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3 years ago

25 Pts + Brainliest for the first correct answer.

Mathematics

1 answer:

NeTakaya3 years ago

8 0

6.)Corresponding

7.)Alternate Interior

8.)Vertical

9.)Alternate Exterior

10.)Adjacent

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Devon made a box with length x+1, width x+3, and height x-3. What is the volume of Devon's box as a function of x?

erica [24]

Answer:

(a)

$V=x^3+x^2-9x-9$

(b)

$x=10$

(c)

$x=\frac{7}{2}$

Step-by-step explanation:

we are given

length is x+1

$L=x+1$

width is x+3

$W=x+3$

height is x-3

$H=x-3$

(a)

we can use volume formula

$V=L\times W\times H$

now, we can plug it

$V=(x+1)\times (x+3)\times (x-3)$

now, we can simplify it

$V=x^3+x^2-9x-9$

(b)

we are given volume =1001

so, we can set V=1001

and then we can solve for x

$V=x^3+x^2-9x-9=1001$

now, we can factor it

$\left(x-10\right)\left(x^2+11x+101\right)=0$

$x-10=0$

$x=10$

(b)

we are given volume

so, we can set

$V=14\frac{5}{8}=\frac{14\times 8+5}{8}$

$V=\frac{117}{8}$

and then we can solve for x

$V=x^3+x^2-9x-9=\frac{117}{8}$

now, we can factor it

$8x^3+8x^2-72x-189=0$

$\left(2x-7\right)\left(4x^2+18x+27\right)=0$

$2x-7=0$

$x=\frac{7}{2}$

8 0

3 years ago

The graph of f(x) = 2x2 + x – 15 passes through the point (0, –15) and one of its zeros is (2.5, 0). What is the other zero of t

pogonyaev

Answer:

x=-3

Step-by-step explanation:

6 0

3 years ago

Prove that for any natural n the number 3^(n+4)−3^n is divisible by 16.

gtnhenbr [62]

Answer:

Proved (See Explanation)

Step-by-step explanation:

Show that 3ⁿ⁺⁴ - 3ⁿ is divisible by 16.

This is done as follows

$\frac{3^{n+4} - 3^n}{16}$

From laws of indices;

aᵐ⁺ⁿ = aᵐ * aⁿ.

So, 3ⁿ⁺⁴ can be written as 3ⁿ * 3⁴.

$\frac{3^{n+4} - 3^n}{16}$ becomes

$\frac{3^n * 3^4 - 3^n}{16}$

Factorize

$\frac{3^n(3^4 - 1)}{16}$

$\frac{3^n(81 - 1)}{16}$

$\frac{3^n(80)}{16}$

3ⁿ * 5

5(3ⁿ)

<em>The expression can not be further simplified.</em>

<em>However, we can conclude that when 3ⁿ⁺⁴ - 3ⁿ is divisible by 16, because 5(3ⁿ) is a natural whole number as long as n is a natural whole number.</em>

3 0

3 years ago

How do you write 2/11 as a decimal using long division

LuckyWell [14K]

Answer:

0.18

Step-by-step explanation: Converting the fraction 2/11 into a decimal is very easy. To get 2/11 converted to decimal, you simply divide 2 by 11.

3 0

3 years ago

Read 2 more answers

Scott divides some 4-digit numbers by 1000. His answer is a decimal every time. Scott says,if you divide a 4-digit number number

Ghella [55]

Answer:

1000, 2000, 3000, .... etc are the 4-digit numbers which when divided by 1000, give whole number answer.

Step-by-step explanation:

Scott divides some 4- digit numbers by 1000 and his answer is a decimal every time.

From this Scott has concluded that if you divide a 4-digit number by 1000, then the answer will never be a whole number.

I think Scott is wrong and the reason is that if we try to divide those 4-digit numbers which are multiples of 1000, i.e. 1000, 2000, 3000, 4000, ... etc. with 1000 then only you will get a whole number answer. (Answer)

3 0

3 years ago