Given:
The function is
[tex]f(x)=2x^3+ax^2-37x-60[/tex]
The binomial [tex]x-4[/tex] is a factor of f(x).
To find:
The value of [tex]a[/tex].
Solution:
If [tex]x-c[/tex] is a factor of f(x), then [tex]f(c)=0[/tex].
It is given that, [tex]x-4[/tex] is a factor of f(x), then [tex]f(4)=0[/tex].
We have,
[tex]f(x)=2x^3+ax^2-37x-60[/tex]
Substituting x=4, we get
[tex]f(4)=2(4)^3+a(4)^2-37(4)-60[/tex]
[tex]f(4)=2(64)+a(16)-148-60[/tex]
[tex]f(4)=128+16a-208[/tex]
[tex]f(4)=16a-80[/tex]
Now,
[tex]f(4)=0[/tex]
[tex]16a-80=0[/tex]
[tex]16a=80[/tex]
[tex]a=\dfrac{80}{16}[/tex]
[tex]a=5[/tex]
Therefore, the value of a is 5.
An angle measures 2° less than the measure of its supplementary angle. What is the
measure of each angle?
Answer:
44 degrees and 46 degrees.
Step-by-step explanation:
Answer:
91 and 89 is the answer.
part 3 of coordinate planes, please help if you know it :)
Answer:
s
Step-by-step explanation:
Tha answer is s
I NEED HELP!!!!! ASAP!!!!!
Answer: 127 11/12
Step-by-step explanation:
1. 1/2 + 3/4 = 2/3
Change 1/2 by by multiplying by 2 to get a common denominator of fourths.
2/4 + 3/4 = 2/3?
5/4 = 2/3?
no
2. 5/8 - 1/4
Change 1/4 by by multiplying by 2 to get a common denominator of eighths.
5/8 - 2/8 = 3/8?
3/8 = 3/8 ?
yes
3/8 x 10 = 30/8
3. 4/5 +7/10 = 1 1/2
Change 4/5 by multiplying by 2 to get a common denominator tenths.
8/10 + 7/10 = 1 1/2?
15 /10 = 1 1/2?
yes
1 1/2 x 10 = 25
4. 2 1/3 - 1 5/6 = 1/6
Change 1/3 by multiplying by 2 to get a common denominator sixths.
2 2/6 - 1 5/6 = 1/6?
3/6 = 1/6
no
100 -2/3 - 1/6 + 30/8 + 25
multiply the thirds by 8. Sixths by 4. Eighths by 3 to get a common denomonator of 24ths.
100 - 16/24 - 4/24 + 90/ 24 + 25 = 125 70/24
create mixed number
127 22/24
reduce
127 11/12
At a local coffee shop, three coffees and two muffins cost a total of $7.00. Two coffees and four
muffins cost a total of $8.00. How much would six cups of coffee and 1 muffin cost?
Answer:
$10.25
Step-by-step explanation:
Set up a system of equations, so 3c + 2m = 7 and 2c + 4m = 8, where c = the cost of coffees, and m = cost of muffins
To solve multiply the first equation by -2(3c + 2m=7) so you get -6c -4m = -14 now add the two equations
-6c - 4m = -14
2c + 4m = 8 notice that -6c + 2c = -4c and -4m + 4m cancels, then -14+8=-6
so we have -4c = -6 so c = $1.50
To solve for m, substitute c = 1.50 so 3(1.50) + 2m = 7, so solve for m so
4.5 + 2m = 7, 2m = 2.5, so m = $1.25
So now solve the final problem 6(1.50) + 1(1.25) = $10.25
write 3450 in scientific notation form. b) write 234 x 10^16 in standard form. c) Population of kuwait is 2.4million. It is 4/5 population of Hong Kong. Calculate the population of kuwiat as percentage of Hong kong population.
Answer:
a; 3.45 * 10^3
b) 2.34 * 10^18
c) 80%
Step-by-step explanation:
a) 3450 in standard form
To write in standard form, we have to place a decimal at the back of the first non-zero number
we have this as ;
3.450
The count of numbers after the decimal point is 3
This will be the power to which 10 will be raised
We have this as;
3.45 * 10^3
b) 234 * 10^16
Let us write 234 in standard form
That will be;
234 = 2.34 * 10^2
So we have ;
2.34 * 10^2 * 10^16
Using the law of indices, we have;
2.34 * 10^(2 + 16) = 2.34 * 10^18
c) From the question, Kuwait is 4/5 of Hong kong’s population
Let Honk Kong’s population be x
4/5 * x = 2.4 million
4x = 5 * 2.4 million
x = 5 * 2.4/4
x = 5 * 0.6
x = 3 million
so writing the population of Kuwait as a percentage of that of Hong kong, we have
2.4/3 * 100%
= 0.8 * 100% = 80%
A hot liquid starts at 93 degrees F. Its temperature decreases at a
constant rate of 9% per minute after it has been placed in a refrigerator.
To the nearest degree, what is the temperature of the liquid after cooling
for 7 minutes? *
Answer:
34.41º
Step-by-step explanation:
0.93 times 9=8.37 degrees per minute
7 times 8.37=58.59
93-58.59=34.41
Find the distance between the points (5,6) and (-10,-6)
Write your answer as a whole number or a fully simplified radical expression. Do not round.
Answer:
ugghhh I think it's a ughhh carrot
-2 [4 - 3x] + 5x - 2
Step-by-step explanation:
Given
-2 [4 - 3x] + 5x - 2
= - 8 + 6x + 5x - 2
= 11x - 10
Hope it will help :)❤
Answer:
11x-10
Step-by-step explanation:
-8+6x+5x-2
11x-10
A motorist drives 146km at a certain speed. She then increase this speed of by 19km/hr and take the same time to travel the next 16km. Find her speed for both part of the journey. Pleaseeeeeeeeeeee helpppppppppppp
Step-by-step explanation:
A motorist drives 146km at a certain average speed she then increases the speed by 9km/h and takes the same time to travel the next 164km.
find her speeds for both parts of the journey.
:
let s = his original speed
then
(s+9) = the increased speed
:
Write a time equation; time = dist/speed
146%2Fs = 164%2F%28%28s%2B9%29%29
cross multiply
164s = 146(s+9)
164s = 146s + 1314
164s - 146s = 1314
18s = 1314
s = 1314/18
s = 73 km/h is his original speed
:
» Which shape is a parallelogram with 4 right angles?
Answer:
rectangle
Step-by-step explanation:
Answer: Rectangle
Step-by-step explanation: Hope this helps ! :)
Find the sum of the arithmetic sequence
-10, -7, -4, -1, 2, 5, 8
All exponential functions can be written in many forms. Write the function f(t)=110(1.35)^{\frac{t}{40}}f(t)=110(1.35) 40 t in the form f(t)=ae^{kt}f(t)=ae kt . Round all coefficients to four decimal places.
Step-by-step explanation:
Given - f(t)=110(1.35)^{\frac{t}{40}}
To find - Write the function in the form f(t)=ae^{kt}. Round all coefficients
to four decimal places.
Proof -
Given that , the function is f(t)=110(1.35)^{\frac{t}{40}}
Now,
We can write it in the form of [tex]f(t) = 110(1.35)^{\frac{t}{40} }[/tex]
By comparing with the form [tex]f(t) = ae^{kt}[/tex] , we get
a = 110.0000
k = [tex]\frac{1}{40}[/tex] = 0.0250
Please help;due today
Answer:
148 degrees
Step-by-step explanation:
360 - 74 - 138 = 148 degrees
Please help thank you :)))
Answer:
x = 25.46
Step-by-step explanation:
[tex]x^2+9^2=27^2\\x^2+81=729\\x^2=648\\\sqrt{x^2} =\sqrt{648} \\x=25.46[/tex]
aiudaaaa pliis
cuanto es 20 = 6 - 5x con explicacion por favor
PLS HELP!! Find the product or type
“impossible"
[2 8 1 , 0 5 -2]
[5 2 1]
Answer:
Step-by-step explanation:
For the multiplication of two matrices, number of columns in 1st matrix should be equal to the number of rows of the 2nd matrix.
In the given question,
1st matrix → [tex]\begin{bmatrix}2 & 8 & 1\\ 0 & 5 & -2\end{bmatrix}[/tex]
Number of columns in this matrix = 3
2nd matrix → [5 2 1]
Number of rows in this matrix = 1
Therefore, number of columns in 1st matrix are not equal to the number of rows in the 2nd matrix.
Therefore, multiplication of matrices given in the picture is "Impossible".
Answer:
impossible
Step-by-step explanation:
accellus
Which of the following fractions represents the product? HELP ASAP will mark brainly
Answer:
maybe A
Step-by-step explanation:
total number of boxes = 12
total number of green boxes = 5
= 5/ 12
Answer:
i did this the answer is C
Step-by-step explanation:
me ayudan con esta operacion? : 14 - 21 ÷ 7 + 105 ÷ 5
Answer:
32
Step-by-step explanation:
helpppppppppppp plzzzzzzzzzzzzzzzzzzz
Answer:
Step-by-step explanation:
[tex]\left[\begin{array}{ccc}7&31\\142&19\end{array}\right][/tex] = 7(19) - 142(31) = - 4269
[tex]\left[\begin{array}{ccc}7&11&21\\55&-8&2\\-16&-1&-9\end{array}\right][/tex] = 7(- 8)(- 9) + 11(2)(- 16) + 21(55)(- 1) - 21(- 8)(- 16) - 7(2)(- 1) - 11(55)(- 9) = 1768
[tex]\left[\begin{array}{ccc}9.07&6.02&2.01\\-30.7&2.5&3.5\\3.55&-1.1&2.35\end{array}\right][/tex] = 9.07(2.5)(2.35) + 6.02(3.5)(3.55) + 2.01(- 30.7)(- 1.1) - 2.01(2.5)(3.55) - 9.07(3.5)(- 1.1) - 6.02(- 30.7)(2.35) = 647.3561
Answer:
I think it’s 6.7
Step-by-step explanation:
Sup I’m a friend….so hey✌️
A certain psychological test measures empathy and emotional intelligence. The score, S, of a randomly selected senior student at a large university has a mean of 123 and a standard deviation of 29. The score, F, of a randomly selected first-year student at a large university has a mean of 104 and a standard deviation of 34.
