A company rents a storage unit. The unit is in the shape of a cube. The formula V=s^3 can be used to find the volume of a cube. Using the formula, determine the volume of the storage unit if the side length (s) is 7 feet.

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Explanation:

The old dimensions of the rectangle were 30 by 15.

The new dimensions are 30+x by 15+x, where x is some positive number.

The new rectangle dimensions multiply to 1000

(30+x)(15+x) = 1000

Use the FOIL rule to expand out the left side like so

(30+x)(15+x) = 1000

450+30x+15x+x^2 = 1000

450+45x+x^2 = 1000

x^2+45x+450

Then lets get everything to one side

x^2+45x+450 = 1000

x^2+45x+450-1000 = 0

x^2+45x-550 = 0

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From here we use the quadratic formula

Plug in a = 1, b = 45, and c = -550.

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(45)\pm\sqrt{(45)^2-4(1)(-550)}}{2(1)}\\\\x = \frac{-45\pm\sqrt{4225}}{2}\\\\[/tex]

[tex]x = \frac{-45\pm65}{2}\\\\x = \frac{-45+65}{2} \ \text{ or } \ x = \frac{-45-65}{2}\\\\x = \frac{20}{2} \ \text{ or } \ x = \frac{-110}{2}\\\\x = 10 \ \text{ or } \ x = -55\\\\[/tex]

Earlier we defined x to be a positive number. This means we ignore x = -55. It makes no sense to add on a negative amount to each dimension.

The only practical answer is x = 10.

So each dimension is increased by 10 feet.

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If x = 10, then the old dimensions of 30 by 15 bump up to 30+10 = 40 by 15+10 = 25

Then note how 40*25 = 1000, which helps confirm we have the correct dimensions.

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Now go back to the question at hand: we want to find the new width. The old width was 30 feet. The new width is 30+x = 30+10 = 40 feet

We know that four snacks and three movie tickets cost $40 dollars, and when you take away 2 snacks but still keep the tickets, its $32.

2 snacks= $8

What i did to find the cost of each ticket is I divided 8 by 2 (8/2) and ended getting $4

1 snack= $4

Now to find the cost of each ticket, i divided 2 snacks ($8) and got this equation:

32 - 8= 24

3 tickets= $24

Now to find the amount for each ticket, i divided 24 by 3 (24/3) and got the answer:

1 ticket= $8

Therefore, snacks are $4 and movie tickets are $8

Thank you! Btw can i please get brainly :3

Answer:

29

Step-by-step explanation:

I subtracted 65 from 36 since the question only gave me 2 numbers and a variable to use.

Step-by-step explanation:

c = 65 - 36

c = 29

C is 29 that is the answer

Answer:

multiply -7 by 6x and then multiply-7 by 7

-7(6x)-7(7)

-42x-49=-133

+49. +49

the 49 cancel out

-42x=-84

divide both sides by -42

-42x/-42=-84/-42

the -42 cancel out

leaving x=2 the negatives cancel out making it positive

Given:

Point A (4, -3) is translated 3 units horizontally and -5 units vertically, rotated 90° clockwise, reflected over the x-axis, and dilated by a factor of 5.

To find:

The rule and coordinates of A'.

Solution:

Let a point be P(x,y).

If a point translated 3 units horizontally and -5 units vertically, then

[tex]P(x,y)\to P_1(x+3,y-5)[/tex]

Then, rotated 90° clockwise.

[tex](x,y)\to (y,-x)[/tex]

[tex]P_1(x+3,y-5)\to P_2(y-5,-(x+3))[/tex]

Then, reflected over the x-axis.

[tex](x,y)\to (x,-y)[/tex]

[tex]P_2(y-5,-(x+3))\to P_3(y-5,x+3)[/tex]

Dilated by a factor of 5.

[tex](x,y)\to (5x,5y)[/tex]

[tex]P_3(y-5,x+3)\to P'(5(y-5),5(x+3))[/tex]

[tex]P_3(y-5,x+3)\to P'(5y-25,5x+15)[/tex]

So, the rule of transformation is

[tex](x,y)\to (5y-25,5x+15)[/tex]

We have a point A(4,-3). So, put x=4 and y=-3.

[tex]A(x,y)\to A'(5(-3)-25,5(4)+15)[/tex]

[tex]A(x,y)\to A'(-15-25,20+15)[/tex]

[tex]A(x,y)\to A'(-40,35)[/tex]

Therefore, the coordinate of point A' are (-40,35).

Step-by-step explanation:

Since Angle DAE = Angle BCE, lines AD amd BC are parallel (by Z-angles).

This means that Angle ADE = Angle CBE (by Z-angles).

We have 2 congruent angles and 1 congruent side (AD = BC, given).

By ASA congruence, triangles AED and CEB are congruent.

B.P. Mathur v. Union Of India

Answer:

0.857 weeks

Step-by-step explanation:

Using the information provided we can create the following equations for the total amount Mallory (M) and Aimee (A) will save after x number of weeks...

M = 35 + 15x

A = 5 + 50x

Now we would need to make both of these equations equal one another and solve for x to calculate after how many week both Aimee and Mallory will have saved the same amount of money

35 + 15x = 5 + 50x  ... subtract 5 and 15x from both sides

30 = 35x  ... divide both sides by 35

[tex]\frac{30}{35}[/tex] or 0.857 = x

Finally, we can see that after 0.857 weeks both Mallory and Aimee will have saved the same amount of money.

*** The process provided is correct but I believe that the actual values for Aimees savings should be $50 and plans to save $5 a week, this would make the final result 1.5 weeks which would make more sense***

Answer:

c = 88

Step-by-step explanation:

c/88 = 44/19

19×c = 44×38

19c = 1672

c = 88

Answer:

B

Step-by-step explanation:

The pattern is x/-3

Answer:

The equation of the linear relationship is y = 3x + 2 ⇒ B

Step-by-step explanation:

To solve the question substitute the x in the equation by the x-coordinate of each point to find y, if y equals the y-coordinate of the point, then the point is on the graph of the equation

A.

∵ y = 2x + 3

→ Use the first point (0, 2)

∵ x = 0

→ Substitute x by 0 in the equation

∴ y = 2(0) + 3

∴ y = 0 + 3 = 3

∵ The y-coordinate is 2

∴ The point (0, 2) does not lie on the graph of the relationship

∴ The equation y = 2x + 3 doesn't represent the equation of the relationship

B.

∵ y = 3x + 2

→ Use the first point (0, 2)

∵ x = 0

→ Substitute x by 0 in the equation

∴ y = 3(0) + 2

∴ y = 0 + 2 = 2

∵ The y-coordinate is 2

∴ The point (0, 2) lies on the graph of the relationship

→ Use the second point (1, 5)

∵ x = 1

→ Substitute x by 1 in the equation

∴ y = 3(1) + 2

∴ y = 3 + 2 = 5

∵ The y-coordinate is 5

∴ The point (1, 5) lies on the graph of the relationship

→ Use the third point (3, 11)

∵ x = 3

→ Substitute x by 3 in the equation

∴ y = 3(3) + 2

∴ y = 9 + 2 = 11

∵ The y-coordinate is 11

∴ The point (3, 11) lies on the graph of the relationship

→ Use the fourth point (2, 7)

∵ x = 2

→ Substitute x by 2 in the equation

∴ y = 3(2) + 2

∴ y = 6 + 2 = 8

∵ The y-coordinate is 7

∴ The point (2, 7) doesn't lie on the graph of the relationship

∴ The equation of the linear relationship is y = 3x + 2

Answer:

x+9

Step-by-step explanation:

I got it right on the quiz

Answer: Option B.

Step-by-step explanation:

A linear function can be written as:

y = a*x + b

where a is the slope and b is the y-intercept.

if the line passes through the points (ax, ay) and (bx, by) then the slope is:

a = (bx - ax)/(by - ay)

In this case, we can see that the line passes through the points:

(1, 3) and (2, 1)

Then the slope is:

a = (1 - 3)/(2 - 1) = -2

y = -2*x + b

In the graph we also can see that the line intersects the y-axis at y = 5, then b = 5.

The line is:

y = f(x) = -2*x + 5.

the inverse function is such that:

g( f(x)) = x

to find the inverse function of a linear equation, we just could isolate x.

y - 5 = -2x

-y/2 + 2.5 = x

Then we could write the inverse function as:

g(x)  = - x/2 + 2.5

Now we need to see which pairs belong to this line. I just will evaluate the function g(x) in different values of x, and see which points belong to the line.

g(9) = -9/2 + 2.5 = -4.5 + 2.5 = -2

(9, -2) belongs to the line.

g(7) = -7/2 + 2.5 = -3.5 + 2.5 = -1

Then (7, -1) belongs to this line.

g(5) = -5/2 + 2.5 = 0

Then the point (5, 0) belong to this line.

We can already see that all these points are in option B, then option B is the correct one.

Answer:

A or B

Step-by-step explanation:

Also i need help to

Answer:

A. [tex]\sqrt{16}[/tex] × [tex]\sqrt{4}[/tex]  

I hope this helps!

Answer:

k = 4

Step-by-step explanation:

The formula for binomial probability distribution is;

P(X = k) = C(n, k) × p^(k) × (1 - p)^(n - k)

Where C(n, k) is the number of possible ways that n number of people choose k.

While p is probability of success

In this question, 20 children want to choose from 4 toys namely tricycle, blocks, a train set, and puzzles.

This means that from binomial probability distribution formula, n = 20 and k = 4.

Given:

A line is perpendicular to the given line and having negative slope.

To find:

The slope of the line.

