Andre wants to make an open box by cutting out corners of a 22 inch by 28 inch poster board and then folding up the sides. The volume V(x) in cubic inches of the open top box is a function of the side length x in inches of the square cutouts. Write and expression for v(x)

Answer:

16

Step-by-step explanation:

Step 1: Start by setting it up with the divisor 2 on the left side and the dividend 32 on the right side.

Step 2: The divisor (2) goes into the first digit of the dividend (3) 1 time(s). therefore, put 1 on top.

Step 3: Multiply the divisor by the result in the previous step (2 x 1 = 2) and write that answer below the dividend.

Step 4: Subtract the result in the previous step from the first digit of the dividend (3-2=1) and write the answer below.

Step 5: Move down the 2nd digit of the dividend (2)

Step 6: The divisor (2) goes on into the bottom number (12), 6 time(s). Therefore, put 6 on top.

Step 7: Multiply the divisor by the result in the previous step (2 x 6 = 12) and write that answer at the bottom.

Step 8: Subtract the result in the previous step from the number written above it. (12-12=0) and write the answer at the bottom.

That is it.

After Dividing 33 by 2 using long division method we get,

quotient = 16 and remainder = 1

Here we have to divide,

33 by 2 through long division method,

Since we know that,

In mathematics, long division is the procedure of dividing big numbers into smaller groups or sections. It is beneficial to divide a difficulty into small and straightforward steps. Dividends, divisors, quotients, and remainders are all part of the long divisions. The dividend in a long division problem is the enormous number that is divided by another integer known as the divisor. The quotient is the outcome of the division, while the remainder is the extra quantity that cannot be divided.

Therefore, proceed the long division,

2 ) 33 ( 16

  - 2

 _____

    1 3

  - 1 2

________

       1

Hence, After long division we get,

quotient = 16 and remainder = 1

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Answer:

4x-12 or 4(x-3)

Step-by-step explanation:

9x+9+2x-7(3+x)

9x+2x+9-21-7x

11x-12-7x

11x-7x-12

4x-12

Answer:

5 because 250 ÷50 equals 5

Step-by-step explanation:

Because its says she took out 50 each week and you divide by 250 by 50 and 50 represents out of her savings account and which equals 5 because the number of weeks and and she had 250 in there 5 weeks ago and she took 50 out each week so its 5 weeks

Answer:

8

Step-by-step explanation:

Answer:

8,10 and 12

Step-by-step explanation:

The numbers are

(x-2)* (x-4)  = x^ -64

Diistributive

x^-4x-2x+8 = x^-64

Subtract x^ on both sides (It will be cancelled)

-6x+8 = -64

Subtract 8 on both sides

-6x=-72

Divide both sides by -6

x=12

12-2=10

12-4=8

 8*10=80                     12*12=144            144-80=64

80+64=144

Answer:

B is the correct answer, as x - 2 in the exponent would move the graph to the right 2.

Answer:

C. 6

Step-by-step explanation:

Constant of Proportionality means the unit rate, but just the number. So to find it would be 1 car has 6 people. So the C.o.p would be 6.

Answer:

The answer is x = -17/6.

Step-by-step explanation:

Given:

5 1/3 + x = 2 1/2 . Using least common denominator.

Now, to solve the equation:

[tex]5\frac{1}{3}+x=2\frac{1}{2}[/tex]

[tex]=\frac{16}{3} +x=\frac{5}{2}[/tex]

Subtracting both sides from 16/3 we get:

[tex]x=\frac{5}{2}- \frac{16}{3}[/tex]

Now, the least common denominator of 2 and 3 is 6.

So, we using this we calculate:

[tex]x=\frac{5\times 3-16\times 2}{6}[/tex]

[tex]x=\frac{15-32}{6}[/tex]

[tex]x=\frac{-17}{6}[/tex]

Therefore, the answer is x = -17/6.

Answer:

Number of Adult's tickets sold on Saturday = 3,356

Number of Children's tickets sold on Saturday = 2, 928

Total number of tickets sold over these two days is 8,938.

