The only factoring you need to do is already done for you:
x² + x - 12 = (x + 4) (x - 3)
What you're asked to do is decompose
(3x - 4) / (x² + x - 12)
into partial fractions, i.e. find a and b such that
(3x - 4) / (x² + x - 12) = a / (x + 4) + b / (x - 3)
Multiply both sides by x² + x - 12 :
3x - 4 = a (x - 3) + b (x + 4)
3x - 4 = (a + b) x + (-3a + 4b)
So we have
a + b = 3
-3a + 4b = -4
and solving this system gives
a = 16/7 and b = 5/7
so you should submit the numbers in bold:
(3x - 4) / (x² + x - 12) = 16 / (7 (x + 4)) + 5 / (7 (x - 3))
Carla can roll 18 pretzels in 12 minutes. How many can she roll in 40 minutes?
Answer: 60
Step-by-step explanation:
To find how much she rolls in 1 minute, you divide 18 by 12. This gets you 1.5. Multiply 1.5 by 40 and you get 60.
THE DOTS SHOWN REPRESENT WHAT KIND OF SEQUENCE?
D is for difference
R is for ratio
Arithmetic is Adding
Geometrical is Multiplying
please help asap , explain how you got the answer .
Answer:
f(x)= -2/5x-4
Step-by-step explanation:
-2/5 is the slope and -4 is the y intercept
Help will give brainlist!
If correct. Thanks!
Answer:
B y=0.5x-1
Step-by-step explanation:
Answer:
Y=-1/2x-1
Step-by-step explanation:
The slope is found using rise/run
Y-int can be found on the graph
Leo gathered data about the weight, in pounds of his suitcase when it was packed for trips lasting different numbers of nights. the data he gathered is organized in the table. (PLEASE ANSWER FOR REAL!!! NO BS LIKE RANDOM LETTERS OR IDK!)
Nights (x) 2, 3, 4, 5, 6
Weight (y) 17, 22, 26, 30, 35
Answer:
y=4.4x+8.4
Step-by-step explanation:
Help plsssssssssssss???
Answer:
Go 6 units to the right and then 8 units up.
Answer:
so Go 6 units to the right and then 8 units up. and then you should get your point on the graph id apreciate brainliest
Step-by-step explanation:
these are two different questions
Please help me on this
Answer:
a: -1,-1
b: 2,3
c:6,7
d: 5, 7
Step-by-step explanation:
Answer:
A -1,-1
B 2,3
C 6,7
D 5,-3
Step-by-step explanation:
You have to plug in each plotted point into the formula that was given to you.
Ex - A is plotted point is (-4,-3) so you plug in (-4+3,-3+2) which will give you (-1,-1)
(THIS IS A TEST I NEED HELP)
In the rectangular prism, PQ is the diagonal. Find the length of
PQ given PR = 7, RS = 4, and QS = 4.
A 4
B 9
C 12
D 15
Answer:
Option (B)
Step-by-step explanation:
Length of PR = 4
RS = 4
QS = 4
For the length of PT,
PT² = RT² + PR² [Since, PT is the diagonal of rectangle PRT]
PT² = QS² + PR² [Since, RT ≅ QS]
PT² = 4² + 7²
PT² = 16 + 49
PT² = 65
Now for the length of PQ,
PQ² = QT² + PT²
PQ² = RS² + PT² [Since, QT ≅ RS]
PQ² = 4² + 65
PQ² = 16 + 65
PQ = √81
PQ = 9
Therefore, length of diagonal PQ is 9 units.
Option (B) will be the answer.
A bag contains 12 red marbles the ratio of red marbles to blue marbles is 4:3 find the number of blue marbles in the bag
Answer:
9
Step-by-step explanation:
this can be written as an equation.
12/x=4/3
and it is just easy now, you see what you multiply 4 by to get 12 and it is 3, so that means you have to multiply 3 by 3
3 times 3 is 9, so the answer is 9
Answer:
Hello There!!
Step-by-step explanation:
First look at the ratios the red marbles ratio is 4 and the blue marbles ratio is 3.
