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]
(3+6i)(4-4i) simplify
Answer:
See picture
Step-by-step explanation:
Hope this helps!
Write the equation of the line in slope-intercept form.
The equation of the line in slope-intercept form is
Sandra and Peter together weigh 275 pounds. Sandra and
Martin together weigh 245 pounds. All three together
weigh 410 pounds. What is Sandra's weight alone?
Answer:
110 pounds
Step-by-step explanation:
Let the weight of Sandra, Peter and Martin be S, P and M pounds respectively.
S +P= 275 -----(1)
S +M= 245 -----(2)
S +P +M= 410 -----(3)
(3) -(1):
S +P +M -(S +P)= 410 -275
S +P +M -S -P= 135
M= 135
Substitute M= 135 into (2):
S +135= 245
S= 245 -135
S= 110
Thus, Sarah weighs 110 pounds.
hihii who knows the answer to this question??
Part A
x = some unknown number
2x = doubling that number
2x+11 = adding on eleven
Answer: 2x+11 = 25=============================================================
Part B
If we knew what x was, then we can compute 2x+11 using the order of operations PEMDAS. Because x is unknown, we follow PEMDAS in reverse to isolate x.
So we'll undo the addition first by subtracting 11 from both sides. Then we undo the multiplication by dividing both sides by 2.
2x+11 = 25
2x+11-11 = 25-11 ..... subtract 11 from both sides
2x = 14
2x/2 = 14/2 ...... divide both sides by 2
x = 7
The number the person thought of was 7. Double 7 to get 14. Add on eleven to get 14+11 = 25.
Answer: x = 7Write the recursive and explicit formulas for the given sequence 4, 7, 10, 13
recursive formula: explicit formula:
a,1 = a,n =
a,n =
Answer:
the answer to your question is 45 over 6
Answer:
45/6 or simplified 15/2
Step-by-step explanation:
what is 492 divided bye 2 someone help me
Answer:
246
Step-by-step explanation:
Given that,
→ what is 492 divided by 2 ?
In mathematical form,
→ 492 ÷ 2
→ 246 {final answer}
Hence, the answer is 246.
Stop and answer this question
The first truck carries 35 tons less rice than the second truck. The number of paddy in the first truck is 2/3 of the amount in the second truck. How many tons of paddy does each cart hold?
First truck = x
Second truck = y
x + 35 = y
x = 2/3y
So
2/3y +35=y
1/3y = 35
y = 35*3
y = 105
And ,
x = 2/3y = 70
plz help??????????????????????
Answer:
Step-by-step explain
i did not do the 1 and 2 srry
Is 4/9 equivalent to 8/16
Answer in the picture.
Question 1 of 10
Using the graph as your guide, complete the following statement.
The discriminant of the function is
101
HA
-10
10
The discriminant of the function is positive
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the discriminant of the function be represented as D
Now , the value of D is
D = ( b² - 4ac )
And , when ( b² - 4ac ) is positive, we get two real solutions
When a quadratic function contacts the x-axis on two different occasions, the function should be positive in this case. When the quadratic function intersects the x-axis precisely on one occasion, the function should be equal to zero.
When the x-axis shouldn't cross the function graph, the function should be smaller than zero.
Hence , the discriminant of the function is positive
To learn more about quadratic equations click :
https://brainly.com/question/25652857
#SPJ7
The complete question is attached below :
Using the graph as your guide, complete the following statement.
The discriminant of the function is
hey i need help on this question even if you can only answer one of the three boxes
but if someone can do 2 or more that would be very apricated
thanks!
Answer:
I don't see boxes?
Step-by-step explanation:
I do not see any boxes sorry for the inconvenience
Graph the lines y=3x+3
~graph
Graph the line using the slope and y-intercept, or two points.
Slope : 3
y intercept = (0 , 3)
graph already attached ✔️
~ nice to help you ^^
Answer:
Step-by-step explanation:
What is the value of x?
A) 3
B) 6
C) 8
D) 1
Answer:
I'm amusing its the answer is C
12. Hannah wants to buy 4 presents for at least $60. She wants to spend an equal amount of money on each present. Write and solve an inequality to show the least amount of money Hannah will spend on each present
Answer: 15
Step-by-step explanation:
So it is pretty much 60/4 which is easy 15 here is the work
1 5
4 6 0
- 4
2 0
- 2 0
0
Answer:
x ≥ $15
Step-by-step explanation:
At least means ≥
4x ≥ $60 Replace the inequality sign with an = sign and solve the equation.
4x = $60
x = $60 ÷ 4
x = $15 Now put the inequality sign back into the problem
x ≥ $15
Find an equation of the vertical line through (4,-9)
Answer:
x = 4
Step-by-step explanation:
Whenever it asks for the equation of a vertical line all you have to do is look at the x point given to you which is 4 and make x = 4, doing this means that this certain vertical line covers all possible y values which includes -9 as well which is why the answer is x=4
It cost Chloe $9.20 to send 92 text messages. How many text messages did she send if she spent $18.00?
who know plz plz !!
Answer:
180 texts
Explanation:
mutiply 92 by 0.10 and you'll get 9.2
So each text costs 10 cents.
Which system of linear inequalities has the point (2, 1) in its solution set?
y less-than negative x + 3. y less-than-or-equal-to one-half x + 3 On a coordinate plane, 2 lines are shown. The first solid straight line has a positive slope and goes through (negative 4, 1) and (0, 3). Everything below the line is shaded. The second dashed straight line has a negative slope and goes through (0, 3) and (3, 0). Everything to the left of the line is shaded.
y less-than negative one-half x + 3. y less-than one-half x. On a coordinate plane, 2 lines are shown. The first solid straight line has a negative slope and goes through (0, 3) and (4, 1). Everything below the line is shaded. The second dashed straight line has a positive slope and goes through (0, 0) and (2, 1). Everything below and to the right of the line is shaded.
y less-than-or-equal-to negative x + 3. y less-than-or-equal-to one-half x + 2 On a coordinate plane 2 solid straight lines are shown. The first line has a positive slope and goes through (negative 4, 1) and (0, 3). Everything below the line is shaded. The second line has a negative slope and goes through (0, 3) and (3, 0). Everything below and to the left of the line is shaded.
y less-than one-half x. y less-than-or-equal-to negative one-half x + 2 On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 2) and (4, 0). Everything below the line is shaded. The second dashed line has a positive slope and goes through (negative 4, negative 2) and (0, 0). Everything below the line is shaded.
Which graph represents the function f (x) = –| x - 3| + 1
Answer:
D
last one
Step-by-step explanation:
PLZ HELP ITS TIMED AND IM STUCK
3. option d
2. option a
5. option f
The ratio of red cars to blue cars in a parking lot was 9 : 7. If there were 72 red cars, how many blue cars were there?
Answer:
56
Step-by-step explanation:
We can mark the blue cars as x, so now, we have 9:7, and 72:x, we can use cross multiplication to get the value of x, 72*7 = 9x, which we can simplify into 504 = 9x, and can divide both sides by 9 to get 56 = x.
Hope it helped!
some more math stuff I don't know of :(
They are both 40°. This is bc 180-65-75=40
Community planners are planning to build a new community garden. They agree that the garden will be rectangular in shape, but the proposed dimensions changed. At the most recent meeting, it was determined that the length would remain at 15.8 yards but that the width would increase by 5.2 yards. So, the garden would now cover an area of 327.65 square yards.
Which equation can be used to determine the original width of the garden, w?
1: 327.65 = 5.2 (w + 15.8)
2: 327.65 = 15.8(w +5.2)
3: 327.65 = 2 (w +21)
Answer:
2)
Step-by-step explanation:
To find the original width, multiply 15.8 by w, and by 5.2.
You'll get 327.65 = 15.8w + 82.16.
Next, do the opposite of the symbol from both sides, 327.65 - 82.16 = 15.8w + 82.16.
The constant is 82.16, and the symbol is +, the opposite of plus is -, and thus subtract the constant from both sides.
You'll get 245.49 = 15.8w.
Now do the opposite of the symbol (a number next to a variable is multiplication, so do division, and divide 15.8 on both sides.
245.49/15.8 = 15.8w/15.8, which equals 15.5373417722.
You have a savings bank account, you have $35.30 in the account to start.
You deposit $17.50. Then you add in another $25 from your birthday.
Then you have to spend $6.99. But then you saved up another $14.75 that
you want to deposit, after all of those transactions what is your current
BALANCE?
Answer: $85.56
Step-by-step explanation:
$35.30 +$17.50= $52.80
$52.80+$25 = $77.80
$77.80-$6.99 = $70.81
$70.81+$14.75 = $85.56
think of two numbers which when add give 5 and substracts give 1
Answer:
3 and 2
Step-by-step explanation:
3+2=5
3-2=1
Hope this helps!!
Write the slope-intercept form of the given line. Include your work in your final answer. Type your answer in the box provided to submit your solution.
Answer:
y=-1/3x+1
Step-by-step explanation:
it is negative because when you find the slope you go down instead of up
What is the Factor of 3/9+8/9
Step-by-step explanation:
the lcm is 9 so....
3/9+8/9
multiply both sides by their lcm which is 9...
so....
9 (3/9)+9 (8/9)
3+8=11
A reflection over the x axis moves the point (-2, 5) to which quadrant?
I
Hiiii!!! Can someone please help mee!! I will give you double points!!!
Answer:
II quadrant
Step-by-step explanation:
Looking at the drawing, you can determine that the point with
coordinates (-2 ; 5) is in the II quadrant
Split 70 into the ratio 3:4? I don't understand ratio :(
Answer:
30:40
Step-by-step explanation:
Item A: item B : total
3 4 3+4
3 4 7
The total is 70
70/7 = 10
Multiply each item by 10
Item A: item B : total
3*10 4 *10 7*10
30 40 70
Answer:
30 and 40
Step-by-step explanation:
3 : 4 means 3 out of every 7 objects and 4 out of every 7.
[tex]\frac{3}{7} (70) = 30[/tex]
[tex]\frac{4}7} (70) = 40[/tex]
what's 12+12+12?
_______
.
Answer:
the answer is ;
12+12+12 = 36
The tape diagram below represents 100%.
100%
?
What percent is represented by the shaded area?
%
Answer:
60% is the answer also give me brainliest plss