The three sides of a triangle of lengths 4, 5, and 7. The triangle is obtuce

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:

A vertical stretch of scale factor 2, followed by a translation of 4 units left and 1 unit down is written as:

g(x) = 2*f(x + 4) - 1

For a general function f(x), a vertical stretch of scale factor K is written as:

g(x) = K*f(x).

Horizontal translation:

For a general function f(x), a horizontal translation of N units is written as:

g(x) = f(x + N).

Vertical translation:

For a general function f(x), a vertical translation of N units is written as:

g(x) = f(x) + N.

So, if we start with a function f(x) and we stretch it vertically with a scale factor of 2, we get:

g(x) = 2*f(x)

Then we translate it 4 units left:

g(x) = 2*f(x + 4)

Then we translate 1 unit down:

g(x) = 2*f(x + 4) - 1

This is the equation for the transformation.

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5x² + x - 6 = 0

Δ = 1² - 4*5*(-6) = 121 = 11²

x' = (-1 - 11) / (2x5) = -12/10 = - 6/5

x" = (-1 + 11) / (2x5) = 10/10 = 1

=> D

The values of x will the function [tex]f (x) = 5x^2 + x - 6[/tex] equal zero are x = - 6/5 and x = 1. Hence option D is true.

Used the concept of a quadratic equation that states,

An algebraic equation with the second degree of the variable is called a Quadratic equation.

Example; ax² + bx + c = 0

Given that the quadratic equation,

[tex]f (x) = 5x^2 + x - 6[/tex]

Now for the values of x at which the function equals zero, we have to find the zeroes of the function by using the factorization method.

[tex]f (x) = 5x^2 + x - 6[/tex]

[tex]f (x) = 5x^2 + (6 - 5)x - 6[/tex]

[tex]f (x) = 5x^2 + 6x - 5x - 6[/tex]

[tex]f (x) = x (5x + 6) - 1 (5x + 6)[/tex]

[tex]f (x) = (5x + 6) (x - 1)[/tex]

Hence, the value of zeroes,

[tex]5x + 6 = 0[/tex]

[tex]5x = - 6[/tex]

[tex]x = \dfrac{- 6}{5}[/tex]

And, [tex]x - 1 = 0[/tex]

[tex]x = 1[/tex]

So, the value of x is x = - 6/5 and x = 1. Hence option D is true.

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Answer:

a=0.7

A Area

0.49

Using the formula

A=a2

Solving fora

a=A=0.49=0.7

Given that 2x + 3 = -1 is a mathematical formula that expresses the equality of two expressions, the value of x in the equation is -2.

An equation is simply a mathematical formula that expresses the equality of two expressions, using the equals sign as a connection between them.

Given the data in the question;

2x + 3 = -1

First, we collect like terms.

2x = -1 - 3

2x = -4

divide both sides by 2
2x/2 = -4/2

x = -4/2

x = -2

Given that 2x + 3 = -1 is a mathematical formula that expresses the equality of two expressions, the value of x in the equation is -2.

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[tex]\qquad\qquad\huge\underline{{\sf Answer}}♫[/tex]

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \: \frac{1}{2} (5 + 13) - 4.5[/tex]

[tex]\qquad \sf  \dashrightarrow \: \frac{1}{2} (18) - 4.5[/tex]

[tex]\qquad \sf  \dashrightarrow \: 9 - 4.5[/tex]

[tex]\qquad \sf  \dashrightarrow \:4.5[/tex]

[tex]\qquad \sf  \dashrightarrow \:(5 + 11) - (24 - 15) \times 3[/tex]

[tex]\qquad \sf  \dashrightarrow \:16 - (9 \times 3)[/tex]

[tex]\qquad \sf  \dashrightarrow \:16 - 27[/tex]

[tex]\qquad \sf  \dashrightarrow \: - 11[/tex]

[tex]\qquad \sf  \dashrightarrow \: {6}^{2} + (3 \times 7) - (9 \div 3)[/tex]

[tex]\qquad \sf  \dashrightarrow \:36 + 21 - 3[/tex]

[tex]\qquad \sf  \dashrightarrow \:57 - 3[/tex]

[tex]\qquad \sf  \dashrightarrow \:54[/tex]

Answer: 47.28 miles

Step-by-step explanation: 5.91 times 8= 47.28

Step-by-step explanation:

a) x = 100 - 43 - 29 + 10

b) 100 - 43 = 57.

57 - 29 = 28.

28 + 10 = 38.

38 feet.

Answer:

7.21

Answer:

733

Step-by-step explanation:

18 - √81 + 9 × 3⁴ - ( 3 - 2 + 9 ) ÷ 2

18 - 9 + 9 × 81 - ( 10 ) ÷ 2

(18 - 9) + (9 × 81) (-10 ÷ 2)

9 + 729 - 5

738 - 5

733

I hope this helps!

Answer:

A. 904.32 ft cubed

Step-by-step explanation:

Answer:

1/4; 25%

Step-by-step explanation:

if a year has four seasons we can say that there are 4 possibilities

spring appears once

this means that the probability that a day chosen at random will be in spring would be 1 out of 4

or 25%

Your answer is

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

height of tress is 20 feet

Step-by-step explanation:

because tan = perpendicular/ height

we see option only 20 feet satisfy it

Answer:

Option D :- 20 feet

Step-by-step explanation:

[tex] \sf \tan ( \theta) = \frac{height}{distance} [/tex]

[tex] \rightarrow \sf \: \tan (\theta) = \frac{20}{50} [/tex]

[tex] \sf \: height \: = 20 \: ft[/tex]

Answer:

90

Step-by-step explanation:

Number of boxes can be filled

= (60 x 50 x 30) ÷ (10x10x10)

= 90

Answer:

90

Step-by-step explanation:

P = L×W×H

=60×50×30

P= 90,000

P= L×W×H

=10×10×10

P=1,000

90,000 ÷ 1,000 = 90

So, 90 pieces of terry in one cartoon

I think it's help

0,15 = 15 : 10 = 15%

Answer:

Step-by-step explanation:

|3x+12|

one is as it is                                     one is the negative value of it

3x + 12                                                   - (3x + 12)

                                                               - 3x - 12

That is because both negative and positive values put in am absolute value become positive.

The value of the absolute value function is given by the expressions A and B where A = 3x + 12 and B = - ( 3x + 12 )

Regardless of the sign, a modulus function returns the magnitude of a number. The absolute value function is another name for it.

It always gives a non-negative value of any number or variable. Modulus function is denoted as y = |x| or f(x) = |x|, where f: R → (0,∞) and x ∈ R.

The value of the modulus function is always non-negative. If f(x) is a modulus function , then we have:

If x is positive, then f(x) = x

If x = 0, then f(x) = 0

If x < 0, then f(x) = -x

Given data ,

Let the modulus function be represented as M

Now , the value of M is

M = | 3x + 12 |  be equation (1)

The absolute value function is defined as

If x is positive, then f(x) = x

If x = 0, then f(x) = 0

If x < 0, then f(x) = -x

So , the two expressions are

A = 3x + 12 and

B = - ( 3x + 12 )

Hence , the absolute value functions are solved

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Answer:

Yes

Step-by-step explanation:

4(3) - 28 = -16

12= -16 + 28

12 = 12

Hope that helps!

Answer:

The distributive property

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

i hope this will help

Answer:

[tex]a=36\: \sf ms^{-2}[/tex]

Step-by-step explanation:

[tex]\textsf{Displacement}\:x=4t^3-27t+8[/tex]

[tex]\implies \textsf{Velocity}\:v=\dfrac{dx}{dt}=12t^2-27[/tex]

[tex]\implies \textsf{Acceleration}\:a=\dfrac{dv}{dt}=24t[/tex]

At the moment the direction of motion of P reverses, the velocity of P will be zero.   Therefore, find the value of t when v = 0:

[tex]\implies v=0[/tex]

[tex]\implies 12t^2-27=0[/tex]

[tex]\implies t^2=\dfrac{27}{12}=\dfrac94[/tex]

[tex]\implies t=\pm\sqrt{\dfrac94}=\pm\dfrac32[/tex]

As time is positive, P reverses when t = 3/2 s

To find acceleration at this time, simply substitute the found value of t into the equation for acceleration:

[tex]\implies a=24(\frac32)[/tex]

[tex]\implies a=36\: \sf ms^{-2}[/tex]

Answer:

A and C

Step-by-step explanation:

Both A and C are the same shape, same size, but C is flipped over. If you were to cut out the two shapes and put them over one another, they would be the same. You can also count the blocks that are in the shape itself to see if they match.

The longer side on both has 2.5 blocks in it, the side is two blocks tall, and the smaller line has 1.5 of the block shown.

I'll will implement a sketch to show you what I mean and submit it here. Look at it if you are still confused

I hope this helps!

-No one

Answer:

x = 36

Step-by-step explanation:

Assuming that line EAF + FAB = 180, we can substitute the lines with their x values to become 3x + 2x = 180 = 5x

Then x = 180/5 = 36

The measure of x for the given angles is 36° so option (D) will be correct.

An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.

The angle is the measurement of the angular distance.

The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.

Given that A is in between of line joining by EB so EAB is a straight line and ∠EAB = 180°.

Now,

∠EAB = 180°

∠EAF + ∠FAB = 180°

3x + 2x = 180

5x = 180

x = 36°

Hence "The measure of x for the given angles is 36°".

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Answer:

Proportional

Step-by-step explanation:

[tex]\frac{10}{24}= \frac{5}{12}[/tex] the ratio is 2:1

5 x 2 = 10

12 x 2=24

The ratios are proportional.

Hope this helps! Please let me know if you need more help, or if you think my answer is incorrect. Brainliest would be MUCH appreciated. Have a great day!

Stay Brainy!

−Kallmekrish

Answer:

The given ratios are proportional

Step-by-step explanation:

To consider the fractions as "proportional", they must be equivalent. Let us assume that the fractions are equivalent. Then, we get;

[tex]\implies \dfrac{10}{24} = \dfrac{5}{12}[/tex]

When using cross multiplication, we get;

[tex]\implies \dfrac{10}{24} = \dfrac{5}{12}[/tex]

[tex]\implies 10 \times 12 = 24 \times 5[/tex]

When simplified, we get;

[tex]\implies 10 \times 12 = 24 \times 5[/tex]

[tex]\implies 120 = 120 \ \checkmark[/tex]

Therefore, the relationship is proportional.

The factored form of the equation 9x⁴y - 6x³y² + 3x²y³ is 3x²y(3x²-2xy+y²).

The product of a constant and two linear expressions in factored form. The roots of the function are the parameters and the x-intercepts of the graph. Often Factoring is referred to as the process of converting a quadratic function to factored form.

We need to write the given expression [tex]9x^4y-6x^3y^2 + 3x^2y^3[/tex] in the factored form, therefore, we will take the common terms out of the given expression,

1. Taking 3 as the common term, we will get,

[tex]9x^4y-6x^3y^2 + 3x^2y^3\\\\= 3 (3x^4y-2x^3y^2 + x^2y^3)[/tex]

2. Taking x² as the common term

[tex]= 3 (3x^4y-2x^3y^2 + x^2y^3)\\\\= 3x^2(3x^2y-2xy^2+y^3)\\\\[/tex]

3. Taking y as the common term,

[tex]= 3x^2(3x^2y-2xy^2+y^3)\\\\= 3x^2y(3x^2-2xy+y^2)\\\\[/tex]

Hence, the factored form of the equation 9x⁴y - 6x³y² + 3x²y³ is 3x²y(3x²-2xy+y²).

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Answer:

Step-by-step explanation:

Formulae

Area of a triangle = 1/2 x base x height

Area of a rectangle = width x length

Question 1

Surface area of square based pyramid = area of base + 4 × area of triangle

⇒ SA = (6 × 6) + 4(1/2 × 6 × 14)

         = 36 + 168

         = 204 yd²

Question 2

Surface area of a cuboid = 2 × base area + 2 × end area + 2 × side area

⇒ SA = 2(10 × 6) + 2(6 × 3) + 2(10 × 3)

         = 120 + 36 + 60

         = 216 mm²

Extra credit question

Surface area of a triangular based prism = base area + 2 × triangle area + 2 × side areas

base area = 3 × 10 = 30 mm²

triangle area = 1/2 × 3 × 2 = 3 mm²

side area = 10 × 2.5 = 25 mm²

⇒ total SA = 30 + (2 × 3) + (2 × 25)

                 = 30 + 6 + 50

                 = 86 mm²

❍ Concept :-

We can solve these questions by using the formulas of area of triangle and rectangle, which will make our work easier. So, we know that,

⠀

[tex] \blue{ \underline{ \boxed{ \begin{array}{cc} \sf1. ~Area_{Triangle} = \dfrac{1} {2} \times b \times h \qquad \: \: \: \: \: \: \: \\ \\ \\ \sf2. \: Area_{Rectangle} = Length \times Breadth \end{array}}}} \\ \\ [/tex]

Using these formulas and figuring out the number of triangles and rectangles in each shape, we will solve this question.

⠀

✰ Solution :-

⠀

1. In this square pyramid, if we closely observe, we will get to know that there are 1 rectangle and 4 triangular faces. Thus,

⠀

[tex]\sf \hookrightarrow Area=6 \times 6 + 4( \dfrac{1}{2} \times 6 \times 14) \\ \\ \\ \sf \hookrightarrow Area=36 + 168 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area= {204 \: yd}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ [/tex]

⠀

2. Now, here, we can use the formula of total surface area for cuboid, i.e.

⠀

TSA = 2( lb + bh + hl )

⠀

[tex]\sf \hookrightarrow Area=2(10 \times 6 + 6 \times 3 + 10 \times 3) \\ \\ \\ \sf \hookrightarrow Area=2(60 + 18 + 30) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area=2 \times 108 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area= {216 \: mm}^{2} \: \: \qquad \qquad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ [/tex]

⠀

Extra Credit Question.

⠀

Here, we can find out the total surface area by finding,

⠀

Base area i.e. length x breadth ( B.A. )

Side area i.e. length x breadth ( S.A. )

triangular area = 1/2 x b x h ( T.A. )

⠀

Now,

⠀

TSA = BA + 2 x S.A. + 2 x T.A.

⠀

[tex]\sf \hookrightarrow Area=(10 \times 3) + 2(10 \times 2.5) + 2(\dfrac{1}{2} \times 3 \times 2) \\ \\ \\ \sf \hookrightarrow Area= 30 + 2 \times 25 + 2 \times 3 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area=30 + 50 + 6 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area= {86 \: mm}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ [/tex]

Answer:

Step-by-step explanation:

29-9=20

9-(-11)=20

50×-20=-1000

-1000+29=-971

Answer:

According to question if we observe, number of red sweets are the least

It 's only 1%

Step-by-step explanation: