Enter the correct answer in the box.
Consider this rational equation.
Use the least common denominator to simplify the rational equation into a standard form quadratic equation.
Replace the values of b and c to create the equation.
Answers
Answer:
[tex]x^2-10x+8=0[/tex]
Step-by-step explanation:
[tex]\frac{1}{x} +\frac{1}{x-2}=\frac{1}{4} \\\\\frac{x-2+x}{x(x-2)} = \frac{1}{4} \\\\\frac{2x-2}{x(x-2)}=\frac{1}{4} \\\\4(2x-2)=x(x-2)\\8x-8=x^2-2x\\0=x^2-2x-8x+8\\0=x^2-10x+8\\x^2-10x+8=0\\[/tex]
Using the least common denominator in simplifying the rational equation, the result of in standard form is: [tex]\mathbf{x^2 -10x + 8 = 0}[/tex]
What is the Least Common Denominator (LCD)?Least common denominator is the smallest common multiple of the denominators of two or more fractions.It is useful when simplifying, adding, subtracting or comparing fractions.Given:
[tex]\frac{1}{x} + \frac{1}{x - 2} = \frac{1}{4}[/tex]
The least common denominator of the two fractions on the left side of the equation is x(x - 2).
Thus:
[tex]\frac{1(x - 2) + x(1)}{x(x - 2)} = \frac{1}{4}\\\\\frac{x - 2 + x}{x(x - 2)} = \frac{1}{4}\\\\\frac{2x - 2}{x^2 - 2x)} = \frac{1}{4}[/tex]
Cross multiply[tex]4(2x + 2) = 1(x^2 - 2x)\\\\8x + 8 = x^2 - 2x\\\\[/tex]
Rewrite in standard form[tex]0 = x^2 - 2x - 8x + 8\\\\0 = x^2 -10x + 8\\\\\mathbf{x^2 -10x + 8 = 0}[/tex]
Learn more about least common denominator on:
https://brainly.com/question/542317
Related Questions
Olivia baked 45 mini-loaves of banana bread to be sliced for snacks at a craft fair. She will place an equal number of loaves in 6 different locations. What if Olivia wants to put only whole loaves at each location? How many loaves will be at each location?
Answers
Answer:
7 whole loaves of bread.
Step-by-step explanation:
Since there are total of 6 locations and each location needs to have the same number of whole loaves of bread we simply need to divide the number of mini-loaves of banana bread by the number of locations like so...
45 / 6 = 7.5
As we can see by the mathematical expression above 45 loaves of bread can be divided into 6, giving each location 7.5 loaves of bread but since each location needs only whole loaves then that would mean that each location would get 7 whole loaves of bread.
PLEASE ANSWER ASAP! LOOK AT THE PIC ATTACHED: (please show work!)
Answers
Answer:
Answer is B
Step-by-step explanation:
Remember, perpendicular lines have opposite slopes. In order to do this, you just need to flip the sign (Change it to the opposite. For example, if it is 3, it would be -3), and change the slope to its reciprocal (For example, if it is 3, it would 1/3). Finally, since the equation is y = 1/2x + 10, the slope would change to -2x... so your answer is B
Pls answer!!
x - y = 5
4x + y = 10
What could x and y equal
Answers
Answer:
I: Slope = 1
x= 5/1 or 5.00000
y= 5/-1 0r 5.00000
2: Slope = -8.000/2.000 or 4.000
x= 5/2 or 2.50000
y= 10/1 or 10.00000
Step-by-step explanation:
The decimal answers are the fraction in decimal form
find perimeter of semicircle if radius is 22 cm
Answers
The perimeter of a circle is equal to 2πR where R is the radius if we want the perimeter of the semicircle we divide by 2 and we get
P=πR=22π=22*3.14=69.08cm
Which of the following is a true statement of two linear equations?
Answers
100% as a fraction in simplest form
Answers
Answer:
1
Step-by-step explanation:
100/100 =
1
srry if wrong but
hope this helps
take care
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
1/10 10% of 1
Step-by-step explanation:
3/4 0.75
0.2 20% of 1
15/10 150% of 1
14/10 1.4
Fraction: 1/10, 3/4, 3/2, 4/5
Decimal: 0.75, 0.2, 1.4
Percentage: 10%, 20%, 150%
(The answer is in the same order as the column, I did not include the boxes that were already filled in)
Determine the distance between 7.3 and 3.5.
A.10.7
B.4.3
C.3.7
D.-3.7
Answers
explination: subtract
Is there anybody from the online schooling called BUZZ? that can help me out at all?
Have a great day! Merry Christmas! <3
Answers
Find the perimeter of a square garden if it’s area is 1369m2?
Answers
Answer:
Step-by-step explanation:
The area formula for a square is
[tex]A=s^2[/tex] where A is the area and s is a side measure. In a square, this side measure is the same (because all 4 sides in a square are the same). Therefore, our formula becomes:
[tex]1369=s^2[/tex]
Take the square root of both sides to find that a side measures 37 m.
The perimeter of a square is to add all 4 sides together (or to multiply the one side by 4):
4 * 37 = 148 m
what is 2.98989 as a fraction
Answers
Answer:
2.98989/1
Step-by-step explanation:
Here is a list of ingredients for making 12 small cakes. 108 g margarine 180 g sugar 200 g plain flour 1 teaspoon baking powder 2 eggs. Joe is going to make 24 of the small cakes. Determine how much margarine he will need. Write your answer in a complete sentence.
Answers
Answer:
216g of margarine
Step-by-step explanation:
From the above question:
12 small cakes required 108g of margarine
If he would be making 24 of the small cakes, hence, that would be calculated as:
12 small cakes = 108g of margarine
24 small cakes = x
Cross Multiply
12 × x = 24 × 108g
x = 24 × 108g/12
x = 216g of margarine
Therefore, he would need 216g of margarine to make 24 of small cakes
what’s the quotent of -3/8 and -1/4
Answers
Answer:
1.5
Step-by-step explanation:
-3/8=-0.375
-1/4=-0.25
the negatives cancel each other out so it is 0.375/0.25
.25 goes into .375 1.5 times, so the answer is 1.5
Have a good day!
It needs to be 20 characters long so I’m just putting this so I can actually submit. The other guy already out the explanation so I’m proud of you and just tryna get points. Anyways the calculator is always available too if you need it
Question 5. Solve x + 9 = -13
Answers
Answer:
x = -22
Step-by-step explanation:
x + 9 = -13
-9 -9
x = -13 - 9
x = -22
Answer: x = -22
Graph the equation.
y =
-3/4
(2+3)(x + 7)
Answers
The equation y = -3/4 (2+3)(x + 7) is graphed in the image below.
What is the range of this function? Help
Answers
Answer:
Range is the extension of the values across the x-y plane. We can see the data extends as far as -13 and as far as 11 so (-13,11)
Given y+6=10(x-9) What is the point used to write the equation?
Answers
Answer:
Point (9, -6)
General Formulas and Concepts:
Algebra I
Point-Slope Form: y - y₁ = m(x - x₁)
x₁ - x coordinate y₁ - y coordinate m - slopeStep-by-step explanation:
Step 1: Define
y + 6 = 10(x - 9)
Step 2: Break Function
Identify Parts
Slope m = 10
Point (9, -6)
9. For the points A(5,0) and B(7,3), calculate the angle between AB
and the x-axis.
Answers
Answer:
Trigonometry question: For the point A (5; 0) and B (7;3) calculate the angle between AB and the x-axis. The answer given in the book is as follows:56.3 degrees.
Meghan earns 20.00 dollars by walking dogs. She uses all of her earnings to buy a shirt for 12.85 dollars and some stickers for 0.65 dollars each. How many stickers does she buy ?
Answers
Answer:
She bought 11 stickers
Step-by-step explanation:
20 - 12.85
7.15
then
7.15/0.65
11
Answer:
the answer is 11 :D
Step-by-step explanation:
Im not sure but please correct me if im wrong!
Given f(x)=7x+12 and Domain={3,6,9} find Range
{21,42,63}
{9,6,3}
{33,54,75}
{19,26,33}
Answers
Answer:
the answer is the 3rd option
range = { 33, 54, 75 }
Write an equivalent expression for 2(1.7x + 3.3) + 5(2.6x + 1.4) by combining like terms
Answers
Answer:
16.4x + 13.6
Step-by-step explanation:
Equivalent Expressions
Algebraic expressions can be given in different forms when applying properties of the basic operations.
The given expression is:
2(1.7x + 3.3) + 5(2.6x + 1.4)
Multiplying both parentheses by the outer factor:
3.4x + 6.6 + 13x + 7
Combining like terms:
16.4x + 13.6
The original and the final expressions are equivalent because they produce the same results
The position data for line 1 was recorded in 1-second intervals. Draw a graph with distance on the y-axis and elapsed time on the x-axis. Reference all distance and time measurements to dot 1. To plot a point, use the circle tool. To draw a line between points, use the line tool. To move a point or line, use the select tool.
Answers
Answer:
Picture
Step-by-step explanation: Plato
Andrew purchased a coat for $50.00 on sale for 25% off. What was the cost of the coat after the discount not including tax?
Answers
Answer:
$ 37.50
Step-by-step explanation:
100% - 25% = 75%
75% = 0.75
50 × 0.75 = $ 37.50
show work what is the gcf of 12x^2 and 15x^3
Answers
Hey there! I'm happy to help!
The greatest common factor is the largest factor that both numbers contain. Let's look at the factors of these terms.
12x²: 1, 12, 2, 6, 3, 4, x, x
15x³: 1, 15, 3, 5, x, x ,x
We see that both of these numbers contain a 3 and 2 x's, so our GCF would be 3x².
Have a wonderful day!
On Saturday, Alicia ran 2 miles. This was 0.3 miles farther than Henry ran. Write and solve an
an addition equation to find out how many miles Henry ran.
Answers
Answer: a - 0.3.
Step-by-step explanation;
Let a represent the number of miles that Alicia ran. The equation will be this: a - 0.3. You will subtract 0.3 from the number of miles that Alicia ran because her amount is 0.3 miles farther than what Henry ran.
What is the derivative of f(x) = 9x^2 + x?
Answers
Answer:
f'(x) = 18x + 1
Step-by-step explanation:
f(x) = 9x^2 +x
f'(x) = 9(2x) + 1
f'(x) = 18x + 1
What determines the pitch of a sound? PLEASE HELP MEH!!
the decibel level
the frequency of vibrations
the amplitude
the medium
Answers
Answer:
Since pitch is such a close proxy for frequency, it is almost entirely determined by how quickly the sound wave is making the air vibrate and has almost nothing to do with the intensity, or amplitude, of the wave. That is, "high" pitch means very rapid oscillation, and "low" pitch corresponds to slower oscillation.
Step-by-step explanation:
please mark me as brainliest thank you
Given the graphs of f(x) =x -7 and g(x) =-5x-1, what is the solution to the equation f() = g(x)?
Answers
Answer:
1
Step-by-step explanation:
x-7=-5x-1
x-(-5x)-7=-1
x+5x-7=-1
6x-7=-1
6x=-1+7
6x=6
x=6/6
x=1
Write an equation in point-slope form of the line that passes through the given point and with the given slope m.
(-4,1) m=4
The equation of the line is ?
Answers
Answer:
An equation in point-slope form of the line that passes through the given point and with the given slope m = 4 will be:
[tex]y-1 = 4(x-(-4))[/tex]
Step-by-step explanation:
Given
The point = (-4, 1)m = 4Using the point-slope form of the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
here:
m = slope(x₁, y₁) = pointsubstituting the values m = 4 and the point (-4, 1) in the point-slope form of the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y-1 = 4(x-(-4))[/tex]
Thus,
An equation in point-slope form of the line that passes through the given point and with the given slope m = 4 will be:
[tex]y-1 = 4(x-(-4))[/tex]
Note: It can further be simplified
[tex]y-1=4\left(x+4\right)[/tex]
Add 1 to both sides
[tex]y-1+1=4\left(x+4\right)+1[/tex]
[tex]y=4x+17[/tex]
A line with a positive slope is parallrl to one of the lines shown. What is its slope? Use the graph shown below. The slope is:
Answers
Answer:
the slope of the blue line is 2/3
Step-by-step explanation:
y2-y1 over x2-x1
6,5 and we have 0,1
5-1/6-0
4/6=2/3