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3 years ago

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Mathematics

1 answer:

irina [24]3 years ago

5 0

The last term is 63 so 3 might be a zero of the function;-

f(3) = 27 - 7*9 - 3*9 +63 = 27 - 63 - 27 + 63 = 0 so 3 is a zero and

therefore (x - 3) is a factor of the volume function.

Long division of the expression by x - 3 gives the quotient:-

x^2 + 4x - 21

Factoring this:-

= ( x + 7)(x - 3)

So the dimensions of the box are, x-3, x-3 and x+7 answer.

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There is 1000cm3 of aluminum available to cast a trophy that will be in the shape of a right square pyramid. Is this enough alum

stealth61 [152]

The 1000 cubic centimeters of aluminium is enough for aluminium a trophy that will be in the shape of a right square pyramid and has a base edge of 10 cm and a slant height of 13 cm.

Step-by-step explanation:

The given is,

Volume of aluminium available is 1000 cubic centimeters

Shape of trophy is right square pyramid

Trophy has a base edge of 10 cm and slant height of 13 cm

Step:1

Formula for volume of right square pyramid,

$Volume, V = a^{2}\frac{h}{3}$ .....................................(1)

Where, a - Base edge value

h - Height of pyramid

From given,

a = 10 cm

h = 13 cm

Equation (1) becomes,

$= 10^{2}(\frac{13}{3} )$

$= (100)(4.333)$

$= 433.33 cm^{3}$

Volume of trophy = 433.33 cubic centimeters

Compare with the volume of available aluminium and volume of right square pyramid,

$Volume of available aluminium > Volume of right square pyramid$

$1000 cm^{3} > 433.33 cm^{3}$

So, the given volume of aluminium is enough to make right square pyramid shaped trophy.

Result:

The 1000 cubic centimeters of aluminium is enough for aluminium a trophy that will be in the shape of a right square pyramid and has a base edge of 10 cm and a slant height of 13 cm.

6 0

3 years ago

Read 2 more answers

Use the distributive property to write an expression that is equivalent to: 3(x + 5)

lana [24]

Answer:

3x=15

Step-by-step explanation:

Here's what I found on google about the distributive property-

To “distribute” means to divide something or give a share or part of something. According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.

Now for the math-

3(x+5)

distribute the numbers- 3(x)+3(5)

solve- 3*5=15

3x+15

3 0

3 years ago

I know that the answer isn't x=0. Please help.

WITCHER [35]

(2x+8)/6=1/3(x+4)

3(2x+8)=6(x+4)

6x+24=6x+24.

0=0.

∴There are no real solutions.

8 0

4 years ago

Someone plz help me

Zina [86]

I thought you said these problems were all different. They look exactly the same to me.

Figure the volume of one of the small blocks, and use that to divide into the whole volume. 

3 1/4 = 13/4 so the box has a volume of 13/4 * 3 * 1 = 39/4 ft^3 

each small block has a volume of (1/4)^3 = 1/64 ft^3 

(39/4) / (1/64) = 624

Hope this helps love.
-Joker7721

This is the explanation.

6 0

3 years ago

Read 2 more answers

Someone please help !!

sdas [7]

Looking at Pascal's Triangle, specifically at the row that starts with 1, 10, etc we see the value 210 in the 4th slot (start the count at 0) since 10-6 = 4

Or you can use the combination formula nCr to get the same result

nCr = (n!)/(r!*(n-r)!)
10C4 = (10!)/(4!(10-4)!)
10C4 = (10!)/(4!*6!)
10C4 = (10*9*8*7*6!)/(4!*6!)
10C4 = (10*9*8*7)/(4!)
10C4 = (10*9*8*7)/(4*3*2*1)
10C4 = 210

Either way, the final answer is Choice C) 210

6 0

3 years ago