Answer:
16 x ^4 − 96 x^ 3 + 216 x ^2 − 216 x + 81
Step-by-step explanation:
Use the binomial expansion theorem to find each term. ∑
∑The binomial theorem states ( a + b ) n = n ∑ k = 0 n C k ⋅ ( a n − k b k ) . 4 ∑ k = 0 4 ! ( 4 − k ) ! k ! ⋅ ( 2 x ) 4 − k ⋅ ( − 3 ) k
Expand the summation. 4 ! ( 4 − 0 ) ! 0 ! ⋅ ( 2 x ) 4 − 0 ⋅ ( − 3 ) 0 + 4 ! ( 4 − 1 ) ! 1 ! ⋅ ( 2 x ) 4 − 1 ⋅ ( − 3 ) + 4 ! ( 4 − 2 ) ! 2 ! ⋅ ( 2 x ) 4 − 2 ⋅ ( − 3 ) 2 + 4 ! ( 4 − 3 ) ! 3 ! ⋅ ( 2 x ) 4 − 3 ⋅ ( − 3 ) 3 + 4 ! ( 4 − 4 ) ! 4 ! ⋅ ( 2 x ) 4 − 4 ⋅ ( − 3 ) 4
Simplify the exponents for each term of the expansion. 1 ⋅ ( 2 x ) 4 ⋅ ( − 3 ) 0 + 4 ⋅ ( 2 x ) 3 ⋅ ( − 3 ) + 6 ⋅ ( 2 x ) 2 ⋅ ( − 3 ) 2 + 4 ⋅ ( 2 x ) ⋅ ( − 3 ) 3 + 1 ⋅ ( 2 x ) 0 ⋅ ( − 3 ) 4
Simplify each term.
= 16 x ^4 − 96 x^ 3 + 216 x ^2 − 216 x + 81
· Jessica has 5x - 3 magazines while Kenya has 4x + 2 magazines. How many
magazines do they have altogether?
Answer:
9x-1
Step-by-step explanation:
solution - jessica has 5x-3 magazines
kenya has 4x+1 magazines
so, magazines do they have together = 5x-3+4x+2
= 9x-1
hence, magazines do they have together = 9x-1
A linear function has the same y-intercept as x + 4y = 20 and its graph contains the
point (7, 7). Find the y-intercept of the linear function.
y-intercept: (0,___)
Answer:
(0,5)
Step-by-step explanation:
x + 4y = 20
4y = -x + 20
y = -1/4x + 5
The y - intercept of the line is 5
(0,5)
-Chetan K
Ned rides his bike 6 miles to the store and 6 miles back. The graph shows the relationship between the distance Ned is from home at any time throughout his trip and the distance he spends riding the bike. Which statement is true about Ned's ride?
A. Ned's speed is constant for the entire ride from 0 to 90 minutes
B. Ned's speed is constant on the interval from 0 to 60 minutes.
C. Ned's speed between the interval from 20 to 40 minutes is the same as his speed over the interval 50 to 90 minutes.
D. Ned's speed over the interval from 20 to 40 minutes is faster than his speed over the interval from 0 to 20 minutes.
Answer:
The answer is D
Step-by-step explanation:
A cant be right because the graph isn't a straight line.
B cant be right because from 0 to 60 the graph the line goes at a(n) upward slope not a straight line.
Although the first part of question c is right, the second part is wrong. From 50-90 the ling goes at a downward slope via decreasing, which isn't equal like it said so question C is wrong.
So the correct answer is D
The equation Y-5 = 6(x+1) is written in point-slope form. What is the equation written in slope-intercept form?
O y = 6x + 11
O y = 6x - 1
O y = 6x - 4
O y = 6x + 6.
Answer:
Option A: y = 6x + 11
Step-by-step explanation:
Given the linear equation in point-slope form, y - 5 = 6(x + 1), and that we must determine its equivalent slope-intercept form, y = mx + b:
First, we must distribute 6 into the parenthesis on the right-hand side of the equation:
y - 5 = 6(x + 1)
y - 5 = 6x + 6
Lastly, we must add 5 to both sides of the equation to isolate y:
y - 5 + 5 = 6x + 6 + 5
y = 6x + 11
Therefore, the slope-intercept form is: y = 6x + 11, which matches Option A.
find the scale of each map: an actual distance of 50 km corresponds to 4 cm on the map.
