The difference of 3 times a number and 17 is 5. Find the number.

Which of the quadratic functions has the narrowest graph?

charle [14.2K]

Answer:

$y=\frac{1}{8}x^2$

Step-by-step explanation:

A quadratic function has the formula ax² + bx + c

To determine if a graph will be narrow or wide, the leading coefficient, a, will be the factor that determines this
The greater the coefficient, the narrower the parabola
The lesser the coefficient, the wider the parabola

Here all of the functions are in the form ax²

In $y=\frac{1}{8}x^{2}$ , our "a" term is $\frac{1}{8}$
In y = -2x², our "a" term is -2
In y = -3x², our "a" term is -3
In $y=\frac{1}{3}x^{2}$ , our "a" term is $\frac{1}{3}$

We can eliminate the two functions with the negative coefficients because they are much smaller than the two functions with the fractions as coefficients, and will therefore open much wider.

We can now compare the two remaining functions, $y=\frac{1}{8}x^2$ and $y=\frac{1}{3}x^2$

Giving the two fractions common denominators would turn them into $y = \frac{3}{24}x^2$ and $y=\frac{8}{24} x^2$
The equation with the larger fraction will be the parabola that is the narrowest. In this case, it is the $y=\frac{8}{24} x^2$ .
Therefore, $y=\frac{1}{8}x^2$ will have the narrowest graph

7 0

3 years ago

What is the circumference of the semicircle in this figure? Express your answer in feet.

Aleksandr-060686 [28]

Diameter of the semicircle: D=6 yd*(3 ft / 1yd)→D=18 ft
Circumference of the semicircle: C=pi*D/2
C=pi(18 ft)/2
C=9pi ft
pi=3.14
C=9(3.14) ft
C=28.26 ft

Answer: Fourth option 28.26 ft

3 0

3 years ago

Help Pleasee<br><br> Reflect shape A in the line x = -2

Cerrena [4.2K]

Answer: Check out the diagram below

The reflected image is shown in red.

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Explanation:

Draw a vertical line through -2 on the x axis. This is the mirror line.

Now focus on the upper right corner of the figure, which is at (-3, -1). Notice how the horizontal distance from this corner point to the mirror line is exactly 1 unit. If we move another 1 unit to the right, then we'll arrive at (-1,-1) which is where the reflected point lands or ends up.

In short, the upper right corner point (-3,-1) reflects over x = -2 to land on (-1,-1)

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As another example, the upper left corner point (-5, -1) will move exactly 4 spaces to the right to get to the mirror line. Then we move another 4 spaces to the right to get to (2,-1).

So the upper left corner (-5,-1) will ultimately move to (2,-1) after the reflection over x = -2.

Apply these steps to the other corner points and you'll end up with what is shown below.

Take note that a point like A(-5,-1) moves to A'(1,-1), and similar to the other points as well. Also, notice that when going from A to B to C, etc we are moving clockwise. We move counterclockwise when going from A' to B' to C' etc. Reflections always swap the orientation.