Answer:
f(x) = 12x³ - 19x² + 17x - 17
Step-by-step explanation:
We can the numerator by multiplying the denominator by the quotient, and then adding the remainder.
We're given a denominator of 4x - 5
a quotient of 3x² - x + 3
and a remainder of -2
so the original numerator is:
(4x - 5)(3x² - x + 3) - 2
= 12x³ - 4x² + 12x - 15x² + 5x - 15 - 2
= 12x³ - 19x² + 17x - 17
Let's test that by dividing it by 4x -5 with long division:
[tex]\ \ \ \ \ \ \ \ \ \ 3x^2 - x + 3\\4x - 5\overline{)12x^3 - 19x^2 + 17x - 17}\\.\ \ \ \ \ \ \ \ \ \underline{2x^3 - 15x^2}\\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ -4x^2 + 17x\\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \underline{-4x^2 + 5x} \\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 12x - 17\\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \underline{12x - 15}\\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2R[/tex]
That matches, so we know our answer's right, and:
f(x) = 12x³ - 19x² + 17x - 17
A model car has a length of 7.25 inches. The actual car is 14.5 feet long. What is the scale of the model car?
Answer:
1:24
Step-by-step explanation:
Convert inches to feet, 7.25 inches is 0.604 feet.
0.604:14.5 needs to become 1:something, so set up 0.604/14.5 = 1/x
Solve for x now by dividing 14.5 by 0.604. You get 24 for x, so the answer is 1:24 scale!
chris sold a watch for $1500 thereby making a profit of 20% calculate the amount chris payed for the watch
In a class of 22 students, 13 have a brother and 15 have a sister. There are 3 students who do not have any siblings. What is the probability that a student has a brother given that they do not have a sister?
Answer:
1/4
Step-by-step explanation:
The probability that a student has a brother given that they do not have a sister 9/7.
How to calculate the probability of an event?Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.
Then, suppose we want to find the probability of an event E.
Then, its probability is given;
[tex]\rm P(E)=\dfrac{Number \ of \ favourable \ events}{Number \ of \ total \ events}\\\\[/tex]
In a class of 22 students, 13 have a brother and 15 have a sister.
There are 3 students who do not have any siblings.
3 students don't have a sibling.
The probability that a student has a brother given that they do not have a sister is;
[tex]\rm P(E)=\dfrac{Number \ of \ favourable \ events}{Number \ of \ total \ events}\\\\ \rm P(E)=\dfrac{13+15-22+3}{22-15}\\\\\rm P(E)=\dfrac{31-22}{7}\\\\ P(E)=\dfrac{9}{7}[/tex]
So, the probability that a student has a brother given that they do not have a sister 9/7.
Learn more about probability here:
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HELP ME PLEASE!!!!!ITS DUE TODAY!!
Answer:
T = 11.77
18% Tip = 2.12
Total with tip = $13.89
This should be right :)
Lmk how I did!
hi everyone i got a 16/20 on a final what percent is that im jw
Answer:
80%
Step-by-step explanation:
The previous owner of Ahmed's new sail boat recalled that the area of sail B was 108 square feet. What is the length of the base of sail B? Use the image below.
Answer:
81 ft
Step-by-step explanation:
Bryan initially filled a measuring cup with 3/10 of a cup of syrup from a large jug. Then he poured 1/10 of a cup back into the jug. How much syrup remains in the measuring cup?
The area of a rectangle is 35x - 20. Find the length and width of the triangle. (Hint: Factor completely) Write your answer as a product. Ex: 8(3x-2).
Please help me get the answers for this
Answer:
B.
Step-by-step explanation:
Somebody help me ASAP noww
Answer:
65
Step-by-step explanation:
That is a 180 split so 180-115=65
Which of the following is equivalent to
8/9
One of these expressions reduces to 1 and the other reduces to –1. Do you know which one is which? How do you know? x + 3 3 + x 3 − x x − 3 x + 3 3 + x = The numerator of the expression 3 − x x − 3 can be written as . 3 − x x − 3 =
Answer:
First Blank: 1
Second Blank: -1 (x-3)
Third Blank: -1
Step-by-step explanation:
The expression [tex]\frac{x+3}{3+x}[/tex] is reduced to 1 and the expression [tex]\frac{3-x}{x-3}[/tex] is reduced to -1.
