Answers
[tex]f(a) = -4a +6a^3 - 15 -4a^2 \\\\\text{By the remainder theorem,}\\\\f\left(\dfrac 53 \right) = -4\left(\dfrac 53 \right) + 6 \left( \dfrac 53 \right)^3 - 15 - 4 \left(\dfrac 53 \right)^2 = -5\\\\\\ \text{Hence}~-5~ \text{is the remainder when f(a) is divided by}~ 3a -5[/tex]
[tex]\\ \sf\longmapsto 3a-5=0[/tex]
[tex]\\ \sf\longmapsto 3a=5[/tex]
[tex]\\ \sf\longmapsto a=\dfrac{5}{3}[/tex]
Using remainder theorem
[tex]\\ \sf\longmapsto f(a)=-4a+6a^2-4a^2-15[/tex]
[tex]\\ \sf\longmapsto f\left(\dfrac{5}{3}\right)[/tex]
[tex]\\ \sf\longmapsto -4(5/3)+2a^2-15[/tex]
[tex]\\ \sf\longmapsto -20/3+2(5/3)^2-15[/tex]
[tex]\\ \sf\longmapsto -20/3+2(25/9)-15[/tex]
[tex]\\ \sf\longmapsto -20/3+50/9-15[/tex]
[tex]\\ \sf\longmapsto (-60+50)/9-15[/tex]
[tex]\\ \sf\longmapsto -10/9-15[/tex]
[tex]\\ \sf\longmapsto -10-135/9[/tex]
[tex]\\ \sf\longmapsto -145/9[/tex]
[tex]\\ \sf\longmapsto 16\dfrac{-5}{9}[/tex]
Remainder=-5
Related Questions
hiroshi borrowed 3 nonfiction books from the library. This was 25% of the books he checked out. how many books did Hiroshi take out?
Answers
Answer:
12 books
Step-by-step explanation:
25% is the same as 1/4
3=25%=1/4
if you multiply 3 by 4 you get 100% or 12
You can also do this by adding 9, aka 3*3, to 3 to get 3*4=12.
Camelle manages her soccer team. she needs to order 4 practice jerseys for each player. There are y players how many total practice jerseys does she need to order?
write and expression
Answers
Answer:
T= total # of jerseys to order
y= # of players
T= 4*y
Total equals 4 times # of players
T= 4y
A man's age is three times his son's age. Ten years ago, he was five times his son's
age. By forming two equations and solving them simultaneously, find both of their ages.
Answers
Answer:
Step-by-step explanation:
son age be x
Aman age is 3x
ten years ago
son age x-10
aman age 3x -10
A.T.Q
5(x-10) = 3x -10
5x -50 = 3x - 10
2x = 40
x =20
3x=60
son present age =20
aman present age = 60
Sam has 3 more than twice the number of baseball cards that Catherine has. Together Sam and Catherine have 51 baseball cards. How many cards do Sam and Catherine each have?
Answers
Answer:
catherine has 16 card and sam also has 16 card
for a brainlist +10 points please help
Answers
Answer:
C. Two smaller atoms come together to form a larger atom that is a different element.
Explanation:
Fusion is a reaction in which two nuclei combine to form a nucleus with the release of energy.
The coordinates of a point change as follows during a dilation:
(-6, 3) ----> (-2, 1)
What is the scale factor?
Answers
Answer:
The answer is D. (6,9)
Step-by-step explanation:
Glad to help
There were 6 teams in a baseball tournament. Each team played against every other team exactly once during the tournament. A team earned 2 points for a win, 1 point for a tie, and 0 points for a loss. What was the total number of points earned by all 6 teams in the tournament?
Answers
Since there were 6 teams in a baseball tournament, and each team played against every other team exactly once during the tournament, and a team earned 2 points for a win, 1 point for a tie, and 0 points for a loss, to determine what was the total number of points earned by all 6 teams in the tournament, since a series of results have not been raised, the following table should be made:
Possible outcomes: 5 wins = 5 x 2 = 10 4 wins and 1 a draw = 4 x 2 + 1 = 9 4 wins and 1 loss = 4 x 2 = 8 3 wins and 2 draws = 3 x 2 + 2 x 1 = 8 3 wins, 1 draw and 1 loss = 3 x 2 + 1 = 7 3 wins and 2 losses = 3 x 2 = 6 2 wins and 3 draws = 2 x 2 + 3 x 1 = 7 2 wins, 2 draws and 1 loss = 2 x 2 + 2 x 1 = 6 2 wins, 1 draw and 2 losses = 2 x 2 + 1 = 5 2 wins and 3 losses = 2 x 2 = 4 1 win and 4 draws = 2 x 1 + 4 x 1 = 6 1 win, 3 draws and 1 loss = 2 x 1 + 3 x 1 = 5 1 win, 2 draws and 2 losses = 2 x 1 + 2 x 1 = 4 1 win, 1 draw and 3 losses = 2 x 1 + 1 x 1 = 3 1 win and 4 losses = 2 x 1 = 2 5 draws = 5 x 1 = 5 4 draws and 1 loss = 4 x 1 = 4 3 draws and 2 losses = 3 x 1 = 3 2 draws and 3 losses = 2 x 1 = 2 1 draw and 4 loss = 4 x 1 = 1 5 losses = 0
Learn more in https://brainly.com/question/6283215
Please help if it's right I'll give brainliest
Answers
Answer:
Since XBC is 55 degrees and triangle BXC is isosolese, angle BCX is also 55 degrees. 180 - 110 = 70
so angle BXC is 70 degrees.
3^x X 9^4 = 3^n
Find n in terms of x
Answers
Answer:
n = x + 8
Step-by-step explanation:
Using the rules of exponents
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]
[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex]
Then
[tex]3^{x}[/tex] × [tex]9^{4}[/tex] = [tex]3^{n}[/tex]
[tex]3^{x}[/tex] ×[tex](3^2)^{4}[/tex] = [tex]3^{n}[/tex]
[tex]3^{x}[/tex] × [tex]3^{8}[/tex] = [tex]3^{n}[/tex]
[tex]3^{x+8}[/tex] = [tex]3^{n}[/tex]
Since bases on both sides are equal, both 3, then equate exponents
n = x + 8
help with this question please?!ASAP
Answers
V = 1/3 (3.14) (4)^2 • 12
V = 200.96 mm^3
Answer:
209.22 mm
Step-by-step explanation:
What was the primary goal of mine workers’ strikes? A. to stop poor pay and dangerous working conditions B. to open new land to mining operations C. to reduce regulations on mining practices D. to advocate for more settlement of the territory Please select the best answer from the choices provided A B C D Mark this and return
Answers
Answer:
The Answer is A, to stop poor pay and dangerous working conditions
2^-5 =
Can someone please help
Answers
Answer:
[tex]\frac{1}{32}[/tex]
Step-by-step explanation:
Using the rule of exponents
[tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex] , then
[tex]2^{-5}[/tex] = [tex]\frac{1}{2^{5} }[/tex] = [tex]\frac{1}{32}[/tex]
class extends value undefined is not a constructor or null
Answers
What? What do you mean?
Find the quotient of 15.75 and 4.5?
Answers
Answer: 3.5
Step-by-step explanation: 15.75 ÷ 4.5 3.5
If a triangle is equilateral, then all the sides in the triangle are congruent.If all the sides in a triangle are congruent, then all the angles are congruent.
Answers
Answer:
Where's the question?
Step-by-step explanation:
Reindeers eat 62 apples an hour, there is 24 hours in a day, how many do they eat
Answers
multiply the numbers and that will be your answer.
A grandfather is ten times older than his granddaughter. He is also 54 years older than
her. How old is each of them?
Answers
Granddaughter = 6
Answer:
The present ages of the granddaughter and grandfather are 6 and 60 years.
Step-by-step explanation:
Let the present age of granddaughter be x years.
So, the present age of grandfather is 10x years.
According to the given condition, we have
10 x = 54 + x
9 x = 54
x = 6
10 x = 60
age of grandfather is 60
age of granddaughter is 6
Hence, the present age of granddaughter is 6 years and that of grandfather is 60 years.
(hope this helps can I pls have brainlist (crown)☺️)
Find the slope given two points: (-9, -2) and (-5,0)
Answers
Answer:
1/7
Step-by-step explanation:
Consider the line passing through these two points. The increase in x (run) from the first to the second is 14; the increase in y (rise) is 2.
Thus the slope of this line is m = rise/run = 2/14, or m = 1/7
Answer:
[tex]m = \frac{1}{2}[/tex]
Step-by-step explanation:
To find the slope using two given sets of coordinates, the following function can be used:
[tex]m = \frac{y2-y1}{x2 - x1}[/tex]
Where x1,y1 are one set of coordinates and x2,y2 are the other set:
[tex]m = \frac{0 - (-2)}{-5 - (-9)}\\[/tex]
[tex]m = \frac{0 + 2}{-5 + 9}[/tex]
[tex]m = \frac{2}{4}[/tex]
This can be simplified down to:
[tex]m = \frac{1}{2}[/tex]
Hope this helps!
Answer the question in the picture below
Answers
Answer:
16.25, 20, 13.75, 12.5, 7.5
Step-by-step explanation:
1cm= 2.5m
6.5x2.5= 16.25
8x2.5= 20
5.5x2.5= 13.75
5x2.5= 12.5
3x2.5= 7.5
Write a formula for the volume V of a prism where B is the area of the base and h is height
Answers
Answer:
a pyramidal prism is 1/3 the volume of a similar rectangular prism of same base and height
so V=(1/3)bh
V=36
H=6
find area of base
36=(1/3)b6
36=2b
divide both sides by 2
18=b
the area of the base is 18 square units
Step-by-step explanation:
the answer is : V= B.h
Use 3.14
Jerry is building a model car. The picture shows one of the wheels for the car. The wheel has a diameter of 30 millimeters.
30 mm
Which is closest to the distance around the outside edge of the wheel?
Answers
We want to find the distance around the outside wheel of the car given that we know its diameter. We will see that this distance is 94.2mm
So the distance around the outside edge of the wheel will be equal to its circumference.
We do know that for a circle of diameter D the circumference is defined as:
C = pi*D
Where pi = 3.14
Here we do know that the diameter is 30 mm, then the circumference of the wheel will be:
C = 3.14*30mm = 94.2 mm
This is the distance around the outside edge of the wheel.
If you want to learn more about circumferences you can read:
https://brainly.com/question/17009561
I'm really confused and need help.
Answers
Answer:
EC = 3
Step-by-step explanation:
Questlon 21 of 25
What are the vertex and x-intercepts of the graph of the function given below?
- 2x - 24
Answers
[tex] - 2 \times - 24 = - 2( \times + 12[/tex])
What percent is x of y?
Remember answer in percent(%)
Answers
Answer:
Step-by-step explanation:
If we do not have any numbers de can think that x and y are any number
y is 100%
x is ?%
? = 100x / y
The percent that is x of y is 100x/y
share £165 in the ratio 2:3
Answers
2:3=£165
2:3 =5
2/5 x 165
=2x33
66
=3/5 x 165
3 x 33
99
answer: 66 : 99
find the slope and y intercept.
Answers
Answer:
the slope is 2
the y intercept is (-4,0)
Step-by-step explanation:
slope is calcuated by rise over run
Y intercept is (-4,0)
Rise over run
How to divide with decimals in the divisor.
Answers
Answer:
Step-by-step explanation:
Move the decimal point in the divisor and dividend. Turn the divisor (the number you’re dividing by) into a whole number by moving the decimal point all the way to ...
Place a decimal point in the quotient (the answer) directly above where the decimal point now appears in the dividend.
Divide as usual, being careful to line up the quotient properly so that the decimal point falls into place. ...
Select the correct range of the function represented by the graph.
Answers
Answer:
[-1,3]
Step-by-step explanation:
Find the length of the third side. If necessary, write in simplest radical form.
Answers
9
Explanation:
9 root 2 = root 81 x root 2 = root 162
Root 162 = 12.7279220614
9^2 + b^2 = 12.7279220614^2
81 + b^2 = 162
b^2 = 81
Root both
B = 9
Simplify 80−−√
4 5√
5 16−−√
5 4√
16 5√
Answers
Answer:
The answer is the 3rd choice
Step-by-step explanation: