Which expression is equivalent to the following complex fraction?
3
-4
x-1
2.
X-1
2-
0
2(X-2)
-4X+7
-4X+7 D.
2(X-2)
4x+7
2(x2-2)
2(x2-2)
4x+7
Answers
Answer:
[tex]\frac{-4x+7}{2(x-2)}[/tex]
Step-by-step explanation:
[tex]For x \neq 1 \\\frac{\frac{3}{x-1}-4}{2-\frac{2}{x-1}}=\frac{\frac{3}{x-1}-\frac{4x-4}{x-1}}{\frac{2x-2}{x-1}-\frac{2}{x-1}}=\frac{\frac{-4x+7}{x-1}}{\frac{2x-4}{x-1}}=\frac{-4x+7}{2(x-2)}[/tex]
The equivalent expression is 2(x - 2) / (-4x + 7).
Option A is the correct answer.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
To simplify the given expression:
[3/(x - 1) - 4] / [2 - 2/(x - 1)]
We need to find a common denominator for the two fractions in the numerator and denominator of the main fraction.
The common denominator for the numerator is (x - 1) and for the denominator is 2(x - 1).
We can then rewrite the expression as:
[3 - 4(x - 1)/(x - 1)] / [2(x - 1) - 2/(x - 1)]
Simplifying the numerator by distributing the -4:
(3 - 4x + 4) / (x - 1)
(-4x + 7) / (x - 1)
Now, simplifying the denominator by finding a common denominator:
2(x - 1) - 2/(x - 1)
= (2x - 2 - 2)/(x - 1)
= 2(x - 2)/(x - 1)
Substituting back into the original expression, we get:
(-4x + 7)/(x - 1) / [2(x - 2)/(x - 1)]
Multiplying by the reciprocal of the denominator:
(-4x + 7)/(x - 1) x (x - 1)/[2(x - 2)]
(-4x + 7)/[2(x - 2)]
Therefore,
The equivalent expression is 2(x - 2) / (-4x + 7).
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Related Questions
The tennis courts are 3 blocks west and 2 blocks south of Miguel’s house. The bike path is 5 blocks east and 2 blocks south of Miguel’s house. How many blocks are the tennis courts from the bike path?
Answers
Answer:
8
Step-by-step explanation:
If Miguel's house is (0,0), then the tennis court is (-3,-2), and the bike path is (5,-2). There fore, we can just count the squares between the tennis court and the bike path, which is 8.
Hope that this helps!
From the coordinate calculation, here tennis courts are 8 blocks far from the bike path.
Given that,
The tennis courts are 3 blocks west and 2 blocks south of Miguel’s house. The bike path is 5 blocks east and 2 blocks south of Miguel’s house. How many blocks are the tennis courts from the bike path is to be detemined.
What is coordinate?
Coordinate, is represented as the values on the x-axis and the y-axis of the graph.
Here on the graph,
Assume that Miguel's house is (0,0),
then accoding to the question the tennis court is (-3,-2), and the bike path is (5,-2).
Now, difference in the position dx = 5 - (-3)
= 8
Thus, from the coordinate calculation, here tennis courts are 8 blocks far from the bike path.
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Select the correct answer from each drop-down menu. Mallory goes to the farmers market every weekend. She buys six apples for $0.75 each and a bagful of oranges that are priced at $1.25 per orange. The total charge is $14.50. Write the equation representing this situation where n represents the number of oranges.
Answers
Answer:
a) The equation for the situation = 14.50 = 4.5 + 1.25n
b) The number of oranges she bought = 8 oranges
Step-by-step explanation:
Where n represents the number of oranges.
The equation is written as
Total charge = $0.75 × 6 + $1.25 × n
$14.50 = $0.75 × 6 + $1.25 × n
14.50 = 4.5 + 1.25n
1.25n = 14.5 - 4.5
1.25n = 10
n = 10 / 1.25
n = 8 oranges
PLEASE HELP. !!!!!!
the 4th option is “A translation 2 units left and 1 unit up
Answers
Hannah has a part-time job making holiday wreaths. This week, she made x medium wreaths, twice as many large wreaths as medium wreaths, and 12 as many small wreaths as medium wreaths. In terms of x, how many wreaths did Hannah make this week?