The two given expressions are [tex]\frac{x+3}{3+x}[/tex] and [tex]\frac{3-x}{x-3}[/tex].
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
Here,
[tex]\frac{x+3}{3+x}=\frac{x+3}{x+3}=1[/tex]
Now, [tex]\frac{3-x}{x-3}=\frac{-(x-3)}{x-3}=-1[/tex]
Therefore, the expression [tex]\frac{x+3}{3+x}[/tex] is reduced to 1 and the expression [tex]\frac{3-x}{x-3}[/tex] is reduced to -1.
To learn more about an expression visit;
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A boat can travel 128.8 miles on 16.1 gallons of gasoline. How far can it travel on 9.4 gallons?
Katheryn fills container X with water. She
wants to pour the water into container Y until
it is full.
PLS PLS PLS PLS PLS PLS helpppp im so confused and just need some help on this.
ill mark u breainliest or whatever ya want just pls answer this with the correct answer its due in like 10 mins
Answer:
14. non- proportional
15.it will take 88 minutes to add 16 seats.
It will take 104.5 minutes to add 19 seats.
Step-by-step explanation:
Let m represent number of minutes.
We have been given that an assembly line worker at Rob's Bicycle factory adds a seat to a bicycle to a rate of 2 seats in 11 minutes.
We will use proportions to solve our given problem.
To find the time taken to add 16 seats, we will in our proportion as:
Therefore, it will take 88 minutes to add 16 seats.
To find the time taken to add 19 seats, we will in our proportion as:
Therefore, it will take 104.5 minutes to add 19 seats
All equilateral triangles are -------- triangles. acute scalene obtuse or right?
Answer:
All equilateral triangles are acute angle triangles.
In the following figure, the value of x is ?
Step-by-step explanation:
Using SOH CAH TOA
sin#=opp/hyp
sin35=x/20
20sin35=x
x=11.4715
x=11.5
Help needed on this question
!!!!!!Help Me Plz!!!!!!
Answer:
angle ABE = 55 degrees
Step-by-step explanation:
(3x-8) + (x+14) = 90
4x+6 = 90
4x = 84
x = 21
angle ABE = 3(21)-8 = 55
Someone help me pls :(
Answer: (3,3)
Step-by-step explanation:
find the value of each variables
Answer:
Step-by-step explanation:
Two similar triangles.
10/26 = y/13
y = 5
x² = 13² - y² = 144
x = 12
An object with a mass of 5.0kg accelerates 8.0m/s2 when an unknown force is applied to what is the force?
Answer:
The correct amount of force i believe is
f= 40 newton
i got the answer by using the formula below
force = mass x acceleration
f=5kg *8.0 m/s^2
Step-by-step explanation:
help me out, please. Thank you!
Answer:
a: 5
b: (0, -2)
c: 3
d: (0, 11)
Step-by-step explanation:
Hope this helps!
There were 30 pairs of jeans on sale for 2/3 of the regular price.
The regular price was $36. What was the sale price?
Answer : $36
Explanation:
To find the sale price we can set up a proportion. 25/100 = x/48. We keep the 100 and 48 both on the bottom of the fraction since they represent the "whole". x represents the discount off the full price of the dress. To solve this proportion, we cross multiply, yielding 48 * 25 = 100x. Alternatively, if you notice that 25/100 simplifies to 1/4, we can use 1/4 in our proportion instead of 25/100, thus, 1/4 = x/48. Then, cross multiplying, we get 48 = 4x, so x = 12. Then we subtract this discount from the original price yielding 48 – 12 = 36; thus, she paid $36 for the dress.
