The perimeter of a rectangle is 12 meters. Find the maximum area of such a rectangle. You must support your answer with calculus; an answer without support will receive no credit

The number of btus which are needed to cool Lucia’s apartment shown in the three-dimensional model are 20,400 btus.

Volume of rectangular prism is the amount of quantity, which is obtained in it in the 3 dimensional space.

Volume of a rectangular prism is the product of its width, height and length.

[tex]V=w\times h\times l[/tex]

Here, (w) is the width of the base (l) is the length and (h) is the height of the rectangular prism.

A three-dimensional model of Lucia’s apartment is shown. The image is attached below for the apartment. The three section are there in the apartment. The volume of this apartment is,

[tex]V=[(20\times12)+(20-9)\times16+(20\times20)]\times10\\V=8160\rm\; ft^3[/tex]

To cool the whole apartment, an air conditioner must provide 2.5 btus per cubic foot. To cool, the 8160 cubic foot apartment the btus needed are,

[tex]n=8160\times2.5\\n=20400\rm\; btus[/tex]

Hence, the number of btus which are needed to cool Lucia’s apartment shown in the three-dimensional model are 20,400 btus.



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Answer:

20,400 BTUs

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

25°-27°= -2°

At noon, the temperature outside was 25 degrees. By 8:00pm, the temperature had dropped 27 degrees. What was the temperature outside at 8:00pm, in degrees?

= 25 - 27

= - 2°

Step-by-step explanation:

I think it will help you.

Look at the example

Let's use mid-term splitation

[tex]\\ \rm\rightarrowtail 6x^2-5x-6[/tex]

[tex]\\ \rm\rightarrowtail 6x^2+4x-9x-6[/tex]

[tex]\\ \rm\rightarrowtail 2x(3x+2)-3(3x+2)[/tex]

[tex]\\ \rm\rightarrowtail (2x-3)(3x+2)[/tex]

Answer:

Step-by-step explanation: 5.6 would be the add on to 27 so since it included the key word '' left'' you'd substract the two and you'd get your answer, just use calculator. You got this!!!

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Answer: yes it would change my answer for what is a better buy

Step-by-step explanation: if you buy a $1.98 large soda for 50¢ off you’ll have a $1.48 soda that is only 30¢ more but the size is significantly larger

The scale factor used for scaling the actual rectangular pool was 4/15 and the length of the scaled rectangle is 9.6 feet.

Suppose the initial measurement of a figure was x units.

And let the figure is scaled and new measurement is of y units.

Since the scaling is done by multiplication of some constant, that constant is called scale factor. Let that constant be 's'.

Then we have:

[tex]s \times x = y\\s = \dfrac{y}{x}[/tex]

Thus, scale factor is the ratio of the new measurement to the old measurement.

For this case, we're specified that:

Dimensions of the original pool = 24 feet wide by 36 feet long

The scaled rectangle's dimension: 6.4 feet width and L feet length (we assume the length be L units).

So, in scale drawing, 24 feet was converted to 6.4 feet. Let the scale factor be 's', then:

[tex]6.4 = s \times 24\\\\s = \dfrac{6.4}{24} = \dfrac{4}{15}[/tex]

Thus, since length is also scaled by same factor(as the whole figure is scaled by constant scale factor assumingly), we get:

Scaled length = s times original length

[tex]L = \dfrac{4}{15} \times 36 = 9.6 \: \rm feet[/tex]

Thus, the scale factor used for scaling the actual rectangular pool was 4/15 and the length of the scaled rectangle is 9.6 feet.

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Answer:

D

Step-by-step explanation:

PLEASE MARK ME AS BRAINLIEST AND HAVE A NICE DAY :)

Answer:

D is correct.

Step-by-step explanation:

The length of arc of the given circle, to the nearest hundreth, is: 2.41 units.

Length of arc = ∅/360 × 2πr, where the radius of the circle is r, and the reference angle is ∅.

We are given the following:

Radius (r) = 3 units

Reference angle (∅) = 46°

Plug in the values into the length of arc formula:

Length of arc = 46/360 × 2π(3)

Length of arc = 2.41 units.

Therefore, the length of arc of the given circle, to the nearest hundreth, is: 2.41 units.

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Answer:

no increase

Step-by-step explanation:

the range is the difference between the largest and smallest values in the data set.

largest value = 9 and smallest value = 3 , then

range = 9 - 3 = 6

replacing 8 by 5 has no effect on the above 2 values , so no change

Answer:

The range would stay the same.

Step-by-step explanation:

The old set is 6 9 3 6 8 6 3

- range is 9-3 = 6.

The new set is  6 9 3 6 5 6 3

which has a range of 9 - 3 = 6.

Answer:

To find the area of a trapezoid, multiply the sum of the bases (the parallel sides) by the height (the perpendicular distance between the bases), and then divide by 2.

Step-by-step explanation:

:) Hope this helps you with what you're working on!

Answer:

well, here's the formula!

Step-by-step explanation:

area = (1/2) · (p + q) · h

Answer:

72

Step-by-step explanation:

1 large cube is 2 x 3 cubes equals 6

length is 3 x 4 x 2 = 24

24 x 3 = 72 for each layer

72 x 2 = 144 smaller cubea

Answer:

4/5

Step-by-step explanation:

Here is how to solve:

We start with a term called Rise over Run. We rise up 4. We then will run to the right 5. We have a slope of 4/5x. If the line is going up, then it will be a positive slope. If the line is going down., then it will be a negative slope. So, the line is going up, so it would be a positive 4/5x

Answer:

Positive slope or (2,3)_(-3,-2)

Step-by-step explanation:

I don't find your question very clear, but I have two possible answers for you.

Positive slope, the type/name of the slope.

(2,3)_(-3,-2), the coordinates.

