The latest thrill ride at a popular theme park takes roller coaster fans on an exciting ride. In the first 20 seconds, it carries its passengers up a 100-meter hill, plunges them down 72 meters, and quickly takes them back up a 48-meter rise. How much higher or lower from the start of the ride are they after these 20 seconds?

HELP ME PLEASE!!!!

Answer:

Vertex form: f(x) = – (x – 3)² – 1  

vertex: (3, -1)

Step-by-step explanation:

Given the quadratic function, f(x) = -x²+ 6x -10:

where a = -1, b = 6, and c = -10

The vertex of a parabola is the point at which the parabola intersects the axis of symmetry. The axis of symmtery occurs at x = h. Therefore, the x-coordinate of the vertex is the same as h.

To find the vertex, (h, k), you need to solve for h by using the formula:  [tex]h = \frac{-b}{2a}[/tex]

Plug in the values into the formula:

[tex]h = \frac{-b}{2a}[/tex]

[tex]h = \frac{-6}{2(-1)} = 3[/tex]

Therefore, h = 3.

Next, to find the k, plug in the value of h into the original equation:

f(x) = -x²+ 6x -10

f(x) = -(3)²+ 6(3) -10

f(x) = -1

Therefore, the value of h = -1.

The vertex = (3, -1).

Now that you have the value for the vertex, you can plug these values into the vertex form:

f(x) = a(x - h)² + k

a =  determines whether the graph opens up or down, and makes the parent function wider or narrower.

h = determines how far left or right the parent function is translated.

k = determines how far up or down the parent function is translated.

Plug in the vertex, (3, -1) into the vertex form:

f(x) = – (x – 3)² – 1  

This parabola is downward-facing, with its vertex, (3, -1) as its maximum point on the graph.

Answer:

9 Should be your answer

Step-by-step explanation:

[tex]2^{2}[/tex] = 4

[tex]3^{2}[/tex] = 9

These will help us as we solve this problem.

Then: 2² + 3² - 2²

= 4 + 9 - 4

= 9

Kind requests:

Please give brainliest :D

Answer:

x = -10

Step-by-step explanation:

-2x - 10y = 20 (plug y=0)

-2x = 20

x = 20/-2

x = -10

Answer:

Step-by-step explanation:

[tex] \frac{ {2x}^{2} - 7x - 4 }{ {x}^{2} - 5x + 4 } \\ \frac{ {2x}^{2} + x - 8x - 4 }{ {x}^{2} - x - 4x + 4} \\ \frac{x(2x + 1) - 4(2x + 1)}{x(x - 1) - 4(x - 1)} \\ \frac{(x - 4)(2x + 1)}{(x - 4)(x - 1)} \\ \frac{2x + 1}{x - 1} \\ [/tex]

Answer:

Step-by-step explanation:

2 people make 2 bikes in 2 hours so  2 people can make 1 bike in 1 hour

So in 6 hours,  2 people can make 6 bikes.

So to make 12 bikes we need  2*2 = 4 people.

Answer:

Step-by-step explanation:

for vertex

x-2=0 gives x=2

when x=2,y=4

vertex (2,4)

axis of symetry

x-2=0

Answer:

<A is not congruent to angles B or C

Step-by-step explanation:

AB ~AC Given

<B ~ <C isosceles Triangle Theorem

The length of the side AB and AC will be congruent with each other. Then the triangle ΔABC will be an isosceles triangle.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The two triangular legs and their opposing angles are congruent in an isosceles triangle.

In triangle ΔABC, then the length of the side AB and AC will be congruent to each other.

AB = AC

Then the triangle ΔABC will be an isosceles triangle.

More about the triangle link is given below.

https://brainly.com/question/25813512

#SPJ2

We want to find and graph the motion equations by finding the ratios.

The graph can be seen at the end of the answer.

We define the rate of change as the rate at which one variable changes with respect to other.

Here, we know that you move 30 meters every 5 seconds, then your rate of change in position is:

r = 30m/5s = 6 m/s

Note that this is a speed.

For your friend, we know that he/she moves 9 meters in 2 seconds, so his/her rate is:

r' = 9m/2s = 4.5 m/s.

Now we need to graph these in a coordinate plane, but these are just numbers, I assume that you want the motion equation graphed.

The motion equations are just given by the rate we just fond times the variable, in this case, the variable is the time in seconds.

Your equation is:

p(t) = (6 m/s)*t

Your friend equation is:

p'(t) = (4.5 m/s)*t

The graphs can be seen below, the green one is the first function, and the blue one is the second.

If you want to learn more, you can read:

Answer:

B. 31.4

Step-by-step explanation:

To find x, the hypotenuse, we need to use sin because we have been given the opposite (the side opposite the angle 35°) and we need to work out the hypotenuse (the longest or slanted side):

SOH, CAH, TOA

sin(θ) = opposite ÷ hypotenuse

Sub in the values (we don't know the hypotenuse so i've called it x):

sin(35) = 18 ÷ x (multiply both sides by x)

x × sin(35) = 18 (divide both sides by sin(35))

x = 18 ÷ sin(35) = 31.38204...

x ≈ 31.4

Hope this helps!

Answer: 166,400,000 1000 bills

$166,400,000,000

Answer:

166,400,000

sry for answering late!

Answer:

pretty sure it's 65

Step-by-step explanation:

They're usually congruent for these type of angles. Also, y would be 50

Answer:

x = 50°

Step-by-step explanation:

y = 65° because the base angles of an isosceles triangle are equal

x = 50° because angles in a triangle add up 180°

Answer:

first multiply 3 with −8 and we get − 24

then find two numbers that if we add or subtract we get + 10 and if we multiply we get − 24

and the numbers are + 12 and −2

then we place those numbers as follow :-

3x²+12x−2x−8

then we group them

(3x2+12x)(−2x−8)

now take the common factor out.

3x(x+4)−2(x+4)

then group the numbers outside of the brackets

(3x−2)(x+4)

And that is the answer:

Proper Solution:-

1.) 3x2+10x−8

2.) 3x2+12x−2x−8

3.) (3x2+12x)(−2x−8)

4.) 3x(x+4)−2(x+4)

5.) (3x−2)(x+4)

Answer:

2373.8 dollars

Step-by-step explanation:

3652 times 35% equals 1272.2 so 3652 - 1272.2 = 2372.8

Answer:

53°

Step-by-step explanation:

As we can see that ∠3 and ∠7 are corresponding angles. Therefore,

Now calculate the angles of ∠3 and ∠7.

Now we can see that ∠3 and ∠1 are alternate angles and ∠7 and ∠1 are alternate exterior angles. Thus, we can say that

Hence the measure of ∠1 is 53°.

♦♦♦♦♦Hope it helps♦♦♦♦♦

Answer:

Yes, because it passes the vertical line test. If we were to draw a vertical line anywhere on the graph, it would only go through one point, so the relation is a function.

Step-by-step explanation:

1. This graph is a function because it passes the vertical line test. The vertical line test is a simple method that is used to determine if a relation is a function or not. A function can one output (y) for every unique input (x). If we were to draw a vertical line anywhere on the graph, and it would only go through one point, then the relation is a function. If it went through multiple points in some areas, it's not a function.

2. Since we can draw a vertical line anywhere and have it pass through one point, this relation is a function.

Answer:

x = 4.5

Step-by-step explanation:

[tex]\frac{x}{3}[/tex] = 1.5 ( multiply both sides by 3 to clear the fraction )

x = 3 × 1.5 = 4.5

Answer:

4 1/8

Step-by-step explanation:

subtracting a whole number with a fraction just means I have to change one of the numbers so they match with the other.

meaning I should change the whole number 5 to a fraction.

I will use the bottom number to figure out what the fraction in the whole number should look like.

5 = 5/1

I want the bottom number to be 8 like the other fraction 7/8

I multiply the top and bottom number of 5/1 by 8, giving me

40/8

now I subtract 40/8-7/8 = 33/8 or 4 and 1/8

Answer:

m∠1 = 107 degrees

m∠2 = 73 degrees

Step-by-step explanation:

1. ∠1 and the angle with 107 degrees are corresponding angles, which are located in the same relative position. They're congruent in measures, so m∠1 = 107 degrees.

2. ∠1 and ∠2 are a linear pair, meaning their angle measures add up to 180 degrees. Given m∠1 = 107 degrees, we just have to subtract 107 from 180 to get m∠2.

Therefore, m∠2 = 73 degrees.

Answer:

5 1/4

Step-by-step explanation:

To convert into an improper fraction, we times the whole number by the denominator and then add the numerator. For the first number, it is 15/4 and the second number is 7/5. Then we multiply 15/4 and 7/5 to get 5 1/4.

Answer:

99/5

Step-by-step explanation:

CONVERT INTO:

33/4 x 12/5

MULTIPLY THE FRACTIONS:

(33x12)

--------------

5

CANCEL TERMS:

(33x3)

-----------

5

SIMPLIFY:

99/5

Answer:

-6√3 - 9√2

Step-by-step explanation:

So you distribute like normal:

-3√3 times 2 is -6√3

-3√3 times √6 is -3√18

You can simplify -3√18 into -9√2

(because 9 can be squared into 3 and you can multiply the 3 with the current 3 into 9)

(Also you have to divide 9 out of 18 since you are simplifying)

So the answer will be -6√3-9√2

Hope this helps!

Answer:

No solutions

Step-by-step explanation:

I hope my answer help you.

Answer:

1.5 Or C :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Step 1: Equation at the end of step 1

Simplifying

60(x + 20) = 3x

Reorder the terms:

60(20 + x) = 3x

(20 * 60 + x * 60) = 3x

(1200 + 60x) = 3x

Solving

1200 + 60x = 3x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3x' to each side of the equation.

1200 + 60x + -3x = 3x + -3x

Combine like terms: 60x + -3x = 57x

1200 + 57x = 3x + -3x

Combine like terms: 3x + -3x = 0

1200 + 57x = 0

Add '-1200' to each side of the equation.

1200 + -1200 + 57x = 0 + -1200

Combine like terms: 1200 + -1200 = 0

0 + 57x = 0 + -1200

57x = 0 + -1200

Combine like terms: 0 + -1200 = -1200

57x = -1200

Divide each side by '57'.

x = -21.05263158

Simplifying

x = -21.05263158

Answer:

forgive me i need points

Step-by-step explanation: