First simplify the rational expression by dividing. The degree in the numerator has to be at least 1 less than the degree in the denominator before you can decompose into partial fractions.
(3x³ - 5x² - 3x - 40) / ((x² + 4) (x - 3)) = 3 + (4x² - 15x - 4) / ((x² + 4) (x - 3))
Now decompose the remainder term into partial fractions:
(4x² - 15x - 4) / ((x² + 4) (x - 3)) = (ax + b) / (x² + 4) + c / (x - 3)
Multiply both sides by the denominator on the left:
4x² - 15x - 4 = (ax + b) (x - 3) + c (x² + 4)
Expand the right side:
4x² - 15x - 4 = ax² + (b - 3a) x - 3b + cx² + 4c
4x² - 15x - 4 = (a + c) x² + (b - 3a) x - 3b + 4c
Then
a + c = 4
b - 3a = -15
-3b + 4c = -4
Solve this system to get
a = 5, b = 0, c = -1
We end up with
(4x² - 15x - 4) / ((x² + 4) (x - 3)) = 5x / (x² + 4) - 1 / (x - 3)
and so
(3x³ - 5x² - 3x - 40) / ((x² + 4) (x - 3))
= 3 + 5x / (x² + 4) - 1 / (x - 3)
Kate and Nora each have a sum of money. The ratio of the amount of money Kate has to that of Nora is 3 : 5. After Nora gives $150 to Kate, the ratio of the amount of money Kate has to that of Nora becomes 7 : 9. Find the sum of money Kate had initially.
Answer:
5 : 3
Step-by-step explanation:
Answer:
$5
Hope this helps!
Solve the following system of equations:
x − 2y = 14
x + 3y = 9
Answer:
(12, - 1)
Step-by-step explanation:
x - 2y = 14 ......... (1)
x + 3y = 9 ......... (2)
(2) - (1)
(x - x) + (3y - ( - 2y)) = 9 - 14
5y = - 5 ⇒ y = - 1
x + 3( - 1) = 9 ⇒ x = 12
(12, - 1)
What is the value of the expression below when w=7 and x=2?
3w - 4x
Answer:
13
Step-by-step explanation:
3(7)-4x
3(7)-4(2)
21-8
=13
There are 15 pieces of fruit in a bowl and 6 of them are apples. What percentage of the pieces of
fruit in the bowl are apples?
A. 0.06%
B. 40%
C. 6%
D. 0.4%
Answer:
40%.
Step-by-step explanation:
There are 6 / 15 apples out of the bowl.
6/15 = 2/5 = 0.4
So, 40% of the fruit in the bowl are apples.
Hope this helps!
Place these number in order from greatest to least.
-7/5, 16, -1, 3.2, -6.5, 0, 3/4,
Answer:
Step-by-step explanation:
First, change the fractions into decimals, then use the knowledge of the number line system to know which is greater or smaller than who.
-7/5 -1.4
3/4 0.75
so the numbers are -1.4, 16, -1, 3.2, -6.5, 0, 0.75
from greatest to least:
= 16, 3.2, 0.75, 0, -1, -1.4, -6.5
Question 3
True or false. A discount will add to the total cost you
will pay for an item.
Answer:
False
Step-by-step explanation:
integer c is 2/3 of the way from A on the integer line. Determine C
A=-23
B=-5
Answer:
Please see picture below
Step-by-step explanation:
find the slope of the line in the given picture, please help soon
Answer:
Step-by-step explanation:
the answer is 48
Last year, the school library had a total of x books. Over the summer, the library acquired another 40 books and now has a total of 1,795 books. Which equation could be used to find x, the number of books the library had last year?
Answer:
1794-40=x?
Step-by-step explanation:
this is genuine answer but a little bit unsure
Last year = x books
This year = x + 40 books
The needed equation is x + 40 = 1,795.
Question 1 (2 points)
Jeff is purchasing a car for $29,175 that will depreciate in value 7.5% each year.
Write a function to model the value P of the carafter t years,
If he decides to sell the car after 6 years, what will be the value of his car? Express your answer as a decimal rounded to the nearest hundredth.
