If f(x) = 2x+7 and g(x) = -3x+5, what is f(g(1))?
1 answer:
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1. 4 3/4 feet = 19/4 feet
2 2/5 feet=12/5 feet.
multiplying them together yields
Part 2:
11.4 ft^2 - 4 1/2 ft^2=
11.4-4.5=6.9 ft^2 = 69/10 ft^2 left after you subtract the decoration in the middle
Now you're trying to find now many rectangular cutouts (that each are 3/8 ft^2) will fit in the remaining space.
You do that by dividing the remaining space left by 3/8:
since you have to have a whole number of cutouts, you round 92/5 down to 90/5, which is 18 cutouts
2 2/5 feet=12/5 feet.
multiplying them together yields
Part 2:
11.4 ft^2 - 4 1/2 ft^2=
11.4-4.5=6.9 ft^2 = 69/10 ft^2 left after you subtract the decoration in the middle
Now you're trying to find now many rectangular cutouts (that each are 3/8 ft^2) will fit in the remaining space.
You do that by dividing the remaining space left by 3/8:
since you have to have a whole number of cutouts, you round 92/5 down to 90/5, which is 18 cutouts
Answer:
Step-by-step explanation:
To sketch a quadratic function we need two things:
1) Nature of the curve
2) Vertex
3) y-intercept
The completing square form of the quadratic equation is:
where,
a represents the nature of the graph it can be maximum or minimum , meaning, if a > 0 then minimum(u shaped curve/happy face) and if a < 0 then maximum(n shaped curve/sad face).
h represents the x-coordinate of the vertex.
k represents the y-coordinate of the vertex.
Now if we compare g(x) with our completing square form we get the following:
When we simply compare the following we get ,
a = 1 , which means a > 0 since 1 is greater than 0 the nature of the curve will be minimum(happy face/u shaped)
h = 4, which means the x-coordinate of the vertex is 4
k = 12, which means the y-coordinate of the vertex is 12
Now we have the nature of the curve, we have the vertex now all we need is the y-intercept.
For y-intercept:
For y-intercept meaning at which point will the graph cross the y-axis(0 , y)
For that we expand the formula and turn it into the standard quadratic equation form by using the formula (a - b)^2
now we compare with the standard quadratic form:
here c is the y-intercept and while comparing we can see that c = 28 ,
so the curve cuts the y-axis at (0 , 28)
So we have all the three things that we need to graph our function.
So we just plot the y-intercept , the vertex , and join the dots. Just a tip draw a dotted line on the x-coordinate of the vertex because the vertex point is also called as a turning point where the graph goes in the opposite direction just like a mirror reflection. I attached 2 images you can check them out. One is handmade(i know i suck at drawing but still xD) , one is sketched by online graphing calculator.
Answer:
10 Square Inches
Step-by-step explanation:
<u>Trapezoid</u>
Base =12 inches
Height =10 inches
Top side= 10 inches.
Area of a Trapezoid
Area of the Trapezoid=110 Square Inches
<u>Rectangle</u>
Base = 12 inches
Height =10 inches.
Area of a Rectangle=Base X Height
=12 X 10
=120 Square Inches
<u>Difference in Area between the two packages</u>
Difference=Area of Rectangle-Area of Trapezoid
=120-110
=10 Square Inches