You already know that there are 12 ratios in the bag so 12÷4=3(1 ratio equals 3 marbles)
Therefore,3×3=9.So the answer is 9 blue marbles.
hope this helps,have a great day!!
~Pinky~
Answer the two following question and will mark Brainliest
Answer:
Max: (-2,5)
Min: (-6,-4)
Answer:
(-2, 5) for the max and (-6, -4) is the min. That if the question is talking about max and min graph points!
Step-by-step explanation:
Hope it helps!
Which statements describe a characteristic of a right pentagonal pyramid? Select two options.
The bases are parallel and congruent.
The segment from the top to the center of the base is perpendicular to the base.
All the faces are congruent pentagons.
The base is a pentagon and the sides are triangles.
The base must be a regular polygon.
Answer:
B and D are correctStep-by-step explanation:
The options:
A. The bases are parallel and congruent.
Incorrect. There are no parallel bases in any pyramidB. The segment from the top to the center of the base is perpendicular to the base.
Correct as its a right pyramidC. All the faces are congruent pentagons.
Incorrect. Only the base is pentagon.D. The base is a pentagon and the sides are triangles.
CorrectE. The base must be a regular polygon.
Incorrect. It is pentagon.Answer:
2 and 4
Step-by-step explanation:
edge 2021
5d-3+2d=4d+9. I need help can you help me solve this problem
Answer:
D=4
Step-by-step explanation:
Answer:
d=4
Step-by-step explanation:
5d - 3 +2d = 4d +9
7d-3=4d+9
-4d -4d
3d-3=9
+3 +3
3d=12
divide both sides by 3
d=4
the ratio of boys to girls is in a class 4:3. There are 35 students in the class. How many students are boys ?
What is the formula?
Answer:
ratio 4x:3x
total= 7x parts = 35(given)
x= 35/7 =5
boys = 4x = 20
girls = 3x = 15
The number of boys are more by 20-15 = 5.
Step-by-step explanation:
Answer:
20 boys 20:15
Step-by-step explanation:
helpful??
Rewrite the equation C = 2nr to show the expression that can be used to find the value of r.
The process is:
C = 2nr
2nr = c
r (2n) = c
[tex]r = \frac{c}{2n} [/tex]
That's the answer☝️☝️☝️☝️
or maybe this one
r = 2n + c
sorry, I'm unsure, it has been too long since I studied that...
Answer:
C = 2nr
you divide by 2n both sides
that means C/2n = 2nr/2n
after that you simplify then it will be C/2n = r
r = C/2n
Are the two triangles similar?
Answer:
No, they are not.
Step-by-step explanation:
Miguel places his 13-foot ladder 5 feet from the edge of his house. How high does the ladder reach? A. 8 feet B. 12 feet C. 13.9 feet D. 144 feet E. 194 feet
Answer:
A - eight feet
Step-by-step explanation:
20 character rule can be dumb sometimes
The Pythagoras is the sum of the square of two sides is equal to the square of the longest side. The height of the house is 12 feet, then the correct option is B.
What is a right-angle triangle?It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function.
Miguel places his 13-foot ladder 5 feet from the edge of his house.
Then the height of the house is given by the Pythagoras theorem.
P² = H² - B²
P² = 13² - 5²
P² = 169 - 25
P² = 144
P = 12
Then the height of the house is 12 feet.
More about the right-angle triangle link is given below.
https://brainly.com/question/3770177
After a 5% discount, a car is on sale for $11,400. What was the price of the car before the discount?
