Move down c units means minus 2 from whole function
f(x) moved down 2 units means f(x)-2
so
f(x)-2=2x²-8-2
f(x)-2=2x²-10
g(x)=2x²-10
We got the value of
by solving the given equations
and
by reduction method.
<h2>
What is reduction method?</h2>
The reduction or elimination approach includes using arithmetic operations between equations to produce equivalent equations with fewer unknowns that are simpler to analyze and evaluate.
Given equations are
.........(1)
...........(2)
We need to find the value of ![e=x+y](https://tex.z-dn.net/?f=e%3Dx%2By)
Simplifying the given equation (2) and we get
................(3)
Now, substitute the equation (3) in equation (1) and we get
![3x+2(26-5x)=26\\\Rightarrow 3x+52-10x=26\\\Rightarrow -7x+52=26\\\Rightarrow -7x=26-52\\\Rightarrow -7x=-26\\\Rightarrow x=\frac{26}{7}](https://tex.z-dn.net/?f=3x%2B2%2826-5x%29%3D26%5C%5C%5CRightarrow%203x%2B52-10x%3D26%5C%5C%5CRightarrow%20-7x%2B52%3D26%5C%5C%5CRightarrow%20-7x%3D26-52%5C%5C%5CRightarrow%20-7x%3D-26%5C%5C%5CRightarrow%20x%3D%5Cfrac%7B26%7D%7B7%7D)
Substitute the value of x in equation (3), we get
![y=26-5\frac{26}{7} \\\Rightarrow y=26-\frac{110}{7}\\\Rightarrow y=\frac{162-110}{7}\\\Rightarrow y=\frac{52}{7}\\](https://tex.z-dn.net/?f=y%3D26-5%5Cfrac%7B26%7D%7B7%7D%20%5C%5C%5CRightarrow%20y%3D26-%5Cfrac%7B110%7D%7B7%7D%5C%5C%5CRightarrow%20y%3D%5Cfrac%7B162-110%7D%7B7%7D%5C%5C%5CRightarrow%20y%3D%5Cfrac%7B52%7D%7B7%7D%5C%5C)
Now adding the values of x and y, we get
![\therefore e=\frac{26}{7}+\frac{52}{7}\\\Rightarrow e=-{[\frac{26+52}{7}]\\\Rightarrow e={[\frac{78}{7}]](https://tex.z-dn.net/?f=%5Ctherefore%20e%3D%5Cfrac%7B26%7D%7B7%7D%2B%5Cfrac%7B52%7D%7B7%7D%5C%5C%5CRightarrow%20e%3D-%7B%5B%5Cfrac%7B26%2B52%7D%7B7%7D%5D%5C%5C%5CRightarrow%20e%3D%7B%5B%5Cfrac%7B78%7D%7B7%7D%5D)
Therefore, the value of
.
To learn more about reduction method from the below link:
brainly.com/question/13107448
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<span>In the statement "A _____ is a pair of equal ratios.", the word that completes is A, proportion. A proportion is a numerical correlation between two numbers. Frequently, these numbers can speak to an examination of things or individuals. For instance, say you strolled into a room brimming with individuals. </span>
You mean the house is 30.5 feet long correct?
30.5 / 25 = 1.22 feet
Therefore, the model is 1.22 feet long.
Answer:
The constant is 140 and it represent the minimum amount of money they'll make from selling hotdogs when the price is not raised.
Step-by-step explanation:
You're given the equation
y = -8x² + 54x + 140
The result from calculating the equation will give you how much money they made at the end of the day. And x is the amount of $1 price increase they had on the hotdog.
So we assume that they didn't raise the hotdog price at all (so x=0), then we would get:
y = -8(0)² + 54(0) + 140
y = 0 + 0 + 140
y = 140
Read further if you want more explanation...
So if they didn't increase their price at all, they would make at least $140.
Now lets plug in x=1 for a $1 increase in price.
we get
y = -8(1)² + 54(1) + 140
y = 186
ok, we see that the amount of money they made increased to $186 when they raise the price.
Now lets check when we raise the price by $2 (x=2)
y = -8(2)² + 54(2) + 140
y = 216
ok, now the revenue increased to $216
Just one last check, lets see what happen when we raise the price by $3 (x=3)
y = -8(3)² + 54(3) + 140
y = 230
Price increased again to $230.
As you can see, the 140 represent the revenue they make when the price is not raised at all (x=0).