Kadeem has a case for art supplies shaped like a rectangular prism. The volume of the case is 100 cubic inches, and it’s height is 5 inches

Witch table has values that could be the length and width of the case?

Answer:

25.46

Step-by-step explanation:

v = a^3 / 6√2

= 216/6√2 = 25.46

The rate of change for the interval between 2 and 6 on the x-axis is 3.

Given

On a coordinate plane, a parabola opens up.

Solid circles appear on the parabola at (negative 4, 14), (negative 3, 9. 5), (negative 2, 6), (0, 2), (1, 1. 5), (2, 2), (4, 6), (5, 9. 5), (6, 14).

A rate of change defines how one quantity changes in relation to another quantity.

The rate of change for the interval between 2 and 6 on the x-axis is;

[tex]\rm Rate \ of \ change =\dfrac{2-14}{2-6}\\\\Rate \ of \ change =\dfrac{-12}{-4}\\\\Rate \ of \ change =3[/tex]

Hence, the rate of change for the interval between 2 and 6 on the x-axis is 3.

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The total cost function is the sum of the two given functions, and this is equal to:

c(t) = 190 + 70*t

We know that:

If she hires both of them for the same time t, then the total cost function will be given by the sum of the two above functions, we will get:

c(t) = p(t) + e(t)

c(t) = (115 + 25*t) + (55*t + 75)

c(t) = (115 + 75) + (55*t + 25*t)

c(t) = 190 + 70*t

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Answer:

2/8 (Simplified to 1/4)

Step-by-step explanation:

There are 8 pieces to this, 2 of these 8 pieces are 6, and 3 which are both multiples of 3. So this gives you 2/8 but as you said you need it simplified so if you divide the top and bottom by 2 that gets you the answer of 1/4.

The equation of the circle in squared form is [tex]\rm (x + 6)^2 + (y + 1)^2 = 38[/tex]. Then the center of the circle is at (-6, -1).

It is a locus of a point drawn at an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.

The equation of the circle is given as

[tex]\rm x^{2} + y^2 + 12x +2y - 1 = 0[/tex]

This can be written as

[tex]\rm x^{2} + y^2 + 12x +2y = 1[/tex]

Add both sides 36 and 1, then

[tex]\rm x^{2} + 12x + 36 + y^2 +2y +1 = 1 + 36 + 1[/tex]

Then we know that

[tex]\rm (a+b) ^2 = a^2 + b^2 + 2ab[/tex]

Then

[tex]\rm (x + 6)^2 + (y + 1)^2 = 38[/tex]

Thus, the center of the circle is at (-6, -1).

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Answer:

answer in picture

Step-by-step explanation:

The height of the boat floating above the seafloor at high tide is 17.5 feet

The ratio of the similar sides of the triangles is equal to a constant. In order to determine how high the boat is, we will use the ratio below;

20/40 =x/35

Determine the value of x

40x = 20 * 35
40x =700

x = 700/40
x = 17.5feet

Hence the height of the boat floating above the seafloor at high tide is 17.5 feet

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Answer:

It's 27.8

Step-by-step explanation:

Answer: 55

Step-by-step explanation:

Answer:

SIMILAR

Step-by-step explanation:

The lines are parallel to each other, and one of the angles are 90 degrees. That is the only info that you get. You need to be able to make sure that another angle besides the 90 degrees is similar. The lines are parallel to each other, meaning that the other two angles should be equal in measure. See, if the angle in the second triangle gets bigger, the lines wouldn't be parallel, would they?

The quadratic equation 2x² + 12x – 3 = 0 can be written as 2(x²+12x+9)=3+18. Then the correct option is A.

It is the method to separate the polynomial into parts and the parts will be in multiplication. And the value of the polynomial at this point will be zero.

Inga is solving the quadratic equation 2x² + 12x – 3 = 0

   2x² + 12x – 3 = 0

        2x² + 12x  = 3

 2x² + 12x + 18 = 3 + 18

2 (x² + 12x + 9) = 3 + 18

The quadratic equation 2x² + 12x – 3 = 0 can be written as 2 (x² + 12x + 9) = 3 + 18. Then the correct option is A.

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for the unit put ft or feet

for question 5, it is 4/8 and 1/2

The sheet used by Mario and Patience which is going to warm up the quickest, and, therefore, bake the cookies the fastest is copper sheet.

The specific heat of a substance is the amount of heat needed, to raise the temperature of the of one gram of substance by unit degree Celsius.

The specific heat capacity of the substance can be given as,

[tex]C=\dfrac{Q}{m\Delta T}[/tex]

Here, (m) is the mass of the substance, (Q) is heat energy and

is the change in temperature.

The above formula can be rewritten as,

[tex]{Q}={m\Delta T}C[/tex]

By this formula, we can say that the heat energy is directly proportional to the specific heat of the substance.

Thus the value of heat energy required to warm up the substance will be higher with the higher value of specific heat and result of it the substance require more time to warm up.

Here, the specific heats of these substances are:

Treated glass = 0. 75 J/g • °C

Aluminum = 0. 90 J/g • °C

Stainless steel = 0. 50 J/g • °C

Copper = 0. 39 J/g • °C

In the above data, the value of specific heat of copper is less than other three substances.

Hence, the sheet used by Mario and Patience which is going to warm up the quickest, and, therefore, bake the cookies the fastest is copper sheet.

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Answer:

x=55  (i think)

Step-by-step explanation:

190=(2x-10)+90

(subtract 90 from 190)

100=(2x-10)

(add 10 to 100)

110=2x

(divide by 2)

55=x

The weight in pounds of the contents in the container is 288 pounds.

The volume of right rectangular prism is obtained by multiplying all 3 dimensional measures of that prism.

Given

A shipping container in the shape of a right rectangular prism has a length of 16 feet, a width of 8 feet, and a height of 4. 5 feet.

The container is completely filled with contents that weigh, on average, 0. 50 pound per cubic foot.

The volume of the right rectangular prism is given by

[tex]\rm Volume = 16\times 8 \times 4.5\\\\ Volume=576 \ ft^3[/tex]

Since the volume obtained is in cubic foot, thus there can be as many as 408 cubic foots inside the container.

Since one cubic foot content weighs around 0.50 pounds, thus,

[tex]\rm 1 \ cubic \ foot=0.50 \ pounds\\\\ 576 \ ft^3=0.50 \times 576 =288 \ pounds[/tex]

Hence, the weight in pounds of the contents in the container is 288 pounds.

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The length of one side of the square room of Rhett for his movie and music collection is (2x+7) feet.

Area of square is the square of its sides length. It can be given as,

[tex]A=a^2[/tex]

Here, [tex]a[/tex] is the length of the side of the square

Rhett decides to build a square room for his movie and music collection. The area of the room is given by the polynomial equation as,

[tex]A=(4x^2 +28x +49)\rm ft^2[/tex]

Find the factors of the above equation using the split the middle term method as,

[tex]A=4x^2 +28x +49\\A=4x^2 +14x+14x +49A=x(2x+7)+7(2x+7)\\A=(2x+7)(2x+7)\\A=(2x+7)^2\rm ft^2[/tex]

Compare it with the area of the square we get,

[tex]a=(2x+7)\rm ft[/tex]

Hence, the length of the square room of Rhett for his movie and music collection is (2x+7) feet.

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Answer:

Step-by-step explanation:

[tex]y=-x^{2} +36[/tex]

can be factored out as (-x-6)(x-6)

x-intercepts are: +6 and -6

represents the two ends of the rainbow

y-intercept: y=36

represents the highest point of the rainbow

[tex]7^6 + 7^5 - 7^4\\\\7^4*7^2 + 7^4*7 - 7^4*1\\\\7^4(7^2 + 7 - 1)\\\\7^4(49 + 7 - 1)\\\\7^4(55)\\\\7^4(11*5)\\\\11*5*7^4\\\\11k\ \text{ where } k = 5*7^4\\\\[/tex]

The result we end up with is 11k which is a multiple of 11.

Therefore, this proves that [tex]7^6 + 7^5 - 7^4[/tex] is divisible by 11.

Answer:

7^4 * 5

You need to factor the answer.

answer:

[tex]\sf x = \frac{2}{7}[/tex]

solving steps:

[tex]\hookrightarrow \sf 7(2x+\frac{1}{7} )=14(3x-0.5)[/tex]

[tex]\hookrightarrow \sf 7(2x)+7(\frac{1}{7} )=14(3x)-14(0.5)[/tex]

[tex]\hookrightarrow \sf 14x + 1 = 42x - 7[/tex]

[tex]\hookrightarrow \sf 14x -42x = - 7-1[/tex]

[tex]\hookrightarrow \sf -28x = -8[/tex]

[tex]\hookrightarrow \sf x = \frac{-8}{-28}[/tex]

[tex]\hookrightarrow \sf x = \frac{2}{7}[/tex]

[tex]\\ \rm\hookrightarrow 7(2x+1/7)=14(3x-0.5)[/tex]

[tex]\\ \rm\hookrightarrow 2x+1/7=2(3x-0.5)[/tex]

[tex]\\ \rm\hookrightarrow 2x+1/7=6x-1[/tex]

[tex]\\ \rm\hookrightarrow 4x=1+1/7[/tex]

[tex]\\ \rm\hookrightarrow 4x=8/7[/tex]

[tex]\\ \rm\hookrightarrow x=8/28=2/7[/tex]

Answer:

c-3

Step-by-step explanation:

Initial value of a function means that it is the y-intercept of the function

Answer:

40w^3

Step-by-step explanation:

I'm assuming you meant w^3 (w to the third power). In that case, you would just add 34 + 13 + 11 - 18 because they are all like terms (coefficients of w^3).

Answer(s):

[tex]\displaystyle y = 3cos\:(2\pi{x} - \frac{\pi}{2}) + 3 \\ y = -3sin\:(2\pi{x} \pm \pi) + 3 \\ y = 3sin\:2\pi{x} + 3[/tex]

Step-by-step explanation:

[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 3 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\frac{1}{4}} \hookrightarrow \frac{\frac{\pi}{2}}{2\pi} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{1} \hookrightarrow \frac{2}{2\pi}\pi \\ Amplitude \hookrightarrow 3[/tex]

OR

[tex]\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 3 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{1} \hookrightarrow \frac{2}{2\pi}\pi \\ Amplitude \hookrightarrow 3[/tex]

You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the sine graph, if you plan on writing your equation as a function of cosine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 3cos\:2\pi{x} + 3,[/tex] in which you need to replase "sine" with "cosine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the sine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the cosine graph [photograph on the right] is shifted [tex]\displaystyle \frac{1}{4}\:unit[/tex]to the left, which means that in order to match the sine graph [photograph on the left], we need to shift the graph FORWARD [tex]\displaystyle \frac{1}{4}\:unit,[/tex]which means the C-term will be positive, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{\frac{1}{4}} = \frac{\frac{\pi}{2}}{2\pi}.[/tex]So, the cosine graph of the sine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 3cos\:(2\pi{x} - \frac{\pi}{2}) + 3.[/tex]Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph hits [tex]\displaystyle [-\frac{1}{4}, 0],[/tex]from there to [tex]\displaystyle [\frac{3}{4}, 0],[/tex]they are obviously [tex]\displaystyle 1\:unit[/tex]apart, telling you that the period of the graph is [tex]\displaystyle 1.[/tex]Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 3,[/tex]in which each crest is extended three units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

I am delighted to assist you at any time.

Answer:

r = 6 ft

Step-by-step explanation:

Answer: 12

Step-by-step explanation:

Using proportions, it is found that the finance charge was of $408.

A proportion is a fraction of a total amount.

In this problem, monthly payments of $158.50 were made for 48 months, hence the total amount paid was of:

48 x $158.5 = $7,608.

The finance charge is the price financed subtracted by the fixed price, hence:

$7,608 - $7,200 = $408.

The finance charge was of $408.

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Answer:

Step-by-step explanation:

Use distributive property: a(b-c) =(a*b) - (a*c)

2(m - 4) + 1  = 2*m - 2*4 +1

                   = 2m - 8 + 1      

Combine like terms

                   = 2m - 7

Since the opposite side of the quadarilateral are equal hence it is a rectangle.

The sum of the external side is equal to the perimeter. The perimeter of the shape is expressed as:

P = 2(l+w)

where:

P = 120cm

If the width is 30cm less than twice it’s length, then;

w = 2l + 30

Substitute

120 = 2(l + 2l + 30)
60 = 3l + 30
3l = 30
l = 10

Recall that:

w = 2l + 30
w = 2(10) + 30
w = 50cm

Since the opposite side of the quadarilateral are equal hence it is a rectangle.

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Answer:

x-intercept(s): (−3,0)

y-intercept(s): (0,12)

Step-by-step explanation:

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

Answer: 2

Step-by-step explanation:

Because 72 : 2 = 36 (Farmer Lito could put 2 tomatoes in each bags)

72 : 5 = 14,4

72 : 10 = 7,2

(Farmer Lito couldn't put there cause there are decimals left)

Answer:

129 degrees

Step-by-step explanation:

Ok, DAE, as given, is 90 degrees. So, BAD would equal 90 as well, so BAC would be 90-51, 39. And because FAE is vertical angle to BAC, FAE is also 39. So 39 + 90 is 129.