Use the Binomial Theorem and Pascal’s Triangle to write each binomial expansion.

_ (2x-3)^3

HELP ASAP

Answer: 6 hours

Step-by-step explanation:

Given : The time taken by Company X to install chairs : [tex]t_1=10\text{ hours}[/tex]

The time taken by Company Y to install chairs : [tex]t_2=15\text{ hours}[/tex]

Then , the time taken (T) by both of them to install the chairs if they work together is given by :-

[tex]\dfrac{1}{T}=\dfrac{1}{t_1}+\dfrac{1}{t_2}\\\\\Rightarrow\ \dfrac{1}{T}=\dfrac{1}{10}+\dfrac{1}{15}\\\\\Rightarrow\dfrac{1}{T}=\dfrac{10}{60}\\\\\Rightarrow\ T=6[/tex]

Hence, it will take 6 hours to the two companies if they working together .

Answer:

1.39x=15

Step-by-step explanation:

each song is worth 1.39 dollers

If there are x songs, the total value would be 1.39x

1.39x=15

Answer:

Mercedes can download new songs for $1.39 each. Write an equation to show how many songs she can download for $15.00.  

15x = 1.39

15 + x = 1.39

1.39x = 15

1.39 + x = 15

Step-by-step explanation:

The equation is the following:

1.39x = 15

15 $ is what you have to download the songs, and each unit is 1.39 $, by clearing the X of the equation, it is 15 / 1.39, and the result is the number of songs that Mercedes can download.

Answer:

8x-6x=-18

8x-6x=2x

2x=-18

-18/2=-9

x=-9

Step-by-step explanation:

Answer:

C)

Explanation:

Movement along a vector is compared by adding, subtracting, multiplying, or dividing the values respectively.

Answer:

5/75 in my opinion. 75 is total of hot drink

Step-by-step explanation:

Answer:

A. Draw line segment AB

Step-by-step explanation:

Please mark brainliest and have a great day!

Answer:

B

Step-by-step explanation:

The Guy Above Got It Wrong On The Exam.

Answer:

Option C.

Step-by-step explanation:

In the given triangles XWV and XYZ we have to prove both the triangles are congruent.

Since side VW ≅ side YZ (Given)

∠WVX ≅ ∠XYZ (Given)

And by AAS theorem, we should prove ∠VXW = ∠YXZ

Since AAS theorem says, if two adjacent or corresponding angles and one opposite side of these angles are equal then the given triangles will be congruent.

Therefore, Option C. will be the answer.

Answer:

Prove that VXW TO YXZ by vertical angles

Answer:

Here's what I get.

Step-by-step explanation:

Part A. Equation in standard form

The question is asking you to find the equation of a straight line that passes through two points

Let x = the number of days

and y = the cost

Then the coordinates of the two points are (2,225) and (5,480).

(i) Calculate the slope of the line

[tex]\begin{array}{rcl}m & = & \dfrac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\& = & \dfrac{480 - 225}{5 - 2}\\\\& = & \dfrac{255}{3}\\\\& = & 85\\\end{array}[/tex]

In other words, the daily rental is $85/day.

(ii) Calculate the y-intercept

[tex]\begin{array}{rcl}y & = & mx + b\\480 & = & 85 \times 5 + b\\480 & = & 425 + b\\b & = & 55\\\end{array}[/tex]

(iii) Write the equation for the line

y = 85x + 55

That is, the cost is $55  plus $85/day

Part B. Equation in function notation

Replace y with ƒ(x)

ƒ(x) = 85x + 55

Part C. Graphing

Let's say you want to plot a graph of the rental cost for up to ten days.

(i) Calculate two points on the graph.

When x = 0, y = 85; when x = 10, y = 905.

(ii) Scale your axes

A good number of intervals is about ten.

Your x-axis should have tick marks at 1-day intervals.

Your largest y-value is 905. Ten intervals would make about $90/interval. However, you should round that up to $100/interval for easy interpolation.

Your y-axis will run from 0 to $1000 in $100 intervals.

Plot your two points and draw a straight line through them.

(iii) Axis labels

x represents the number of days, so the label on the x-axis could be "No. of days."

y represents the cost of renting the boat, so the label on the y-axis could be "Rental cost."

Your graph should resemble the one below.

Answer:

I believe it's A.

Step-by-step explanation:

Because look at the parts: The number x /  is equal to / another number n / plus / the square root of 3.

Hope my answer has helped you!

For this case we must express in an algebraic way the following expression:

"The number x is equal to another number n plus the square root of 3"

So:

The same "x" number is represented as:

[tex]x =[/tex]

A number "n" plus the square root of three is represented as:

[tex]n + \sqrt {3}[/tex]

So, the complete expression is:

[tex]x = n + \sqrt {3}[/tex]

Answer:

Option A

Answer:

7.08

Choice A

Step-by-step explanation:

From the right-angled triangle we have been given the following;

One angle - 33 degrees

The hypotenuse - 13 units

We are required to determine the length of the side, opposite the angle, marked x.

Using the Mnemonic; SOHCAHTOA

The sine of an angle is; (opposite side)/(hypotenuse)

Therefore;

sin 33 = x/13

x = 13 * sin 33

x = 7.080

Answer: A

Step-by-step explanation:

[tex](0. \infty)[/tex]

Since this is a logarithmic function, the domain is [tex](0. \infty)[/tex]. But what is the domain of a function? The domain of a function is the set of inputs. This is so, because for any logarithmic function[tex]y=log_{a}(x)[/tex], x must be greater than 0. So this function is continuous and has an x-intercept at [tex](1,0)[/tex], and y increases as x increases. Finally, its graph is shown below.

Answer:

P (−11, 13), Q (−17, −19), R (23, 27)

Step-by-step explanation:

we know that

The reflection of a figure across the x-axis has the following rule

(x,y) -----> (x,-y)

so

P(-11,-13) -----> P(-11,13)

Q(-17,19) -----> Q(-17,-19)

R(23,-27) ----> R(23,27)

Answer:

P (−11, 13), Q (−17, −19), R (23, 27)

Step-by-step explanation:

Got it right on my test :)

Answer:

Step-by-step explanation:

(–1)8 + (–1)7 + –16 + –14 – (–1)2 = -8 -7 -16 -14 +2 = -45+2 = - 43

Answer: Hiking was most prefered between ages 20-29

Answer:

Step-by-step explanation:

Given that a survey asked two age groups which summer sport they most preferred. the results are shown in the table below.

We have to find which sport was most preferred by people by ages 20-29 and what is the relative frequency within this age group

From the table we find that age group 20-29 prefers s

ski        15           [tex]\frac{15}{268}[/tex]

Swim    88          [tex]\frac{88}{268}[/tex]

Kayak   42          [tex]\frac{42}{268}[/tex]

Hike    123          [tex]\frac{123}{268}[/tex]

Total   268          1

We find that hike liking are more in this age group

Relative frequency calculated as frequency/268 is shown above.

Answer:

the zeros are -3,-1, and 1

Step-by-step explanation:

zeros are nothing more that where the function crosses or touches the x-axis

Answer: Third Option

-3, -1, 1

Step-by-step explanation:

By definition, the zeros of a function f(x) are all the values x for which f(x) = 0.

In other words, the zeros of a function f(x) are the intersections of the graph of f(x) with the axis of x.

Therefore, to identify the zeros of the function shown, identify the values of x in which the graph intersects the horizontal axis.

You can see in the graph that these intersections occur in

[tex]x = -3\\x = -1\\x = 1[/tex]

Finally the zeros are: -3, -1, 1

The polynomial remainer theorem says that a polynomial [tex]p(x)[/tex] leaves a remainder of [tex]p(c)[/tex] when divided by [tex]x-c[/tex]. When [tex]x=2[/tex], we have

[tex]2x^3+ax^2+3x-5=4a+17[/tex]

[tex]x^3+x^2-2x+a=a+8[/tex]

Both operations leave the same remainder, which means

[tex]4a+17=a+8\implies3a=-9\implies\boxed{a=-3}[/tex]

Then the remainders are both 5.

A function means that each x can only have one y-value

B, C, and D are NOT functions because they have x-values that have multiple y-values.

For example

B. has two values for -4:

(-4, 8) and (-4, -8)

C. has two values for 9:

(9, -1) and (9, 2)

D. has two values for 5:

(5, -7) and (5, 9)

This makes A. the only function

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Area = x + 3 + [tex]\frac{2}{5x}[/tex]

Step-by-step explanation:

Volume = 5x² + 15x + 2

Height = 5x

Area = Volume ÷ Height

Area = 5x²/5x + 15x/5x + 2/5x

Area = x + 3 + 2/5x

Answer:

x+3+2/5x

Step-by-step explanation:

Answer:

B: Exponential decay

Step-by-step explanation:

Answer:

exponential decay

Step-by-step explanation:

[tex]f(x)= 2(\frac{1}{2})^x[/tex]

[tex]f(x)= ab^x[/tex] is an exponential function, where 'a' is the initial value and 'b' is the exponential factor

When the value of 'b' is between 0 and 1 then it is exponential decay

when the value of 'b' is greater than 1 then it is an exponential growth

In the given exponential function , the value of b is 1/2 that is 0.5

The value of 'b' is between 0 and 1 so it is an exponential decay

Answer:

The answer to your problem is 13%

There are 4 male freshmen and 30 students total.

Divide the amount of male freshmen by the amount of students and turn it into a percentage.

4/30= 0.1333 = 13%

Answer:

Step 1: Factor left side of equation.

(5x−1)(3x−5)=0

Step 2: Set factors equal to 0.

5x−1=0 or 3x−5=0

x=

1 /5

or x=

5 /3

Answer:::::::::

x=5/3 or x=1/5

Answer:

(6, 3)

Step-by-step explanation:

Given the 2 equations

3x + 6y = 36 → (1)

3x - 6y = 0 → (2)

Add the 2 equations term by term to eliminate the y- term

(3x + 3x) + (6y - 6y) = (36 + 0)

6x = 36 ( divide both sides by 6 )

x = 6

Substitute x = 6 into either of the 2 equations and solve for y

(1) : 18 + 6y = 36 ( subtract 18 from both sides )

6y = 18 ( divide both sides by 6 )

y = 3

Solution is (6, 3)

Answer:

the solution is (6, 3)

Step-by-step explanation:

Subtract the second equation from the first, as indicated:

 3x+6y=36

-( 3x-6y=0)

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

      12y = 36.  Then y = 36/12 = 3.  

Subbing 3 for y in the second equation, we get 3x - 6(3) = 0, or 3x = 18, or x = 6.

Thus, the solution is (6, 3).

Answer:

540 degrees

Step-by-step explanation:

We can find the sum of the interior angles by using the formula (n - 2) * 180.

n: represents the total number of angles in the polygon

We can determine that polygon contains 5 angles, which means you would substitute the n variable with. Then you would simply follow the order of operation (ex: parentheses first, multiplication next, etc.) to find our answer.

(5 - 2) * 180

Solve the contents inside the parentheses first, as mentioned above.

(5 - 2) * 180

(5 - 2) = 3

So, we are left with

3 * 180

Now you'd multiply 3 * 180 and the product of that represents the sum of the measures of the interior angles of the polygon.

3 * 180 = 540

In conclusion, the sum of the measures of the interior angles is 540 degrees.

Answer:

540

Step-by-step explanation:

Answer:

Answer: The Answer Is B

Answer:

I think is D is the best answer

Answer:

1

Step-by-step explanation:

To evaluate (g ￮ f)(0), substitute x = 0 into f(x) then substitute the value obtained into g(x), that is

f(0) = 5(0) + 1 = 0 + 1 = 1, then

g(1) = 1³ = 1

Answer:

31 aces

Step-by-step explanation:

To find the number of aces you would expect, take the probability of an aces and multiply by the number of tries

1/13 * 400 =30.76923

Rounding up, approximately 31 aces

Answer:

30 times

Step-by-step explanation:

1/3 * 400

30.76923

31 times

Answer:

8 * 2

Step-by-step explanation:

When you draw the rectangle make it an 8 units by 2 units rectangle.

Answer:

x=13°

Step-by-step explanation:

If BE is an angle bisector, then it divides the angle into two equal angles. This means that

∠ABE=∠EBC

Since ∠ABE=2x+20 and ∠EBC=4x-6, we have

2x+20=4x-6

2x-4x=-6-20

-2x=-26

2x=26

x=13°

Answer:

a. 50 mph.

b. 16 mph.

Step-by-step explanation:

Convert minutes to hours using dimensional analysis:

[tex]\displaystyle \rm 24 \; minutes \times \frac{1\; hour}{60\; minutes} = \frac{2}{5}\; hours[/tex].

Average speed is distance traveled over time taken:

[tex]\displaystyle \text{Average Speed} = \frac{\text{Distance Traveled}}{\text{Time Taken}} = \rm \frac{20\; miles}{\dfrac{2}{5}\; hours} = (20 \times \frac{5}{2})\; mph= 50\; mph[/tex].

Similarly,

[tex]\displaystyle \text{Time Taken} = \rm 75 \; minutes \times \frac{1\; hour}{60\; minutes} = \frac{5}{4}\; hours[/tex].

[tex]\displaystyle \text{Average Speed} = \frac{\text{Distance Traveled}}{\text{Time Taken}} = \rm \frac{20\; miles}{\dfrac{5}{4}\; hours} = (20\times \frac{4}{5})\; mph= 16\; mph[/tex].

Step-by-step explanation:

Use the distance formula:

d² = (x₂ − x₁)² + (y₂ − y₁)²

d² = (-3 − -12)² + (-8 − -11)²

d² = 9² + 3²

d² = 90

d = 3√10