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mart [117]
3 years ago
13

Henry and reiko both used 1 yard of ribbon to make bows. write two different fractions to show that Henry and reiko use the same

amount of ribbon
Mathematics
1 answer:
Natalka [10]3 years ago
4 0
To show that they used the same amount of ribbon you could take the 1 yard and divided into different sized equal groups.

1 yard divided by four equals 1/4 yard for each of four ribbons.

1 yard divided by six equals 1/6 yard for each of six ribbons.

You could have ribbons the size of 1/4 our yard and 1/6 yard, but you would have different amounts of each.
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For the data in the table, write an equation for the direct variation.
melisa1 [442]

The equation of direct variation is,

\begin{gathered} y=kx \\ k=\frac{y}{x} \end{gathered}

Substitute the values of <em>y</em> and <em>x</em>.

\begin{gathered} k=\frac{5.4}{4} \\ k=1.35 \end{gathered}

So, the obtained equation will be <em>y</em>=1.35(x).

Let's check with the values of <em>x</em>.

1) If <em>x</em>=4

\begin{gathered} y=1.35x \\ y=1.35(4) \\ y=5.4 \end{gathered}

2) If <em>x</em>=2

\begin{gathered} y=1.35x \\ y=1.35(2) \\ y=2.7 \end{gathered}

3) If <em>x</em>=-2

4 0
1 year ago
Let g(x) = 2x and h(x)= x^2 -4. find (g o h)(0)
finlep [7]
The answer is -8

====================================================

Explanation:

There are two ways to get this answer

Method 1 will have us plug x = 0 into h(x) to get
h(x) = x^2 - 4
h(0) = 0^2 - 4
h(0) = 0 - 4
h(0) = -4
Then this output is plugged into g(x) to get
g(x) = 2x
g(-4) = 2*(-4)
g(-4) = -8 which is the answer
This works because (g o h)(0) is the same as g(h(0)). Note how h(0) is replaced with -4
So effectively g(h(0)) = -8 which is the same as (g o h)(0) = -8

-----------------------

The second method involves a bit algebra first
Start with the outer function g(x). Then replace every x with h(x). On the right side, we will replace h(x) with x^2-4 because h(x) = x^2-4

g(x) = 2x
g(x) = 2( x )
g(h(x)) = 2( h(x) ) ... replace every x with h(x)
g(h(x)) = 2( x^2-4 ) ... replace h(x) on the right side with x^2-4
g(h(x)) = 2x^2-8
(g o h)(x) = 2x^2-8

Now plug in x = 0
(g o h)(x) = 2x^2-8
(g o h)(0) = 2(0)^2-8
(g o h)(0) = 2(0)-8
(g o h)(0) = 0-8
(g o h)(0) = -8

Regardless of which method you use, the answer is -8

5 0
3 years ago
5x4 – 7x3 – 5x2 + 5x + 1 = 0
olya-2409 [2.1K]
20 - 21 - 10 + 5x +1= 0
5x = 10
x = 2
5 0
3 years ago
What is the radius of a hemisphere with a volume of 19160 ft', to the nearest tenth<br> of a foot?
irina1246 [14]
I think the answer is 20.9
6 0
3 years ago
4x + 3 = 4x + 15 solve for x<br> Plese help
ira [324]

<span>4x - 15 = 3 </span>
<span>4x = 3 + 15 </span>
<span>4x = 18 (divide both sides by 4 to get x) </span>
<span>4x/4 = 18/4 </span>
<span>x = 4.5 </span>
4 0
3 years ago
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