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4. Ray needs help creating the second part of the coaster. Create a unique parabola in the pattern f(x) = (x − a)(x − b). Describe the direction of the parabola and determine the y-intercept and zeros.


5. Create a graph of the polynomial function you created in Question 4

Answer:

Step-by-step explanation:

Break up the shape into a trapezoid and rectangle:

Trapezoid area = (Top + Bottom) * Height / 2

= (9 + 20) * (21-16) / 2

= 29 * 5 / 2

= 72.5

Rectangle area = Length * Width

= 20 * 16

= 320

Combining, the total area = 72.5 + 320

= 392.5 in^2

Answer:

A = 392.5 in²

Step-by-step explanation:

The composite figure is made up of a rectangle and a trapezoid.

Calculate the area of the rectangle:

[tex]\begin{aligned}\textsf{Area of a rectangle}&=\sf length \times width\\&=20 \times 16\\&=320\; \sf in^2\end{aligned}[/tex]

Calculate the area of the trapezoid:

[tex]\begin{aligned}\textsf{Area of a trapezoid}&=\dfrac{\text{base}\;a+\text{base}\;b}{2} \times \text{height}\\&=\dfrac{9+20}{2} \times (21-16)\\&=\dfrac{29}{2} \times 5\\&=72.5\; \sf in^2\\\end{aligned}[/tex]

Therefore, the area of the composite figure it the sum of the area of the rectangle and the area of the trapezoid:

[tex]\begin{aligned}\textsf{Total area of composite figure}&=\textsf{Area of rectangle}+\textsf{Area of trapezoid}\\&=320+72.5\\&=392.5 \; \sf in^2\end{aligned}[/tex]

Therefore, the area of the composite figure is 392.5 in².

Answer:

There are 6 congruent triangles in a regular hexagon.

The triangles are equilateral (all sides are equal in length).

Using side length of equilateral triangle formula:

[tex]\sf x=\sqrt{\dfrac{4}{3}h^2}[/tex]

where x is the side length and h is the height

[tex]\sf \implies x=\sqrt{\dfrac{4}{3}\cdot 6^2}[/tex]

[tex]\sf \implies x=\sqrt{48}[/tex]

[tex]\sf \implies x=4\sqrt{3} \ units[/tex]

Therefore, perimeter = 6 × 4√3 = 24√3 units

Radius = side length of triangle = 4√3 units

Side Be a

[tex]\\ \rm\rightarrowtail h=\dfrac{\sqrt{3}}{2}a[/tex]

[tex]\\ \rm\rightarrowtail 6=\dfrac{\sqrt{3}}{2}a[/tex]

[tex]\\ \rm\rightarrowtail 12=\sqrt{3}a[/tex]

[tex]\\ \rm\rightarrowtail a=12/\sqrt{3}[/tex]

[tex]\\ \rm\rightarrowtail a=4\sqrt{3}[/tex]

Perimeter:-

The value of the dilated line segments P'Q', A'B' and M'N' are 4 cm. 3 cm and 6 cm

Dilation is the increase or decrease in the size of an figure or object.

A dilation with a scale factor of 2 is applied to the three line segments shown to form P'Q', A'B', and M'N'.

Hence:

P'Q' = scale factor * PQ = 2 * 2 = 4 cm

A'B' = 2 * 1.5 = 3 cm

M'N' = 2 * MN = 2 * 3 = 6 cm

The value of the dilated line segments P'Q', A'B' and M'N' are 4 cm. 3 cm and 6 cm

Find out more on dilation at: https://brainly.com/question/10253650

S=0,5ha

4.06=0,5ha

ha=8.12

a=8.12/h

Answer:

  3/4

Step-by-step explanation:

You can form the product, then cancel common factors, or you can cancel common factors before you form the product.

__

  [tex]5\times\dfrac{3}{20}=\dfrac{15}{20}=\dfrac{3\cdot5}{4\cdot5}=\boxed{\dfrac{3}{4}}\\\\\textsf{or ...}\\\\5\times\dfrac{3}{20}=\dfrac{5}{20}\cdot\dfrac{3}{1}=\dfrac{1}{4}\cdot\dfrac{3}{1}=\boxed{\dfrac{3}{4}}[/tex]

Answer:

58km

Step-by-step explanation:

perimeter of rectangle= 2x(l+b)

2x(28+1)

2x29=58

Answer:

y=-2x-1

Step-by-step explanation: This is because of rise/run. This means rise, count up or down until you hit the line that is horizontal to where your line intersects a whole point. Then run, what you count horizontal matches with your rise count. This means we can count 2/1 and since it's going down it's negative. So the slope is -2 and the y-intercept is -1 because it intersects through the y-intercept -1.

Answer:

The answer is -1.5

Step-by-step explanation:

Hope that helps.

Answer:

Step-by-step explanation:

-3/4 + (-3/4) remove parentheses

-3/4- 3/4 calculate the difference

-3/2 or - 1 1/2 or -1.5

Answer:

2.

Step-by-step explanation:

This is called the ambibuous case where  2 sides are given and angle opposite one of these sides.

2 traingles are possible.

Answer:

According to the graph:

H^2 + 10^2 = 21^2

Solve as:

H = 18.19 feet

So the height is 18.19 feet

Answer:

[tex]\boxed{\sf{y=2x+7}}[/tex]

Step-by-step explanation:

Use a slope formula and slope-intercept formula.

Slope-intercept formula:

[tex]\sf{y=mx+b}[/tex]

The m represents the slope.

The b represents the y-intercept.

Slope formula:

[tex]\sf{\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

[tex]\sf{y_2=9}\\\\\sf{y_1=(-3)}\\\\\sf{x_2=1}\\\\\sf{x_1=(-5)}[/tex]

Rewrite the problem down.

[tex]\sf{\dfrac{9-(-3)}{1-(-5)}=\dfrac{9+3=12}{1+5=6}=\dfrac{12}{6}=2 }[/tex]

y=2x+7

I hope this helps you! Let me know if my answer is wrong or not.

Answer:

8.49 and No

Step-by-step explanation:

C² - b² = a² (pythagorus rule rearranged for a²)

9² - 3² = a²

81 - 9 = a²

a² = 72

a = 8.49 and no they aren't a triple.

Answer:

140.80

Step-by-step explanation:

Not completely sure if my answer is correct

Answer:

assuming they only have to pay for parking once, 8 friends can go, if each person has to pay for parking and ticket only 5 people can go, Im assuming it'll be 8 for the answer tho I hope I'm right

There are 8 people can go to the amusement park.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given:

Total amount = $285.75

Parking = $13.75

Price of ticket per person = $34.

So, money left after paying for parking

=285.75 - 13.75

= 272

Now, number of people in amusement park

= 272/34

=8

Hence, 8 people can go to the amusement park.

Learn more about unitary method here:

https://brainly.com/question/22056199

#SPJ6

Answer: A. Obstacle

Step-by-step explanation: They have the same meaning.

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Point Form:

[tex](0,7),(-13,-97)[/tex]

Equation Form:

[tex]x=0,y=7\\x=-13,y=-97[/tex]

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    y-(8*x+7)=0

Equation of a Straight Line

Solve   y-8x-7  = 0

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.'

n this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  y-8x-7  = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 7/1 so this line "cuts" the y axis at y= 7.00000

 y-intercept = 7/1  =  7.00000

Calculate the X-Intercept :

When y = 0 the value of x is 7/-8 Our line therefore "cuts" the x axis at x=-0.87500

 x-intercept = 7/-8  = -0.87500

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 7.000 and for x=2.000, the value of y is 23.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 23.000 - 7.000 = 16.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

   Slope     = 16.000/2.000 =  8.000

Geometric figure: Straight Line

 Slope = 16.000/2.000 = 8.000

 x-intercept = 7/-8 = -0.87500

 y-intercept = 7/1 = 7.00000

Pull out like factors :

  -x2 - 5x - 7  =   -1 • (x2 + 5x + 7)

Trying to factor by splitting the middle term

2.2     Factoring  x2 + 5x + 7

The first term is,  x2  its coefficient is  1 .

The middle term is,  +5x  its coefficient is  5 .

The last term, "the constant", is  +7

Step-1 : Multiply the coefficient of the first term by the constant   1 • 7 = 7

Step-2 : Find two factors of  7  whose sum equals the coefficient of the middle term, which is   5 .

     -7    +    -1    =    -8

     -1    +    -7    =    -8

     1    +    7    =    8

     7    +    1    =    8

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Find the Vertex of   y = -x2-5x-7

Parabolas have a highest or a lowest point called the Vertex .   Our parabola opens down and accordingly has a highest point (AKA absolute maximum) .    We know this even before plotting  "y"  because the coefficient of the first term, -1 , is negative (smaller than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two  x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is  -2.5000  

Plugging into the parabola formula  -2.5000  for  x  we can calculate the  y -coordinate :

 y = -1.0 * -2.50 * -2.50 - 5.0 * -2.50 - 7.0

or   y = -0.750

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = -x2-5x-7

Axis of Symmetry (dashed)  {x}={-2.50}

Vertex at  {x,y} = {-2.50,-0.75}

Function has no real roots

Solve Quadratic Equation by Completing The Square

3.2     Solving   -x2-5x-7 = 0 by Completing The Square .

Multiply both sides of the equation by  (-1)  to obtain positive coefficient for the first term:

x2+5x+7 = 0  Subtract  7  from both side of the equation :

  x2+5x = -7

Now the clever bit: Take the coefficient of  x , which is  5 , divide by two, giving  5/2 , and finally square it giving  25/4

Add  25/4  to both sides of the equation :

 On the right hand side we have :

  -7  +  25/4    or,  (-7/1)+(25/4)

 The common denominator of the two fractions is  4   Adding  (-28/4)+(25/4)  gives  -3/4

 So adding to both sides we finally get :

  x2+5x+(25/4) = -3/4

Adding  25/4  has completed the left hand side into a perfect square :

  x2+5x+(25/4)  =

  (x+(5/2)) • (x+(5/2))  =

 (x+(5/2))2

Things which are equal to the same thing are also equal to one another. Since

  x2+5x+(25/4) = -3/4 and

  x2+5x+(25/4) = (x+(5/2))2

then, according to the law of transitivity,

  (x+(5/2))2 = -3/4

We'll refer to this Equation as  Eq. #3.2.1  

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

  (x+(5/2))2   is

  (x+(5/2))2/2 =

 (x+(5/2))1 =

  x+(5/2)

The answer is: Yes, all conditions for inference are met.

I think you meant solve [tex](4^2)x(2^9)[/tex]

Answer:

8192

Step-by-step explanation:

Given:

[tex]\left(4^2\right)x\left(2^9\right)[/tex]

Solution:

[tex]\left(4^2\right)x\left(2^9\right)[/tex]

[tex]=4^2x \:2^9[/tex]

[tex]4^2=16[/tex]

[tex]=16x \:2^9[/tex]

[tex]2^9=512[/tex]

[tex]=16x\:512[/tex]

[tex]\mathrm{Multiply\:the\:numbers:}\:16\cdot \:512=8192[/tex]

[tex]=8192[/tex]

~lenvy~

Answer:

=> 8192

Step-by-step explanation:

Given :

(4²)x(2⁹)

=> (16)x(512)

=> 16.512

=> 8192

Answer:

(2x,2y)

Step-by-step explanation:

Hope this helps!!!

Answer:

48%

Step-by-step explanation:

there are 250 cars in total 50+70 is 120 (the red  or blue cars)

so there are 120 "yes" out of 250 total of 120 divided by 250 equal 0.48 or 48%

Answer:

10 hours

Step-by-step explanation:

multiply b 2 then divided the miles and time and add to the total to get the time and miles you need

Check the picture below.

Answer:

p = 35

Step-by-step explanation:

the midsegment WY is half the measure of VZ , that is

WY = [tex]\frac{1}{2}[/tex] VZ ( substitute values )

p - 21 = [tex]\frac{1}{2}[/tex] (p - 7) ← multiply through by 2 to clear the fraction

2p - 42 = p - 7 ( subtract p from both sides )

p - 42 = - 7 ( add 42 to both sides )

p = 35

Answer:

4 ways

Step-by-step explanation:

Given

Possible combinations

Answer:

Step-by-step explanation:

[tex]y=ab^x\\x=0,y=4\\4=ab^0\\4=a(1)\\a=4\\y=4b^x\\x=2,y=256\\256=4b^2\\b^2=\frac{256}{4} =64\\b=\pm8\\y=4(8)^x\\or\\y=4(-8)^x[/tex]

Answer:

Step-by-step explanation:

16% of 250

250% of 16

Both outcomes are same so the answer is True

Let's check

16% of 250

250% of 16

Yes true

Answer:

1062

Step-by-step explanation: Find the area of each side then add it all up