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2 years ago

5

If I wanted to change the vertex of a quadratic function from (2,3) to (-1,6), what form would you use and what would you do to

it?

1 answer:

vampirchik [111]2 years ago

3 0

This is a translation and it is most easily done with the vertex from of the equation. change vertex to (-1,6): y=a(x+1)+6

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Solve the equation for x by graphing -2x + 3 = -3(-x) - 2

adoni [48]

Answer:

x = 1

Step-by-step explanation:

There are a couple of ways to solve this. One is to graph the left side of the equation, graph the right side of the equation, and look for the point where those graphs intersect. It is at x = 1. The first attached graph shows this solution.

__

Another method for solving such an equation is to subtract one side from the other and look for the value of x that makes the resulting expression zero.

(-2x +3) -(-3(-x) -2) = 0

A graphing calculator doesn't need to have this simplified. If it is simplified, it becomes ...

-5x +5 = 0

So, the graphed line is y = -5x+5. Its x-intercept is x=1, the solution of the original equation. The graph of this is shown in the second attachment.

6 0

2 years ago

A theater group made appearances into cities the hotel charge before tax and the second city was 1500 higher than the first the

Svetlanka [38]

Answer:

The hotel charge in each city before tax was <u>$5125</u> of the first city and <u>$3625</u> of the second city.

Step-by-step explanation:

Given:

A theater group made appearances into cities the hotel charge before tax and the second city was 1500 higher than the first.

The tax of the first city was 6% and the tax of the second city was 10%.

Total hotel tax paid for two cities with $670.

Now, to find the hotel charge in each city before tax.

Let the hotel charge in first city before tax be $x.$

And the hotel charge in second city before tax be $y.$

<em>So, as the hotel charge of the second city was 1500 higher than the first.</em>

<em>Thus</em>,

$y=x-1500$ ........(1)

<em>And as given, the tax of the first city was 6% and the tax of the second city was 10%, total hotel tax paid for two cities with $670.</em>

6% of $x$ + 10% of $y$ = $670.

$\frac{6x}{100} +\frac{10y}{100} =670$

$0.06x+0.10y=670$

Substituting the value of $y$ from equation (1) we get:

$0.06x+0.10(x-1500)=670$

$0.06x+0.10x-150=670$

$0.16x-150=670$

<em>Adding both sides by 150 we get:</em>

$0.16x=820$

<em>Dividing both sides by 0.16 we get:</em>

$x=5125.$

<em>The hotel charge in first city before tax = $5125.</em>

Now, substituting the value of $x$ in equation (1) we get:

$y=x-1500$

$y=5125-1500$

$y=3625.$

<em>The hotel charge in second city before tax = $3625.</em>

Therefore, the hotel charge in each city before tax was $5125 of the first city and $3625 of the second city.

5 0

3 years ago

<img src="https://tex.z-dn.net/?f=f%28n%29%3D3%5En" id="TexFormula1" title="f(n)=3^n" alt="f(n)=3^n" align="absmiddle" class="la

andrezito [222]

Answer:

$24(f(n))$

Step-by-step explanation:

$f(n+3) = 3^{n+3}\\f(n+1) = 3^{n+1}$

so

$f(n+3) - f(n+1) = 3^{n+3} - 3^{n+1}$

$= 27(3^n) - 3(3^n)$

$= 24(3^n)$

$= 24(f(n))$

hope this helped! :)

4 0

1 year ago

2 2/3× 4 1/5 help me plzzzzz!!!

Rus_ich [418]

First let's multiply the whole numbers 2 and 4. Obviously that is 8. Now let's put aside the whole number and multiply fractions.

2/3 x 1/5 is equal to 2x1/3x5 so it's 2/15 which is already in simplest form.

So your final answer is 8 and 2/15 :)

If this was helpful would you mind marking mine as brainliest please? It helps me rank up a lot!

8 0

2 years ago

A bag contains 6 green counters, 4 blue counters and 2 red counters. Two counters are drawn from the bag at random without repla

Svetach [21]

Answer:

24.24%

Step-by-step explanation:

In other words we need to find the probability of getting one blue counter and another non-blue counter in the two picks. Based on the stats provided, there are a total of 12 counters (6 + 4 + 2), out of which only 4 are blue. This means that the probability for the first counter chosen being blue is 4/12

Since we do not replace the counter, we now have a total of 11 counters. Since the second counter cannot be blue, then we have 8 possible choices. This means that the probability of the second counter not being blue is 8/11. Now we need to multiply these two probabilities together to calculate the probability of choosing only one blue counter and one non-blue counter in two picks.

$\frac{4}{12} * \frac{8}{11} = \frac{32}{132}$ or 0.2424 or 24.24%

8 0

2 years ago