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Related Questions

Last year 950 people attended a town's annual parade. This year 1,520 people attended. What was the percent increase in attendance from last year to this year?

Answers

Answer: 60% increase

Step-by-step explanation: look up calculator soup if you have more questions like this

A quadratic function y = f(x) is plotted on a graph and the vertex of the resulting
parabola is (6, -3). What is the vertex of the function defined as
g(x) = f(-x) - 3?

Answers

Answer: (-6, - 6)

Step-by-step explanation:

Here we have two transformations, and the first step will be to explain those transformations:

Reflection over the y-axis.

For a function f(x), the reflection over the y-axis is written as:

g(x) = f(-x)

Then if we initially had a point (x, y), the transformed point will be (-x, y).

Vertical translation.

We can define a vertical translation of N units as:

g(x) = f(x) + N

if N > 0, the translation is up.

If N < 0, the translation is down.

Then if we start with a point (x, y), the transformed point will be (x, y + N)

In the case of this problem we have g(x) = f(-x) - 3

This means that N = -3

Then if we initially had the vertex at the point (6, - 3)

The transformed point will be: changing the sign of the x-component and subtracting 3 in the y-component, then the transformed vertex point is:

(-6, -3 - 3) = (-6, - 6)

The vertex of the resulting  parabola will be (-6, -6)

Rule of reflection

Given the function y= f(x), plotted on a graph and the vertex of the resulting

parabola is (6, -3), if this coordinate is reflected over the y-axis, the reflection rule will be:

[tex](x,y) \rightarrow (-x, y)[/tex]The coordinate (6, -3) under this translation will give (-6, -3)

To get the corresponding function [tex]g(x) = f(x) - 3\\[/tex]

[tex]g(x) = [(-6, -3) - 3]\\g(x) = (-6, -3-3)\\g(x) =(-6, -6)[/tex]

Hence the vertex of the resulting  parabola will be (-6, -6)

Learn more on reflection here: https://brainly.com/question/14460986

What's the solution to -182=2(1+2x)-2

Answers

-182=2(1+2x)-2

2*1=2
2*2x=4x

-182=4x+2-2
-182=4x
-45.5=x

Answer: [tex]x = -\frac{91}{2}[/tex]

Step-by-step explanation:

If you have any questions, feel free to ask :)

Step 1: Add [tex]2[/tex] to both sides.

[tex]-182 + 2 = 2(1 + 2x)[/tex]

Step 2: Simplify [tex]-182 + 2[/tex] to [tex]-180[/tex].

[tex]-180 = 2(1 + 2x)[/tex]

Step 3: Divide both sides by [tex]2[/tex].

[tex]-\frac{180}{2} = 1 + 2x[/tex]

Step 4: Simplify [tex]\frac{180}{2}[/tex] to [tex]90[/tex].

[tex]-90 = 1 + 2x[/tex]

Step 5: Subtract [tex]1[/tex] from both sides.

[tex]-90 - 1 = 2x[/tex]

Step 6: Simplify [tex]-90 - 1[/tex] to [tex]-91[/tex].

[tex]-91 = 2x[/tex]

Step 7: Divide both sides by [tex]2[/tex].

[tex]-\frac{91}{2} = x[/tex]

Step 8: Switch sides.

[tex]x = -\frac{91}{2}[/tex]

~I hope I helped you :)~

A plumber uses the expression 48 + 25h to determine the number of dollars to charge each customer. If h= 2.5, how much does the customer pay

Answers

Answer:

$110.5

Step-by-step explanation:

48 + 25(2.5)

48 + 62.5

=110.2

Answer:

The answer is 110.5

Step-by-step explanation:

48+25(2.5)=110.5

A plane set off to Portland at a speed of 232 mph. On the
return flight of 12 hours, the plane cruised at 204 mph.
How many hours long was the flight to Portland?

Answers

Answer:

The flight to Portland takes 10.6 hours.

Step-by-step explanation:

To find the time of flight to Portland we need to calculate the distance traveled by using the equation:

[tex] x = v*t [/tex]

Where:

v: is the speed = 204 mph (return flight)

t: is the time = 12 h (return flight)

[tex] x = v*t = 204 mi/h*12 h = 2448 mi [/tex]

Now, we can find the time of flight to Portland using v = 232 mph:

[tex]t = \frac{x}{v} = \frac{2448 mi}{232 mi/h} = 10.6 h[/tex]

Therefore, the flight to Portland takes 10.6 hours.

I hope it helps you!