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3 years ago

Which statement is true about the extreme value of the given quadratic equation?

Mathematics

1 answer:

ICE Princess25 [194]3 years ago

3 0

Answer:

Option B. The equation has a maximum value with a y-coordinate of -21.

Step-by-step explanation:

The correct quadratic equation is

$y=-3x^{2}+12x-33$

This is a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

Convert to vertex form

Factor -3

$y=-3(x^{2}-4x)-33$

Complete the square

$y=-3(x^{2}-4x+2^2)-33+12$

$y=-3(x^{2}-4x+4)-21$

Rewrite as perfect squares

$y=-3(x-2)^{2}-21$

The vertex is the point (2,-21)

therefore

The equation has a maximum value with a y-coordinate of -21

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Find two positive numbers whose product is 36 and whose sum is a minimum.

alukav5142 [94]

Let one of the numbers be x. The other number cab then be represented as 36-x (x+36-x = 36).
The product can then be represented as y = x(36-x) or y=36x-x2

The maximum or minimum is always on the axis of symmetry which has the formula x=-b/2a.
In our case, the axis of symmetry is -36/-2, so x=18.

If one number is 18 and the 2 numbers add to 36, the other number is 18 as well.
So the 2 numbers are 18 and 18 and the maximum product is 324,

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2 years ago

Nora bought a cartoon character lunchbox for $40. A price guide says it is worth $32. What's the percent decrease?

son4ous [18]

Answer:

It might be 8

Step-by-step explanation:

40-32=8

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3 years ago

In this line of ,the ratio of red circles to blue circles is 1:3 , How many more red circles would need to be added to make the

avanturin [10]

8 more red circles because if you have 9 red circles and 3 blue ones the ratio would be 9:3 and if you simplify that down to 3:1 that’s the answer. So you would need to add 8 more red circles

5 0

3 years ago

in february,Robbins and Myers,Inc.executed a 2-for-1 split.janine had 470 shares before the spilit.each share was worth $69.48.

aleksley [76]

<span>After the split, Janine had 960 share worth $34.74. Since they doubled the amount of share, but decrease the amount of each share, Jane didn't gain or lose any money during the event.</span>

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3 years ago

Which graph best represents the function f(x)=2x ?

yan [13]

Answer:

Step-by-step explanation:

The best - well, only way- is to check a few points.

Namely -1 (unless your eyesight is really poor!), 0, 1, 2, and 3.

$f(x) = 2^x\\f(-1) = 2^-^1 = \frac12\\f(0) =2^0 =1\\f(1)= 2^1=2\\f(2)=2^2=4\\f(3)=2^3= 8$

Now you can mark all these points in each graph (well, you could if they were on paper and not on a screen) and see which one of the lines passes through all of them. Spoiler alert, it's the B graph.

A represents $2(2^x) = 2^{x+1}$ , B is the one you want, C is $\frac{2^x}2 = 2^{x-1}$ and D looks like $4^x = 2^2^x$

3 0

2 years ago