Step-by-step explanation:

Here, the number of tickets sold on FRIDAY:

Adult Ticket sold = 1,678

Children's Tickets sold = 976

So, the total number of tickets sold on Friday  

= Sum of ( Adult + Children's ) tickets  = 1,678  + 976 = 2,654 ....  (1)

The number of tickets sold on SATURDAY:

Adult Ticket sold =   2 times as many as the number of adult tickets sold

on Friday

=  1,678 x 2  = 3,356

Children's Tickets sold = 3 times as many as the number of children's

tickets sold on Friday.

=  976  x 3 = 2, 928

So, the total number of tickets sold on Saturday  

= Sum of ( Adult + Children's ) tickets  = 3,356 + 2,928 = 6, 284 ....  (2)

Now, the total number of tickets booked in these two days :

Sum of tickets booked on (Friday + Saturday)

= 2,654 +  6, 284  =   8,938

Hence, total number of tickets sold over these two days is 8,938.

Answer:

(- 10, 5 )

Step-by-step explanation:

Given the 2 equations

5x + 12y - 10 = 0 ( add 10 to both sides )

5x + 12y = 10 → (1)

2x - 3y + 35 = 0 ( subtract 35 from both sides )

2x - 3y = - 35 → (2)

Multiplying (2) by 4 and adding to (1) will eliminate the y- term

8x - 12 y = - 140 (3)

Add (1) and (3) term by term

5x + 8x + 12y - 12y = 10 - 140, that is

13x = - 130 ( divide both sides by 13 )

x = - 10

Substitute x = - 10 into either (1) or (2) and solve for y

Substituting in (1)

5(- 10) + 12y = 10

- 50 + 12y = 10 ( add 50 to both sides )

12y = 60 ( divide both sides by 12 )

y = 5

Solution is (- 10, 5 )

Answer:

1/3 of a bag of dog food last will last for [tex]\frac{1}{6}[/tex]

Step-by-step explanation:

Given:

Number of  dog bag food used per day by Monroe Pet Store to feed the dog= 2

To find:

Number of days  1/3 of a bag of dog food last=?

Solution:

Let the number days for which the [tex]\frac{1}{3}[/tex] of bag of food lasts be x

For one day= 2 bags

for x days = [tex]\frac{1}{3}[/tex]

By cross multiplication method

[tex]2x=\frac{1}{3}[/tex]

[tex]x=\frac{\frac{1}{3}}{2}[/tex]

[tex]x=\frac{1}{3}\times\frac{1}{2}[/tex]

[tex]x=\frac{1}{6}[/tex]

Answer:

Add 7 black beads

Step-by-step explanation:

Since we can only change the number of black beads, decide how many black beads you will add based on how many white beads there are.

There are three white beads in the picture.

Total beads we will have (b meaning black)     b : 3

                                  Ratio black : white beads 3 : 1

Use the common ratio, which is a number that both sides of the original ratio multiply by to get to the new ratio.

Find common ratio by dividing total by ratio white beads: 3/1 = 3

Multiply ratio black beads by common ratio. 3 X 3 = 9

We need 9 black beads in total.

Check answer

9 : 3     Both sides divisible by 3; reduce ratio

= 3 : 1        Correct ratio

There will be a total of 9 black beads, but we already have 2 black beads:

(9 total) - (2 original) = (7 to add)

Therefore we need to add 7 black beads.

To make the ratio of black to white beads 3:1, you need to add 1 more black bead.

To make the ratio of black to white beads 3:1, we need to determine how many more black beads need to be added. Currently, the ratio is 2:3, which means for every 2 black beads, there are 3 white beads. Let's say we have 2x black beads and 3x white beads. To make the ratio 3:1, we need to have 3 black beads for every 1 white bead. This means we need to add x more black beads. Setting up the equation 2x + x = 3(3x), we can solve for x to find out how many more black beads are needed.

Simplifying the equation, we get 2x + x = 9x. Combining like terms, we have 3x = 9x. Subtracting 3x from both sides, we get 0 = 6x. Dividing both sides by 6, we find that x = 0. Since we need an integer value for x, it means we need to add 1 more black bead to make the ratio 3:1.

Therefore, you need to add 1 more black bead to make the ratio of black to white beads 3:1.

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Sin is negative where as cos is positive in the 4th quadrant.

Step-by-step explanation:

Sin, cos and tan are all positive in the 1st quadrant. Sin is only positive in the 2nd quadrant. Tan is only positive in the 3rd quadrant.Cos is only positive in the 4th quadrant.

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Keywords: graphs, sin, cos, quadrant

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The graphs of sin and cos, while similar in shape and period, are shifted horizontally due to their phase difference. This directly affects their signs in different quadrants, revealing their interconnected nature and dependence on the unit circle representation.

Similarities in Graphs:

Shape: Both sine and cosine graphs share the same sinusoidal wave pattern, meaning they oscillate up and down between their maximum and minimum values.

Period: Both functions have the same period of 2π radians or 360 degrees, meaning they complete one full cycle within this interval.

Amplitude: Both have an amplitude of 1, meaning they oscillate between -1 and 1 on the y-axis.

Shift and Relationship between Signs:

Phase Shift: The cosine graph is essentially the sine graph shifted to the left by π/2 radians (or 90 degrees). This explains why their peaks and troughs don't coincide perfectly.

Signs in Quadrants: This phase shift plays a crucial role in determining the signs of sin and cos in different quadrants:

Quadrant I (0° to 90°): Both sin and cos are positive as they increase in value.

Quadrant II (90° to 180°): Sin remains positive as it continues increasing, but cos becomes negative as it decreases.

Quadrant III (180° to 270°): Both sin and cos are negative as they decrease in value.

Quadrant IV (270° to 360°): Sin becomes positive as it increases, but cos remains negative as it continues decreasing.

Underlying Connection:

These relationships can be further explained by their definitions based on the unit circle:

Sine: sin(θ) represents the y-coordinate of a point on the unit circle when the angle θ is measured from the positive x-axis counterclockwise.

Cosine: cos(θ) represents the x-coordinate of the same point.

Therefore, as θ moves around the circle, the signs of sin and cos change based on their positions relative to the axes.

S = {1R, 2R, 2R, 4R, 5R, 6R, 1B, 2B, 3B, 4B, 5B, 6B, 1Y, 2Y, 3Y, 4Y, 5Y, 6Y}

Step-by-step explanation:

As there are 6 outcomes of die and 3 outcomes for spinner, the total sample space will have following elements:

n(S) = 6*3 = 18

Each outcome of die will combined with either of the colors

Let R stand for red color

Let B be for blue color

Let Y be for yellow color

So, the outcomes will be:

S = {1R, 2R, 2R, 4R, 5R, 6R, 1B, 2B, 3B, 4B, 5B, 6B, 1Y, 2Y, 3Y, 4Y, 5Y, 6Y}

Keywords: Sample space, Probability

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Answer:

A B C

X can't be equal to - 1

There are 2 answers: choice B and choice F

==========================================

Explanation:

Assuming the second "x+1" is all in the denominator, this will cancel with the first "x+1" in the numerator. I'm using the rule that x/x = 1 where x is nonzero.

What happens after the canceling is that f(x) = x-2. This is a linear equation with positive slope (the slope is 1).

The positive slope means the line goes up as we read it from left to right. As x gets larger, y does too. So we can say [tex]\text{ as } x \to \infty \text{ , } y \to \infty[/tex]

Going in reverse, as x heads off to negative infinity, y does the same as well. Therefore, [tex]\text{as } x \to -\infty \text{ , } y \to -\infty[/tex]

Below is the graph attached as an image to help visually verify the two answers. Note the hole at x = -1 which is due to the fact that this x value makes the original unsimplified version of f(x) to be undefined. Recall that we cannot divide by zero so x+1 cannot be equal to zero.

Answer:

x+2y

20 character minimum

Answer:

The sum of x and twice y

x+2y

35

Step-by-step explanation:

The equation is in point slope form.

The slope is -3.

Answer:

[tex]9c^{8} -30c^{10} + 25c^{12}[/tex]

Step-by-step explanation:

We can use formula (a-b)² = a² -2ab + b².

In our example a = 3c^4 and b = 5c^6

[tex](3c^{4} - 5c^{6})^{2} = [3c^{4} ]^{2} - 2*3c^{4} *5c^{6} + [5c^{6}]^{2}=\\=9c^{8} -30c^{10} + 25c^{12}[/tex]

Expanding and combining the like terms, the expression becomes [tex]9c^{8} - 30c^{10} + 25c^{12}[/tex] .

Given expression is [tex](3c^{4} - 5c^{6} )^{2}[/tex] .

Using Formula -  [tex](a - b)^{2}[/tex]  = [tex]a^{2} - 2ab + b^{2}[/tex]

Expanding the expression, we have -

[tex]9c^{8} - 2*3c^{4}*5c^{6} + 25c^{12}[/tex] [Using the above hypothesis]

[tex]9c^{8} - 30c^{10} + 25c^{12}[/tex]  

As we can see that there is no like terms or common terms in the expansion of the equation, thus we have the final expression as [tex]9c^{8} - 30c^{10} + 25c^{12}[/tex] .

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Answer:

f(x)<=-1/3x+1

Step-by-step explanation:

so to test this you can do

0<=-1/3(0)+1

0<=1

so it's true

Answer:

y [tex]\leq[/tex] [tex]\frac{-1}{3}x[/tex] + 1

Step-by-step explanation:

To find the inequality represented by the graph, we need to find the linear equation that represents the blue line.

As we can see, the:

y intercept: (0, 1)

x intercept: (3, 0)

So the slope of the equation is:

[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

= [tex]\frac{0-1}{3-0}[/tex] = [tex]\frac{-1}{3}[/tex]

So use the slope and the slope-point formula, we find the linear expression

The standard form is: y = mx+ b

<=> y = [tex]\frac{-1}{3}[/tex] x + b

Substitute the point (0, 1) to find b, we have:

b= y - [tex]\frac{-1}{3}[/tex] x

<=> b= 1 - 0 =1

So the linear equation is: y = [tex]\frac{-1}{3}[/tex] x + 1

After that, we need to take a test point form the shaded area and evaluate the expression. Let the point be: (1, 2), we have:

2 = [tex]\frac{-1}{3} *1[/tex] +1

<=> 2=[tex]\frac{2}{3}[/tex]

We know that 2 > [tex]\frac{-1}{3}[/tex]  this means that the left inequality sign is ≥ , so the  inequality represented by the graph:

y [tex]\leq[/tex] [tex]\frac{-1}{3}x[/tex] + 1

Answer: D

Step-by-step explanation:

The number of different 3-digit numbers you can make using the digits 5, 3 and 2 is 6

There are 3 different digits.

And each digit can only be selected once.

This means that the first number can be any of the three, the second number can be any of the remaining 2 and the last can be the last digit

So, we have:

Ways = 3 * 2 * 1

Evaluate

Ways = 6

Hence, the number of different 3-digit numbers you can make using the digits 5, 3 and 2 is 6

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To find a pricing option with the same unit price as 4 lemons for $0.79, we calculated the unit price per lemon as $0.1975. None of the provided pricing options match this unit price, as they are all significantly higher.

We need to determine the equivalent unit price per lemon to match the store's offer of 4 lemons for $0.79. First, we calculate the unit price for one lemon by dividing the total price of the bag by the number of lemons. So, $0.79 divided by 4 gives us a unit price of $0.1975 per lemon.

Now, let's use this unit price to check which pricing option results in the same unit price. We must find a scenario where each lemon costs $0.1975.

An access fee of $4 and a per-unit price of $4 with 2 units bought would have a unit price of $4, which is too high.

An access fee of $9 and a per-unit price of $4 with 3 units bought would also have a unit price of $4, again too high.

An access fee of $24 and a per-unit price of $3 with 4 units bought would have a unit price of $3, which is also higher than $0.1975.

For the bundle size of 4 units with a bundle price of $36, we would have a unit price of $9 ($36 divided by 4), which is much higher.

The scenario with an access fee of $32 and a per-unit price of $16 for 4 units is also incorrect since the unit price is $16.

None of the given pricing options have a per-unit price of $0.1975.

let x = the angle

let 2x = supplement of the angle

x + 2x = 180

3x = 180

x = 60

The angles measure is 60 degrees.

Hope this helps!

Answer:20000

Step-by-step explanation:

30+1000+4000

Answer:

25.36

Step-by-step explanation:

Answer:

[tex]\sqrt{x} 643.14=25.360205046489667529081701292151‬[/tex]

Step-by-step explanation:

Answer:

7 has the highest probability

Explanation:

When two dices are rolled simultaneously,

The possible outcomes are:

{1,1}, {1,2}, {1,3}, {1,4}, {1,5}, {1,6}

{2,1}, {2,2}, {2,3}, {2,4}, {2,5}, {2,6}

{3,1}, {3,2}, {3,3}, {3,4}, {3,5}, {3,6}

{4,1}, {4,2}, {4,3}, {4,4}, {4,5}, {4,6}

{5,1}, {5,2}, {5,3}, {5,4}, {5,5}, {5,6}

{6,1}, {6,2}, {6,3}, {6,4}, {6,5}, {6,6}

The sum of digits are

1 2 3 4 5 6 7

2 3 4 5 6 7 8

3 4 5 6 7 8 9

4 5 6 7 8 9 10

5 6 7 8 9 10 11

6 7 8 9 10 11 12

It is noted that 7 is common in every series,

therefore, 7 has the highest probability

Answer:

The solution in the attached figure

see the explanation

Step-by-step explanation:

we have

[tex]y < -\frac{1}{2}x+2[/tex]

The solution of the inequality is the shaded area below the dashed line

[tex]y=-\frac{1}{2}x+2[/tex]

The slope of the dashed line is negative [tex]m=-\frac{1}{2}[/tex]

The y-intercept of the dashed line is the point (0,2)

The x-intercept of the dashed line is the point (4,0)

using a graphing tool

The solution in the attached figure

Remember that

Any point that lie on the shaded area is a solution of the inequality and if a point is a solution of the linear inequality, then the point must satisfy the inequality

Answer:

Your answer choices are:

(2, 3)

(2, 1)

(3, –2)

(–1, 3)

Step-by-step explanation:

YOUR ANSWER IS

(3, -2)

I hope this helps!

Answer:

The answer is four.

Step-by-step explanation:

II + II= IIII

Answer:

the answer is 4

Step-by-step explanation:

if you have 2 candy bars and are given 2 more you will get 4

Answer:

20100 decimeters

Step-by-step explanation:

1 kilometer=10,000 decimeters

2 1/100=201/100

201/100*10,000=20100

Answer:

[tex]\large\boxed{2\dfrac{1}{100}\ kilometers=20100\ decimeters}[/tex]

Step-by-step explanation:

[tex]PREFIXES\\\\mega\ (M)=10^6\\\\kilo\ (k)=10^3\\\\hecto\ (h)=10^2\\\\deko\ (da)=10\\\\decy\ (d)=10^{-1}=0.01\\\\centi\ (c)=10^{-2}=0.01\\\\mili\ (m)=10^{-3}=0.001\\\\mikro\ (\mu)=10^{-6}=0.000001[/tex]

[tex]2\dfrac{1}{100}=2.01\\\\2\dfrac{1}{100}\ km=2.01\ km=2.01\cdot10000\ dm=20100\ dm\\\\1\ kilometers=10000\ decimeters[/tex]

Answer:

574

Step-by-step explanation:

All your doing is subtracting!

Answer:

Her mouth

right ?!

that was not hilarious but okey

Answer:

She forgot to shut her dum dum bubble gum chromosome flip phone no home smash mouth up.

Step-by-step explanation: