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lisov135 [29]
3 years ago
5

Amelia claims that if she doubles the length and width of the base of a rectangular prism and triples the height, she has increa

sed the volume by a factor of 12 (2 × 2 × 3). What would you tell her?
Mathematics
1 answer:
julia-pushkina [17]3 years ago
3 0

Answer:

Step-by-step explanation:

(2L)(2W)(3H) = 12LWH.

Amelia gets it.

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Type the correct answer in each box
Luba_88 [7]

Answer:

We know that the equation of the circle in standard form is equal to <em>(x-h)² + (y-k)² = r²</em> where (h,k) is the center of the circle and r is the radius of the circle.

We have x² + y² + 8x + 22y + 37 = 0, let's get to the standard form :

1 - We first group terms with the same variable :

(x²+8x) + (y²+22y) + 37 = 0

2 - We then move the constant to the opposite side of the equation (don't forget to change the sign !)

(x²+8x) + (y²+22y) = - 37

3 - Do you recall the quadratic identities ? (a+b)² = a² + 2ab + b². Now that's what we are trying to find. We call this process <u><em>"completing the square"</em></u>.

x²+8x = (x²+8x + 4²) - 4² = (x+4)² - 4²

y²+22y = (y²+22y+11²)-11² = (y+11)²-11²

4 - We plug the new values inside our equation :

(x+4)² - 4² + (y+22)² - 11² = -37

(x+4)² + (y+22)² = -37+4²+11²

(x+4)²+(y+22)² = 100

5 - We re-write in standard form :

(x-(-4)²)² + (y - (-22))² = 10²

And now it is easy to identify h and k, h = -4 and k = - 22 and the radius r equal 10. You can now complete the sentence :)

5 0
3 years ago
Erica collected a total of $180 for her favorite charity over the first 3 months of the year. She collected the same amount in t
ankoles [38]
X+x+3x= 180
5x= 180
x= 36

3(36)= 108
Your answer is D. $108
4 0
3 years ago
Read 2 more answers
Solve each equation by completing the square <br>r² = –12r - 35​
Fittoniya [83]

Answer:

r = - 7, r = - 5

Step-by-step explanation:

Given

r² = - 12r - 35 ( add 12r to both sides )

r² + 12r = - 35

To complete the square

add ( half the coefficient of the r- term )² to both sides

r² + 2(6)r + 36 = - 35 + 36

(r + 6)² = 1 ← take the square root of both sides )

r + 6 = ± 1 ( subtract 6 from both sides )

r = - 6 ± 1, thus

r = - 6 - 1 = - 7 or r = - 6 + 1 = - 5

7 0
3 years ago
1.3 Dominic buys a calculator costing £7.50, 3 packets of pens costing £1.80 for each packet and
Naddika [18.5K]
I believe the answer is .60
4 0
3 years ago
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A motorboat moves across the lake constant speed. When it begins, it is 64 km from the shore. After 17 minutes it is 30 km from
aliya0001 [1]
Idk but i have to answer 091
8 0
3 years ago
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