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3 years ago

How do i rewrite the sum in the form a(b+c) such that the integers b and c have no common factor. 24+16?

Mathematics

2 answers:

Rus_ich [418]3 years ago

8 0

Answer:

$8\cdot (3+2)$

Step-by-step explanation:

Find the greatest common factor of numbers 24 and 16:

$24=2\cdot 12=2\cdot 2\cdot 6=\underline{2\cdot 2\cdot 2}\cdot 3\\ \\16=2\cdot 8=2\cdot 2\cdot 4=\underline{2\cdot 2\cdot 2}\cdot 2$

These two numbers have the greatest common factor (all underlined factors)

$GCF(24,16)=2\cdot 2\cdot 2=8$

So,

$24=8\cdot 3\\ \\16=8\cdot 2$ and

$24+16=8\cdot (3+2)$

Note that numbers 3 and 2 have no common factors.

densk [106]3 years ago

5 0

Answer:

8(3+2)

Step-by-step explanation:

We need to write the sum in the form a(b+c) such that the integers b and c have no common factor.

Given sum is 24+ 16

Now we find out Greatest common factor for both 24 and 16

24 -> 2 times 2 times 2 times 3

16 -> 2 times 2 times 2 times 2

GCF is 2 times 2 times 2 = 8

WE put the common factor 8 outside and divide both numbers by 8 and put is inside the parenthesis

$8(\frac{24}{8} +\frac{16}{8} )$

$8(3+2)$

we got 24 +16 in the form of a(b+c) that is 8(3+2)

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3 years ago

1.) What is the equation of the path of firework #1? Write your equation in general form.

valina [46]

1. I'm assumig that the paths are perfect parabolas

this means that their general forms can be written in $y=ax^2+bx+c$

it's easier to find vertex form first then expand to get general form

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vertex is (10,50), so (h,k)=(10,50) and h=10, k=50

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to find the value of $a$ , subsitute another point

(0,0)

$0=a(0-10)^2+50)$

$0=100a+50$

$a=\frac{-1}{2}$

so the equation in vertex form is $h_1=\frac{-1}{2}(t-10)^2+50$

expand to get general form

$h_1=\frac{-1}{2}(t^2-20t+100)+50$

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$h_1=\frac{-1}{2}t^2+10t$

same as last time

vertex is (10,72) so (h,k)=(10,72) so h=10 and k=72

equation is $h_2=a(t-10)^2+72$

find $a$

use another point

(0,22)

$22=a(0-10)^2+72$

$22=100a+72$

$-50=100a$

$a=\frac{-1}{2}$

so the equation in vertex form is $h_2=\frac{-1}{2}(t-10)^2+72$

range is the numbers that h is allowed to be

think about what h represents. it represents the height of the rocket

from the graph, we can see that the lowest possible height is 0yd and the highest height is 50yd

so range is 0 to 50 or 0≤h≤50

domain is the numbers that t is allowed to be

think about what t represents. it represents how long the rocket has been flying

it will stop flying when it hits the ground or at t=20

it starts flying at t=0

so domain is from 0 to 20 or 0≤t≤20

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3 years ago

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Fynjy0 [20]

Answer:

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Step-by-step explanation:

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Hope this helped for you!

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