Answer:
a = 3, b = -18
Step-by-step explanation:
You can start by getting a common denominator in the fractions [tex]\frac{x+1}{x-2}[/tex] and [tex]\frac{x-4}{x+2}[/tex]. You can multiply the first one by [tex]\frac{x+2}{x+2}[/tex] to get [tex]\frac{(x+2)(x+1)}{x^2-4}[/tex]and you can multiply the second by [tex]\frac{x-2}{x-2}[/tex] to get [tex]\frac{(x-4)(x-2)}{x^2-4}[/tex]. You can simplify the fractions:
[tex]\frac{(x+2)(x+1)}{x^2-4}[/tex] - [tex]\frac{x^2+3x+2}{x^4-4}[/tex]
[tex]\frac{(x-4)(x-2)}{x^2-4}[/tex] - [tex]\frac{x^2-6x+8}{x^2-4}[/tex]
Now we can rewrite the equation:
[tex]2-\frac{x^2+3x+2}{x^2-4} -\frac{x^2-6x+8}{x^2-4}[/tex]
and combine the terms with the same denominator:
[tex]2+\frac{-x^2-3x-2-x^2+6x-8}{x^2-4}[/tex]
[tex]2+\frac{-2x^2+3x-10}{x^2-4}[/tex]
Now, to add the two into the fraction, we multiply it by [tex]x^2-4[/tex] to get [tex]2x^2 - 8[/tex].
[tex]\frac{2x^2-8-2x^2+3x-10}{x^2-4}[/tex]
And simplify:
[tex]\frac{3x-18}{x^2-4}[/tex]
a = 3, b = -18
The value of the integers a and b are 3 and - 18 respectively.
What do you mean by algebraic expressions ?
Algebraic expression is an equation which consists of variables and the arithmetic operations such as division , multiplication , etc.
Firstly , let's find out a common denominator in the fractions , [tex]\frac{x+1}{x-2}[/tex] and [tex]\frac{x-4}{x+2}[/tex] .
The first one can be written as :
= [tex]\frac{x+1}{x-2}[/tex] × [tex]\frac{x+2}{x+2}[/tex]
= [tex]\frac{(x+1)(x+2)}{x^{2} - 4}[/tex]
and the second one can be written as :
= [tex]\frac{x-4}{x+2}[/tex] × [tex]\frac{x-2}{x-2}[/tex]
= [tex]\frac{(x-4)(x-2)}{x^{2} - 4}[/tex]
The expression will be :
= 2 - [tex]\frac{x+1}{x-2}[/tex] - [tex]\frac{x-4}{x+2}[/tex]
= 2 - [tex]\frac{(x+1)(x+2)}{x^{2} - 4}[/tex] - [tex]\frac{(x-4)(x-2)}{x^{2} - 4}[/tex]
= [ 2 (x²- 4) - (x+1) (x+2) - (x-4) (x-2)]/ [(x²- 4)]
= [2x² - 8 - x² - 3x - 2 - x² + 6x - 8] / [(x²- 4)]
By simplifying it , we get :
= [tex]\frac{3x-18}{x^{2} - 4}[/tex]
If we compare it with the given form which is [tex]\frac{ax + b}{x^{2} -4}[/tex] we get :
[tex]\frac{3x-18}{x^{2} - 4}[/tex] = [tex]\frac{ax + b}{x^{2} -4}[/tex]
or
3x - 18 = ax + b
or
The values of a and b are :
a = 3 and b = -18.
Therefore , the value of the integers a and b are 3 and - 18 respectively.
Learn more about algebraic expressions here :
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help please! if it’s correct ill give brainliest
Answer:
[tex]radius = \sqrt{ {15}^{2} + {36}^{2} } = 39 \\ area = 4 \times {39}^{2} \times \pi = 19103.76[/tex]
Savannah gave the cashier $20 to pay for 3 pairs of socks. The cashier gave her $5.03 in change. Each pair of socks cost the same amount. What is the cost in dollars and cents for each pair of socks? Once you solve the problem, circle/highlight your answer.
Answer: $4.99
Step-by-step explanation:
The amount that Savannah paid for the 3 pairs of socks will be gotten by subtracting $5.03 from $20 which will be:
= $20 - $5.03
= $14.97
Since each paid of socks cost thesame amount, the cost of each pair of socks will be:
= $14.97/3
= $4.99
Each pair of socks cost $4.99
PLEASE ANSWERRRRRRRRRRRRRRRRRRRRRRRRRRR
Answer:
215 cm^2
Step-by-step explanation:
Area for triangles: 1/2(b)(h)
Area for parallelograms: (b)(h)
18 - 6 - 5 = 7
20 - 10 = 10
1/2(7)(10)
1/2(70)
35
18(10)
180
180 + 35 = 215
Thank you for the Points but please stop taking answers from people who need help... Its not very kind
3. Simplify:
a) 4a - 3b + a - 2b
Answer:
4a-3b+a-2b
5a-3b-2b
5a-3b-2b
5a-5b
solution: 5a-5b
Carlos is NOT correct because
Answer:
He is wrong because for the last part of foil he multiplies 3 times 3 and got 6 instead of 9.
Solve for X please help
Answer:
x = 10
Step-by-step explanation:
First square both sides of the equation...
[tex]2\sqrt{x + 8} = 3\sqrt{x - 2} \\(2\sqrt{x + 8})^{2} = (3\sqrt{x - 2})^{2} \\ 4(x + 8) = 9(x - 2)\\4x + 32 = 9x - 18\\-5x = -50\\x = 10[/tex]
how do you find the height of a triangle (to calculate area)?
Answer:
The height of the triangle could be found by the Pythagoras theorem, where the result is, with the data of the exercise:
Height of the triangle = 10.392And the area of the triangle is:
Area of the triangle = 31.176 units^2Step-by-step explanation:
When you have two measurements of a triangle, as the case in the picture, you can find the third with the Pythagoras theorem, which is:
(opposite leg)^2 + (adjacent leg)^2 = hypotenuse^2As you can see in the picture, the measurement of the hypotenuse is 12, and the opposite leg could be 6, for this reason, we're gonna clear the adjacent leg of the formula above:
(opposite leg)^2 + (adjacent leg)^2 = hypotenuse^2(adjacent leg)^2 = hypotenuse^2 - (opposite leg)^2Now, we can replace the values in the formula obtained:
(adjacent leg)^2 = hypotenuse^2 - (opposite leg)^2(adjacent leg)^2 = 12^2 - 6^2(adjacent leg)^2 = 144 - 36(adjacent leg)^2 = 108Now, as we just need the adjacent leg, we take the square root of both sides:
adjacent leg = [tex]\sqrt{108}[/tex]adjacent leg = 10.392 approximately.Now, with these data, we can find the area of the triangle with the next formula:
Area of a triangle = (base * height) / 2And we replace the measurements:Area of a triangle = (6 * 10.392) / 2Area of a triangle = 31.176As the image does not contain units, it would be simply this number, however, you should know that the area units are usually given squared, for example: in^2 or ft^2.
The quality control manager of at Long John Silver's restaurant wants to analyze the length of time that a car spends at the drive-thru window waiting for an order. It is determined that the mean time spent at the window is 59.3 seconds with a standard deviation of 13.1 seconds. The distribution of time at the window is skewed right. The quality control manager wishes to use a new delivery system designed to get cars through the drive-thru system faster. A random sample of 40 cars results in a sample mean time spent at the window of 56.8 seconds. What is the probability of obtaining a sample mean of 56.8 seconds or less, assuming that the population mean is 59.3 seconds
Answer:
0.11314
Step-by-step explanation:
The Long John Silver's restaurant parameters are;
The mean time spent at the window, μ = 59.3
The standard deviation, σ = 13.1
The time distribution is skewed right
The number of cars in the sample, n = 40 cars
The mean time spent at the window with the delivery system, [tex]\overline x[/tex] = 56.8 seconds
The Z-value for a mean time of 56.8 seconds is given as follows;
[tex]Z=\dfrac{\bar{x}-\mu }{\dfrac{\sigma }{\sqrt{n}}}[/tex]
Therefore, we get;
[tex]Z=\dfrac{56.8-59.3 }{\dfrac{13.1 }{\sqrt{40}}} \approx -1.20697620617[/tex]
Therefore, the z-value ≈ -1.21
From the normal probability table, we have;
P([tex]\overline X[/tex] ≤ 56.8) = P(Z < -1.21) = 0.11314
The probability of obtaining a sample mean of 56.8 second or less, assuming that the population mean is 59.3 seconds P([tex]\overline X[/tex] ≤ 56.8) = 0.11314.