Answer:
$11,970 is the price of the car before the discount
Step-by-step explanation:
HELPP! I need an explanation an answer quicck
Answer:
C. -1,-2
Step-by-step explanation:
Help Plz 10pts will be given
Answer:
Is the first one 3 over 7
Step-by-step explanation:
e owner of a skatepark wants to increase her entry fee of $5 Buy in increments of $0.50 currently the skate park has an average of 500 paying customers per week the equation (500 - 25x)( $5 + $0.50x) give me the estimated weekly income where X is the number of $0.50 entry fee price increases if the entry fee is increased to $7.50 what will be the expected average number of paying customers each week
Answer:
375 paying customers
Step-by-step explanation:
First you need to find how much the fee was increased from $5.00 to $7.50
7.5 - 5 = 2.5
Then how many times the pay increase goes into that number to find your X value
2.5/.5 = 5
Now that we have found our x value lets plug it into the equation to find the money the park will make in increments of 1
500 - 25(1) = 475
500 - 25(2) = 450
500 - 25(3) = 425
500 - 25(4) = 400
500 - 25 (5) = 375
Answer:
375
Step-by-step explanation:
Calcium-41 is being used in studies testing the effectiveness of drugs for preventing osteoporosis. The half-life of calcium-41 is 100,000 years. If 20 grams of calcium-41 are present initially, how long would it take until only 2 grams
remains?
Answer:
332,193 years
Step-by-step explanation:
From the question above, we are to calculate the time in an half life question, hence, the formula is given as
t = In(Nt/No) ÷ -(In2/t½)
Where
t = time is takes for an substance to decay or reduce
Nt = Amount of sample after time = 2g
No = Initial amount of sample = 20g
t½ = Half life = 100,000 years
Hence,
t = In(2/20) ÷ (In 2/ 100,000)
t = 332192.80948874 years
Approximately = 332,193 years
Solve by using substitution. Express your answer as an ordered pair.
Answer:
(1, -2)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Algebra I
Solving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
4x + y = 2
y = x - 3
Step 2: Solve for x
Substitution
Substitute in y: 4x + (x - 3) = 2Combine like terms: 5x - 3 = 2Isolate x term: 5x = 5Isolate x: x = 1Step 3: Solve for y
Define equation: y = x - 3Substitute in x: y = 1 - 3Subtract: y = -2please help i’ll give brainliest please tysm :))
Answer:
Grape juice has 180 containers.
Step-by-step explanation:
Given that the ratio of containers of orange juice to containers of grape juice in a store is 5 orange juices to 4 grape juices.
i.e.
Orange Juice containers : Grape Juice containers = 5 : 4
Total containers = 405
It means if we divide 405 by 9, we get the 9 equal parts of 45.
i.e. 405 / 9 = 45
as
Orange Juice containers : Grape Juice containers = 5 : 4
It means the share of Grape Juice containers is 4 parts out of 9 parts.
Thus, multiply 45 by 4 to determine the number of containers grape juice have:
45 × 4 = 180 containers
Therefore, grape juice has 180 containers.
add 2f+5g+7h and 3f+6g+8h
Answer:
Step-by-step explanation:
Add the like terms
5f+11g+15h
Which equation is not linear
A. -4x + 2y =7
B. x/4 =y
C. X=-5
D. 2/x + 3/y
[ that's / not a division it's a fraction bar]
Identify the constant of proportionality.
Answer:
14
Step-by-step explanation:
If you divide -28 and -2, you get 14 which is the constant of proportionality. You can try to multiply -4 and 14 to check which you get -56. The graph shows that and it's the correct answer!
A fundraiser is being held to support a local nonprofit organization. Admission costs $10, and each raffle ticket costs $3. There are no other possible costs. If an event-goer pays the admission fee and buys x number of tickets, what type of function should be used to model the total amount spent by the event-goer at the event?
Answer:
y= 10+ 3x
10 is the admission fee
3x is the cost for each ticket
y is the total
The function for the total cost (y) spent by the event-goer at the event is
y = 3x+10
What is a function?A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output.
Given that, Admission costs $10, and each raffle ticket costs $3. There are no other possible costs.
Let the total cost be y,
Therefore, establishing the function, for x number of tickets.
y = 3x+10
Hence, the required function is y = 3x+10
For more references on function, click;
https://brainly.com/question/21145944
#SPJ6
PLEASE HELP!!
What is the slope for runner 1 and runner 2 ?
Kaylee put $240.00 in a bank account that gains 25%
interest annually.
How much interest will be accumulated in a year?
S???
If Kaylee makes no withdrawals, how much money will be
in the account after a year?
$???
Answer:
S=720
Step-by-step explanation:
25$ of 240 =60
60×12months=720