Answer:
[tex]\huge\boxed{ \sf x^4+28x^3+294x^2+1372x+2401}[/tex]
explanation:
[tex]\sf (x+7)^4[/tex]
[tex]\hookrightarrow \sf (x+7) (x+7) (x+7) (x+7)[/tex]
[tex]\hookrightarrow \sf (x^2 +14x+49)(x+7)(x+7)[/tex]
[tex]\hookrightarrow \sf (x^3 +14x^2+49x+7x^2+98x+343)(x+7)[/tex]
[tex]\hookrightarrow \sf (x^3 +21x^2 +147x +343)(x+7)[/tex]
[tex]\hookrightarrow \sf x^4 + 21 x^3 + 147x^2 + 343x + 7x^3 + 147x^2 + 1029x+ 2401[/tex]
[tex]\hookrightarrow \sf x^4+28x^3+294x^2+1372x+2401[/tex]
note: just keep multiplying and simplifying with patience.
[tex](x + 7)^{4} [/tex]
Write 4 as a sum
[tex] {(x + 7)}^{2 + 2} [/tex]
Use [tex] \boxed{ \pmb{ {a}^{m + n} = {a}^{m} \times {a}^{n} }}[/tex] to expand the expression
[tex] {(x + 7)}^{2} \times {(x + 7)}^{2} [/tex]
Use [tex] \boxed{ \pmb{(a + b)^{2} = {a}^{2} + 2ab + {b}^{2} }}[/tex] to expand the expression
[tex] ( {x}^{2} + 14x + 49) \times ( {x}^{2} + 14x + 49)[/tex]
Multiply the parentheses
[tex] {x}^{4} + 14 {x}^{3} + {49x}^{2} + 14 {x}^{3} + {196x}^{2} + 686x + {49x}^{2} + 686x + 2401[/tex]
Collect like terms
[tex] {x}^{4} + {28x}^{3} + {294x}^{2} + 1372x + 2401[/tex]
Which equation describes a line with a slope of 2/5 and a y-intercept at (0, 4)?
Answer:
y=2/5x+4
Step-by-step explanation:
because 4 would be where the line crosses the number 4 on the y axis which puts it at the back and the slope is x because it increases by an amount indescribable.
WILL GIVE BRAINLIEST IF CORRECT PLEASE ANSWER!!!!!
Find the value of cos I rounded to the nearest hundredth, if necessary.
Answer: 41.40962211 or 41.41
Step-by-step explanation:
Cos i = 30/40
x = Cos ^-1 (30/40)
x = 41.41 or 41.40962211
WILL GIVE BRAINLIEST IF CORRECT PLEASE ANSWER!!!!!
The triangle below is isosceles, Find the length of side x to the nearest tenth.
Answer: 3.5
Step-by-step explanation:
Solve
v < 45. Graph the solution.
The solution is
someone helppp
Answer:
The solution is v ≤ 81.
Graph it on a number line by writing a closed circle above the number 81 with a line moving to the left (sorry I'm bad at explaining, just comment if you don't get it)
Step-by-step explanation:
5/9v ≤ 45
Divide 5/9 on both sides
v ≤ 81
A diner has collected data about customer coffee-drinking habits. They have calculated that P(cream) = 0. 5, P(sugar) = 0. 6, and P(cream or sugar) = 0. 7. Determine the P(cream and sugar). 0. 4 0. 5 0. 6 0. 7.
Probability of an event is the measure of its chance of occurrence. The value of the probability P(cream and sugar) is given by: Option A: 0.4
What is the addition rule of probability for two events?For two events A and B, we have:
Probability that event A or B occurs = Probability that event A occurs + Probability that event B occurs - Probability that both the event A and B occur simultaneously.
This can be written symbolically as:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
For the considered case, the probabilities are:
P(cream) = 0. 5P(sugar) = 0. 6P(cream or sugar) = 0. 7Thus, we get;
P(cream or sugar) = P(cream) + P(sugar) - P(cream and sugar)
0.7 = 0.5 + 0.6 - P(cream and sugar)
P(cream and sugar) = 1.1 -0.7 = 0.4
Thus, the value of the probability P(cream and sugar) is given by: Option A: 0.4
Learn more about probability here:
brainly.com/question/1210781
Emma sold all the parasols in the store for $84. She brought new
parasols from the stockroom and decided to increase the price of a
parasol to $13.
Which of the following equations represents the total amount, t, Emma
will have earned after selling the additional, p, parasols?
A. t = 84 + 13p
B. t = 84 + (p + 13)
C. t = 84 × 13p
D. t = 84 + [tex]\frac{p}{13}[/tex]
Answer: B. Emma sold all the parasols in the store for $84. She brought new parasols from the stockroom and decided to increase the price of a parasol to $13.
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
First, she earned $84
She bought new parasols and increase the price of each parasol by $13-> she will earn $13p by selling p additional parasols
->total amount = 84+13p
Apply the distributive property to factor out the greatest common factor.
