Using the binomial theorem, expand the expression (4 + y) to the power of 4

Answers

Answer 1

Answer:

When raised to the power of 4, the binomial (4 + y) expands to:

[tex]y^4 + 16y^3 + 96y^2 + 256y + 256[/tex]

Step-by-step explanation:

[tex](4 + y)^4 \\= (y^2 + 8y + 16)^2\\= y^4 + 8y^3 + 16y^2 + 8y^3 + 64y^2 + 128y + 16y^2 + 128y + 256\\= y^4 + 16y^3 + 96y^2 + 256y + 256[/tex]


Related Questions

A group of students are standing in rows. There are as many students in a row as there are rows. If there are 64 students in the group, how many students are standing in pach row?
A. 4
B 6
C. 8
D 12.​

Answers

Answer:

B..im pretty sure

Step-by-step explanation:

First it cant be D because 12 x __ = 64. There is no whole number multiplied by 12 that equals 64. So cross that out. then it's not B because 6 x ___ = 64. So also cross that out. the only thing u have left is 4 and 8. Then u can cross out A because the group of students has to be the same number of rows. Which is 8 x 8 aka B. The answer is B

Answer:

B

Step-by-step explanation:

Which of the following is a true statement about the rhombus shown

Answers

Answer:

Option D is the correct answer

Step-by-step explanation:

Since, diagonals of a rhombus bisects at right angles.

[tex]\therefore m\angle STP = 90\degree \\ [/tex]

9514 1404 393

Answer:

  D)  m∠STP = 90°

Step-by-step explanation:

In general, the diagonals of a rhombus are different lengths and the corner angles are not 90°. (The exception in both cases is when the rhombus is a square.)

However, it is always true that the diagonals are perpendicular bisectors of each other, so all angles at T are 90°.

  m∠STP = 90°

a store buys shirts for $12 each and marks up the price by %25. what is the price for a shirt at this store??

Answers

Answer:

Step-by-step explanation:

The price of the shirt at the store is $16

12 x .25 = 4

4 + 12 = 16

7 (x+y) - 7 x with all the steps plz

Answers

Answer:

7y

Step-by-step explanation:

7x+7y-7x=0+7y=7y

Answer:

7y

Step-by-step explanation:

7(x+y)-7x  - Distribute 7 through the peretheses

7x+7y-7x  - since two opposites add up to 0, remove them from the             expression

= 7y

Help a birb. Get a crown.

Answers

Answer:

6.

in 24/4=6,

24 is the dividend

4 is the divisor

6 is the quotient

in 4*6 = 24,

4 and 6 are the factors

24 is the product

7. division is an operation on two numbers to find the quotient

8. fact family is a group of related facts using the same numbers

9. multiplication is an operation on two numbers to find the product

Answer:

6. 24/4 = 6

7.24

8.4

9.6

4 * 6 = 24,

4 și 6 sunt factorii

24 este produsul

7. împărțirea este o operație pe două numere pentru a găsi coeficientul

8. familia de fapte este un grup de fapte conexe care utilizează aceleași numere

9. multiplicarea este o operație pe două numere pentru a găsi produsul

Step-by-step explanation:

Charlie can run 2 laps every 10 minutes and 4 laps every 28 minutes. How long will it take for Charlie to run 3 laps.

Answers

Answer:

19min

Step-by-step explanation:

Write an inequality. Marianda is packing eggs in cartons. Each carton holds 12 eggs. She has already filled 3 cartons. How many more eggs does she need to fill at least 17 cartons?

Answers

14 x 12= 168. (she already filled 3 cartons. so, 17-3 =14.) she needs 168 eggs to fill the other 14 cartons.

PLease im almost out of time

Answers

There is no question so currently, I am unable to help you.

I WILL GIVE BRAINLIST!
Showthat (1+i)2 = 2i

Answers

Answer:

(1+i)2=2i

Step-by-step explanation:

Since the 2 is on the outside of the) then that means it is multiplying and if you multiply 1x2 it will equal.2

Then if you were to multiply 2 x the i it will get 2i then you add it to get 2i

Answer:

Use formula (a + b)² = a² + 2ab + b²

(1 + i)² =1² + 2*1*i + i² =1 + 2i + (-1) =2i

Assume that random guesses are made for six multiple choice questions on an SAT​ test, so that there are nequals6 ​trials, each with probability of success​ (correct) given by pequals0.2. Find the indicated probability for the number of correct answers. Find the probability that the number x of correct answers is fewer than 4.

Answers

Answer:

0.2 +-4

Step-by-step explanation:

The required probability is 0.8826 that the number x of correct answers is fewer than 4.

What is probability?

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

There are n equals 6 ​trials, each with a probability of success​ (correct) given by p equals 0.2.

This is a direct application of Binomial distribution with sample size (n) = 6 and P(success) = p = 0.35

Let X be a Binomial random variable.

X ~ Binomial (n = 6, p = 0.35)

We have to determine, P(X < 4)

Using Excel we discover this probability,

⇒ P(X < 4) = P(X ≤ 3) = BINOMDIST (3, 6, 0.35, 1) = 0.8826

⇒ P(X < 4) = 0.8826

Therefore, the required probability is 0.8826

Learn more about probability here:

brainly.com/question/11234923

#SPJ5

HELPPPPPPPPPPPPPPPPPPPPPPPPPPPHEL

Answers

Answer:

15 degrees

Step-by-step explanation:

90-75= 15

........

Joshua rents an apartment in an all-brick building in the city. The value of the
belongings in the apartment is about $25,000. If Joshua wants to insure his
belongings while renting, how much will he have to pay for insurance per
year?
Annual Premium per $100 of coverage
Brick
Steel
Mixed
Wood
Area
Building Contents Building Contents Building Contents Building Contents
rating
10.39 0.43 0.5
0.54
0.55 0.65 0.66 0.76
Suburb | 0.45 0.52 0.56 0.63 0.72 0.74 0.83 0.85
Rural 0.6 0.69 0.71 0.8 0.89 0.91 1
1.02
City
A. $107.50
B. $150.00
C. $173.50
D. S178.65

Answers

Answer:

107.5

Step-by-step explanation:AOPED

Clara buys a sweater that is on sale for 1/4 off She says the total amount she
will pay will be equal to 3/4 of the original price of the sweater.
Is she correct?

Answers

I believe she is but I’m not entirely sure so maybe do some work on it

What is the solution to the equation represented by the model below?


x = negative 14
x = negative 2
x = 2
x = 14

Answers

Answer:

2x + 4

To model 2x+4, you need :

2 positive x-tiles to represent 2x.

4 positive unit tiles to represent 4.

3x+(-1)

To model 3x+(-1), you need :

3 positive x-tiles to represent 3x.

1 negative unit tile to represent (-1).

if its wrong sorry u can report me

What is the solution for this inequality?

need help fast please!​

Answers

Answer:

[tex]x\geq -4[/tex]

Step-by-step explanation:

[tex]-10x\leq 40[/tex]

divide by -10, which means you need to flip the inequality sign since youre dividing by a negative number

[tex]x\geq -4[/tex]

Answer:

The anwer is D

Step-by-step explanation:

up up up......

Solve the proportion. 8/11 = 4/y + 2

Answers

Answer:

[tex]y=-\frac{22}{7}[/tex]

Step-by-step explanation:

Suppose that y varies directly with x and y = 12 when x = -2. What is x when y = -6?

Answers

X=1

Explanation:
Conduct a ratio, -2/12=x/-6

You have to find the x in this ratio so you will multiply -2 and -6 together, and multiply 12 and x together and make them equal to eachother. It would look like this.
(-6)(-2)=12x
12=12x
x=1

I hope this is right and I’m sorry if I’m wrong:((

For the right triangle shown, which equation is correct?
1. all answers are correct
2. cos(53) = x/16
3. cos(53) = sin(37)
4. sin(37) = 16/x

Answers

Answer:

3.37

Step-by-step explanation:

x+37+16+90=180

x+143=180

×=180-143

x = 37

Find the exact values of the six trigonometric ratios of the angle in the triangle 160 and 164

Answers

Answer:

[tex]\sin \theta = \frac{40}{41}[/tex], [tex]\cos \theta = \frac{3}{82}[/tex], [tex]\tan \theta = \frac{80}{3}[/tex], [tex]\cot \theta = \frac{3}{80}[/tex], [tex]\sec \theta = \frac{82}{3}[/tex], [tex]\csc \theta = \frac{41}{40}[/tex]

Step-by-step explanation:

We notice that figure represents a right triangle, the hypotenuse has a length of 164 units and the leg opposite to [tex]\theta[/tex] has a length of 160 units. The sine of [tex]\theta[/tex] is:

[tex]\sin \theta = \frac{160}{164}[/tex]

[tex]\sin \theta = \frac{40}{41}[/tex]

The leg adjacent to [tex]\theta[/tex] is determine by the Pythagorean Theorem:

[tex]r = \sqrt{164^{2}-160^{2}}[/tex]

[tex]r = 6[/tex]

Then, the cosine of [tex]\theta[/tex] is:

[tex]\cos \theta = \frac{6}{164}[/tex]

[tex]\cos \theta = \frac{3}{82}[/tex]

Lastly, we determine the remaining trigonometric ratios by using these identities:

[tex]\tan \theta = \frac{\sin \theta}{\cos \theta}[/tex] (1)

[tex]\cot \theta = \frac{1}{\tan \theta}[/tex] (2)

[tex]\sec \theta = \frac{1}{\cos \theta}[/tex] (3)

[tex]\csc \theta = \frac{1}{\sin \theta}[/tex] (4)

If we know that [tex]\sin \theta = \frac{40}{41}[/tex] and [tex]\cos \theta = \frac{3}{82}[/tex], then the trigonometric ratios are, respectively:

[tex]\tan \theta = \frac{\frac{40}{41} }{\frac{3}{82} }[/tex]

[tex]\tan \theta = \frac{80}{3}[/tex]

[tex]\cot \theta = \frac{1}{\frac{80}{3} }[/tex]

[tex]\cot \theta = \frac{3}{80}[/tex]

[tex]\sec \theta = \frac{1}{\frac{3}{82} }[/tex]

[tex]\sec \theta = \frac{82}{3}[/tex]

[tex]\csc \theta = \frac{1}{\frac{40}{41} }[/tex]

[tex]\csc \theta = \frac{41}{40}[/tex]

PLEASE HELP I GIVE BRAINLIEST

Answers

Answer:

y = 11

Step-by-step explanation:

Perimeter = 6 + 5y + y + 2 + 4y + 3

                = 10y + 11

10y + 11 = 121

10y = 121 - 11

     = 110

y = 110 ÷ 10

y = 11

Help please! This has to do with the Pythagorean theorem.

Answers

Answer:15.62 units

Step-by-step explanation:

just the two legs squared = diagonal squared, so then square root the diagonal so u get a real number

Hurry and anwser plz

Answers

Answer:

D

Step-by-step explanation:

103+103=206

360-206=154

154 divided by 2 equals 77 degrees aka D.

Hope this helped! :)

the answer should be D

Perform the indicated operation.
1 1/7x 2 4/5

Answers

Explanation: none




Answer: The answer would be 3.2

Identify the independent and dependent variable of the following graph. Indicate whether the graph rises, falls, or is constant.
A person's core body temperature (°F) in relation to time of day

a. Independent Variable: time of day, Dependent Variable: temperature Graph falls until morning and then steadily rises throughout the day.


b. Independent Variable: time of day, Dependent Variable: temperature Graph is constant and then rises.

c. Independent Variable: time of day, Dependent Variable: time of day Graph is constant and
then rises.

d. Independent Variable: temperature, Dependent Variable: time of day
Graph falls until morning
and then steadily rises throughout the day.​

Answers

Answer:

d number is the correct answer of the question

One serving of yogurt is 95 calories. How many calories are in 2.5 servings of yogurt ?

Answers

Answer:

237.5 calories

Step-by-step explanation:

One serving has 95

so 2.5 serving has

2.5×95= 237.5

Plz mark brainliest

thanks

An evergreen tree is supported by a wire extending from 1.5 feet below the top of the tree to a stake in the ground. The wire is 24 feet long and forms a 58° angle with the ground. how tall is the tree?​

Answers

Answer:

Approximately [tex]21.9\; \rm ft[/tex] (assumption: this tree is perpendicular to the ground.)

Step-by-step explanation:

Refer to the diagram attached (not drawn to scale.)

Label the following points:

[tex]\rm S[/tex]: stake in the ground.[tex]\rm A[/tex]: top of the tree.[tex]\rm B[/tex]: point where the wire is connected to the tree. [tex]\rm C[/tex]: point where the tree meets the ground.

Segment [tex]\rm SB[/tex] would then denote the wire between the tree and the stake. The question states that the length of this segment would be [tex]24\; \rm ft[/tex]. Segment [tex]\rm AB[/tex] would represent the [tex]1.5\; \rm ft[/tex] between the top of this tree and the point where the wire was connected to the tree.

The question is asking for the height of this tree. That would correspond to the length of segment [tex]\rm AC[/tex].

If this tree is perpendicular to the ground, then [tex]\rm \angle A\hat{C}S =90^\circ[/tex]. Triangle [tex]\rm \triangle BCS[/tex] would be a right triangle with segment [tex]\rm SB[/tex] as the hypotenuse.

The question states that the angle between the wire (segment [tex]\rm SB[/tex]) and the ground (line [tex]\rm SC[/tex]) is [tex]58^\circ[/tex]. Therefore, [tex]\rm \angle A\hat{S}C = 58^\circ[/tex].

Notice, that in right triangle [tex]\rm \triangle BCS[/tex], segment [tex]\rm BC[/tex] is the side opposite to the angle [tex]\rm \angle B\hat{S}C = 58^\circ[/tex]. Therefore, the length of segment [tex]\rm BC\![/tex] could be found from the length of the hypotenuse (segment [tex]\rm SB[/tex]) and the cosine of angle [tex]\rm \angle B\hat{S}C = 58^\circ\![/tex].

[tex]\displaystyle \cos\left(\rm \angle B\hat{S}C\right) = \frac{\text{length of $\mathrm{BC}$}}{\text{length of $\mathrm{SB}$}} \quad \genfrac{}{}{0em}{}{\leftarrow\text{opposite}}{\leftarrow \text{hypotenuse}}[/tex].

Rearrange to obtain:

[tex]\begin{aligned}& \text{length of $\mathrm{BC}$} \\ &= (\text{length of $\mathrm{SB}$}) \cdot \cos\left(\angle \mathrm{B\hat{S}C}\right)\\ &= \left(24\; \rm ft\right) \cdot \cos\left(58^\circ\right) \approx 20.35\; \rm ft\end{aligned}[/tex].

In other words, the wire is connected to the tree at approximately [tex]20.3\; \rm ft[/tex] above the ground.

Combine that with the length of segment [tex]\rm AB[/tex] to find the height of the entire tree:

[tex]\begin{aligned}&\text{height of the tree} \\ &= \text{length of $\mathrm{AC}$} \\ &= \text{length of $\mathrm{AB}$} + \text{length of $\mathrm{BC}$}\\ &\approx 20.35\; \rm ft + 1.5\; \rm ft \\ &\approx 21.9\; \rm ft\end{aligned}[/tex].

For which equations is 8 a solution? Select the four correct answers.

Answers

X + 2 = 10
X - 4 = 10
3x = 24
X/8 = 1
Those 4 are the correct answers

Answer:

x+2=10

x-4=4

3x=24

x/8=1

Step-by-step explanation:

What is a reasonable amount of Miles on a used car that you are planning on purchasing

Answers

Answer:

1000 or more

Step-by-step explanation:

because the motor is is good shape

Suppose an ice cream cone is 10 cm deep with a diameter of 4cm. How much ice cream can fit into the cone without it overflowing?

Answers

Answer:

6 inches tall and has a diameter of 2 inchces

Step-by-step explanation:

8 gallons equals how many pints?​

Answers

Answer:

38

Step-by-step explanation:

Answer:

8 gallons equals 64 pints since there are 8 pints in a gallon

Step-by-step explanation:

take care

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