Solution:

We know that, product of slopes of two perpendicular lines is -1.

[tex]m_1\cdot m_2=-1[/tex]

[tex]m_1=-\dfrac{1}{m_2}[/tex]

It means, one slope is opposite and reciprocal of other.

Slope formula:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

From the given graph it is clear that, blue line passes through (0,3) and (2,4). So, slope of blue line is

[tex]m_B=\dfrac{4-3}{2-0}[/tex]

[tex]m_B=\dfrac{1}{2}[/tex]

The slope of blue line is [tex]\dfrac{1}{2}[/tex]. So, slope of the line which is perpendicular to the blue line is -2, which is negative.

From the given graph it is clear that, red line passes through (0,4) and (4,3). So, slope of red line is

[tex]m_R=\dfrac{3-4}{4-0}[/tex]

[tex]m_R=\dfrac{-1}{4}[/tex]

The slope of blue line is [tex]-\dfrac{1}{4}[/tex]. So, slope of the line which is perpendicular to the blue line is 4, which is positive.

Therefore, the slope of the line which is perpendicular to the given line and having negative slope, is -2.

Answer:

the answer is 12k²r¹⁴.........

Answer:

81

Step-by-step explanation:

area of top triangle = 1/2 x 8 x 9 = 36

area of rhombus = 9 x 5 = 45

sum of areas = 81

Answer:

a. are for the same time period

Answer:

[tex]x=12(\sqrt2-1)[/tex]

Step-by-step explanation:

The given equation is :

[tex]\sqrt{2} x-7+x=5[/tex]

Add 7 to both sides of the equation.

[tex]\sqrt{2} x-7+x+7=5+7\\\\\sqrt{2} x+x=12[/tex]

Taking x common from both sides of the equation.

[tex]x(\sqrt{2} +1)=12\\\\x=\dfrac{12}{\sqrt2+1}[/tex]

Multiplying both numerator and denominator by [tex]\sqrt2-1[/tex]

[tex]x=\dfrac{12}{\sqrt2+1}\times \dfrac{\sqrt2-1}{\sqrt2-1}\\\\=\dfrac{12(\sqrt2-1)}{2-1}\\\\=12(\sqrt2-1)[/tex]

Hence, the value of x is [tex]12(\sqrt2-1)[/tex].

Answer:

take one finger and than the other and how may fingers do you have now 2

Responder:

$ 131.25

Explicación paso a paso:

Dado que :

Importe pagado tras sucesivos descuentos del 10% y 20%

Sea el costo original = x

Importe final tras ambos descuentos = 94,5

Primer descuento = (1 - 0.1) x = 0.9x

Segundo descuento: (1 - 0.2) de 0.9x = 0.8 de 0.9x = 94.5

Es decir ; 0,8 * 0,9x = 94,50

0,72x = 94,50

Dividir ambos lados por 0,72

0,72x / 0,72 = 94,50 / 0,72

x = 131,25

Por lo tanto, precio original = $ 131.25

Answer:

The number of clay flower pots = x = 19

The number of ceramic flower pots = y = 16

Step-by-step explanation:

Let

The number of clay flower pots = x

The number of ceramic flower pots = y

Tara bought 35 flower pots

= x + y = 35

x = 35 - y

The gardening store sells clay flower pots, which hold 2 litres of dirt, and ceramic flower pots, which hold 7 litres. Tara bought 35 flower pots, which will hold a total of 150 litres of dirt.

Hence:

2x + 7y = 150.... Equation 2

Substitute 35 - y for x in Equation 2

2 (35 - y) + 7y = 150

70 - 2y + 7y = 150

-2y + 7y = 150 - 70

5y = 80

y = 80/5

y = 16 flower pots

x = 35 - y

x = 35 - 16

x = 19 flower pots

The number of clay flower pots = x = 19

The number of ceramic flower pots = y = 16

Answer:

The number of clay flower pots = 19

The number of ceramic flower pots = 16

Step-by-step explanation:

Answer:

the first one

Step-by-step explanation:

☺️☺️☺️☺️☺️☺️☺️☺️☺️☺️

Answer:

8 pounds

Step-by-step explanation:

3 ft board = 2lb

12 ft board is 4 times more so

2x4 = 8 lb

Answer:

y= -5/1 + 1.90

Step-by-step explanation:

The y-intercept is hard to tell

But the rest is right

Answer:

I have a picture if that helps

Step-by-step explanation:

Answer:

y=-7x-2

Step-by-step explanation:

I assume you need the equation for the line, so that's what I'm solving for here.

1. Start by putting the slope and the coordinates into point slope form, which is y-y1=m(x-x1)

y+30=-7(x-4)

2. Distribute -7 to (x-4) (or multiply x and -4 by -7).

y+30=-7x+28

3. Subtract 30 from both sides to get y by itself.

y=-7x-2

Answer:

180 degrees

Step-by-step explanation: