Answer:
[tex]\frac{5x+2}{3x^2+4x-4}= \frac{2}{3x-2}+\frac{1}{x+2}[/tex]
Step-by-step explanation:
Ooook, step 1: write the denominator as a product, or we're not going anywhere. Can't spot any two factor by staring at it, so quadratic formula it is.
[tex]x= \frac13(-2 \pm \sqrt{4+12})=\frac13(-2\pm4) = -2;\frac23[/tex]
We got our toots, let's split the denominator now: [tex]3x^2+4x-4 = (3x-2)(x+2)\\[/tex]
Now it's all a matter of writing down what we need:
[tex]\frac{5x-2}{3x^2+4x-4}=\frac{5x-2}{(3x-2)(x+2)} = \frac{A}{3x-2}+\frac{B}{x+2} = \frac{A(x+2)+B(3x-2)}{(3x-2)(x+2)}=\frac{Ax+2A+3Bx-2B}{(3x-2)(x+2)} =\frac{(A+3B)x+(2A-2B)}{(3x-2)(x+2)}[/tex]
Here comes the fun part. Two ways: the fast and loose, and the long one.
Fast and loose: let's look only at the numerators of the 3rd to last and first step: [tex]A(x+2)+B(3x-2) = 5x+2[/tex] If we plugged a convenient value, let's say [tex]x=-2[/tex] the coeffcent of A would disappear, and we would be able to find B. Let's do it. [tex]A(-2+2) + B(3(-2)-2) = 5(-2)+2 \rightarrow -8B =-8 B=1[/tex]
At this point we have B, let's pick a different value of x, let's say 1, to get A:
[tex]A(3) + 1(1) = 7 \rightarrow 3A=6 \rightarrow A=2[/tex]
More traditional: Pick the first and last numerators: [tex]5x+2 = (A+3B)x+(2A-2B)[/tex]. Stare at them long enough and pick your favourite excuse to justify the following system (two polynomials are equal if the coefficents are equal, polynomials create a vector space of base [tex](1,x,x^2...)[/tex]
[tex]\left \{ {A+3B=5} \atop {2A-2B=2}} \right.[/tex]
Again, [tex]A=2, B=1[/tex] is a solution.
Either way, the solution is:
[tex]\frac{5x+2}{3x^2+4x-4}= \frac{2}{3x-2}+\frac{1}{x+2}[/tex]
The sum of two numbers is 13 and their diffrence is 3. what are the two numbers?
Answer: Hello!
The two numbers are 8 and 5 .
Step-by-step explanation:
Mark me brainest please. Hope I helped! Hope you make an 100%
Anna♥
Mary spent a total of $354.30 for a party. She spent $200.90 on food, plus an additional $30.68 for each hour of the party. How long was the party?
Answer:
About 5 hours
Step-by-step explanation:
Hope it helps
!!!!!!!!!!!!!!!!!!!3
Answer:
C. y - 1 = -4(x - 2)
Step-by-step explanation:
1. To find which line equation doesn't go through through the two points, we plug in the values of x to see if we get the value of the y.
A:
[tex]y=-4(3)+6[/tex] [tex]y = -12 + 6[/tex] [tex]y = -6[/tex] ✓ [tex]y = -4(1)+6[/tex] [tex]y = -4 + 6[/tex] [tex]y = 2[/tex] ✓B:
[tex]y+6=-4(3-3)[/tex] [tex]y + 6 = -4(0)[/tex] [tex]y + 6 = 0[/tex] [tex]y + 6 - 6 = 0 - 6[/tex] [tex]y = -6[/tex] ✓ [tex]y + 6 = -4(1-3)[/tex] [tex]y + 6 = -4(-2)[/tex] [tex]y + 6 = 8[/tex] [tex]y = 2[/tex] ✓C:
[tex]y-1=-4(3-2)[/tex] [tex]y-1=-4(1)[/tex] [tex]y-1=-4[/tex] [tex]y = -3[/tex] ✕Therefore, the answer is C. y - 1 = -4(x - 2).
Help help help quickly
Answer:
x > 15
Step-by-step explanation:
first step is to subtract 9 from each side to get:
x/3 > 5
now multiply each side by 3 to get:
x > 15
What is the estimated sum of 503, 472, 486, 499, 539, and 522?
Answer:
3020
Step-by-step explanation:
round to the nearest 10
503 to 500
472 to 470
486 to 490
499 to 500
539 to 540
522 to 520
Last minute homework due please help.
Answer:
8. 124 degrees
9. 48 degrees
10. 55 degrees
11. 120 degrees
12. 50.5 degrees
13. 118.7 degrees
Match the expressions to their factored forms. Drag the items on the left to the correct location on the right.
Answer:
(x-6)(x+6) pairs with x^2-36
9x^2-1 pairs with (3x-1)(3x+1)
4(x+2)(x-2) pairs with 4x^2-16
Step-by-step explanation:
Solve for b.
8b−1=24b+4
ans = -7
Answer:
Step-by-step explanation:
yeah your answer was wrong so you clearly need help
8b-1=24b+4
subtract 4 from both sides
8b-5=24b
subtract 8b from both sides
-5=16b
divide by 16
b=-5/16
Answer:
b = -5/16
Step-by-step explanation:
8b - 1 = 24b + 4
8b - 24b = 4 + 1
-16b = 5
16b = -5
b = -5/16
Which proportion is not true?
A) BC/CD=FG/GH
B) AC/CD=EG/GH
C) BD/FH =AD/EH
D) AB/AE=EF/BF
Answer:
c I think that is the answer
b. 6 times the sum of 12 and 8
Answer:
120
Step-by-step explanation:
12+8 = 20
20*6 = 120
What is the perimeter of PQR? Show your work.
5. Find the triangle similar to AABC at the right.
Answer:
the answer is b
Step-by-step explanation:
what is 3(a+b)-2(a-b)
Answer:
a + b
Step-by-step explanation:
3(a+b)-2(a-b)
=> 3a + 3b - 2a - 2b
=> a + b
Therefore, a + b is our answer
Answer:
a + 5b
Step-by-step explanation:
3(a + b) - 2(a - b) ← distribute both parenthesis
= 3a + 3b - 2a + 2b ← collect like terms
= a + 5b
The first four terms of an arithmetic sequence are given.
27,32,37,42,...
What is the 60th term of the sequence?
What expression is equivalent to 42+18
I think the answer is 20+40...
You need to collect at least 32 shells to create a necklace. Your friend gave you 14 and you already had 6. How many more shells do you need to make a necklace? *
Josh runs 7 miles in 60 minutes. At the same rate, how many miles would he run in 24 minutes?
Answer:
2.8 milesStep-by-step explanation:
Josh runs 7 miles in 60 minutes. At the same rate, how many miles would he run in 24 minutes?
7 : 60 = x : 24
x = 7 * 24 : 60
x = 2.8 miles
Solve 2x^2 + 5x – 3 = 0
Answer:
Step-by-step explanation:
Solve for Z:
4 > 5Z + 34
help me so hard
Answer:
Isolate the variable by dividing each side by factors that don't contain the variable.
Inequality Form:
Z < − 6
Interval Notation:
( − ∞ , − 6 )
Step-by-step explanation:
Answer:
z<-6
Step-by-step explanation:
4-5Z>34
-5z>34-4
-5z>30
z<-6
Find the coordinates of the vertices of the triangle after a rotation
270° counterclockwise about the origin.
Answer:
it is a
Step-by-step explanation:
The coordinates of the triangle ΔC'D'E' will be (2, 1), (5, -3), and (2, -1). Then the correct option is C.
What is a transformation of a shape?A point, line, or mathematical figure can be converted in one of four ways, and each has an effect on the object's structure and/or position.
Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.
The triangle ΔCDE is shown below.
The triangle ΔC'D'E' after a rotation 270° counterclockwise about the origin.
The triangle ΔCDE and ΔC'D'E' are shown on the graph.
The coordinates of the triangle ΔC'D'E' will be (2, 1), (5, -3), and (2, -1). Then the correct option is C.
The transformation of the triangle is given below.
More about the transformation of the shape link is given below.
https://brainly.com/question/27224339
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What is 0.375 as a whole percent?
Answer:
0.375 is 37.5 % of 1
Step-by-step explanation:
a. For y = 5+ 80 when x = 4, what does y equal?
b. For a = 3 - 5c when c = -0.5, what does a equal?
c. For n = 2d2 – 5 when d = -2, what does n equal?
n
d. For v = -3(1 – 3) when r = -1, what does v equal?
a. y = 5x + 80 = 5*4 + 80 = 20 + 80 = 100
b. a = 3-5c = 3 - 5*(-0.5) = 3 - (-2.5) = 3 + 2.5 + 5.5
c. n = 2d² - 5 = 2*(-2)² - 5 = 2* 4 - 5 = 8 - 5 = 3
d. v = -3(1-3r) = -3(1-3(-1)) = -3(1+3) = -3*4=-12
Which fraction and decimal forms match the long division problem? 15) 8.000 75, 50 45, 的一 5 O A. 8 and 0.53 15 O B. B. 15 and 0.53 8 O c. 15 and 0.533 8 O D. 8 and 0.53 15
Answer:
The correct answer is AAAA
Answer:
A.
[tex] \frac{8}{15} and \: 0.53[/tex]
Crystal has played the piano for 15 years. Jane has played for 3 years. How many
times longer has Crystal played the piano I need equation: and answer
Answer:
15/3=5
Step-by-step explanation:
Crystal has played the piano for 5 times longer than Jane.
find the unit rate for this problem
45 tacos for 15 people ______ to is per person
No link please!!!
Answer:
45/15 = 3
Step-by-step explanation:
3 tacos per person
Answer:
3 tacos for 1 person
Step-by-step explanation:
45 tacos / 15 people
Divide the top and bottom by 15
(45/15) / ( 15/15)= 3/1
3 tacos for 1 person
what would the answer be
Answer:
60
Step-by-step explanation:
A line that includes the points (z,2) and (–8,–5) has an undefined slope. What is the value of z?
Answer: z = -8
Step-by-step explanation:
A line with an "undefined slope" is one that is vertical to the x axis. It has a slope that is undefined because there is no change in x for all points on the line. The slope is the Rise over the Run, and in this case there is no :Run." That means dividing by zero, so it is undefined.
Since x foes not change, the unknown point (z,2) would be (-8,2).
z = -8
Can you write 8x=1 as a quadratic equation?
Answer:
yes
Step-by-step explanation:
The root of the given linear equation can be made to be a repeated root of a quadratic equation:
(8x -1)² = 0
A car agency shows a new car with a price of AED 45,000. The company predicted that the cost of the
car would depreciate 10% each year for three years and then depreciate 8% each year after that. Find
the value of the vehicle in 8 years.
HELP ME PLSSS
Answer:
$8640
Step-by-step explanation:
Step 1:
The total amount of the car currently is $45,000. The car depreciates by 10% for the next 3 years. Then multiply 3 to 45,000.
3 × 45,000 = 135,000
The price then decreases by 10%. So, find 10% of 135,000
[tex]10\% = \frac{10}{100}[/tex]
[tex]135000=\frac{135000}{1}[/tex]
[tex]\frac{10}{100}\times \frac{135000}{1}[/tex]
Cross cancel the zeros
[tex]\frac{10}{1}\times \frac{1350}{1}[/tex]
Multiply across
[tex]10\times1350 = 13500[/tex]
Therefore, for the three years, the cars price is now $13,500.
Step 2:
The next step is the same as the first one. But now the car currently is $13,500. And The car depreciates by 8% for the next years. We have to find the value in 8 years. Then multiply 8 to 13,500.
8 × 13,500 = 108,000
Now, find 8% of 108,000
[tex]8\% = \frac{8}{100}[/tex]
[tex]108000=\frac{108000}{1}[/tex]
[tex]\frac{8}{100}\times \frac{108000}{1}[/tex]
Cross cancel the zeros
[tex]\frac{8}{1}\times \frac{1080}{1}[/tex]
Multiply across
[tex]8\times1080 = 8640[/tex]
Therefore, the value of the vehicle in 8 years is $8640.
1/3(12-9y) distributive property
Answer:
4 - 3y
Step-by-step explanation:
[tex]\frac{1}{3}[/tex] (12 - 9y) ← multiply each term in the parenthesis by [tex]\frac{1}{3}[/tex]
= 4 - 3y
The simplification of 1/3(12-9y) using distributive property is 4 - 3y
What is distributive property?According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
For example, 2( x +y ) can be simplified as 2 × x + 2 × y
= 2x + 2y. This is distributive property.
Similarly, ⅓( 12- 9y) can be simplified as
(1/3 × 12) - (1/3 × 9y)
= 4 - 3y
Therefore 1/3(12-9y) is equivalent to 4 - 3y
learn more about distributive property from
https://brainly.com/question/2807928
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