Answers
Answer:
Total number of wreaths = 3.5 wreaths
Step-by-step explanation:
Given:
Number of medium wreaths = x
Number of larger wreaths = 2[Number of medium wreaths]
Number of small wreaths = [1/2][Number of medium wreaths]
Find:
Total number of wreaths
Computation:
Total number of wreaths = Number of medium wreaths + Number of large wreaths + Number of small wreaths
Total number of wreaths = Number of medium wreaths + 2[Number of medium wreaths] + [1/2][Number of medium wreaths]
Total number of wreaths = x + 2x + 0.5x
Total number of wreaths = 3.5 wreaths
A wire attached to the top of a pole reaches a stake in the ground 20 feet from the foot of the pole and makes an angle of 58° with the ground. Find the length of the wire.
Answers
cos 58 = 20/length of rope
length of rope = 20/cos 58 degrees
= 37.74 feet
In a bag there are blue sweets and red sweets. The ratio of blue sweets to red sweets is 5:3 What fraction of the sweets are blue?
Answers
Answer:
5/8
Step-by-step explanation:
SUM OF RATIOS = 5 + 3 = 8
fraction of blue sweet = blue sweet ratio / sum of ratios = 5/8
two rectangles have a scale factor of 4:1. If the area of the larger rectangle is 156cm^2, what is the area of the smaller rectangle?
A. 26.75 cm^2
B. 31 cm^2
C. 9.75 cm^2
D. 39 cm^2
Answers
Answer:
c=9.75cm^2
Step-by-step explanation:
156/16 because you are deivding each side by 4 and 4x4=16 and the area is 156
Find the equation of the line that is parallel to the line
y = 3x + 3 and passes through the point (10,1). Write the
equation in slope-intercept form.
Answers
9514 1404 393
Answer:
y = 3x -29
Step-by-step explanation:
The parallel line will have the same slope: 3. The y-intercept can be found from ...
b = y -mx
b = 1 -(3)(10) = 1 -30 = -29
Then the slope-intercept equation is ...
y = 3x -29
Can anyone help me out?
Answers
Answer:
55° because 2and 6 are corresponding angles (they are equal)
6 and 8 are vertically opposite angles (they are equal)
Step-by-step explanation:
hope this is helpful
need an answer asap will give the first answer brainliest
Answers
Answer:
The answer would be the first one.
m = -3n
Step-by-step explanation:
Answer:
m = -3n
Step-by-step explanation:
-6 = (-3)2 True
-12 = (-3)4 True
-18 = (-3)6 True
Which of these quadrilateral types must have all four sides congruent?
A. Rectangle, square
B. Parallelogram, rectangle, square, rhombus
C. Square, rhombus
D. Rectangle, square, rhombus
Answers
C. Square, a rhombus is the right answer.
What does it mean that all four sides are congruent?A rhombus is a parallelogram in which all four sides are congruent. Shaped like a diamond. A square is a parallelogram with four congruent sides and four right angles. In other words, squares are rectangles and diamonds.
Exactly all the shapes on the four sides are called squares. Each type of figure here is a square type. The lengths of the congruent sides are the same. If parallel sides are drawn as lines, they never intersect.
Two triangles are congruent If the corresponding sides have the same length and the corresponding angles are the same, then the two triangles are congruent.
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What is the measure of x?
Answers
Answer:
x = 10
Step-by-step explanation:
(segment piece) x (segment piece) = (segment piece) x (segment piece)
4*x = 5*8
4x = 40
Divide by 4
4x/4 = 40/4
x = 10
Mariya is solving the quadratic equation by completing the square.
4x2-20x+3=0
4x2-20x=-3
A(x2-5x)=-3
Mariya is solving the quadratic equation by completing the square.
4x2-20x+3=0
4x2-20x=-3
A(x2-5x)=-3
What is the value of A?
-20
3
4
5
Answers
Answer:
4
Step-by-step explanation:
just 4 -_-
4x^2-20x
=4(x^2-5x)
so the value is 4
By solving the quadratic equation, the value of A is 4
Option (3) is correct.
What is a quadratic equation?A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is [tex]ax^{2}+bx+c=0[/tex], where a and b are the coefficients, x is the variable, and c is the constant term.
Given quadratic equation
[tex]4x^{2} -20x+3=0[/tex]
⇒ [tex]4x^{2} -20x=-3[/tex]
By taking 4 as common in [tex]4 x^{2}[/tex] and 20x
⇒ [tex]4(x^{2} -5x)=-3[/tex]...................(1)
According to the question by solving the quadratic equation. Mariya got, [tex]A(x^{2} -5x)=-3[/tex] .....................(2)
By comparing equation 1 and 2 we can clearly see that A = 4
Hence, by solving the quadratic equation, the value of A is 4
Option (3) is correct.
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Someone pls help me ill give out brainliest pls don’t answer if you don’t know
Answers
Answer:
B
Step-by-step explanation:
√256=16
√289=17
Answer:
b.√256 and √289 . play basketball
Jaclyn used the slope formula to find the slope of the line through the points given in the table.
A 2-column table with 2 rows. Column 1 is labeled x with entries 0, negative 3. Column 2 is labeled y with entries 4, 0.
1. Point 1: (0, 4); Point 2: (negative 3, 0). 2. Slope = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction = StartFraction 0 minus 4 Over negative 3 minus 0 EndFraction = StartFraction negative 4 Over negative 3 EndFraction. 3. Slope = four-thirds.
In which step did Jaclyn make an error?
Answers
Answer: She didn't make an error.
Step-by-step explanation:
She just didn't I got it right.
Answer:
answer is D
Step-by-step explanation:
can some one pls help me with this i need help
Answers
Answer:
9/8 cup peanuts were used
The amounts are:
Correct
Correct
Incorrect
A 5-pack of granola bars costs $3.55. What is the unit price?
Answers
Answer:
0.71 is the unit price
Step-by-step explanation:
all u gotta do is divide 3.55 by 5 to find out how much it cost each:)))
hope this helps!!!!
please mark brainiest<3
On a math exam, Joel had a score of 90, which was exactly 2 standard deviations above the mean. The standard deviation for the test is 3.
Answers
Answer:
84
Step-by-step explanation:
Score = 90
Standard deviation = 3
Score = mean + 2(standard deviation)
90 = mean + 2(3)
90 = mean + 6
Mean = 90 - 6
Mean = 84
20 POINTS PLEASE ANSWER!
Answers
Answer:
area = 15 units ^2
Step-by-step explanation:
you look at width times height (just count the blocks vertical and horizontal)
width = 3 units
height = 5 units
area = 15 units ^2
For each of the following quadrilaterals, select all the properties that must be true.
Answers
This is the answer to the qjestion
3 / 1/3 dividend by 1 / 1/5
Answers
(pls help i’m suffering) 3.06a Finding Standard Form by Completing the Square
Classify each as Circle, Quadratic (parabola) or other
(x - 5)2 + (v - 2) = 16
= 100
22 - x = 25
(x - 2) - (y + 5)= 10
y = 2x + 5
Answers
Step-by-step explanation:
A circle equation is represented by
[tex]x {}^{2} + {y}^{2} = r {}^{2} [/tex]
A circle have both terms to the 2nd. degree
The 1st equation, 2nd equation, 4th equation are circles.
A quadratic is represented by
[tex] {x}^{2} + bx + c[/tex]
A quadratic equation only has one term that is second degree.( meaning if x and y are both to the 2nd degree, it will not be a quadratic, it will be a circle.
The 3rd equation is a quadratic.
The fifth equation has a leading coefficient at the degree of 1 so it is other(linear)
This language derives from the area of a square being its side length multiplied by itself. The word "quadratic" comes from quadratum, the Latin word for square.