25% = 25/100
25100=x48
14=x48
(1) * (48) = (4) * (x)
48 = 4x
(48)/4 = (4x)/4
12 = x
The discount is $12.
$48 – $12 = $36
PLEASEE HELPPP
find the solution to the system of equations
Please help
Please
Which 2 segment are parallel?
Please
Answer:
E and D
Step-by-step explanation:
(PLEASE HELP) What is the value of x?
Enter your answer in the box.
x =
Answer:
x = 12
Step-by-step explanation:
(10x - 20)° + (6x + 8)°= 180°
(Linear pair angles)
(10x - 20 + 6x + 8)°= 180°
(16x - 12)°= 180°
16x - 12 = 180
16x = 180 + 12
16x = 192
x = 192/16
x = 12
Answer:
so x would equal 12
Step-by-step explanation:
(10x - 20)° + (6x + 8)°= 180°
so you are going to want to combine like terms which would be
10x and 6x, and 20,8
10x+6x=16x
20-8=12
16x-12=180
now you want to get 12 on the opposite side of the equal side so you add (since it is negative) 12 to each side
which gets rid of the first 12
16x=180+12
now you can add 180+12
and you get 192
so now we want to get x by itself in order to do that you must divide
you are going to divide by 16 an each side and the 16 cancels out the first 16
16x/16=192/16
x=192/16
and 192 divided by 16 is 12
so you answer is
x=12
Hope this made sense :)
Find the unknown side length, x. Write your answer in simplest radical form. A. 3 B. Sqrt 34 C 6 D.Sqrt 41 Please select the best answer from the choices provided
Answer:
Attach a picture of the shape for the sides already known...
Step-by-step explanation:
i need help telling if these are true or false
Answers:
FalseTrueFalseTrue======================================================
Explanations:
Point A is located at (0,1). It then moves to A' which is at (0,3). Note the y coordinate goes from y = 1 to y = 3, so the scale factor is 3/1 = 3 instead of 4. Therefore, the claim is false.Point A is at (-4,4). It moves to (-2,2). Each coordinate of (-4,4) is cut in half to get (-2,2). Cutting a value in half is the same as multiplying by 0.5, so point A fits the description. Let's find out if point B does as well. B is at (2,4) and it moves to B' (1,2); we can see that point B has its coordinates cut in half as well. Points C and D also work to fit the description (I'll let you check those coordinates) which means overall, quadrilateral ABCD dilates with a scale factor of 0.5 to get to quadrilateral A'B'C'D'. The answer here is "true".Point W is at the location (-1,1). Triple each coordinate to get (-3,3) which is where point W' should be located if we applied the dilation of scale factor 3. However, the diagram shows W' is not at (-3,3). It seems to be fairly close to (-2,2) if anything. We don't need to check the other points, but I recommend you do so just for practice. The answer here is "false".Because the scale factor is 0.25 = 1/4, this means "scale factor of 0.25" is the same as "scale factor of 1/4". That tells us to "multiply each coordinate by 1/4" which in turn is equivalent to "divide each coordinate by 4". Point E is at (-4,4) which moves to (-1,1) when we divide each coordinate by 4. Note how point E' is at (-1,1). So E moves in the proper way according to the instructions given to us. Points M, W and O also move in a similar fashion after we divide their coordinates by 4. The answer here is "true".PLEASE HELP ME!!!
Determine whether the function rule models discrete or continuous data.
Function # 1: A movie store sells DVDs for $15 each. The function C(d) = 15d relates the total cost of movies to the number purchased d.
Function # 2: A produce stand sells roasted peanuts for $2.99 per pound. The function C(p) = 2.99p relates the total cost of the peanuts to the number of pounds purchased p.
A.) Functions # 1 models discrete data. Function # 2 models continuous data.
B.) Functions # 1 models continuous data. Function # 2 models continuous data.
C.) Functions # 1 models continuous data. Function # 2 models discrete data.
D.) Functions # 1 models discrete data. Function # 2 models discrete data.
Answer:
the answer is a tell me if this helps!!