Answer:
y-intercept: 10
concavity: function opens up
min/max: min
Step-by-step explanation:
1.) The definition of a y-intercept is what the resulting value of a function is when x is equal to 0.
Therefore, if the function's equation is given, to find y-intercept simply plug in 0 for the x-values:
y intercept ( f(0) )= 10
2.) In order to find concavity (whether a function opens up or down) of a quadratic function, you can simply find the sign associated with the x^2 value. Since 2x^2 is positive, the concavity is positive. This is basically possible, since it is identifying any reflections affecting the y-values / horizontal reflections.
3.) In order to find whether a quadratic function has a maximum or minimum, you can use the concavity of the function. The idea is that if the function opens downwards, the vertex would be at the very top, resulting in a maximum. If a function was open upwards, the vertex would be at the very bottom, meaning there is a minimum. Like the concavity, if the value associated with x^2 is positive, there is a minimum. If it is negative, there is a maximum. Since 2x^2 is positive, the function has a minimum.
Step-by-step explanation:
- Pick two whole points on the graph
- Then, use this formula: Y2 - Y1
X2 - X1
- Finally, you're given a solution (slope)
Answer: A) 18.2 minutes
B) 4.5 minutes.
Step-by-step explanation:
A) Maxine can mow one lawn in 24 minutes, so the rate of work is:
1/24 of the lawn per minute.
Sammie can mow one lanw in 36 minutes, so the rate of work is:
1/36 of the lawn per minute.
The amount of the lawn that each has left to lawn by the minute x is:
Maxine = 1 -(1/24)*x
Sammie = 1 - (1/36)*x
we want to find the value of x such that:
2*(1 - (1/24)*x) = 1 - *(1/36)*x
which means that the amount that Sammie has left is two times the amount that Maxine has left to mow.
2 - (1/12)*x = 1 - (1/36)*x
2 - 1 = (1/12 - 1/36)*x
1/0.055 = x = 18.2
by the minute 18.2
B) Similar to before, here the rates are:
For Maxine, R = 1/6
For Sammie, R = 1/9
The amount they have left to mow by minute x is:
Maxine = 1 - (1/6)*x
Sammie = 1 - (1/9)*x
We want to solve, similar to before.
2( 1 - (1/6)*x) = 1 - (1/9)*x
2 - (1/3)*x = 1 - (1/9)*x
2 - 1 = (1/3 - 1/9)*x
1 = (2/9)*x
1*9/2 = x = 4.5
So here the solution is 4.5 minutes. Hope this helps
You can find percentages with a calculator, or without a calculator:
Non-calculator:
To find a percentage of a number without a calculator, you divide the number by the percentage's number equivalent. For example, to find 10% of a number you divide by 10, to find 25% of a number you divide by 4 (because 25% is 1/4 of 100%), to find 50% you divide by 2, and 1% is dividing by 100, etcetera. You can then use the initial percentage's to find more complex percentages, so to find 30% you would divide by 10 and then multiply that by 3, and 75% would be dividing by 4 and multiplying that be 3.
Calculator:
If you have a calculator when you are asked to find the percentage, there is a much simpler way. All percentages have a decimal equivalent because you can picture all percentages as being fractions over 100, and therefore if you divide that number by 100 you get its decimal. On a calculator, if you multiply a number by a decimal multiplier, you get that percentage. For example, if you want to find 25% of a number on a calculator, you would multiply that number by 0.25.
I hope this explains things well enough! Let me know if I missed anything out :)
Ted is 6 years old.
4x6=24+6=30