Answer:
1 cm: 12.5 km
Step-by-step explanation:
Okay just find what the length of one cm equates to so
4/4=1
50/4=12.5
it's like making a unit measurement but yknow its scaling
so one cm (one unit in a way) equals 12.5 km.
what is? -6 = x + 6
this is one step equation addition / subtraction
[tex] \: \: \: \: \: [/tex]
x = - 12
refer to the attachment
refer to the attachmenthope it helps[tex]\sf \longmapsto-6 = x + 6[/tex]
Flip the equation[tex]\sf \longmapsto \: x+6=−6[/tex]
Subtract 6 from both sides[tex]\sf \longmapsto \: x+6−6=−6−6[/tex]
[tex]\sf \longmapsto \: x=−12[/tex]
[tex] \boxed{ \sf \: x=−12}[/tex]
PLEASE HELP!!!!!!!!!!!!!!!!!!!!
Answer:
I think it's c
Step-by-step explanation:
because that looks like a good answer.
Sorry for the spam, I just really need help.
help plssss PLSS I BEG YOu
Answer: Just Try to Do somthing because i cant tell you the Answer
Step-by-step explanation:
Please help me :) Im only giving brainliest to correct answers, and No LiNkS.
Gravity is measured in squares units..
Using the other units given, meters and seconds, gravity would be : meters per second squared
Answer:
meters per second
Step-by-step explanation:
Which statements about the function fare true? Check
all that apply.
The domain of f(x) is {all real numbers).
Answer:
see explanation
Step-by-step explanation:
The following statements are true
The domain of f(x) is all real numbers
The range of f(x) is all real numbers
f(2) = 4
locate x = 2 on the x- axis, go vertically up to meet the line at (2, 4 ) , then
f(2) = 4
What is the slope of the line?
3x-4y=73x−4y=7
Answer:
67x-7y2x-f8
Step-by-step explanation:
5. Find the triangle similar to AABC at the right. Question 5
Answer:
b
Step-by-step explanation:
If you multiple each side by 3 then they will equal the numbers that b has
how do i do this pls explain the steps
Answer:
[tex]a^{\frac{15}{2} }[/tex]
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]
([tex]a^{\frac{1}{2} }[/tex] × a)^5
= [tex](a^{\frac{1}{2}+1) }[/tex]^5
= [tex](a^{\frac{3}{2}) } ^{5}[/tex]
= [tex]a^{\frac{15}{2} }[/tex]
One-half of the sum of a number and 12 is less than 27. What is the number? Write as an inequality.
Answer:
Call the number we need to find a.
Inequality: (12 + a) ÷ 2 < 27
<=> 12 + a < 54
<=> a < 54 - 12
<=> a < 42
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Each friend will pay 13.60 dollars.
Step-by-step explanation:
68/5 is 13.6
convert
b) 25 m³ to ft³
c) 11 ft² to in²
Answer:
conversions are below
Step-by-step explanation:
b) 25 m³ = 882.867 ft³
c) 11 ft² = 1584 in²
please help me in questions 16 and 17 only and i’ll mark you as brainliest i promise
Answer:
16. Domain: [-3,5] and range : [-5,3]
17. Domain: [0,4] and range: [0,4]
1.Find the missing fraction, decimal, or percent. Reduce fractions to the lowest terms.
Question: 93% what is the equivalent fraction and decimal?
Hint: separate your answers for the missing information with a comma make sure not to have
additional spaces in your answers. Ex: 93/100,93 Ex: 93%,.93 Ex: 93/100,93%*
Answer:
93/100 as a fraction. 0.93 as a decimal.
Step-by-step explanation:
BRAINLIEST
Two questions to solve
Please no trolling
Answer:
Step-by-step explanation:
question 13:
the triangle with x is a 30-60-90 triangle which means
x= 17√3
then the traingle with y and z is a 45-45 triangle
z=34
y= 34√2
question 14:
x= 18√3
z=9
y= 18
74.88 is what percent of 72?
Answer:
104%
Step-by-step explanation:
Put the following numbers in order:
3.28, -4/5, -7.1, 0, 11/12, π, .889753, -4 1/3 help please!
In order of smallest to largest.
1) -7.1
2) -4 1/3
3) -4/5
4) .889753
5) 11/12
6) 0
7) π
8) 3.28
9. The
school is planning on taking 684 students on the field trip. If the bus can only hold 43
students, how many buses will they need?
Answer:
16
Step-by-step explanation:
Answer:
16 buses
Step-by-step explanation:
684/43 = 15.9
Help?
I tried : 3b^2(2b-1)(2b+1) and it was wrong ):
Answer:
b(3b−10)(b−1)
Step-by-step explanation:
b(3b−10)(b−1)
I 3) Give the steps you will use to separate the variable and the solve the equation.
a) у/3 = 4
b) Zn - 6 = 8
pls pls pls pls give step by step answer I will mark brainlist
(1)
Multiply both sides by 3
y = 4 * 3
Simplify 4 * 3 to 12
y = 12
(2)
There are two possibilities for both z & n.
Solving for z:
add 6 to both sides
2n = 8 + 6
simplify 8 + 6 to 14
zn = 14
divide both sides by n
z = 14/n
Solving for n:
add 6 to both sides
zn = 8 + 6
simplify 8 + 6 to 14
zn = 14
divide both sides by z
n = 14/z
Company X tried selling widgets at various prices to see how much profit they would
make. The following table shows the widget selling price, x, and the total profit
earned at that price, y. Write a quadratic regression equation for this set of data,
rounding all coefficients to the nearest tenth. Using this equation, find the profit, to
the nearest dollar, for a selling price of 14.25 dollars.
Regression equations are used to represent the relationship between the x and y variables.
The quadratic regression equation is [tex]\mathbf{y =-6.407 X^2 +216.721 X -975.561}[/tex]The profit for a selling price of $14.25 is $812To determine the quadratic regression equation, we make use of a graphic calculator
Using a graphing calculator, we have the quadratic regression equation to be [tex]\mathbf{y =-6.407 X^2 +216.721 X -975.561}[/tex]
When the selling price is $14.25, it means that:
[tex]\mathbf{x = 14.25}[/tex]
So, we have:
[tex]\mathbf{y =-6.407 \times 14.25^2 +216.721 \times 14.25 -975.561}[/tex]
Evaluate the exponents
[tex]\mathbf{y =-6.407 \times 203.0625+216.721 \times 14.25 -975.561}[/tex]
Evaluate the products
[tex]\mathbf{y =-1301.0214375+3088.27425 -975.561}[/tex]
Evaluate like terms
[tex]\mathbf{y =811.6918125}[/tex]
Approximate to the nearest dollar
[tex]\mathbf{y =812}[/tex]
Hence, the profit for a selling price of $14.25 is $812
Read more about regression equations at:
https://brainly.com/question/7656407
need help please and thank you!!
Answer:
x=125
Step-by-step explanation:
Since the sum of the angles is 720 degrees, you can set up the following equation:
120+100+120+120+x+(x+10)=720
2x+470=720
2x=250
x=125
Sam earns $.75 for each call he makes for a telemarketing service. He hopes to make at least $100 each day. Write an inequality to represents the number of calls he must make each day. (Let c equal the number of calls. )
Find an expression which represents the difference when (-x+9y) is subtracted from (-6+4y)
Answer:
x - 5y - 6
Step-by-step explanation:
- 6 + 4y - ( - x + 9y) ← distribute parenthesis by - 1
= - 6 + 4y + x - 9y ← collect like terms
= x - 5y - 6
In Dominic’s classroom, there are 5 rows of desks. There are 5 desks in each row. In all, 5 classrooms in his school have the desks set up the same way. Write an expression with an exponent that shows the total number of desks in these 5 classrooms.
Use words, numbers, and/or pictures to show your work. Write your answer on the paper provided.
Answer:
5^(3) is the exponent form which equals 125desks
Step-by-step explanation:
A row has 5 desks
A classroom has 5 rows of desks= 5*5 desks
The school has 5 classrooms
=5*5+5*5+5*5+5*5+5*5 desks
=5^(2)+5^(2)+5^(2)+5^(2)+5^(2)
=5[5^(2)]
=5^(3) = 125 desks