Answer:
a = ![\frac{1}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D)
Step-by-step explanation:
Aside from the standard, quadratic form,
![y = ax^2 + bx + c](https://tex.z-dn.net/?f=y%20%3D%20ax%5E2%20%2B%20bx%20%2B%20c)
Parabolas can also be written as
![y = a(x-h)^2+k](https://tex.z-dn.net/?f=y%20%3D%20a%28x-h%29%5E2%2Bk)
Where a is the scale factor, h represents the distance that the parabola has been translated along the x axis, and k represents the distance the parabola has been shifted up and down the y-axis.
Looking at the table, we see that the function appears to be concave up around x = 2. That means that h in this case is 2. The function is shifted down by -4, because the lowest point on the parabola is (2, -4)
Now we have to solve for a using any points on the table besides x = 2
I will use (4, -3) because it's the easiest option
![- 3 = a(4-2)^2-4\\-3 = a(2)^2-4\\-3 = 4a - 4\\1 = 4a\\a = \frac{1}{4}](https://tex.z-dn.net/?f=-%203%20%3D%20a%284-2%29%5E2-4%5C%5C-3%20%3D%20a%282%29%5E2-4%5C%5C-3%20%3D%204a%20-%204%5C%5C1%20%3D%204a%5C%5Ca%20%3D%20%5Cfrac%7B1%7D%7B4%7D)
Answer:
1 is the coefficient.
There is no number Infront of variable.Hence if there is no number thrlere is 1. xysquare 1 is the coefficient,X and y are base and square is Exponent.
Answer:
, Required equation
The number of people Mark invited to the party = 13
Step-by-step explanation:
According to the question,
Total amount spent = (Price of bunch of ballons)+(cost per gift) x (Number of persons)
Given: Total amount spent =$72.95 , Price of bunch of ballons =$6.00 ,
cost per gift =$5.15
thus,
, Required equation
To solve , first
subtract 6 from both sides, we get
![66.95=5.15x\\\\\Rightarrow\ x=\dfrac{66.95}{5.15}\\\\\Rightarrow\ x=13](https://tex.z-dn.net/?f=66.95%3D5.15x%5C%5C%5C%5C%5CRightarrow%5C%20x%3D%5Cdfrac%7B66.95%7D%7B5.15%7D%5C%5C%5C%5C%5CRightarrow%5C%20x%3D13)
The number of people Mark invited to the party = 13
Answer:
Option C is correct.
The value of x nearest to tenth is, 21.4 units
Step-by-step explanation:
In a given right angle triangle;
by definition of tangent ratio i,e ![\tan \theta = \frac{opposite side}{Adjacent side}](https://tex.z-dn.net/?f=%5Ctan%20%5Ctheta%20%3D%20%5Cfrac%7Bopposite%20side%7D%7BAdjacent%20side%7D)
![\tan 25^{\circ} = \frac{10}{x}](https://tex.z-dn.net/?f=%5Ctan%2025%5E%7B%5Ccirc%7D%20%3D%20%5Cfrac%7B10%7D%7Bx%7D)
![0.46630765815 = \frac{10}{x}](https://tex.z-dn.net/?f=0.46630765815%20%3D%20%5Cfrac%7B10%7D%7Bx%7D)
or
units
Therefore, the value of x nearest to tenth is, 21.4 units
Answer:
![approx. = 85.28 {ft}^{2}](https://tex.z-dn.net/?f=approx.%20%3D%2085.28%20%7Bft%7D%5E%7B2%7D%20)
Step-by-step explanation:
You can think of this as adding the area of the rectangular portion of the deck (length x width) and the semicircular portion (πr^2)/2.
(l×w)+(πr^2)/2
(10×7)+((π2^2)/2
79+2π
![approx. = 85.28 {ft}^{2}](https://tex.z-dn.net/?f=approx.%20%3D%2085.28%20%7Bft%7D%5E%7B2%7D%20)