22c+33d =
Answer:
Step-by-step explanation:
First find the GCF of 22 and 33
22 = 2 * 11
33 = 3 *11
GCF = 11
Distributive property:a*(b+c)=(a*b) + (a*c)
22c + 33d = 11 * 2c + 11 * 3d
= 11*(2c + 3d)
how does identifying the mean on an ordered-value bar graph help you find the mean on a dot plot?
Answer:
To find the mean, add up all the values and then divide by the number of values. The median is the value that is exactly..
SOLVE BOTH
if f(x)=2x+8, find f(5)
if f(x)=3x+4, find f(8)
Answer:
Step-by-step explanation:
simple! plug in the 5 for x, f(5)=2(5)+8
f(5)=10+8
f(5)=18
f(8)=3(8)+4
f(8)=28
A project manager must select four analysts from her group to write four
different software functions. There are 5 junior and 8 senior analysts in her group.
The first and fourth functions can be written by any of the analysts. The second
function must be written by a senior person and the third function must be written
by a junior person. How many ways are there for her to assign the analysts to the
functions if no person can be assigned to more than one function?
Using the Fundamental Counting Theorem, it is found that there are 4,440 ways to assign the analysts.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
In this problem:
With the first function being written by a senior, we have that: [tex]n_1 = 8, n_2 = 7, n_3 = 5, n_4 = 10[/tex].With the first function being written by a junior, we have that: [tex]n_1 = 5, n_2 = 8, n_3 = 4, n_4 = 10[/tex].Hence:
N = (8 x 7 x 5 x 10) + (5 x 8 x 4 x 10) = 4400.
There are 4,440 ways to assign the analysts.
To learn more about the Fundamental Counting Theorem, you can check https://brainly.com/question/24314866
Solve the inequality if possible 6 (x + 3 )<5x+18+x
Answer:
x < 3
Step-by-step explanation:
6(x + 3) < 5x + 18 + x
6x + 18 < 6x + 186x + 6x < 18 + 1812x < 36x < 36 ÷ 12x < 3At a bowling alley, there is a flat fee of
$
5.00
to rent shoes. In addition, it costs
$
1.25
for each game bowled.
Which equation shows the total cost (
c
) for the number of games (
g
) one bowls?
Answer:
I don't see any answer options, but the total cost should be:
c = $5.00 + $1.25g
Step-by-step explanation:
Assuming that the cost is for one person playing g games, and that person needs to rent 1 pair of shoes, the cost should be:
c = $5.00 + $1.25g
Need help!
Find the volume!
Answer:
volume of cylinder is = πr²h
= π4²6 = π x 16 x 6 = 96π yd³
Find the distance covered by a car in 3x hours is 27x³ + 9x² - 3x Find the rate of the car. Show your solution.
Answer:
distance = 27x³ + 9x² - 3x , time = 3x ,
rate =?
[tex]distance = rate \times time \\ \\ rate = \frac{distance}{time} \\ \\ r = \frac{d}{t} \\ \\ r = \frac{27 {x}^{3} + 9 {x}^{2} - 3x}{3x} \\ \\ r = \frac{3x(9 {x}^{2} + 3x - 1) }{3x} \\ \\ r = 9 {x}^{2} + 3x - 1[/tex]
So; The rate of the car equal (9x²+3x-1)
Para las celebraciones del barrio de Santiago se junto cierta cantidad de dinero que se distribuirá de la siguiente forma:?
Answer:
4,767
Step-by-step explanation:
6 Xavier earns $12.50 for each lawn he mows. If he mowed 8 lawns last week, how
much money did he earn? Show your work.
Answer:
12.50x2.50x8=w
Step-by-step explanation:
12.50×8=100
Answer:
$100
Step-by-step explanation:
12.50 multiplied by 8.
Hurry please!
A) - 1
B) 1
C) 0
D) undefined
What is the mass of Cl2
Answer:
molar mass of carbon-12
Step-by-step explanation:
A Cubic Polynomial with rational coefficients has the roots 6 + SQRT6 and 2/3 FInd one additional root.
SHOW STEPS PLEASE O_O
This is because of the rule that if we have rational coefficients, then one root of [tex]a+\sqrt{b}[/tex] must have a conjugate pair of [tex]a-\sqrt{b}[/tex]. Multiplying the conjugates will have the square roots cancel out.
For more information, check out the difference of squares rule.
-13 = -3h + 2 solve for h
Step-by-step explanation:
-13 = -3h + 2
3h - 13 = 2
3h = 15
h = 5
Answer:
-5
Step-by-step explanation:
-13 = -3h + 2 First, move the positive two (we get rid of a + by using a -)
-2 -2
-15 = -3h -3 is divided (opposite of multiplication is division)
----- ------
3 3
-5 = h Now we have our answer :)
Inez and her friends are buying ride tickets at an amusement park. Order these options from best buy to worst.
Option A: 18 tickets for $13.50
Option B: 36 tickets for $30.00
Option C: 60 tickets for $39.00
Explain if she correct or not. If she is correct, justify her claim. If she is not correct, explain her error and state the correct GCF.