I hope this answers your question ^^

Answer:

step by step solution:

(r/p)(9) = (9+1)²/(9-4) = 100/5 = 20

(q.s)(3) = (-2(3)+7).(3(3)² - 5(3)) = 1×12 = 12

(q/r)(-1) = (-2(-1) + 7)/(-1+1)² = 9/0 = Undefined

(t + s)(4) = -(4)² + 4(4) + 9 + 3(4)² -5(4) = -16 + 16 +9 + 48 - 20= 37

(s o p)(8) = s(p(8)) = s(8-4) = s(4) = 3(4)² -5(4) = 48 - 20 = 28

(q o t)(7) = q(t(7)) = q(-(7)² + 4(7) + 9) = q(-12) = -2(-12) + 7= 24+7 = 31

(r o u)(1) = r(u(1)) = r(1+6) = r(7) = (7+1)² = 64

(t o s)(0) = t(s(0)) = t(0) = 9

(u-p)(-3) = (-3)³ + 6(-3) - (-3) + 4 = -27 -18 + 3 + 4 = -38

(u o r)(-2) = u(r(-2)) = u((-2+1)²) = u(1) = 1 + 6 = 7

(q o q)(6) = q(q(6)) =q (-2(6) + 7) = q(-5) = -2(-5) + 7 = 17

END

Answer:

3

Step-by-step explanation:

it is 3 because if the x value is 5 then the y value is 3

Answer:

The area of the base is 24 [tex]cm^{2}[/tex]

The volume is 168 [tex]cm^{3}[/tex]

Step-by-step explanation:

The area of the base is found by solving [tex]0.5*6*8[/tex], because that is the formula for the area of a triangle.

The volume is found by multiplying the area of the base by the height: [tex]24*7=168[/tex]

Answer:

9/10.

Step-by-step explanation:

3 3/4 ÷ (1 2/3 + 2 1/2)​

= 3 3/4 / ( 5/3 + 5/2)

= 3 3/4 / ( 10/6 + 15/6)

= 3 3/4 / 25/6

= 15/ 4 / 25/6

= 15/4 * 6/25

= 90/100

= 9/10.

Answer:

a)

Step-by-step explanation:

Given:  Step 3

(JK)² = LK · MK  and  (LJ)² = LK · ML

Step 4

Addition property of equality

(JK)² + (LJ)² = LK · MK + LK · ML

Step 5

Distributive property

(JK)² + (LJ)² = LK (MK + ML)

Option A

addition property of equality

So

And

Distributive property

Hence option A is correct

Answer:

option 3

Step-by-step explanation:

6(3√5)

Answer:

4

Step-by-step explanation:

First, rewrite the equation with -5 substituted for A:    (-5)^2 +5(-5) +4
Next, simplify that equation:      25 -25 +4
Simplify this further: 4

When A=-5, the solution is 4.

The total number of nickles that Alice has got for this case is 14. The total amount of money from those nickle and dimes that Alice hold is $1.9

A dollar is further divided into some majorly used parts as:

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

For this case, we're specified that:

Suppose that she has got 'x' nickles.

Then, as it is given that she has 2 more nickles than dimes, therefore, we get:

number of nickles = 2 + number of dimes

x = 2 + 12 = 14

Thus, Alice has got  12 dimes and 14 nickles.

Similarly, we have:

Thus, the total amount of money she got is $1.2 + $0.7 = $1.9

Thus, the total number of nickles that Alice has got for this case is 14. The total amount of money from those nickle and dimes that Alice hold is $1.9

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#SPJ4

Yosef should have multiplied the x-values by 80 to get the y-values.

Tables are told used to arrange ungrouped data.

From the given table, we can find the equation by using the coordinate points (1, 80) and (1, 160)

The standard equation of a line is  y = mx + b

m is the slope

b is the y-intercept

Slop = 160-80/2-1

Slope = 80

For the y-intercept

160 = 80(2) + b

b = 0

The required equation is y = 80x

This means that Yosef should have multiplied the x-values by 80 to get the y-values.

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Answer:

A

Step-by-step explanation:

Answer:

Step-by-step explanation:

as i think it is triangle which means the sum of interior angle 180

14x+13+4x+13+6x+2=180

24x+28=180

24x=152

x=6.2

Answer:

2.744 cubic milimeters

Step-by-step explanation:

Here,

Length ( l ) = 1.4 mm

Base ( b ) = 1.4 mm

Height ( h ) = 1.4 mm

l = b = h = 1.4 mm = a

To find : Volume

This shape is a cube.

Formula : -

Volume of cube = a³

Volume of cube

= 1.4³

= 1.4 x 1.4 x 1.4

= 2.744 cubic milimeters

[tex] \huge\fbox\orange{ANSWER} [/tex]

[tex] \mathsf \purple{v = l \times w \times h}[/tex]

[tex] \mathsf \pink{v = 1.4 \times 1.4 \times 1.4}[/tex]

[tex] \mathsf \purple{v = 2.744 {mm}^{3} }[/tex]

2.74 cubic millimeters

Answer:

The smallest number by which 256 must be divided so that the quotient is a perfect cube is 4.

Step-by-step explanation:

Pythagorean Theorem: a^2 + b^2 = c^2

a = 23 m

b = 11 m

c^2 = (23 m)^2 + (11 m)^2 = 650 m^2

c = sqrt(650 m^2) = 25.5 (rounded to nearest tenth)

It has a ratio of 1:4, meaning for every x, you'd get 4 from your y

Answer: 13.5 in

Step-by-step explanation:

The formula for the volume of a cone is: V = π*r^2*(h/3).

Therefore, when the given numbers are plugged in, it becomes:

1144.53 = (3.14)(9^2)(h/3).

Solving this for h, we get the answer of 13.5 in