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Otrada [13]
3 years ago
9

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

h_1=a(t-10)^2+50

to find the value of a, subsitute another point

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

0=100a+50

a=\frac{-1}{2}

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expand to get general form

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

h_1=\frac{-1}{2}t^2+10t-50+50

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





2.

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




3.

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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