Answer:
p= 18,275
Step-by-step explanation:
The function would be p=29,175(-0.925)^t. You would then substitute t for 6 and solve from there to get p=18,275.
Did it help at all?
solve the following equation 3(x+6) =4(2x-8)
Answer:
x=10
Step-by-step explanation:
3(x+6)=4(2x-8)
3x+18=8x-32
8x-3x=18+32
5x=50
x=10
Answer:
3x+18=8x-32
18+32=8x-3x
50=5x
x=10
Nellle has her hair styled by her hair stylist. The styling costs $85 and Nellie wants to leave a 30% tip. There is a tax rate of 6%.
and tip?
Answer:
115.60
Step-by-step explanation:
for a tip 85x 0.30=25.50
tax 85x0.06=5.10
total extra money 5.10+25.50=30.60
total money payed 85+30.60=115.60
Hope this helped
Please mark Brainlist
find the measure of the acute angles pls help
Answer:
60 degrees
and
52 degrees
Emily is buying cold-weather gear for her family. she pays $100 for 5 pairs of waterproof gloves that each cost the same amount. four of the pairs of gloves are mittens.which expression represents the total cost of four pairs of mittens
Answer:
the 4 pairs cost 80$
Step-by-step explanation:
Ps. My name is Emily
Answer:
yeetjdjsjsjdjdjjssjsbjsjshssujsidsjsnjsnsnsjdudbejdhdd
The equivalent of (-8)-4.(-8)2
The equivalent value of the expression (-8)-4.(-8)² is 768
what is expression?An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.
Given:
(-8)-4.(-8)²
Using properties of integers
(-8-4)*(-8* -8)
=(-12) * (-64)
= 768
Hence, the equivalent value is 768.
Learn more about expression here:
https://brainly.com/question/24242989
#SPJ1
A nest of ants has been growing exponentially in such a way that it's population,P, as a function increasing on average more or less than 1600 ants per week? Enter the value per week to the nearest tenth.
Not sure question is complete, assumptions however
Answer and explanation:
Given the above, the function of the population of the ants can be modelled thus:
P(x)= 1600x
Where x is the number of weeks and assuming exponential growth 1600 is constant for each week
Assuming average number of ants in week 1,2,3 and 4 are given by 1545,1520,1620 and 1630 respectively, then we would round these numbers to the nearest tenth to get 1500, 1500, 1600 and 1600 respectively. In this case the function above wouldn't apply, as growth values vary for each week and would have to be added without using the function.
On one hand, the function above could be used as an estimate given that 1600 is the average growth of the ants per week hence a reasonable estimate of total ants in x weeks can be made using the function.
It took Mrs. Harpole 35 minutes to grade
four student essays. How long will it take
her to grade all her classes, 80 students?
Answer:
700 minutes or 11.67 hours
Step-by-step explanation:
35/4=8.75
8.75*80=700
Write a two-column proof
Given: ∠1 and ∠2 are supplementary, m∠1 = 135°
Prove: m∠2 = 45°
Notice:
Unfortunately I’ve never written a two-column proof before. So I can’t do that. Let me know if what I can do helps at all though.
Step-by-step explanation:
A supplementary angle is an angle made up of two angles that have measures that add up to 180°. m∠2 = 45° because 45° added to 135° equals 180°. Therefore making it a supplementary angle. Meaning that m∠2 = 45° is true. Sorry if this doesn’t help. I tried my best.
Here's a graph of a linear function.
Write the
equation that describes that function.
Express it in slope-intercept form.
Answer:
y = 1/2x + 3Step-by-step explanation:
As per graph, using the points (-6, 0) and (0, 3) we determine that:
the y-intercept is 3 and the slope is m = (3-0)/(0 - (-6)) = /3/6 = 1/2So the equation is:
y = mx + by = 1/2x + 3Which best explains how you know that A(-1,6) is on the same line as a B( -3,10) and C (-5,14)
Answer:
To get from A to B and from B to C, you move left 2 units and then up 4 units.
Step-by-step explanation:
hope this helps :)
Please help me!!
A. 2 and 4 only
B. all of them
C. 1 only
D. 2, 3, 4, only
Answer:
D
Step-by-step explanation:
Supplementary means 180 degree. Thus, you have to find the two angle that equals 180.
Answer:
I think it is 1 only [B.]
Step-by-step explanation:
I'm not sure, but I hope this helps!
$650,000 was stolen from 1st Trust American Bank during a heist. The bank robbers got away clean and sped away traveling at a constant rate of 70 miles per hour. What the robbers did not realize is that one of the bank bags had a GPS tracking device inside of it. Once the police locked on to the signal of the tracking device they took off after the robbers traveling at a constant rate of 90 miles per hour. If the robbers already had a 30 mile head start, how long will it take the police to pass them and force them off the road to be arrested?
Answer:
The time taken before the police force the robbers off the road is 1.5 hours
Step-by-step explanation:
The speed with which the robbers were travelling = 70 miles per hour
The speed with which the police went after the robbers = 90 miles per hour
The distance with which the robbers were in front of the police before the police came after them = miles
Let t represent the time in hours the police force the robbers off the road, we have;
30 + 70 × t = 90 × t
30 = 90 × t - 70 × t = (90 - 70) × t = 20 × t
30 = 20 × t
20 × t = 30
t = 30/20 = 1.5
t = 1.5 hours
The time taken before the police force the robbers off the road = t = 1.5 hours
Answer:
The time taken before the police force the robbers off the road is 1.5 hours
Step-by-step explanation:
sarah reads 6 stories in 8 day
salma reads 11 stories in 8 days
how many stories can salma read more than sarah in 24 days?
Find the slope of the line that passes through the points (2, 1) and (-1,-1).
O
02
O 2/3
Answer:
0
Step-by-step explanation:
m=y2-y1 / x2-x1
m= -1-1/-1-2
m=0/-3
m=0
write down 45 in the Scientific Notation
Answer:
4.5x10^1
The first value should be less than 10
Please help! Will mark Brainliest.
Combine and Simplify: 48 (1/4x - 1/3y - 2/6x - 3/8y - 2/3
Answer:
Okay Somebody Needs To Get The Guy Below OFF OF HERE
Step-by-step explanation:
How to write vertex form when given to choices of “a” in a question ex: write the vertex form of the function where a=1 or a= -1 and H and K are integers? And the vertex is (-1,4)
Answer:
Step-by-step explanation:
Vertex form of quadratic equation is
[tex]y = a(x-h)^2 + k[/tex]
where h and k are the x and y coordinates of the vertex, respectively.
so in this problem
if a=1 and Vertex is (-1,4) means h= -1 and k = 4
the equation will be
[tex]y = 1 (x-(-1))^{2} + 4[/tex]
[tex]y = (x+1)^2 + 4[/tex]
if a=-1 and Vertex is (-1,4) means h= -1 and k = 4
the equation will be
[tex]y = -1 (x-(-1))^{2} + 4[/tex]
[tex]y = -(x+1)^2 + 4[/tex]
45 Points- Geometry
HELP ME
S<--->T
T<--->S
Same thing
4Both sides a equivalent therefore both triangle areas are also equivalent
9514 1404 393
Explanation:
The missing reasons are ...
3. Reflexive property of congruence. A segment is congruent to itself.
4. SSS postulate. The three corresponding sides are shown congruent, so the triangles are congruent.
What is the length of segment AB? (1 point)
Coordinate grid shown from negative 8 to positive 8 on both x axis and y axis at intervals of 1. A straight line labeled AB is drawn. A is the ordered pair 0, 6 and B is the ordered pair 7, 0.
Group of answer choices
Square root of 13
Square root of 85
14
13
Answer:
Square root of 85
Step-by-step explanation:
We can envision the segment AB as the hypotenuse of a right triangle with a height of 6 units and a length of 7 units. We can use the Pythagorean Theorem to solve for the length of segment AB which is similar to distance formula.
6^2 + 7^2 = c^2
36 + 49 = c^2
c^2 = 85
c = Square root of 85.
should i come out to my parents as bi O,o
Answer:
i did and it was the best thing ive ever done
Step-by-step explanation:
Answer:
yes, it feels so much better
Step-by-step explanation:
can someone help me with my geometry test please... on my page. Would love you forever lol