Suppose we randomly select one senior student and one first-year student.
Calculate the mean of the difference D = S – F.
μD = 17.7482
μD = 19
μD = 44.6878
μD = 227
Answer: The answer is 19
Step-by-step explanation: EDGE2020
The mean of the difference D = S - F is 19, which is the correct option (B).
What is the standard deviation?A standard deviation (σ) is a measure of the distribution of the data in reference to the mean.
To calculate the mean of the difference D = S - F, we need to find the expected value of the difference between two random variables, one representing the scores of senior students and the other representing the scores of first-year students.
Here,
μS = 123
μF = 104
The mean of the difference is the difference of the means, so we have:
μD = μS - μF
μD = 123 - 104
μD = 19
Therefore, the mean of the difference D = S - F is 19.
Learn more about the standard deviation here:
brainly.com/question/16555520
#SPJ3
What is sin 74°?
HELPPO
WILL GIVE BRAINLIST
Find the indicated term of each sequence by repeatedly multiplying the first term by the common ratio. Enter your answer to 5 decimal places if necessary. Use a calculator.
−30, 6, −1.2, ...; 5th term
The 5th term of the sequence is
Answer:
-0.048
Step-by-step explanation:
-30 * -1/5 = 6
6 * -1/5 = -1.2
(Remember -30 is first term so we subtract 1 from 5 in the exponent)
-30 * (-1/5)^4 = -0.048
What is the solution set of the equation x2 + 3x - 4 = 6?
A.
{-5, 2}
B.
{-2, -1}
C.
{2, 7}
D.
(5, 10)
If y is directly proportional to Vx, and y = 25 when x = 3, find x when
y = 100
9514 1404 393
Answer:
x = 48
Step-by-step explanation:
It looks like your proportion is ...
y = k√x
Then k can be found as ...
k = y/√x = 25/√3
__
For y = 100, the value of x can be found from ...
100 = (25/√3)√x
4√3 = √x . . . . . . . . . . multiply by √3/25
48 = x . . . . . . . . . . . . . square both sides
The variables x and y vary inversely. Use the given values to write an equation relating x and y. Then find y when x=−3.
x=−4, y=−6
The variables x and y vary inversely. Use the given values to write an equation relating x and y. Then find y when x=−3.
x=−4, y=−6
Answer:
xy-3x=40, x=5
x(y-3)=40
y-3=(40/x)
y=(40/x)+3
y=(40/5)+3
y=8+3
y=11
If the variables x and y vary inversely then when x=-3 and y =-8
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Since x and y vary inversely, we can write the equation:
x y = k, where k is a constant of variation.
Using the given values, we can find k:
(-4)(-6) = k
k = 24
So the equation relating x and y is:
x y = 24
To find y when x = -3, we substitute x = -3 into the equation and solve for y:
(-3) y = 24
y = -8
Therefore, when x = -3, y = -8.
To learn more on Equation:
https://brainly.com/question/10413253
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Raul is cutting boards for a project. He has a board that measures 8 feet and is cutting it into 3/4 foot pieces. How many whole pieces of 3/4 foot will he be able to cut?
Answer:
10
Step-by-step explanation:
1 board = 3/4 foot = 0.75 of a foot
x boards = 8 feet
1/x = 0.75 / 8 feet Cross multiply
0.75 x = 8 Divide both sides by 0.75
x = 8/0.75
x = 10 2/3 boards.
We are told to throw the fractional board away so Raul will get 10 pieces from an 8 foot piece of lumber.
Find the value of x for this trapezoid.
Mrs. Johnson measured 3 rectangular rooms that she wants to tile. What is the total area of the rooms?
Answer:
Find the area of each room and add the areas
Step-by-step explanation:
Please find the full question in the attached image
the area of rectangle is length x breadth. The area of each room would be found and the three areas would be added together
for example ,
dimension of room 1 = 5 x 3
dimension of room 2 = 2 x 3
dimension of room 3 = 4 x 5
area of room 1 = 15
area of room 2 = 6
area of room 3 = 20
total area = 15 + 6 + 20 = 41
Matthew is going to shop rite with $15.He brought a package of croissants for $1.99.The cost of a box of Digiorno pizza is $4.00. What is the maximum number of digiorno pizzas can he buy?
Answer:
he would only be able to buy 2 boxes of pizza
Step-by-step explanation:
Subtract $1.99 from the $15 he has.
$15 - $1.99 = $13.01
Divide $13.01 by $4.00
$13.01/$4.00 = 3.25
There is a decimal in the final answer which means its not a whole pizza. So, the max he would be able to buy is 2 bokes of pizza
Which quadrilaterals are considered parallelogram
Answer: Rectangle, Rhombus, Square
Step-by-step explanation: