Mathematics High School

Multiply the binomial and find the coefficients
(X+y)^1=__×+__y

(×+y)^2=__x^2+__xy+__y^2

(X+y)^3=__×^3+__×^2y+__y^3

(×+y)^4=__×^4+__x^3y+__x^2y^2+__xy^3+__y4

Answers

Answer 1
We can use the pascal triangle to solve this problem.
 
 For this case, rewriting each binomial we have:
 (x + y) ^ 1 = 1x + 1y

 (x + y) ^ 2 = 1x ^ 2 + 2xy + 1y ^ 2

 (x + y) ^ 3 = 1x ^ 3 + 3x ^ 2y + 3xy ^ 2 + 1y ^ 3

 (x + y) ^ 4 = 1x ^ 4 + 4x ^ 3y + 6x ^ 2y ^ 2 + 4xy ^ 3 + 1y4

Related Questions

What does the underlined conjunction connect in the sentence? The family enjoyed fishing, but they loved hiking during their trip. A. sentences B. predicates C. subjects D. direct objects

Answers

the answer is c objects

Find the slope of the line graphed below

Answers

4/6, but the simplified form of it is 2.3

The slope of the line is 2/3

To find the slope of the line, first choose two points that are on the line. For this example we'll use (0, -4) and (6, 0). Now use the slope formula with these two points to find the slope.

m(slope) = (y2 - y1)/(x2 - x1)

m = (0 - -4)/(6 - 0)

m = (0 + 4)/(6 - 0)

m = 4/6

m = 2/3

What constant term should be used to complete the square? x 2 - 5x + _____ = 7

Answers

For this case we have an expression of the form:
 x ^ 2 - 5x + _____ = 7
 To complete the square, we must add to both sides of the equation a constant of the form:
 (b / 2) ^ 2
 We have then:
 x ^ 2 - 5x + (-5/2) ^ 2 = 7 + (-5/2) ^ 2
 Rewriting we have:
 x ^ 2 - 5x + 6.25 = 7 + 6.25
 x ^ 2 - 5x + 6.25 = 13.25
 Answer:
 The constant term that should be used to complete the square is:
 6.25
the correct answer is 25/4 so  choose letter B  as you answer have beautiful day.

10 POINTS!!! FULL ANSWER IN STEP BY STEP FORMAT!! ALL PARTS A, B, C, D, E

Answers

The first thing to do is to get the graph. That's below. That is a very wicked looking graph. I'm not sure what happens at 0. I'm not sure it is continuous at 0. That's something to make a fuss over because x = 0  is one of the x intercepts.

y = - x^(2/5)(x(5/5) + 7).
y = - x^(2/5)(x + 7)
So one of the x intercepts is 0 and the other one is -7.

The reasons are known because the factors can be equated to 0. It does not look to me like there is exact symmetry. There is a local minimum however at what the graph says is (-2,-6.5 or so)
You could differentiate that to find the exact point, but you are not asked for that.

So the domain is from -∞ to zero and 0 to plus ∞ I think you have to exclude 0 even though it is an x intercept. 

The graph decreases from -∞ < x < -2
It increases from -2 < x < 0
It decreases form 0< x < ∞

You flipped a coin 70 times and recorded 23 heads. What is the experimental probability of flipping tails?

ANY HELP IS APPRECIATED!
Please show work

Answers

The experimental probabilities relies on the fact of actual occurrence of the experiment and events. It is the ratio of the number of times an event is occurring to the total number of times that activity has been repeated for.
thus:
experimental probability of our case will be:
P(H)=(# of times of occurrence of the event)/(# of trials)
=23/70
So the probability of getting a head in the experiment is 23/70=0.33

A number cube is rolled 120 times. The number 4 comes up 47 times. What is the experimental probability of rolling a 4? What is the theoretical probability of rolling a 4?

A. 47/120; 1/30
B. 47/120; 1/6 ******
C. 4/47; 1/6
D. 1/6; 47/120

Am I Correct? 

Answers

Yes you are.
(Your answer is B, right?)

A number cube is rolled 120 times. The number 4 comes up 47 times.

We have to determine the experimental probability of rolling a 4.

The formula to evaluate probability of an event is given by:

Probability  = [tex] \frac{Favourable outcomes}{Total outcomes} [/tex]

So, Probability of rolling a 4 = [tex] \frac{ Total number of times when 4 appears}{Total number of times number cube rolled} [/tex]

= [tex] \frac{47}{120} [/tex]

Now, we have to find the theoretical probability of rolling a 4.

Total number of outcomes of number cube = {1,2,3,4,5,6}

Probability of rolling a 4 = [tex] \frac{1}{6} [/tex]

So, Option B is the correct answer.

Madeline is financing $321,800 to purchase a house. How much money will she save over the life of a 20 year fixed rate loan by buying five points with the rate of 4.23% instead of not buying points with the rate of 5.18%? Round to the nearest dollar. (show work)

A= $39,984
B= $23,894
C= $36,697
D= $36,766

Answers

Did you get an answer yet?

Anyone know the answer?

Answers

Hi there your answer would be d
The answer is D. 77. 

What do the graphs of sine and cosine have in common with the swinging you see?
Which reasons did you think of?

Answer:
The high and low points repeat in a pattern.
The cycle repeats at equal time intervals.
The swinging motion is smooth, unabrupt.

Answers

Final answer:

The graphs of sine and cosine functions have similarities with the swinging motion such as repeating patterns at equal time intervals and smoothness.

Explanation:

The graphs of sine and cosine functions have several similarities with the swinging motion you observe:

Both the high and low points in the graphs of sine and cosine functions repeat in a pattern, just like the motion of a swing repeating from its highest to lowest points.The cycle of both graphs repeats at equal time intervals, just like the swinging motion of a swing that takes the same amount of time to swing back and forth.The swinging motion of a swing is smooth and uninterrupted, just like the graphs of sine and cosine functions.

These similarities are because simple harmonic motion, which includes swinging, is closely related to sine and cosine waves.

Learn more about The Link between Simple Harmonic Motion and Waves here:

https://brainly.com/question/37843140

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Need help please asap.

Answers

quadrilateral
trapezoid
isosceles trapezoid
parallelogram

Simplify: x+2/x2-6x-16 ÷ 1/9x

Answers

[tex]\dfrac{x+2}{x^2-6x-16}:\dfrac{1}{9x}=\dfrac{x+2}{x^2-8x+2x-16}\cdot9x=\dfrac{x+2}{x(x-8)+2(x-8)}\cdot9x\\\\=\dfrac{x+2}{(x-8)(x+2)}\cdot9x=\dfrac{1}{x-8}\cdot9x=\dfrac{9x}{x-8} [/tex]

There are 5 cars to be displayed in 5 parking spaces, with all the cars facing the same direction. of the 5 cars, 3 are red, 1 is blue, and 1 is yellow. if the cars are identical except for color, how many different display arrangements of the 5 cars are possible?

Answers

For questions like these, I believe you use permutations. Basically you mutiply all the numbers in the set together. so in this case there are five, so you multiply numbers 1-5 together in order to get the total arrangements possible.

For example :
[tex]1 \times 2 \times 3 \times 4 \times 5 = 120[/tex]
There you go :)
Final answer:

The question relates to combinatorial mathematics and asks for possible arrangements of 5 cars of three different colors. Treating identical colors as one entity, we find that there are 6 ways to arrange the color groups and another 6 ways to arrange the red cars among themselves, resulting in 36 possible arrangements.

Explanation:

The subject of this question is combinatorial mathematics. We're asked how many different arrangements there are if we have 5 cars to be displayed in 5 parking spaces, with the condition that the cars are identical besides their color; 3 of them are red, 1 is blue, and 1 is yellow.

Since three cars are identical (red ones), we treat them as one. So initially, we have three 'entities' to arrange: the red group (of 3 cars), the blue car, and the yellow car. These can be arranged in 3! (which means 3 factorial, or 3 * 2 * 1) = 6 ways.

