Use the binomial theorem to expand expressions 1-4 and answer question 5.

1. (3x^2 +y)^3
2. (5x^4 +2y^5)^4
3. (x^3 +4y^2)^5
4. (x-2y)^6
5. find the coefficient of x^3 y^4 in the expansion of (2x+5y^2)^5

Answer:

Step-by-step explanation:

An radical expression usually involves a radicand which is the number or expression inside the radical symbol √ and an index which is the number outside the radical symbol indicating the root, the radicand raised to the power of the reciprocal of the index.

But in the case of expression "U-2/5" it's not a radical expression as is. It's a fractional expression with variable U and a constant -2/5.

It can be written as √(U-2)/5 or U- √(2/5) if you want to express it as an radical expression.

Option A) In the graph for each value of x there is exactly one value of y

So the function is  a One to One function.

A function is a procedure or a relation that links each element of a non-empty set A, at least one element of another non-empty set B, to another element of the first non-empty set A. In mathematics, a relation f between two sets, A and B, is referred to as the function's domain and co-domain. For all values of a and b, f = (a,b)|

A function f is said to be injective if it maps different items in its domain to other elements; for example, f = f implies x1 = x2. Alternatively, every element of the function's codomain is at most one of its domain's elements.

If some function output value corresponds to more than one input value, the function is said to be many-to-one (sometimes written as "many-one"). If the domain of f contains two different values a and b such that f(a)=f, the function f is many-to-one in symbols (b).

In the graph for each value of x there is exactly one value of y

So the function is  a One to One function.

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Answer: $32.75

Step-by-step explanation:

If each call costs $0.08 and you make 280 minutes worth of calls this month you'll have made $22.04 worth of phone calls plus the monthly access fee ($10.35) if you add both those fees you'll be left with a bill of $32.75.

I hope this answer helped you. :)

Answer:

$32.75

Step-by-step explanation:

10.35 + (0.08×280)

Two equations that have the same solution as the given equation are;

2.3p – 10.1 =  6.49p – 4

230p – 1010 = 650p – 400 – p

Both sides of an equation will remain equal, when both sides are

multiplied by the same amount.

The given equation: 2.3·p - 10.1 = 6.5·p - 4 - 0.01·p

Simplifying the above equation by collecting like terms gives;

2.3·p - 10.1 = 6.5·p - 0.01·p - 4 = 6.49·p - 4

2.3·p - 10.1 = 6.49·p - 4

Multiplying both sides of the original equation by 100 gives

100 × (2.3·p - 10.1) = 100 × (6.5·p - 4 - 0.01·p)

230·p - 1010 = 650·p - 400 - p

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The distance from the top of the tree of height 30 tall to the end of the shadow is 50.

Distance is the length between two point.

To calculate the distance from the top of the tree to the end of the shadow, we use the formula below.

Note: The tree and the shadow form a right angle.

Formula:

Where:

From the question,

Given:

Susbtitute these values into equation 1

Hence, the distance from the top of the tree to the end of the shadow is 50.

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Answer: x=0

Step-by-step explanation:

2(2)=4

4+x=4

-4 on both sides

so x=0

Answer:

B) x = 0

Step-by-step explanation:

We will get our equation in here first. Our equation is:

2 * 2 + x = 4

We simplify the multiplication giving us:

4 + x = 4

Finally, we subtract 4 from both sides to find the value of x. We get:

x = 0.

So the correct answer is B) x = 0.

Hope this helped!

Answer:

0

8

0

9

0

9

9

098098809667906432

Answer:

-15y

Step-by-step explanation:

The square root of any squared number is always the number itself.

So in this case, it is -15y

Brainliest please. It'll help a lot.

Answer:

---------------------------------

Simplify the expression:

We know the square root is never negative and since y is positive, we get:

Answer:d. 120x+60=780

Step-by-step explanation:

120 cost per x hours

Flat Rental cost 60

120x+60=780

-60 as the flat rate which won’t change based on time.

120x=720

Divided by a rate of 120 per hour

x=6 hours

Answer: free allah long live

Step-by-step explanation:

46564

The domain and range of the function on the table are the ones in options B and C.

Domain: {-3, 1, 5, 7}

Range: {2, 4, 5, 9}

For a function y = f(x), we define the domain as the set of the inputs, this is, the set of the possible values of x.

On the other hand, the range is the set of the outputs, this is, the set of the possible values of y.

Then the domain is just the set of the values of x on the table:

Domain: {-3, 1, 5, 7}

And the range is the set of the values of y on the table:

Range: {2, 4, 5, 9}

Then the correct options are C and B.

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Option D, x + y = -2 is the equation in standard form passing through the (-1,-1) and parallel to y = -x - 5.

The process of expressing a specific element in mathematics in the most typical way is known as standard form. Every element of mathematics, including big and small numbers, equations and lines, is designated in a standard form.

A standard form is a way of expressing a certain mathematical idea, such as an equation, number, or expression, in a way that adheres to a set of rules. The standard form is used to clearly represent extremely large or extremely small numbers.

To write an equation in standard form passing through the (-1,-1) and parallel to y = - x - 5, we need to find y-intercept form first

We know that parallel lines have same slope, so

y - y1 = m(x - x1)

y -(-1) = -1(x -(-1)

y + 1 = -x - 1

y = -x - 2

y + x = -2

Thus, Option D, x + y = -2 is the equation in standard form passing through the (-1,-1) and parallel to y = -x - 5.

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Answer:

-3w2-11w-3

Step-by-step explanation:

take w2 and w as variables. you can substitute it as w2=y and w=X then expand brackets

2y-8x-8-5y-3x+5

note that the signed changed at the second part because it was expanded with the minus sign which is basically like -1, so it changes the signs

then you collect like terms:

2y-5y-8x-3x-8+5= -3y-11x-3

now put substitute back w2=y and w=X

-3w2-11w-3

if it won't be a problem solving with w2 and w, then you skip the substitution part and solve the same

The simplest form of the given expression is (- 8n² +n +1)

Simplification is the process of making simple an expression, terms or equations so as to easy for solving or evaluating.

There are some steps for simplification such as removing parenthesis, collecting like terms, addition or subtraction of like terms and so on.

We are given an expression, ( -7n² - 8n -8) + (- n² + 9n +9)

In order to simplify, we first remove the parenthesis and get

- 7n² - 8n -8 - n² + 9n +9

in the next we will collect like terms

- 7n² - n² -8n +9n - 8 +9

We now add or subtract like terms

- 8n² + n+1

this is the simplest form of the given expression.

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It's a good idea to utilize the 13 cm measurement that Martha used for her scale illustration. This is because it would be simpler to measure the flag's stripes. The American flag has 13 stripes, thus each one is 1 centimeter wide.

Flags can be as big as 20 feet by 38 feet, although most are between 3 feet by 5 feet and 5 feet by 8 feet in size. The standard size for an American flag flown outside a home is 3 x 5.

A flag's rectangular design assures that even a moderate breeze would cause it to move, making it readily apparent to everyone else. Additionally, the shape is efficient in terms of production costs, according to a number of flag designers.

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The measure of each angle X and Y are x = 32 degrees and y = 58 degrees

From the question, we have the following parameters that can be used in our computation:

The above statements mean that

x + y = 90

y = 2x - 6

Substitute the known values in the above equation, so, we have the following representation

x + 2x - 6 = 90

Evaluate the like terms

3x = 96

Divide both sides by 3

x = 32

Substitute x = 32 in the equation y = 2x - 6

y = 2 * 32 - 6

Evaluate the equation

y = 58

Hence, the measure of the angle y is 58 degrees

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Answer:

if the scale used 1/4 inch = 3 feet, then what is the perimeter of the actual garden? AI Recommended Answer: The perimeter of the actual garden is 144 feet.

Step-by-step explanation:

A system of equations to model this scenario is given as follows -

x + y = 320

7x + 10y = 2900

        {m} - slope                 {c} - intercept along the y - axis.

Given is that on one day at a local minigolf course, there were 320 customers who paid a total of $2,900. The cost for a child is $7 per game and the cost for an adult is $10 per game.

Let {x} represents the number of children and {y} represents the number of adults who played that day. We can write the given system of equations as -

x + y = 320

7x + 10y = 2900

Therefore, a system of equations to model this scenario is

x + y = 320

7x + 10y = 2900

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well, we know that 37.5% have finished it, that leaves unaccounted for 100% - 37.5% = 62.5%.

now, of those 62.5% fellows only 40% have finished only half of it, how many are those?

well, what's 62.5% of 32?   what's 40% of that much?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{62.5\% of 32}}{\left( \cfrac{62.5}{100} \right)32}\implies 20 ~\hfill \stackrel{\textit{40\% of 20}}{\left( \cfrac{40}{100} \right)20}\implies \text{\LARGE 8}[/tex]

Answer:

[tex]y1 = 4 \\ x1 = 3[/tex]

[tex]y - y1 = m(x - x1)[/tex]

[tex]y - 4 = 0(x - 3)[/tex]

[tex]y - 4 = 0[/tex]

[tex]y = 4[/tex]

The bridge opening times when there are 60 minutes in an hour will be 45/60 and 10/60.

From the information, a boat will pass the Colby drawbridge and then the Wave drawbridge and then the Wave drawbridge.

From the table, Colby is on the 3/4 hour. This will be:

= 3/4 × 60

= 45

Also, Wave Bridge will be:

= 1/6 × 60

= 10

Therefore, it's 45/60 and 10/60 because we know that the common denominator is 60 then 3/4 of an hour is 45mins then 1/6 of an hour is 10.

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Complete question

On the Dell River, a boat will pass the Colby drawbridge and then the Wave drawbridge and then the Wave drawbridge. Rename each of the two drawbridge opening times. There are 60 minutes in an hour, so use 60 as a common denominator. Then, rename each opening time using another common denominator

Bridge name:

1. Asher Cross

2. Colby

3. Rainbow

4. Red Bank

5. Wave

Time of Opening:

1. On the hour

2. On the 3/4 hour

3. On the 2/3 hour

4. On the 1/4 hour

5. On the 1/6 hour

A 90% confidence interval for the population mean is; CI = (163.355, 166.655)

The formula to find the confidence level here is;

CI = x' ± z(s/√n)

Where;

CI is confidence  level

z-score at confidence level

x' is sample mean

s is standard deviation

n is sample size

We are given;

Sample mean; x' = 165

Sample size; n = 20

standard deviation; s = 4.5

z at CL of 90% = 1.645

Thus;

CI = 165 ± 1.645(4.5/√20)

CI = 165 ± 1.655

CI = (163.355, 166.655)

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a) The portion of the garden is made up of beef steak tomatoes is 8.

b) he Equation for beef steak tomatoes is 4/5 x (portion of tomatoes).

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

Portion of Garden have Tomatoes = 2/3

and, 4/5 of the tomato plants are beefsteak tomatoes.

a) The total section in model is 15.

so, Tomatoes in the garden = 2/3 x 15

                                               = 10

and, the portion of the garden is made up of beef steak tomatoes

= 10 x 4/5

= 8 portion.

b) The Equation for beef steak tomatoes

= 4/5 x (portion of tomatoes)

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Answer:

d. [tex]90^{\circ}[/tex]

Step-by-step explanation:

This is the definition of perpendicularity.

The total displacement made by her to go from home to the school is given by the sum of the distances of P to Q, Q to R and then R to S.

The total displacement is obtained as the distance that she walks to go to the school from her home.

The check-points that she passes to go to the school are given as follows:

Hence the total displacement is given by the sum of each of these distances.

These distances are calculated using the formula for the distance between two points, given as follows:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

In which [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the coordinates of each point.

The problem is incomplete, hence the answer is given in general terms.

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