PLEASE HELP ME OUT!!!!
Answer:
Marcia is not correct.
See explanation below.
Step-by-step explanation:
The terms are
2x²
4xy
8xy^4
The terms broken down into products of prime factors are:
2x² = 2 × x × x
4xy = 2 × 2 × x × y
8xy^4 = 2 × 2 × 2 × x × y × y × y × y
To find the GCF, we circle the common factors of the three terms (here we use bold type instead of circling.)
2x² = 2 × x × x
4xy = 2 × 2 × x × y
8xy^4 = 2 × 2 × 2 × x × y × y × y × y
The GCF is the products of the circled (bold) factors.
GCF = 2x
Marcia's answer is the Least Common Multiple.
For the LCM, you use all factors that are common and not common with the larger exponent.
LCM = 2 × 2 × 2 × x × x × y × y × y × y = 8x²y^4
Marcia's mistake is that she calculated the LCM instead of the GCF.
Answer:
Marcia is not correct.
The explanation is above.
Answer:
See below.
Step-by-step explanation:
2x^2, 4xy, and 8xy^4
She is incorrect.
The GCF is 2x.
She found the greatest term, rather than the greatest factor.
-hope it helps
What is the slope of the line that goes through (-5,-5) and (5,-7)
Answer: The slope would be -1/5
Heres a graph
Hope this helps!
If X = 6 cm and Z = 10 cm, what is the length of Y?
A. 8 cm
B. 8 cm
C. 10 cm
D. 6 cm
Answer:
If XYZ is a triangle, then Y = 8 cm
Step-by-step explanation:
X^2 + Y^2 = Z^2, by the Pythagorean Theorem.
Z, in this equation, represents the hypotenuse; the hypotenuse must be the longest side, and we can therefore eliminate C, 10 cm, without even beginning. Then, we may plug the given values in.
(6)^2 + Y^2 = 10^2
36 + Y^2 = 100
Y^2 = (100 - 36) = 64
Y = 8 cm
I hope this helped! :)
The diameter, D, of a sphere is 15 cm. Calculate the sphere's volume, V.
Use the value 3.14 for a, and round your answer to the nearest tenth. (Do not round any intermediate computations.)
Answer: 1766.3
Step-by-step explanation:
The following is proportional b. Fill in the missing table, equation and verbal
3.
Graph
11
10
number of Insta posts
time (days)
days.
Mrs Manuel makles
Equation : k=
Time (days)
Insta post every
Equation
Insta post (#)
5
2
6
9
For questions 4-7, use the equation y =54X
4. Find y when x = 8
5. Find x when y = -20
6. Fill in the table.
Answer:
yx=8 and xy=20 so that is the correct answer
Help need answers asap
Answer:
x = 25
y = 6
Step-by-step explanation:
< B = < M
2x - 20 = 30
2x = 50
x = 25
AB = LM
7y - 8 = 2y + 22
5y = 30
y = 6
Victor's class is going on a field trip.
They will ride on the city bus twice,
once going and once coming back.
The one-way bus trip costs 35€ per
child and 50¢ per adult. There are
24 students, 4 parents, and 1 teacher
4
going on the trip. How much money
will they need for everyone to ride
the bus?
Answer:
2180
Step-by-step explanation:
35x24=840
50x5=250
add those tou get 1090
multiply by 2
2180
The table shows the distance a cyclist rides her bicycle over time. Is the rate of change in distance with respect to time constant? What does the rate of change represent?
Bike Riding Distance
Time
(minutes) Distance
Traveled (ft)
1 1120
2 2240
3 3360
4 4480
A. The rate of change is constant and represents a speed of 1120 ft/min. The cyclist rides her bike at a rate of 1120 ft/min.
B. The rate of change is constant and represents a speed of 3360 ft/min. The cyclist rides her bike at a rate of 1120 ft/min.
C. The rate of change is constant and represents a speed of 2240 ft/min. The cyclist rides her bike at a rate of 1120 ft/min.
D. The rate of change is constant and represents a speed of 4480 ft/min. The cyclist rides her bike at a rate of 1120 ft/min.
From the relationship between the distance and time, the rate of change is constant and represents a speed of 1120 ft/min. The cyclist rides her bike at a rate of 1120 ft/min.
What is a linear equation?A linear equation is in the form:
y = mx + b
Where y,x are variables, m is the rate of change and b is the initial value of y.
Let y represent the distance travelled by the bike after x minutes.
From the table:
Rate of change = (4480 - 1120) / (4 - 1) = 1120 ft/min
The rate of change is constant and represents a speed of 1120 ft/min. The cyclist rides her bike at a rate of 1120 ft/min.
Find out more on linear equation at: https://brainly.com/question/14323743
choices are
A. 3/22
B. 6/23
C. 4/7
D. 3/7
please help
Answer: D
Step-by-step explanation:
There are 14 students who chose vanilla, and 6 of those are male. 6/14 = 3/7.