What is a quadratic function?f(x) = ax2 + bx + c, where a, b, and c are numbers and an is not equal to zero, is a quadratic function. A parabola is the shape of a quadratic function's graph. Although the "width" or "steepness" of a parabola can vary as well as its direction of opening, they all share the same fundamental "U" form.
From the given table we can get the dy/dx which is the slope (m) ,
Therefore,
dy/dx = (7 - 10 ) / ( 4 - 3 )
dy/dx = -3
Now,
( y - y1 ) = m ( x - x1 )
Putting the value from the table,
( y - 10 ) = -3 ( x -5 )
=> y - 10 = -3x + 15
=> 3x + y = 25
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44
Match each ratio with its simplest form.
12:15
20:36
18:24
Pls answer ASAP I need to finish this today and I’m stuck
Answers
20 : 36 = 5 : 9
18 : 24 = 3 : 4
A jazz concert brought in $167,000 on the sale of 8,200 tickets. If the tickets sold for $15 and $25 each, how many of each type of ticket were sold?
Answers
Answer:
x=3800, y=4400
Step-by-step explanation:
X+y=8200 equation 1
15x+25y=167000 equation 2
x=8200-y isolate x in equation 1
15(8200-y)+25y=167000 substitute value of x from equation 1 into equation 2
123000-15y+25y=167000
10y=44000
y=4400
solve for x by inserting y value into either equation.
x+y=8200
x+4400=8200
x=3800
Check answer:
15x+25y=167000
15(3800)+25(4400)=167000
57000+110000
167000=167000
Pls help I don’t know how to do this
Answers
The right answer is a i think i don't known step by step
Step-by-step explanation:
a
a
please help I will give brainlist
Answers
Answer:
Your answer will be B
Step-by-step explanation:
Because you find the difference between 14 and 22 or the difference between 22 and 30 or the difference between 30 and 38. and so on then it will be 8
You then say ok 8 times x so for example 8×1 = 8 then you say ok 22 - 8= 22. So it will be 8x+14...
I hope this helped if not tell me please....❤
Answer: Option B (y=8x+14)
Step-by-step explanation:
To solve these kind of question we just simply keep on inserting the values of x and if we get the required value of y that is in the table that equation is our answer, For example lets take Option A,
y = 8x
If we insert x = 0 we get,
y = 8(0)
y=0
but in the table it says we get 14 so option A is incorrect
Like this we keep checking for more values and all the values of x satisfy our equation in Option B like this,
y=8x+14
y=8(0)+14
y=14
y=8x+14
y=8(1)+14
y=8+14
y=22
y=8x+14
y=8(2)+14
y=16+14
y=30
and so on. Now your answer would be Option B.
THE CREDIT GOES TO (IjlalHashmi)
Michael needs to decide which paint to buy.He found two advertisements, paint A in a 5l drum for R109,95 and paint B in a 20l drum for R599,00.
Which paint will be cheaper per liter?show all calculations.
Answers
Answer:
paint a is cheaper
Step-by-step explanation:
cost price of 1 liter of paint A = 109,95 / 5L
=21.99
cost price of 1 liter of paint B = 599 / 20L
= 29.95
paint A < paint B
An icicle is 12 inches long and melts at a rate of 1/4 inch per hour
Answers
Answer:
It will take 48 hours for the entire icicle to melt.
Step-by-step explanation:
12 divided by 1/4 = 48
The linear equation to model the situation is f(x) = -1/4x + 12
Complete questionWrite a linear equation in slope-intercept form to model the situation. An icicle is 12 inches long and melts at a rate of 1/4 inch per hour.
How to determine the linear equation?The given parameters are:
Length = 12 inchesRate = 1/4 inch per hourThe above means that:
Y-intercept (c) = 12Slope (m) = -1/4A linear equation is represented as:
f(x) = mx + c
Where f(x) represents the function and x represents the number of hours.
So, we have:
f(x) = -1/4x + 12
Hence, the linear equation to model the scenario is f(x) = -1/4x + 12
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Please help me find the answers
For the mean median mode range mm max q1
Answers
Everything has been explained in there
Is 3:5 and 5:7 equivalent
Ratios
Answers
Answer:
no its not equal
