What is 10+10 and what is 4+5

Explain how you could write a quadratic function in factored form that would have a vertex with an x-coordinate of 3 and two dis

skad [1K]

The definition of quadratic function is given by:

 $(1) \ f(x)=ax^{2}+bx+c \\ \\ where \ a, b, c \ are \ real \ values$ 

So the problem asks for two conditions:

1. Write the quadratic function in factored form. 
2. The vertex has an x-coordinate of 3.

Then the equation (1) must be written as follows:

 $f(x)=(x-m)(x-n) \\ \\ where \ m \ and \ n \ are \ the \ roots$ 

To satisfy the two conditions:

$\frac{m+n}{2}=3$

So we are free to choose the value of one root, say:

$m=1$

Thus:

$n=6-1=5$

Finally, the answer is:

$f(x)=(x-1)(x-5)$

The graph of this function is shown in the figure below.

4 0

3 years ago

Read 2 more answers

Item 18 you and your friend are selling tickets to a charity event. you sell 7 adult tickets and 16 student tickets for $120. yo

quester [9]

Answer:

$4

Step-by-step explanation:

The two purchases can be written in terms of the cost of an adult ticket (a) and the cost of a student ticket (s):

7a +16s = 120 . . . . . . . . price for the first purchase

13a +9s = 140 . . . . . . . . price for the second purchase

Using Cramer's rule, the value of s can be found as ...

s = (120·13 -140·7)/(16·13 -9·7) = 580/145 = 4

The cost of a student ticket is $4.

_____

Comment on Cramer's Rule

Cramer's rule is particularly useful for systems that don't have "nice" numbers that would make substitution or elimination easy methods to use. If you locate the numbers in the equation, you can see the X-patterns that are used to compute the numerator and denominator differences.

The value of a is (16·140 -9·120)/(same denominator) = 1160/145 = 8. I wanted to show you these numbers so you could see the numerator X-pattern for the first variable.

__

Of course, graphical methods can be quick and easy, too.

8 0

3 years ago

During a school lunch, the cafeteria sold two-fifths as many white milks as chocolate milks. If there were 35 milks sold, how ma

anyanavicka [17]

Hello!

As we can see, they sell 2/5 as many white milks and chocolate milks. We can write this as the ratio 2:5. As you can see, we are given the total, which is 35. The total of the ratio in simplest form is 7 (2+5). As you can see, we have to multiply by 5 to get that 7 to 35. Therefore we multiply each part of the ratio by 5 to get our final answer. We can have w represent the white milks while c represents the chocolate milks.

$\frac{w}{c} = \frac{2}{5}$ · $\frac{5}{5}$ = $\frac{10}{25}$

Therefore there were 25 chocolate milks sold (just to verify 10 is 2/5 of 25).

I hope this helps!

3 0

3 years ago

Instructions: Given the following roots solve for the quadratic equation. Can I maybe get a hand on this one? My teacher didn't

Blizzard [7]

Do you wanna graph or noi

7 0

3 years ago

The area of a circular sun spot is growing at a rate of 1,400 km^2/s. . (a) How fast is the radius growing at the instant when i

dsp73

In solving a, we must get the formula needed then substitute the given so we have

A=πr2

dA/dt=1,400 km2/s

then solve for dA/dt

1400 km2/s=2π(8000 km)dr/dt

drdt≈0.028 km/s

In solving b, its just the same as solving the letter a, the only difference is that the radius is not given so we get the formula for A, then substitute

640,000 k=πr2⟹r≈451.352 km

Then solve for dAdt

1,400 km2/s=2π(451.352 km)drdt⟹drdt≈0.494 km/s

8 0

3 years ago