Starfish have about 15,000 tiny feet that help them move around the ocean floor. The table shows the distance traveled by a starfish over a given time.

Answer:

  a.  4, 6

  b.  -72

  c.  (5, 3)

  d.  Graph A

Step-by-step explanation:

To answer these questions, it is useful to start by factoring the equation.

  y = -3x² +30x -72 . . . . given

  y = -3(x² -10x +24) . . . . factor out leading coefficient

  y = -3(x -4)(x -6)

The x-intercepts are the values of x that make the factors zero:

  x = 4, 6

__

The y-intercept is the constant in the equation: -72.

__

We know the x-coordinate of the vertex is the midpoint between the x-intercepts: (4+6)/2 = 5. The y-coordinate can be found by evaluating y at that x-value.

  y = -3(5 -4)(5 -6) = -3(1)(-1) = 3

The vertex is (5, 3).

__

The graph that has the correct vertex and x-intercepts is Graph A.

Answer:

x^2 - 5x -36

Step-by-step explanation:

multiply x-9 by x to get x^2 -9x. multiply x-9 by 4 to get 4x-36. add these two together to get x^2 - 9x + 4x - 36. simplify to get x^2 - 5x -36

Answer:

X=22.5

Step-by-step explanation:

Y=kX

20=15k

k=4/3

For X when Y=30

30=4/3×X

Cross multiply

4X=90

X=22.5

Answer:

given slope of 2 and a y intercept of 0

f(x) = 2x

[tex] \: \: \: \: [/tex]

[tex]elipse \: \: \: with \: \: the \: \: center (3, - 4)[/tex]

The length of major axis of the ellipse 2√32.

The length of minor axis of the ellipse 2√18.

What is an ellipse?

The standard form of the ellipse is defined as;

x² / a² + y² / b² = 1

Where, a < b

Minor axis of the ellipse = 2a

And, Major axis of the ellipse = 2b

Given that;

The equation of the ellipse is,

(x−3)² / 18 + (y+4)² /32 = 1

Now,

We can compare with the standards form of an equation of ellipse, we get;

a² = 18

a = √18

And, b² = 32

b = √32

Clearly, √18 < √32

That is; a < b

So, The minor axis of the ellipse = 2a

                                                  = 2√18

And, The major axis of the ellipse = 2b

                                             = 2√32

Therefore,

The length of major axis of the ellipse 2√32.

The length of minor axis of the ellipse 2√18.

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Answer:

a is 2 b is 5 ď is 3 e is 5 and that is it this is not the correct awns

Answer:

[tex]1,325\geq 26x+270[/tex]

Step-by-step explanation:

Step-by-step explanation:

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Answer:

y=-5/2x+2

y+3= -5/2. (x-2)

Step-by-step explanation:

Answer:

y=-5/2x+2

Step-by-step explanation:

y=mx+b, where m is slope, b is y-int and y and x are variables.

Step 1: plot your points

Step 2: draw a line thru them

Step 3: find the slope. -5/2. And your y-int. +2

Hope that helps! Brainliest is appreciated :)

Answer: 40

Step-by-step explanation: if 8 stops complete 20% of the map 100% is 5 times that so 8x5 is 40 so 40 stops in total

The total number of stops in her trip is 40.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Amy has just completed stop 8 and the map shows she is 20% complete.

let the total number of stops be x

So, 20% of x = 8

20/100x= 8

1/5x = 8

x= 40

Hence, the total number of stops in her trip is 40.

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Step-by-step explanation:

Here

5x+16+7x-3+6x+5 = 180(being sum of triangle)

or, 18x=180-18

or, x= 162/18

so, x = 9

now,

here,

<ACD = <ACB(diagonals of parallelogram bisect eachother)

or, <ACD = 7x-3

or, <ACD = 7×9-3

or, <ACD = 63-3

So, <ACD = 60°

Answer:

AB ≈ 5.6 cm

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos62° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AB}{BC}[/tex] = [tex]\frac{AB}{12}[/tex] ( multiply both sides by 12 )

12 × cos62° = AB , then

AB ≈ 5.6 cm ( to 1 dec. place )

Step-by-step explanation:

422 - 115

= 307

The taste of new York made $307 more than pizzeria italiano

Answer:

its half way correct. get rid of the dot on the 2.

Step-by-step explanation:

the point (2, -6) is where the dot is supposed to be located. the 2 is the x point. and the -6 is the y point. so u go to the right 2 and then u go down 6. so the point is where the lowest dot is located

[tex]y= -\frac{3x}{2} +1[/tex]

Answer:

Yes, it is a solution.

Step-by-step explanation:

Plug in 2 into x and 6 into y, because 2 is the x value of the ordered pair and 6 is the y value of the ordered pair.

1st linear equation: 2+6=8, this is true.

2nd linear equation: 3x2-6=0, this is also true.

Therefore, since the ordered pair is a solution to both equations, it is a solution of the linear system.

Answer:

  x = {-2 5/6, +2}

Step-by-step explanation:

To use the quadratic formula, it is helpful to write the equation in standard form.

  (2x +1)(3x +1) = 35

  6x^2 +5x -34 = 0 . . . . . . . subtract 35 and simplify. a=6, b=5, c=-34

The quadratic formula tells you the values of x are ...

  [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-5\pm\sqrt{5^2-4(6)(-34)}}{2(6)}\\\\=\dfrac{-5\pm\sqrt{841}}{12}=\dfrac{-5\pm29}{12}\\\\\boxed{x=\left\{-\dfrac{17}{6},2\right\}}[/tex]

Answer:

is there a pic?

Step-by-step explanation:

we are able to see

Answer: where’s the question

Answer:

y+4=-5/6(x-8)

Step-by-step explanation:

y-y1=m(x-x1)

y-(-4)=-5/6(x-8)

y+4=-5/6(x-8)

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Answer:

i believe its 2 but i might be wrong sorry if i am

Step-by-step explanation:

I think it could be number 1 or number 2

Answer:

Step-by-step explanation:

equation for tiger shark:

for each additional year, it grows by 2.5 cm so that would be shown as 2.5x. also it starts at 55 so you would have to add 55 to that 2.5x.

the equation would be y = 2.5x + 55

equation for hammerhead:

do the same process with the other numbers. this would be

y = 5x + 25

solve with elimination:

subtract the two equations, which would eliminate the y variable

y = 5x + 25

- (y = 2.5x + 55)

you get

0 = 2.5x - 30

solve that for x

2.5x = 30

x = 12 years

so the years that have passed is 12. to find the length, plug in x = 12 into one of the equations:

y = 5x + 25 becomes y = 5 * 12 + 25 = 60 + 25 = 85

so they will be 85 cm long each.

Answer:

Rate of change is correct; it's -3. And when the x-value is 8, the y-value is just a value, not a coordinate point. It's one number. -3 would not be the answer, and i dont know what the answer would be, but it's between greater than -14 and less than -23. Hope this helps!!

Step-by-step explanation:

Im not good at explaining things without it sounding very confusing... sorry.

Answer:

13 in12

Step-by-step explanation:

Answer:

51, 53, 55, 58, 60

Step-by-step explanation:

The minimum is the lowest value in the data set, that is 51

The maximum is the largest value in the data set, that is 60

The median is the middle value of the data, arranged in ascending order. If there is no exact middle then it is the average of the 2 values either side of the middle.

51, 51, 53, 53, 54, 55, 55, 56, 58, 58, 58, 59, 60

                                     ↑ middle

median = 55

The lower quartile is the middle value to the left of the median

51, 51, 53, 53, 54, 55

               ↑

Q₁ = [tex]\frac{53+53}{2}[/tex] = [tex]\frac{106}{2}[/tex] = 53

The upper quartile is the middle value of the data to the right of the median

56, 58, 58, 58, 59, 60

                 ↑

Q₃ = [tex]\frac{58+58}{2}[/tex] = [tex]\frac{116}{2}[/tex] = 58