Fill in the table of values so that this is a proportional relationship with k=3/2 X. Y. *blank*. 0 2. *blank*. *blank*. 6. -2. *blank*

Answer:

The maximum height of the basketball is of 24.25 feet.

Step-by-step explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

[tex]f(x) = ax^{2} + bx + c[/tex]

It's vertex is the point [tex](x_{v}, y_{v})[/tex]

In which

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

[tex]y_{v} = -\frac{\Delta}{4a}[/tex]

Where

[tex]\Delta = b^2-4ac[/tex]

If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].

Height of the basketball:

Given by the following function:

[tex]h(t) = -4t^2 + 10t + 18[/tex]

Which is a quadratic function with [tex]a = -4, b = 10, c = 18[/tex]

What is the maximum height of the basketball?

y(in this case h) of the vertex. So

[tex]\Delta = b^2-4ac = 10^2 - 4(-4)(18) = 388[/tex]

[tex]y_{v} = -\frac{388}{4(-4)} = 24.25[/tex]

The maximum height of the basketball is of 24.25 feet.

Answer:

80 ft²

Step-by-step explanation:

You are given the formula

a = (1/2)bh

Just plug in the base and height, then multiply

a = (1/2) * 8 *20

a = (1/2) * 160

a = 80 ft²

Answer:

80 [tex]ft^{2}[/tex]

Step-by-step explanation:

Area = [tex]\frac{1}{2} bh[/tex]

Area = [tex]\frac{1}{2}[/tex] 8 · 20

Area = [tex]\frac{1}{2}[/tex] 160

Area = 80 [tex]ft^{2}[/tex]

Answer:

Step-by-step explanation:

Answer:

X+(X+1)+X+2)=30

Step-by-step explanation:

Answer:

Given the following algebraic expression 5x² + 10 Which statement is true?

a. The coefficient is 5. ( true)

b. The constant is 2

C. The power is 10

d. The constant is 5

Answer:

dh/dt =  0.4 m/min

Step-by-step explanation:

The volume of the cone is:

V(c) = (1/3)*r² *h              if always  h = 3r    then    r = h/3

The volume of the cone as a function of h will be:

V(h)  =  (1/3)* (h/3)²*h

V(h) =  (1/27)*h³

The increasing rate of the volume is equal to the rate of sand added the:

D(V)/dt   = (1/27)*3*h²*dh/dt

D(v) / dt  =  10 m³/min

h =  15 m      and   dh/dt is the rate of increasing of the height

By substitution

10 m³/min  = ( 1/9)* 225 * dh/dt  (m²)

dh/dt =  90 / 225   m/min

dh/dt =  0.4 m/min

Answer:

f(x) = (x+5)^2 +12

The minimum value is 12

Step-by-step explanation:

f(x)=x^2+10x+37

The vertex will be the minimum value since this is an upwards opening parabola

Completing the square by taking the coefficient of x and squaring it adding it and subtracting it

f(x) = x^2+10x  + (10/2) ^2 - (10/2) ^2+37

f(x) = ( x^2 +10x +25) -25+37

    = ( x+5) ^2+12

Th is in vertex form y = ( x-h)^2 +k  where (h,k) is the vertex

The vertex is (-5,12)

The minimum is the y value or 12

Answer:

Step-by-step explanation:

From the given information:

a)

Assuming the shape of the base is square,

suppose the base of each side = x

Then the perimeter of the base of the square = 4x

Suppose the length of the package from the base = y; &

the height is also = x

Now, the restriction formula can be computed as:

y + 4x ≤ 99

The objective function:

i.e maximize volume V = l × b × h

V = (y)*(x)*(x)

V = x²y

b) To write the volume as a function of x, V(x) by equating the derived formulas in (a):

y + 4x ≤ 99   --- (1)

V = x²y          --- (2)

From equation (1),

y ≤ 99 - 4x

replace the value of y into (2)

V ≤ x² (99-4x)

V ≤ 99x² - 4x³

Maximum value V = 99x² - 4x³

At maxima or minima, the differential of [tex]\dfrac{d }{dx}(V)=0[/tex]

[tex]\dfrac{d}{dx}(99x^2-4x^3) =0[/tex]

⇒ 198x - 12x² = 0

[tex]12x \Big({\dfrac{33}{2}-x}}\Big)=0[/tex]

By solving for x:

x = 0 or x = [tex]\dfrac{33}{2}[/tex]

Again:

V = 99x² - 4x³

[tex]\dfrac{dV}{dx}= 198x -12x^2 \\ \\ \dfrac{d^2V}{dx^2}=198 -24x[/tex]

At x = [tex]\dfrac{33}{2}[/tex]

[tex]\dfrac{d^2V}{dx^2}\Big|_{x= \frac{33}{2}}=198 -24(\dfrac{33}{2})[/tex]

[tex]\implies 198 - 12 \times 33[/tex]

= -198

Thus, at maximum value;

[tex]\dfrac{d^2V}{dx^2}\le 0[/tex]

Recall y = 99 - 4x

when at maximum x = [tex]\dfrac{33}{2}[/tex]

[tex]y = 99 - 4(\dfrac{33}{2})[/tex]

y = 33

Finally; the volume V = x² y is;

[tex]V = (\dfrac{33}{2})^2 \times 33[/tex]

[tex]V =272.25 \times 33[/tex]

V = 8984.25 inches³

Answer:

Time taken for pump B to empty pool = 1 hour.

Step-by-step explanation:

Given:

Time taken for pump A to empty pool = 4 hour

Time taken together = 48 minutes = 48 / 60 = 4/5 hour

Find:

Time taken for pump B to empty pool

Computation:

Assume;

Time taken for pump B to empty pool = a

1/4 + 1/a = 1 / (4/5)

1/4 + 1/a = 5/4

1/a = 5/4 - 1/4

1/a = (5 - 1) / 4

1/a = 1

a = 1

Time taken for pump B to empty pool = 1 hour.

Answer:

Area of triangles 1 = 18 ft²

Area of triangles 2 = 16 in²

Area of triangles 3 = 90 yd²

Step-by-step explanation:

Given:

1] Height of triangle = 4 ft

Base of triangle = 9 ft

2] Height of triangle = 4 in

Base of triangle = 8 in

3] Height of triangle = 12 yd

Base of triangle = 15 yd

Find:

Area of triangles

Computation:

Area of triangles = (1/2)(Base)(Height)

Area of triangles 1 = (1/2)(4)(9)

Area of triangles 1 = 18 ft²

Area of triangles 2 = (1/2)(4)(8)

Area of triangles 2 = 16 in²

Area of triangles 3 = (1/2)(12)(15)

Area of triangles 3 = 90 yd²

Answer:

[tex]\text{A. }y=1.30x+1.50[/tex]

Step-by-step explanation:

The two ringtones will cost her a total of [tex]0.75\cdot 2=1.50[/tex] and is a fixed amount. The relationship between the cost and number of songs only is [tex]y=1.30x[/tex] and therefore the answer is [tex]\boxed{\text{A. }y=1.30x+1.50}[/tex]. You can also directly find the answer by finding the y-intercept (in this case [tex]1.50[/tex]), as no other answer choices include the term [tex]1.50[/tex], so A must be the correct answer.

Answer:

Let the retail cost be x and the wholesale cost be y

Step-by-step explanation:

x = y + 0.50y

x = 1.50y

Therefore the retail cost is 1.50 times the wholesale cost.

Answer:

z=3

Step-by-step explanation:

1. collect like terms

5z-5=25-5z

2. Move the variable to the left hand side and change its sign

5z-5+5z=25

3. Collect like terms

10z=25+5

4. Divide both sides of the equation by 10

z=3

The solution to the equation is z = 3.

To solve for z in the equation 3z - 5 + 2z = 25 - 5z, we can simplify and combine like terms on both sides:

3z + 2z + 5z = 25 + 5

Combining the terms on the left side gives:

10z = 30

Next, we isolate the variable z by dividing both sides of the equation by 10:

(10z)/10 = 30/10

This simplifies to:

z = 3

Therefore, the solution to the equation is z = 3.

To know more about equation:

https://brainly.com/question/10724260

#SPJ6

Answer:

[tex]3 + \frac{1}{2\sqrt{3} } + \frac{1}{5\sqrt[5]{81} }[/tex]

Step-by-step explanation:

Just to make it easier to see, [tex]\sqrt{x} = x^{\frac{1}{2} }[/tex] and [tex]\sqrt[5]{x} = x^{\frac{1}{5} }[/tex]  This way we could more easily use the power rule of derivatives.

So if f(x) = [tex]x^{2} +x^{\frac{1}{2} } +x^{\frac{1}{5} }[/tex] then f'(x) will be as follows.

f'(x) = [tex]x^{1} +\frac{1}{2} x^{-\frac{1}{2} } +\frac{1}{5} x^{-\frac{4}{5} } = x +\frac{1}{2x^{\frac{1}{2} }} +\frac{1}{ 5x^{\frac{4}{5} }} = x +\frac{1}{2\sqrt{x}} +\frac{1}{ 5\sqrt[5]{x^4} }[/tex]

to find f'(3) just plug 3 into f'(x) so [tex]3 + \frac{1}{2\sqrt{3} } + \frac{1}{5\sqrt[5]{81} }[/tex]

Answer:

61.05

Step-by-step explanation:

1/20 = 5/100 = 0.05

61+0.05 = 61.05

Answer:

Correct.

Step-by-step explanation:

It looks good to me.

Good job!

Answer:

Just plus everything together

X-3+4X+4+2X+1

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

0.2x+5>2

Step-by-step explanation:

0.2 is the same as 2/10;

(2/10)x>2-5

(2/10)x>-3

2x>-30

X>-15( since -15 is lesser than -14,-13,-12 and so on. the sign should be >

Answer:

Step-by-step explanation:

a= 2qr^3 quotent 6p^2

[tex]{ \bf{ \underbrace{Given :}}}[/tex]

Radius of the circle "[tex]r[/tex]" = 10 cm.

[tex]{ \bf{ \underbrace{To\:find:}}}[/tex]

The circumference of the circle.

[tex]{ \bf{ \underbrace{Solution :}}}[/tex]

[tex]\sf\orange{The\:circumference \:of\:the\:circle\:is\:20\:π\:cm.}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

We know that,

[tex]\sf\purple{Circumference\:of\:a\:circle \:=\:2πr }[/tex]

[tex] = 2 \: \pi \times 10 \: cm \\ \\ = 20 \: \pi \: cm[/tex]

Therefore, the circumference of the circle is 20 π cm.

[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♡}}}}}[/tex]

9514 1404 393

Answer:

  А. Зп > 9

Step-by-step explanation:

The inequality of A may or may not be true. (It is true only if n > 3.) All of the others are definitely false.

Answer:

35

Step-by-step explanation:

AEC and AEB form a straight angle(180°)

180-40=140

AEV and AED are equal

140 divided by 4 = 35

9514 1404 393

Answer:

  Division A

Step-by-step explanation:

Suppose last year's revenue for the company was 100 units.

Last year's Division A revenue was 0.60×100 = 60. This year's revenue is 1-35% = 65% of last year's, so is ...

  60 × 0.65 = 39 . . . . units

__

Last year's Division B revenue was 0.40×100 = 40. This year's revenue is 1-5% = 95% of last year's, so is ...

  40 × 0.95 = 38 . . . . units

__

At 39 units this year, Division A still has the higher revenue than Division B at 38 units.

9514 1404 393

Answer:

  x -10y = 5 . . . . . infinite number of solutions

Step-by-step explanation:

We can put each equation into standard form by dividing it by its x-coefficient.

  x -10y = 5 . . . . first equation

  x -10y = 5 . . . . second equation

Subtracting the second equation from the first eliminates the x-variable to give ...

  (x -10y) -(x -10y) = (5) -(5)

  0 = 0 . . . . . . . true for all values of x or y

The system has an infinite number of solutions. Each is a solution to ...

  x -10y = 5.

Answer:

1.) A negative linear pattern

2.) Y = - 0.298X1 + 22.241

3.) slope = - 0.298 ; intercept = 22.241

Kindly check explanation

Step-by-step explanation:

Fitting the time series data using technology, the regression equation obtained is :

Y = - 0.298X+ 22.241

Where ; y = percentage of adults who smoke

x = year

Comparing with the linear equation model :

y = b1x + b0

y = - 0.298x + 22.41

-0.298 = slope

22.41 = intercept

The mean squared error, MSE = 0.512

To achieve, percentage users of 12% or less :

y = 12

Y = - 0.298X+ 22.241

12 = - 0.298X + 22.241

12 - 22.241 = - 0.298X1

-10.241 = - 0.298X

X = 10.241 / 0.298

X = 34.365

X = 35 years

From the model OSHA is not on target to meet it's goal as it will take 35 - 11 = 24 years from the last year of the data to achieve a smoker percentage less Than 12%

Answer:

0.9836

Step-by-step explanation: