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kupik [55]
2 years ago
11

Mr. Petrov was trying to choose between two different plans for dollhouses for his daughter. Both dollhouses have a rectangular

prism base with a length of 6 inches, width of 6 inches, and height of 5 inches. Dollhouse 1 has a triangular prism top. The triangular base has a base of 6 inches and height of 4 inches. The prism has a height of 6 inches. Dollhouse 2 has a square pyramid top with a base of 6 inches by 6 inches and height of 4 inches. Which statements are true about the dollhouses? Select three options. The space inside dollhouse 1 can be found using the equation V = 6 (6) (5) + one-half (6) (6) (4). The space inside dollhouse 1 can be found using the equation V = 6 (6) (5) + one-third (6) (6) (4). The space inside dollhouse 2 can be found using the equation V = 6 (6) (5) + one-half (6) (6) (4). The space inside dollhouse 2 can be found using the equation V = 6 (6) (5) + one-third (6) (6) (4). The space inside dollhouse 1 is 24 inches cubed greater than the space inside dollhouse 2.
Mathematics
2 answers:
Dmitriy789 [7]2 years ago
7 0

Answer:

(4). The space inside dollhouse 1 is 24 inches cubed greater than the space inside dollhouse 2.

As the correct equation should add up to 192 dolls house 1 and 168 for dolls house 2; 192 -168 = 24 cubed inches.

Dolls house 1 =  6(6)(5) + one thirds of 6(6) =180+ 12 =192 cubed inches.not 334 as shown in equation 1

Dolls house 2 = should be V= 6(6)5 - one third of 6(6) = 180-12 =168 cubed inches not 188 as shown in equation 2

Where all the other listed answers in question are incorrect as they add up to 334 or 188.

Step-by-step explanation:

dh1+2 rectangle = 6 x 5 x 4 = 120

Volume of triangle

V = 0.5 X b X a X h. = 0.5 x 6 x 6 x 4 = 72sq^3 + 120-sq^3 = 192sq^3

Volume of the Pyramid/rectangle dh = lwh/3

= 6x6x4=144/3=48sq^3 +  120sq^3= V = 168sq^3

Both A + B = V= 192sq^3, B=168sq^3

To calculate the volume of a triangular prism, measure the width and height of a triangular base, then multiply the base by the height by 1/2 to determine the triangle's area. Next, measure the height of the triangular prism and multiply this by the triangle's area to get the volume.

To calculate the volume of a pyramid with a rectangular base, find the length and width of the base, then multiple those numbers together to determine the area of the base. Next, multiply the area of the base by the height of the pyramid. Take that result and divide it by 3 to calculate the pyramid's volume

Gnesinka [82]2 years ago
6 0

Answer:

A: The space inside dollhouse 1 can be found using the equation V = 6 (6) (5) + one-half (6) (6) (4).

D: The space inside dollhouse 2 can be found using the equation V = 6 (6) (5) + one-third (6) (6) (4).

E: The space inside dollhouse 1 is 24 inches cubed greater than the space inside dollhouse 2.

Step-by-step explanation:

ANSWERS ARE <u>A, D, E !!</u>

i just took it on EDGE 2020 - hope it helps :)

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Tyrell Otis deposited his IRS refund check for $760 at 5% and made no other deposits or withdrawals. How much simple interest di
Helga [31]

Answer:

He earned $114 in interest.

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Step-by-step explanation:

Initial balance (b): $760

Interest rate (i): 0.05

Period (n): 3 months

Simple interest applications yield the same amount in interest every period. Therefore, the total simple interest earned can be defined by:

I = n*B*i\\I= 3*760*0.05\\I=114

The final amount (A) in the account is the initial balance plus the interest earned in 3 months.

A = 760 +114\\A=874

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6 0
2 years ago
A statistics professor drew a random sample of 81 observations and found that x with bar on top equals 62 s equals 15. Estimate
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3 0
2 years ago
ANSWER ALL 5 PARTS.
N76 [4]
A function f from a set A to a set B is defined as a relation that assings to each element  x in the set A exactly one element y in the set B. The set A is called the domain of the function while the set B is the range. So we have five statements and need to find some functions. Melissa decides to reserve a patch in her vegetable garden for growing bell peppers. If each side of the tomato patch is x feet, then we have a square patch as shown in the Figure below.

1.a) Write the function Wa(x) representing the width of the bell pepper patch.

We know that she wants its width to be half the width of the tomato patch. Let x be the width of the tomato patch, then the function that matches this statement is:

\boxed{Wa(x)=\frac{x}{2}}

1.b) Write the function La(x) representing the length of the bell pepper patch.

In this case Melissa wants <span>its length to exceed the length of the tomato patch by 2 feet. To do this we enlarge the length of the tomato patch 2 feet. Therefore the function is the following:

</span>\boxed{La(x)=x+2}
<span>
2. Ar</span>ea of the bell pepper patch in terms of x.

Given that the bell pepper patch is a rectangle, then t<span>he area of a rectangle is the product of the length and width. So:

</span>A=(\frac{x}{2})(x+2) \\ \\ \therefore \boxed{A=\frac{x(x+2)}{2}}
<span>
3. C</span><span>ombined area of the tomato patch and the bell pepper patch.

This function is the sum of both the area of the tomato patch and the bell pepper patch. So:

</span>Aar(x)=x^{2}+\frac{x(x+2)}{2} \rightarrow Aar(x)=x^{2}+ \frac{x^{2}}{2}+x \rightarrow Aar(x)=\frac{3x^{2}}{2}+x \\ \\ \therefore \boxed{Aar(x)=\frac{x(3x+2)}{2}}
<span>
4. W</span>rite the function Aa(x) for the remaining planting area in the garden.

The remaining planting area in the garden are the rectangles in red. So we need to subtract the width of the bell pepper patch from the width of the tomato patch and multiply it by 2. In mathematical language this is given by:<span>

</span>Aa(x)=2(x-\frac{x}{2}) \rightarrow Aa(x)=x

5. 
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Given that <span>Melissa wants the area of the bell pepper patch to be 31.5 square feet, then it is true that:

</span>31.5=\frac{x(x+2)}{2} \rightarrow x^{2}+2x-64=0 \\ \\ solving \ for \ x: \\ x=7.06
<span>
Therefore the area of the remaining space is:

</span>\boxed{Aa(7.06)=7.06ft^{2}}

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timofeeve [1]

We need to find the quotient of the given division problem.

\frac{x^{3}-3x^{2}+3x-2}{x^{2}-x+1}

In order to find its quotient, we will use long division.

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First of all, we put x in the quotient as x^{2} goes into x^{3}, x times.

So, we get:

x^{2}-x+1)x^{3}-3x^{2}+3x-2(x

\text{ ..................}x^{3}-x^{2}+x

Upon subtracting, we get:

\text{....................}-2x^{2}+2x-2

We can see that x^{2} goes into -2x^{2}, -2 times, therefore, the next term in the quotient will be -2. This makes our quotient as (x-2).


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