Given the three points (0,3), (4,15), (5,33), determine the equation of the parabola they represent. State the direction the parabola opens. A) The equation is f(x)=3x^2−33/4x+3, and the parabola opens upward B)The equation is f(x)=−3x^2+9x+3, and the parabola opens downward C)The equation is f(x)=−4x^2−13x+3, and the parabola opens downward. D)The equation is f(x)=3x^2−9x+3, and the parabola opens upward.

Answer:

a) FC ←→ and BD ←→ are distinct lines that intersect.

b) B , C and D are distinct points that are collinear.

c) Another name for plane [tex]X[/tex] is plane AEF.

d) E , A , F and C are distinct points that are coplanar.  

Step-by-step explanation:

The first step to solve this question is to look carefully at the picture.

For a) :

We can see that the line FC and the line BD intersect at the point C.

We can write :

a) FC ←→ and BD ←→ are distinct lines that intersect (we can see more lines that intersect with FC ←→ in the picture such as AC ←→  or AE ←→).

For b) :

We can see that the line BD ←→ passes through the points B , C and D (B , C and D are collinear points).  

We can write :

b) B , C and D are distinct points that are collinear.

For c) :

We can name any plane using three points which are contain in the plane but this three points must not be collinear points.

We can name the plane [tex]X[/tex] using the points A , E and F (this is a possible solution).

We can write :

c) Another name for plane [tex]X[/tex] is plane AEF.

Finally, for d) :

Two or more points are coplanar wherever they belong to the same plane.

In the picture, the points A , E , F and C belong to the plane [tex]X[/tex].

We can write :

d) E , A , F and C are distinct points that are coplanar.

Answer:

g(x) = -2|x+1| -3

Step-by-step explanation:

f(x) = |x|

y = f(x) + C C < 0 moves it down

y = |x| -3  for  shifting down 3

y = f(x + C) C > 0 moves it left

y = |x+1| -3 for move it left 1

y = Cf(x)  C > 1 stretches it in the y-direction

y = 2|x+1| -3 to stretch it 2 vertically

y = −f(x)  Reflects it about x-axis

y = -2|x+1| -3

We start off with f(x) = |x|

c < 0 means move down

y = f(x) + c

3 units down

After: y = |x| - 3

c > 0 means move left

y = f(x + c)

1 unit left

After: y = |x + 1| - 3

c > 1 means y direction stretch

y = cf(x)

2 unit stretch

After: y = 2|x + 1| - 3

Reflect across x-axis can be stated as y = -f(x)

After: y = -2|x + 1| - 3

Best of Luck!

Step-by-step explanation:

Hey there!!!

Here,

Firstly, Shift n to right side and -4 to the left side, because we always try to have variable as positive.

[tex] - 8+4 = + 5n-n[/tex]

Now, Simplify them.

[tex] - 8 + 4 = 5n - n[/tex]

[tex] - 4 = 4n[/tex]

You should divide now.

[tex]n = \frac{ - 4}{4} [/tex]

Therefore the value of n is -1.

{ As now you can keep it on left side. We generally find the vallue of variable by keeping it on left side. But we kept it right side in solution to avoid our confusion because if we kept it on left side and you would get harder to find the value at last as we need to transpose (-) to the right side value of n}.

Hope it helps...

Answer:

38.3

Step-by-step explanation:

multiply l x w to get your answer then just round. Hope it helps!!

Answer:

750 miles

Step-by-step explanation:

Ronald

Rental fee = fixed cost + variable cost

= $25 + $0.05x

Where x = number of miles

Dixon

Rental fee = fixed cost + variable cost

= $40 + $0.03x

How many miles must they both drive for their rental fees to be the same?

Equate the two equations

$25 + $0.05x = $40 + $0.03x

Collect like terms

0.05x - 0.03x = 40 - 25

0.02x = 15

Divide both sides by 0.02

x = 15 / 0.02

= 750 miles

Answer:

Step-by-step explanation:

2x - 8 + 9

2x + 1

Answer:

YOUR ANSWER IS 2x+1

HOPED THAT HELPED☺

Step-by-step explanation:

2(x-4) +3^2

multiply 2 to(x-4)

solve for 3^2

2x-8+9

add -8to9

2x+1

x = a number

4(x + 5) = x - 1

Now, let's distribute the 4

4x + 20 = x - 1

Subtract x and 20 from both sides.

3x = -21

Divide both sides by 3

x = -7

Answer:

37 mph

Step-by-step explanation:

Step 1:

74 ÷ 2

Answer:

37

Hope This Helps :)

Answer:

48 meters squared or 48m^2

(Both are correct. Whichever you prefer is fine.)

Step-by-step explanation:

The formula to find area is A=height*base

So since the base = 6 and height = 8

Just multiply to combine the two

6*8=48

If you want to show with only numbers write this.

A=b*h

6*8=48

48 meters squared or 48m^2

Answer:

Step-by-step explanation:

2 + 4 > 8

6 > 8

not true

Answer:

5

Step-by-step explanation:

Replace variables with integers

(-2) - (-7)

Solve.

-2 - (-7) --> -2 + 7 --> 5

Answer: it becomes a positive

Step-by-step explanation:

Answer:

The number is 76

Step-by-step explanation:

Answer:

The Ford Mustang can travel at a faster rate.

Step-by-step explanation:

160/2 = 80/1   miles/hour -Ford Mustang

210/3 = 70/1    miles/hour - Toyota Corolla

Answer:

ANSWER:-

Step-by-step explanation:

AB+BC=AC

17+9

=26 is the answer.

Answer:

The range is { 7,8}

Step-by-step explanation:

The range of the functions is the output values

We do not list the repeated values more than one and normally list them from smallest to largest

The range is { 7,8}

Answer:

26

Step-by-step explanation:

APPLY PEMDAS:

Evaluate the numbers in the parentheses before evaluating the whole equation.

[tex](9+33-6)-3-7\\\\36 - 3 -7\\\\33-7\\\\\boxed{26}[/tex]

Hope this helps.

then try -21.4 that should work

Answer:

See below.

Step-by-step explanation:

f(x) = -|x + 9|

compared to

f(x) = |x|

has a graph that opens downward in an upside down V shape.

It has been moved 9 units left compared to the graph of f(x) = |x|.

It reflects over the x-axis.

Answer:

reflective

Step-by-step explanation:

This statement shows the reflective property.

She works 10 hour per day

Answer: 45 Seconds

Step-by-step explanation: Because if you do 3/4=0.75 or 75%. Knowing that a minute is 60 seconds long. 75% of 60 is 45 Seconds.

Hope this helped!

Answer:

answer of your question is

-x= -7

Answer:

___________________

Answer:

[tex]9[/tex]

Step-by-step explanation:

So we have the expression:

[tex]\sqrt{6-25t}[/tex]

And we want to find the value of the expression when t is -3.

So, substitute -3 for t:

[tex]\sqrt{6-25(-3)}[/tex]

Multiply:

[tex]=\sqrt{6+75}[/tex]

Add:

[tex]=\sqrt{81}[/tex]

Evaluate:

[tex]=9[/tex]

So, our answer is 9.

And we're done!

Answer:

There is a 1 in 5 chance that the letter will be I.

Step-by-step explanation:

There are ten letters in the word and 2 are I's. 2/10 simplifies to 1/5.

Answer:

2/10 or 20%

Step-by-step explanation:

if you were to pick at random

out of all i would have a 20 percent chance to be chosen

Answer:

The Answer to 17 1/3 x 8 is 138.67

There is not enough context to answer the second question.