However, within the red group, those 3 red cars can be arranged amongst themselves in 3! = 6 ways.

Therefore, to get the total number of arrangements, we multiply these results together, giving us: 6 * 6 = 36 different arrangements.

Learn more about Combinatorial Mathematics here:

https://brainly.com/question/32415345

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Aubrey has a new art box in the shape of a rectangular prism. The box is 5 inches, by 8 inches, by 2 inches. How much volume is not take-up by the eraser if the dimension of the eraser is 5.5 inches^3

Answers

I think the answer is 74.5

volume of the rectangular prism = base area * height

base area = length * breadth

volume of the rectangular prism = length * breadth * height

volume of the rectangular prism = 5*8*2 = 80 inches ^3

volume of taken up by the eraser = 5.5 inches^3

volume that is not take-up by the eraser = 80-5.5 = 74.5 inches^3

What is EC if AC = 12, BC = 5, and DC = 4?

A. 30
B. 9
C. 15
D. 7

Answers

we need to find ED first

the formula for this would be (AB +BC)*BC = (ED+DC)*DC

lets replace the letters with the given numbers:

If AC = 12 and BC = 5 then AB = 12-5 = 7

so we get:
(7+5) *5 = (ED+4)*4

12*5 = (ED+4)*4

60 = (ED+4)*4

60/4 = (ED+4)

15 = ED +4

ED = 15-4 = 11

now add ED + DC to get EC

11+4 = 15
 The answer is C. 15

When i am divided into 22, the remained is one. when i am added to 5, the answer is an even number. what number am i? * 5 7 9 10 4 2/5?

Answers

Working with the given answers we can find the correct answer. Indeed, it is a comfortable and cozy way to solve this problem. We have given 5, 7, 9, 10, 4 and 0.4. Among these numbers, if we take 7 we can see that when 22 is divided into that, 1 is remaining and when we sum up 7 and 5, the result is 12, which is an even number. The correct answer is 7

Answer:

Number is 23.

Step-by-step explanation:

We have been given the information when a number is divided by 22 the remainder is 1.

And when it is added to 5  it will give us an even number.

So, the number 23 if we take when divided by 22 it will give the remainder 1.

And when added to 5 it will give 23+5=28 which is an even number.

So, the number is 23.

"the placement test for a college has scores that are normally distributed with a mean of 600 and a standard deviation of 60.if the college accepts only the top 1​% of​ examinees, what is the cutoff score on the test for​ admission?"

Answers

Given that only the top 1% are admitted, the cutoff will be as follows:
the z-score is given  by:
z=(x-μ)/σ
where:
μ-mean
σ-standard deviation
P(x>X)=1-P(z<Z)=0.01
⇒P(z<Z)=1-0.01=0.99
thus:
the value of z that corresponds to 0.99 is 2.33
thus:
2.33=(x-600)/60
solving for x we get:
139.8=x-600
x=739.8
thus the cutoff was 739.8


Isabel is purshing a 5 pound bag of dog food.how many 8- ounce servings can she feed her dog (1lb=16oz

Answers

1 pound = 16 ounces
16 ounces / 8 ounces = 2 servings per pound

5 pound bag x 2 servings per pound = 10 total servings

A tunnel is in the shape of a parabola. The maximum height is 16 m and it is 16 m wide at the base, as shown below.

What is the vertical clearance 7 m from the edge of the tunnel?

Answers

Answer: 15.75 m

Explanation:

1) Since the vertex is at the origin, i.e point (0,0), and the simmetry axis is paralell to the vertical axis, you know that the canonical equation of the parabola is:

y = -4px², where p is the focal distance.

You can also use y = ax², where a = -4p.

2) Using y = ax², you can find a from the fact that at x = 8 (one edge of the tunnel), y = - 16 ( negative value of the height).

Substitute those values (8,16) in the equation y = ax², and you get:

- 16 = a (8²) ⇒ a = - 16 / 64 = - 1/4

Therefore, the equation of the parabola is: y = (-1/4)x².

3) To find the vertical clearance at 7 m from the edge of the tunnel, you must realize that the x-coordinate is x = 8 - 7 = 1.

Then, find y for x = 1:

y = (-1/4)(1²) = - 1/4 = - 0.25

That is the y-coordinate; the clearance is the 16m - 0.25m = 15.75m

What is the place value of the digit 4 in 6,296.04

Answers

Hoi!

The digit 4 is in the hundredths place, since it's behind a decimal.

Place value in front of a decimal goes as:

Ones, tens, hundreds, thousands, etc

Place value behind a decimal goes as:

Tenths, Hundredths, Thousandths, etc

The digit 4 in 6,296.04 is in the hundredths place, representing four hundredths or 4/100. This can also be expressed in scientific notation as 4 x 10⁻².

The place value of the digit 4 in 6,296.04 is in the hundredths position. This is because the digit 4 is two places to the right of the decimal point. In a decimal number, the first place to the right of the decimal point is the tenths place, the second is the hundredths place, and it continues with thousandths, ten-thousandths, and so on. Therefore, in the number 6,296.04, the 4 represents four hundredths, or 4/100, which can also be written in scientific notation as 4 × 10⁻².

Which kind of function best models the data in the table? Use differences or ratios.


A. linear
B. quadratic
C. exponential
D. none of the above

Answers

The data in the table represents a C. exponential function. In an exponential function, as x-values increase, y-values get greater and greater. The y-values increase more rapidly as x-values increase linearly.
The answer would be B. Hope this helps :)

Identify the values that create ordered pairs that are solutions to the equation 3x - 5y = 20.

(5,y) (x,2)

Answers

X=10 Y=1

thats your answer hope it helps ;P
3x - 5y = 20

(5; y)  -  put x = 5 to the equation

3 · 5 - 5y = 20
15 - 5y = 20  |-15
-5y = 5  |:(-5)
y = -1

Answer: (5; -1)

(x; 2)  -  put y = 2 to the equation

3x - 5 · 2 = 20
3x - 10 = 20    |+10
3x = 30    |:3
x = 10

Answer: (10; 2)

Which graph shows the same end behavior as the graph of f(x) = 2x6 – 2x2 – 5?

Answers

[tex]Given \ function : \ f(x) = 2x^6-2x^2-5[/tex]

In order to find the end behavior of the graph, we need to find the degree of the given function and the leading coefficent.

Degree of the given function is the highest power of the variable.

We have variable x there.

Highest power of x is 6.

So, we can say:

Degree = 6 ( an even degree)

And leading coefficent is the coefficent of highest power term.

We have highest power term is 2x^6.

So, the leading coefficent is : 2 (Positive number)

For even degree and positive leading coefficent, end behaviour is

x --> ∞  f(x) = +∞

x-->-∞   f(x) = +∞

Answer:

The answer is A on edg

Step-by-step explanation:

just took the test

Will give brainliest!  pts to the correct answer! Are quadratic equations already in rectangular form? I'm asked to eliminate the parameter t from these two questions to get it into the rectangular equation with x and y. Is it possible?
x(t) = 0.5t^2+0.4t-87.30
y(t)= 0.4t^2+0.1t +29.44

Answers

[tex]\bf x(t)=0.5t^2+0.4t-87.30\implies x(t)=\cfrac{1}{2}t^2+\cfrac{2}{5}t-\cfrac{873}{10} \\\\\\ x=\cfrac{1}{2}\left( t^2+\cfrac{4}{5}t+\boxed{?}^2 \right)-\cfrac{873}{10}[/tex]

so, as you already know, we'll borrow from our good friend Mr Zero, 0, to get that missing value for the perfect square trinomial,

[tex]\bf x=\cfrac{1}{2}\left[ t^2+\cfrac{4}{5}t+\left( \cfrac{2}{5} \right)^2-\left( \cfrac{2}{5} \right)^2 \right]-\cfrac{873}{10} \\\\\\ x=\cfrac{1}{2}\left[t^2+\cfrac{4}{5}t+\cfrac{4}{25}-\cfrac{4}{25} \right]-\cfrac{873}{10} \\\\\\ x=\cfrac{1}{2}\left[t^2+\cfrac{4}{5}t+\left( \cfrac{2}{5} \right)^2\right]-\cfrac{2}{25}-\cfrac{873}{10} \\\\\\ x=\cfrac{1}{2}\left[t^2+\cfrac{4}{5}t+\left( \cfrac{2}{5} \right)^2\right]-\cfrac{4369}{50}[/tex]

[tex]\bf x=\cfrac{1}{2}\left( t+\frac{2}{5} \right)^2-\cfrac{4369}{50}\implies x+\cfrac{4369}{50}=\cfrac{1}{2}\left( t+\frac{2}{5} \right)^2 \\\\\\ 2x+\cfrac{4369}{25}=\left( t+\frac{2}{5} \right)^2\implies \sqrt{2x+\cfrac{4369}{25}}=t+\cfrac{2}{5} \\\\\\ \sqrt{2x+\cfrac{4369}{25}}-\cfrac{2}{5}=t[/tex]

[tex]\bf -------------------------------\\\\ y(t)=0.4t^2+0.1t+29.44\implies y=\cfrac{2}{5}t^2+\cfrac{1}{10}t+\cfrac{736}{25} \\\\\\ y=\cfrac{2}{5}\left( \sqrt{2x+\cfrac{4369}{25}}-\cfrac{2}{5} \right)^2+\cfrac{1}{10}\left( \sqrt{2x+\cfrac{4369}{25}}-\cfrac{2}{5} \right)+\cfrac{736}{25}[/tex]

HELP PLEASE Simplify the rational expression. State any excluded values. x^2-12x+35/x^2-3x-10

Answers


[tex]\frac{{x}^{2} - 12x + 35 }{ {x}^{2} - 3x - 10 } [/tex]
Factorise both the term by splitting the mid term and you'll get


[tex] \frac{ {x}^{2} - 5x - 7x + 35}{ {x}^{2} - 5x + 2x - 10 } \\ = \frac{x(x - 5) - 7(x - 5)}{x(x - 5) + 2(x - 5)} \\ = \frac{(x - 7)(x - 5)}{(x + 2)(x - 5)} \\ = \frac{x - 7}{x + 2} [/tex]

Algebra question ( Matrices and Determinants ) 20 points

Answers

The correct answer is option A

The answer is as following 
The new matrix is 2 rows and 2 columns . i.e. it is 2*2 matrix
The element a₁₁ =5*2 + 0*2 = 10
The element a₁₂ = 5*-1 + 0*-2 = -5
The element a₂₁ = 3*2 +-5*2 = -4
The element a₂₂ = 3*-1 + -5*-2 = 7

The new matrix will be [tex] \left[\begin{array}{ccc}10&-5\\-4&7\end{array}\right] [/tex]

The window is 60 inches wide. What is the width of the window in feet.

Answers

The width of the window in feet is 5 feet.
The Width Of The Window In Feet Is 5 Feet Because Every Foot Is 1 Inch.

60 Divided By 12 = 5

Answer: 5 Feet

I would appreciate it if someone could please check my work on this calculus problem! My steps/answers are in green.

Answers

A. Correct.
B. Some error in evaluation. The result should be near 2.10592505299.
C. Your final answer should have ln(2) in the denominator. The evaluation should be near 1.354326176.
D. Need ln(4) in the denominator everywhere. The evaluation should be near 79.408765453.

Write the expression in complete factored form 5(y-7)+b(y-7)

Answers

the answer is (y-7)(5+b)

A toy company produces two kites whose shapes are geomaetrically similar. Find the length of the missing size of similar kite.

Answers

your answer is x=17.5

Brian wants to build a ramp that leads to a storeroom 5 meters above the ground. He wants the ramp to be 10 meters long. What should the angle of elevation of the ramp be?

15°


30°


45°


60°

Answers

Answer:

It would be 30

Step-by-step explanation:

I did it on plato

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