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2 years ago

Hill can make 2/5 a dozen cookies in 1/3 hour, what is his rate per hour

Mathematics

1 answer:

Setler [38]2 years ago

3 0

Answer:1 1/5 dozen cookies a hour

Step-by-step explanation: hope it helps

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Can you see an easy way to work out the value of <img src="https://tex.z-dn.net/?f=%5Csqrt%7B%201%5E3%20%2B%202%5E3%20%2B%203%5E

Lina20 [59]

We have the sum of cubes identity

$a^3 + b^3 = (a + b) (a^2 - ab + b^2)$

and observing that 1 + 4 = 2 + 3, we have

$1^3 + 4^3 = (1 + 4) (1^2 - 4 + 4^2) = 5 \times 13$

and

$2^3 + 3^3 = (2 + 3) (2^2 - 6 + 3^2) = 5 \times 7$

Then

$\sqrt{1^3+2^3+3^3+4^3+5^3} = \sqrt{5\times13 + 5\times7 + 5\times5^2} = \sqrt{5 \times (20 + 25)} \\\\ ~~~~~~~~ = \sqrt{5^2 \times (4 + 5)} = \sqrt{5^2\times9} = \sqrt{5^2\times3^2} = 5\times3 = \boxed{15}$

Alternatively, we have the well-known sum of cubes formula

$\displaystyle \sum_{i=1}^n i^3 = \frac{n^2(n+1)^2}4$

The sum under the square root is this sum with $n=5$ . Then

$1^3+2^3+3^3+4^3+5^3 = \dfrac{5^2\times6^2}4 = 225 = 15^2$

and so the square root again reduces to 15.

5 0

2 years ago

How do I solve 5x=-4y+4;x=1,2,3

lesya692 [45]

X=1
5=-4y+4
4y=-1
y=-1/4

x=2
10=-4y+4
4y=-6
y=-3/2

x=3
15=-4y+4
4y=-11
y=-11/4

7 0

3 years ago

Read 2 more answers

X^2 -10x -24 =0 A. (x-4)^2=49 B. (x-5)^2=16 C. (x-5)^2 =49 D. (x-8)^2=64

blondinia [14]

Answer:

Step-by-step explanation:

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3 years ago

Write an equation of the line that is:

Marysya12 [62]

$a)\\y=4x+1\\a=4\\new\ y=bx+c\\if\ parallel a=b\\y=4x+c\\substituting\point\ (2,3)\\3=4*2+c\\c=-5\\y=4x-5\\b)\\2y-6x=9\\2y=6x+9\\y=3x+4,5\\a=3\\new\ y=bx+c\\if\ parallel a=b\\y=3x+c\\substituting\ point\ (-2,1)\\1=4*(-2)+c\\c=9\\y=3x+9\\ c)\\y=4x+3\\a=4\\new\ y=bx+c\\if\ parallel a=b\\y=4x+c\\c=-3\\y=4x-3\\e)\\2y-4x=8\\2y=4x+8\\y=2x+4\\a= 2 \\new\y=bx+c\\if\ perpendicular b=-1/a\\y=- \frac{1}{2} x+c\\point(6,-6)\\-6=-1/2*6+c\\c=-3\\y=-1/2x-3\\f)\\2y-5x=15\\2y=5x+15\\y=\frac{5}{2}x+\frac{15}{2}$

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3 years ago

In 2 months, Mica spent a total of $305.43 on groceries. She spent $213.20 in the first month. How much did she spend in the sec

Marina86 [1]

92.23 becuase if u subtract 213.20 by 305.43 it gives you the answer

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3 years ago

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