Answer:
x = 10
y = 70
Step-by-step explanation:
By using the vertical angles theorem we know that x+ y +10 = 90, also simplified to x + y = 80
and 2x + y = 90
By using the substitution method on x + y = 80, it will be y = -x + 80
When you put into the equation 2x + y = 90 you will get 2x -x +80 = 90
Then it will simplify to x = 10
After that plug 10 into x + y = 80 to 10 + y = 80 and get y = 70
For this case what we should do is find the cost per ounce.
For this, we can use the following rule of three:
5 ounces ----------------------> 2.50 $
1 oz ------------------------> x
From here, we clear the value of x.
We have then:
![x = (\frac{1}{5}) * (2.50)\\x = 0.5](https://tex.z-dn.net/?f=%20x%20%3D%20%28%5Cfrac%7B1%7D%7B5%7D%29%20%2A%20%282.50%29%5C%5Cx%20%3D%200.5%20%20%20)
Answer:
The unit cost per ounce is given by:
x = 0.5 $ / ounce
Answer:
![\{\frac{4}{9} \}](https://tex.z-dn.net/?f=%5C%7B%5Cfrac%7B4%7D%7B9%7D%20%5C%7D)
Step-by-step explanation:
First off, we are given a parabola by definition:
![f(x) = 9x^2 + 4x + k \\ a = 9, b = 4, c = k;](https://tex.z-dn.net/?f=f%28x%29%20%3D%209x%5E2%20%2B%204x%20%2B%20k%20%5C%5C%20a%20%3D%209%2C%20b%20%3D%204%2C%20c%20%3D%20k%3B)
Since
, our parabola has an upward opening.
Should we think about it graphically, it will be no wonder that we should pay our attention to the points of the parabola intersecting the abscissa axis. In other words, we need our vertex to intersect the x axis only once per se.
The vertex:
![V_{x} = \frac{-b}{2a} = \frac{-4}{2 * 9} = - \frac{2}{9} \\ V_{y} = 9V_{x}^2 + 4V_{x} + k = 9(- \frac{2}{9})^2 + 4(- \frac{2}{9}) + k = 9 * \frac{4}{9^2} - \frac{8}{9} + k = \frac{4}{9} - \frac{8}{9} + k = - \frac{4}{9} + k](https://tex.z-dn.net/?f=V_%7Bx%7D%20%3D%20%5Cfrac%7B-b%7D%7B2a%7D%20%3D%20%5Cfrac%7B-4%7D%7B2%20%2A%209%7D%20%3D%20-%20%5Cfrac%7B2%7D%7B9%7D%20%5C%5C%20V_%7By%7D%20%3D%209V_%7Bx%7D%5E2%20%2B%204V_%7Bx%7D%20%2B%20k%20%3D%209%28-%20%5Cfrac%7B2%7D%7B9%7D%29%5E2%20%2B%204%28-%20%5Cfrac%7B2%7D%7B9%7D%29%20%2B%20k%20%3D%209%20%2A%20%5Cfrac%7B4%7D%7B9%5E2%7D%20-%20%5Cfrac%7B8%7D%7B9%7D%20%2B%20k%20%3D%20%5Cfrac%7B4%7D%7B9%7D%20-%20%5Cfrac%7B8%7D%7B9%7D%20%2B%20k%20%3D%20-%20%5Cfrac%7B4%7D%7B9%7D%20%2B%20k)
As a result, our
is parametric.
suits us because
. If
, we do not have any roots at all. We have two roots if
.
<span>272mi/68mi/hr= 4 hr
Example:
Calculate the acceleration of a boat that has been cruising at 15 m/s but speeds up to 45 m/s in about 6 seconds. Don’t forget your units, m/s2. In order to calculate the acceleration of the boat we first have to identify the suited formula for acceleration in this scenario. </span>
<span>Hence, a = vf – vi / t. Vi = 15 m/s Vf = 45 m/s T = 6 seconds </span>
<span>Solution: </span>
<span>A = 45 m/s – 15m/s / 6s </span>
A = 5m/s^2<span>
</span>