QUICK WILL MAKE BRAINLIEST!!
FILL IN THE BLANK (HURRY NEED TURNED IN BY 9:06 ITS 9:04)
Million dollar ________?
Answer:
What does it mean but just Million dollar?
Step-by-step explanation:
PLEASE someone help me with this
Answer:
I CAN ACTUALLY HELP FOR ONCE!!!! [tex]30m^{3}[/tex]
Step-by-step explanation:
Answer:
30m^3
Step-by-step explanation:
Dawn is going scuba diving. Which situation would be modeled by a positive number?
on the dive boat deck
at the water line
underwater near a reef
on the ocean floor
Answer:
Step-by-step explanation:
on the dive boat deck :)
What is the area of the rectangle
Answer:
B) [tex]\frac{15}{4}[/tex]
Step-by-step explanation:
Area of a rectangle formula:
A = bh
Given:
b = [tex]2\frac{1}{2}[/tex]
h = [tex]1\frac{1}{2}[/tex]
Work:
A = bh
A = [tex](2\frac{1}{2} )(1\frac{1}{2} )[/tex]
A = [tex]\frac{15}{4}[/tex]
I really need helppppp
Answer:
The correct answer is C.
Step-by-step explanation:
In the equation of a circle, if the variable [tex]x[/tex] and [tex]y[/tex] are added or subtracted by any number before being squared, the entire circle with be translated in the opposite amount that was added or subtracted to the circle. For example, [tex](x-8)^2 + (y-8)^2[/tex] shifts the center 8 to the right and up of the origin, [tex](x+1)^2+(y+4)^2[/tex] shifts the center 1 to the left and 4 down of the origin. Since the circle represented in the graph is centered directly on the origin, that means the equation will have [tex]x^2+y^2[/tex], which helps you eliminate choices A and C. For the equation of a circle, the radius is the value of the constant on the right side of the equal sign taken to its square root. Since the radius of this circle is 8, that means the constant at the right side of the circle would be 64 or [tex]8^2[/tex], so the correct answer would be choice C: [tex]x^2+y^2=8^2[/tex].
Convert 81° to radians.
Answer: 9π/20 radians
How to: Convert from degrees to radians using the ratio π/180 .
Have a great day !
What is the center and radius of the following
circle:
(x +4)2 + (-2) = 4?
Answer:
x = -1
Step-by-step explanation:
Answer:
That is not a circle; it has no y term
My guess:
center = (h, k) = (-4, 2)
r = √4 = 2
Step-by-step explanation:
If I had to guess what you intended:
(x + 4)² + (y - 2)² = 4
The standard equation for a circle is
(x - h)² + (y - k)² = r²
(h, k) is the center and r is the radius
center = (h, k) = (-4, 2)
r = √4 = 2
I need help with this work !!!
Answer:
16. B
17. C
18. D
19. B
20. D
Find the value of x in the isosceles triangle shown below
Answer:
The answer is 12
Hope it helps
Answer:
x = 12
Step-by-step explanation:
Since the 2 legs and base angles are congruent the triangle is isosceles.
The line from the vertex to the base is a perpendicular bisector dividing the triangle into 2 right triangles.
Using Pythagoras' identity in either of the 2 right triangles with legs 3 and [tex]\frac{1}{2}[/tex] x , hypotenuse [tex]\sqrt{45}[/tex] , then
([tex]\frac{1}{2}[/tex] x )² + 3² = ([tex]\sqrt{45}[/tex] )²
[tex]\frac{1}{4}[/tex] x² + 9 = 45 ( subtract 9 from both sides ²)
[tex]\frac{1}{4}[/tex] x² = 36 ( multiply both sides by 4 to clear the fraction )
x² = 144 ( take the square root of both sides )
x = [tex]\sqrt{144}[/tex] = 12
Timed Test
Which type of discontinuity occurs at x = 5?
Answer:
D
Step-by-step explanation:
Based off of previous responses and my incorrect answer, I am going to say the answer is D.
Answer: d
Step-by-step explanation: edge
so i have a pic i need 1a plz i am giving a bunch of my points plz give it real asap
Answer:
.
Step-by-step explanation:
Answer:
What???? (confusion)
I need help pleasee!! Asap!
The midpoints of a rectangle always form parallelogram.
Malik, who is 5 feet tall, stands 15 feet from a mirror. In
the mirror, he can see the reflection of the top of a tree,
which he measures to be 92 feet away from the mirror. round your answer to the nearest hundredth
Find the are of this compound shape below *
Answer:
52 cm²
Step-by-step explanation:
First, we find the area of the bottom rectangle. We see it's 4 high and 10 wide, so 4x10 is 40. Then, we see that the small figure in the top right has a height of 4 and width of 3, so 4x3 = 12, add those and you get 52.
Michael’s favorite cereal is Cinnamon Toast Crunch. His mom buys him a big box for a special treat, and he wants to figure out exactly how much cereal is in the box. The box has a volume of 384 cubic inches. The height is 12 inches and the length is 8 inches. What is the width?
Answer:
he made a good choice, the width is: 4 inches
Step-by-step explanation:
12 x 8 x _4_ = 384
50 POINTS!!!!
A rectangular garden has length twice as great as its width. A second rectangular garden has the same length as the first garden and width that is 4 meters greater than the width of the first garden. The second garden has area of 120 square meters. What is the length of the two gardens? Enter your answer in the box. m=
Answer:
24 meters
Step-by-step explanation:
First we need to show width and length as variables.
let width of garden 1 = W
let length of garden 1 = L
let width of garden 2 = w
let length of garden 2 = l
Now make equations that are explained in the question
L = 2W
l = L
w = W + 4
l × w = 120
Now with that we can find l and w.
Now by looking at the factors of 120, find the factors that work throughout the question.
That is 12 and 10.
l=12
w=10
This means that...
L=12
W=6
Now the answer is 24 meters
Answer:
12m
Step-by-step explanation:
just took the test
Please help.
Determine which lines are parallel and which are perpendicular. Explain your reasoning.
Answer:
Parallel: a and b, p and q, p and r, q and r
PErpendicular: p&a, p&b, q&a, q&b, r&a, r&b
Step-by-step explanation:
Parallel lines have the same slope so both of the lines would be going in the same direction and will never cross each other.
Perpendicular lines cross at a 90 degree angle.
Technically you do not know if q&a and q&b are perpendicular because you do not know if there is a 90 degree angle
Answer:
Parallel lines are equally spaced out in the same direction so it would be p,q, and r, Purpendicular Lines intersect at a 90 degee angle so it would be q and a, q and b, r and b, and r, and so on
Step-by-step explanation:
cual es el resultado de 5-4(6-12)
Answer:
29
Step-by-step explanation:
5-(4*(6-12))=29
Answer:
La respuesta es 29, espero que esto ayude.
Find the median of the data in the box plot below. Cookies A horizontal boxplot titled Number of cookies eaten by each contestant, is plotted along a horizontal axis marked from 2 to 30, in increments of 1. A left whisker extends from 5 to 6. The box extends from 6 to 22 and is divided into 2 parts by a vertical line segment at 8. The right whisker extends from 22 to 25. All values estimated.
Diagrammatic representation of the summarized box plot is attached below :
Answer:
Range = 20
Median = 8
Step-by-step explanation:
The median value of a box plot is obtained at the point where a vertical line divides the box into two parts. In the boxplot Given the median of the representation is 8. This is the point where the vertical line divides the box.
The range of the distribution is the difference between the maximum and minimum value :
Minimum (starting point of whisker) = 5
Maximum (end point of whisker) = 25
Range = 25 - 5 = 20
expand and simplify (3x+4)(2x+3)
Answer:
answer is 6x^2+17x+12
Step-by-step explanation:
3x(2x+3)+4(2x+3)=6x^2+9x+8x+12=6x^2+17x+12
pls help me with this thnx
Answer:
Shop B has a better value for their baked beans.
Step-by-step explanation:
Shop A:
5 kg = 5.65
1 kg = 5.65 / 5
= 1.13 pence
Shop B:
2 kg = 2.02
1 kg = 2.02 / 2
= 1.01 pence
HELP ME ASAP I NEED HELP NOW
Zeros:
x = -2
x = 6
Smaller zero: -2