Their GCF is 6 and the sum is 66
Step-by-step explanation:
Answer:
m < 49/12
Step-by-step explanation:
The portion of the quadratic formula under the square root sign is the discriminant.
If the discriminant is > 0 then there are two real roots.
b² -4ac > 0
-----------------------------
7² - 4(3)m > 0
49 - 12m > 0
Subtract 49 from both sides
-12m > -49
Divide both sides by -12
(when multiplying or dividing by a negative the inequality must be reversed)
m < 49/12
So basycilly slope intercept form is y=mx+b where m=slope and b=y intercept
slope=-1
subsiute
y=-1x+b
y=-x+b
so we are given the point (-3,2)
x=-3 and y=2 is one solution
subsitue and solve for b
2=-(-3)+b
2=3+b
subtract 3 from both sides
-1=b
the slopt inercetp form is y=-x-1
Answer:
a. ![(1,0.25)](https://tex.z-dn.net/?f=%281%2C0.25%29)
b. ![y = 0.25x](https://tex.z-dn.net/?f=y%20%3D%200.25x)
Step-by-step explanation:
Given
The data in the table
Solving (a): The coordinate that represents the unit rate
The unit rate is when its 1 pound
This is so because the unit rate is dollars per pounds.
<em>Hence, the coordinate is </em>
<em></em>
Solving (b): Equation of the graph
First, we calculate the slope (m)
![m = \frac{y_2 - y_1}{x_2 - x_1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D)
Where:
![(x_1,y_1) = (1,0.25)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%20%3D%20%281%2C0.25%29)
![(x_2,y_2) = (4,1.00)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29%20%3D%20%284%2C1.00%29)
![m = \frac{y_2 - y_1}{x_2 - x_1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D)
![m = \frac{1.00 - 0.25}{4 - 1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B1.00%20-%200.25%7D%7B4%20-%201%7D)
![m = \frac{0.75}{3}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B0.75%7D%7B3%7D)
![m = 0.25](https://tex.z-dn.net/?f=m%20%3D%200.25)
The equation is then calculated as thus:
![y - y_1 = m(x - x_1)](https://tex.z-dn.net/?f=y%20-%20y_1%20%3D%20m%28x%20-%20x_1%29)
This gives:
![y - 0.25 = 0.25(x - 1)](https://tex.z-dn.net/?f=y%20-%200.25%20%3D%200.25%28x%20-%201%29)
![y - 0.25 = 0.25x - 0.25](https://tex.z-dn.net/?f=y%20-%200.25%20%3D%200.25x%20-%200.25)
Make y the subject
![y = 0.25x](https://tex.z-dn.net/?f=y%20%3D%200.25x)
<em>Hence, the equation of the graph is: </em>
<em></em>