
995 = 105 + (n-1) 10
so, we get,
n = 900/10
=90
Hence, It occurred 90 times does the digit 5 occur in all the numbers from 100-999 .
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complete question:
How many times does the digit 5 occur in all the numbers from 100-999 ?
A local animal shelter has many cats and dogs. The shaded part represents the percent of animals that are dogs. If there are 82 dogs, how many animals are there in total?
Answer:
weel if you divide 82 by 2 then it you will get the number of cats which is 41 then add 82 + 41 =123
Step-by-step explanation:
mark me brainliest
-5 1/5 + 3.7 + 5 1/10 how to solve
Answer:
to find the answer u have to simplify
A farmer wants to increase the area of His rectangular pen but keep the pen a rectangular shape. He decides to a 5.7 yards of fencing
to the width of the pen but the length will remain 9.5 yards. The new area will be 77.9 square yards.
Which can be used to determine the original width of the pen?
5.7 (W+9.5) = 77.9
S95219
9.5 (W + 5.7) = 77.9
Using the equation for the area of a rectangle, the original width of the pen is determined by:
9.5 (W + 5.7) = 77.9
The area of a rectangle of length l and width w is given by:
[tex]A = lw[/tex]
In this problem:
Increases the width by 5.7 yards, hence [tex]w = w + 5.7[/tex], in which w is the original width.The length remains at 9.5 yards, hence [tex]l = 9.5[/tex].The area is of 77.9 square yards, hence [tex]A = 77.9[/tex]Then:
[tex]A = lw[/tex]
[tex]9.5(w + 5.7) = 77.9[/tex]
For a similar problem, also involving the area of a rectangle, you can check https://brainly.com/question/10489198
Use synthetic division to find the result when 3x^3 + 4x^2 - 5x - 2 is divided by x + 2
Check the picture below.
A) y = 5x
B) y = 10x
C) y = 7.5x
D) y = 30x
There are 350 students graduating on Sunday. 84% of the students are graduating with Bachelor’s degree in Business. How many students are getting their Bachelor's degree in Business?
Answer:
294 students
Step-by-step explanation:
To find percentage, convert the percent to a decimal and multiple the total number of students
80% --> 0.8
350*0.8 = 294 students
9514 1404 393
Answer:
294
Step-by-step explanation:
84% of 350 is ...
0.84 × 350 = 294
294 students are getting their Bachelor's degree in Business.
__
Additional comment
If your calculator does not have a % key, you can perform the multiplication by converting the percentage to a decimal or using it as a fraction. The % symbol is interchangeable with /100, so 84% = 84/100. Of course, this is eighty-four hundredths, which can also be written 0.84.
Any spreadsheet will accept direct input of numbers with an attached % symbol, so you can use one of those for this calculation, also.
What’s the solution to 2x - 2 > 2x + 4 ?
Answer:
This inequality isn't correct.
Step-by-step explanation:
2x - 2 > 2x + 4
Substituting any value for x, the result will be incorrect.
Actually,
2x - 2 < 2x + 4 is correct.
2x - 2x < 4 + 2
0 < 6