What is the slope of the line?

Answer:

0.5 seconds

Step-by-step explanation:

Equation: h(t) = -5t²+5t=10

Where h(t) is in meter, t is in seconds.

The driver will reach maximum height when d[h(t)]/d(t) = 0

From the equation,

d[h(t)]/d(t) = -10t+5

Therefore,

-10t+5 = 0

Solve for t

-10t = -5

10t = 5

t = 5/10

t = 0.5 seconds.

Hence the height will be maximum in 0.5 seconds.

Answer:

45 miles in 1 hour

Step-by-step explanation:

135/3 = 45

45 miles in 1 hour

Answer:

[tex](-9.5,2.63)[/tex]

Step-by-step explanation:

In essence, this problem asks one to find the vertex of the given equation. An easy way to find the vertex of a quadratic equation in standard form is to complete the square.

Completeting the square involves grouping the quadratic and linear term, then factoring out the coefficient of the quadratic term. After doing so, one will add a term to make the grouped terms a perfect square trinomial and then balance the equation. Finally, one will simplify the equation and get the quadratic equation in vertex form. From there, finding vertex is quite easy, the x-coordinate is the additive inverse of the quadratic term, and the y-coordinate is the constant.

Once a quadratic equation in standard form has been converted to vertex form by the process of completing the square, its equation is amongst the lines of the following,

[tex]a(x-k)^2+h[/tex]

(k, h) is the vertex of the parabola.

The quadratic equation in standard form,

[tex]2x^2+19x+42.5[/tex]

Group the quadratic and linear terms,

[tex](2x^2+19x)+42.5[/tex]

Factor out the coefficient of the quadratic term,

[tex]2(x^2+9.5x)+42.5[/tex]

Add a term to make the grouped part a perfect square trinomial, then balance the equation,

[tex]2(x^2+9.5x+22.5625)+42.5-2(22.5625)[/tex]

Simplify,

[tex]2(x^2+9.5x+22.5626)+42.5-45.125[/tex]

[tex]2(x+9.5)^2+2.625[/tex]

The vertex of the equation is the following,

[tex](-9.5,2.625)[/tex]

Rounded,

[tex](-9.5,2.63)[/tex]

Answer:

what they said^

Step-by-step explanation:

Answer: 60

Step-by-step explanation:

ball =x

bat = y

x + y = 90

and

equation II is

3 x + 2 y =210

By multiplying by 3 to equation I both sides

we get equation III as

3( x + y) = 3 ( 90 )

3x + 3y =270 III

subtract II and III

we get 3x+3y=270

- 3x+2y=210

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

0+y= 60

y =60

cost of bat is y ie = 60

and cost of ball ,is

let put value of y in equation I

x+60=90

x=90-60

x=30

cost of ball is 30

The set of parametric equations representing the skater's jump is:

x = 52t

y = 5 + 16t²

We have,

Let's denote the time as t.

Horizontal motion:

The skateboarder's horizontal velocity remains constant throughout the jump, so the horizontal position (x) can be represented as:

x = vt

where v is the horizontal velocity, which in this case is 52 ft/s.

Vertical motion:

The vertical position (y) can be determined using the equations of motion under constant acceleration.

The skateboarder experiences acceleration due to gravity (g) acting downward.

The initial vertical position is 5 ft, and the initial vertical velocity is

0 ft/s.

Using the equation of motion:

[tex]y = y_0 + vy_0t + 0.5gt^2[/tex]

Substituting the given values:

y = 5 + 0t + 0.5(32)t²

y = 5 + 16t²

Thus,

The set of parametric equations representing the skater's jump is:

x = 52t

y = 5 + 16t²

Learn more about equations here:

https://brainly.com/question/17194269

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Answer:

T = -3

Step-by-step explanation:

No explanation needed ...

Answer:

It's 12.

Step-by-step explanation:

90-18=72

72/6 =12

Question:

Discus the advantages and disadvantages of histograms versus stem-and-leaf plots

Answer:

C. Stem-and-leaf plots are easier to make and and can contain more information than histograms. However, they are not very useful for large data sets

Step-by-step explanation:

A stem and leaf plot is a graphical presentation of quantitative data similar to an histogram. However, a stem and leaf plot retains and present the values of the original in the data set such that individual data values can be seen and can then be used to make analysis

The stem and leaf plot consists of a stem and a leaf  arranged in the order of place value, such that the numbers having a common highest place value are arranged on a row in a stem and leaf plot and therefore a stem and leaf plot is easier to make or construct than an histogram

However, it is very rare to find stem and leaf plots having more than 50 datasets or observations.

Answer:

I think it's A

Step-by-step explanation:

Sorry if I'm wrong

we know that

1 ft--------> is equals to 12 in

the ramp is 12 inches tall----------> 1 ft tall

A ramp measures------------------>  6 ft long

applying the Pythagorean theorem

c²=a²+b²

where

c-----> 6 ft long

a----> horizontal distance

b-----> 1 ft tall

a²=c²-b²------> a²=6²-1²-----> a²=35------> a=√35------> a=5.92 ft

the answer is

5.92 ft

Answer:

6.08 or so

Step-by-step explanation:

The height is 1 foot, while the length is 6 feet.

You can use the Pythagorean Theorum to solve this, as you plug in the values.

The theorum states that A squared plus B squared = C squared, where A is  the length, and B is the width. (It doesn't matter if A is the width and B is the length either.)

So if we plug in the values:

1 squared plus 6 squared = C squared.

1 + 36 = 37

Since it is C squared, we can find the square root of 37, which is something like 6.0827625302982196889996842452021.

So usually we round to the hundredths place, so we can use 6.08.

Answer: There is a total of 36 slices of pizza.

Answer:

a) 0.3.

b) 1.117287138  to  9 dec. places.

d)3.

Step-by-step explanation:

a and d: the powers 1/3 and 0.333... is  the cube root.

c: 0.5 = the square root.

b is found using a calculator

Answer:

a) 24

b) 10

c) 12/13

d) 5/13

e) 12/5

Step-by-step explanation:

a) We can see that the leg opposite <C is AB, and we are given AB = 24

b) We can see the leg adjacent to <C is AC, and we are given that AC = 10

c) The trig function sine is equal to

[tex]\frac{opposite}{hypotenuse}[/tex]

The opposite, AB, is 24, and the hypotenuse, BC, is 26. We can plug those numbers in:

[tex]sin(c) = \frac{24}{26} = \frac{12}{13}[/tex]

d)The trig function cosine is equal to

[tex]\frac{adjacent}{hypotenuse}[/tex]

The adjacent, AC, is 10, and the hypotenuse, BC, is 26. We can plug those numbers in:

[tex]cos(c) = \frac{10}{26} = \frac{5}{13}[/tex]

d)The trig function tangent is equal to

[tex]\frac{opposite}{adjacent}[/tex]

The opposite, AB, is 24, and the adjacent, AC, is 10. We can plug those numbers in:

[tex]tan(c) = \frac{24}{10} = \frac{12}{5}[/tex]

Answer:

Mean: 45.8 (rounded to the tenth place)

Median: 46

Mode: 46

Range: 84

Step-by-step explanation:

Answer:

First we solve the radius and then we use the formula for finding the equation of circle.

Answer:

3775 in²

Step-by-step explanation:

The surface area of the ramp :

Area of rectangle = 20 * 23 = 460 in²

Area of rectangle = 20 * 23 = 460 in²

Area of rectangle = 25 * 23 = 575 in²

Bottom rectangle = 60 * 23 = 1380 in²

For the trapezium: (front and rear)

1/2 (base 1 + base 2) * height

Base total = 20+ 20+ 20= 60

1/2(60)*15 = 450 in²

Total surface Area :

(460 + 460 + 575 + 1380 + 450 + 450) in² = 3775 in²

Answer:

She earns $ 37.5  by walking 50 laps

Step-by-step explanation:

This method is called unitary method.

If we know the value of 1 unit of an item we can calculate any number of units of item.

For 1 lap she earns 75 cents.

She walks 50 laps.

She earns for 50 laps = 50*75= 3750 cents

Now we have to converts cents into Dollars for convenience.

1$ = 100 cents

3750 /100 = $ 37.5

Answer:

60degrees

Step-by-step explanation:

SInce our reference angle is <V;

Opposite = WU = 7√3

Hypotenuse= WV = 14

Using the SOH CAH TOA identity

son m<V = opposite/hypotenuse

sin m<V = 7√3/14

sin m<V = √3/2

m<V = arcsin(√3/2)

m<V = 60degrees

Hence the measure of angle V is 60degrees

Answer:

b² =  13.2

Step-by-step explanation:

5.8²+b²=14.4²

33.64+b²=207.36

-33.64       -33.65

b²= √173.71

b² = 13.1799089526

b² =  13.2

Answer:

4√6

Step-by-step explanation:

cot60➜4√2/t

➜1/√3=4√2/t

➜t=4√2√3

➜t=4√6

Answer:

[tex]2\sqrt{2}[/tex] = t

Step-by-step explanation:

Sin(30) = t / [tex]4\sqrt{2}[/tex]

Sin(30) * [tex]4\sqrt{2}[/tex] = t

[tex]2\sqrt{2}[/tex] = t

Hope this helps!

Answer:

arithmetic

Step-by-step explanation:

geometric sequences grow really fast in a short amount of time while arithmetic sequences have a steady growth over any period of time

Answer:

This is an arithmetic sequence and the common difference is equal to 2.

Given:

Consider the line segment YZ with endpoints Y(-3,-6) and Z(7,4).

To find:

The y-coordinate of the midpoint of line segment YZ.

Solution:

Midpoint formula:

[tex]Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]

The endpoints of the line segment YZ are Y(-3,-6) and Z(7,4). So, the midpoint of YZ is:

[tex]Midpoint=\left(\dfrac{-3+7}{2},\dfrac{-6+4}{2}\right)[/tex]

[tex]Midpoint=\left(\dfrac{4}{2},\dfrac{-2}{2}\right)[/tex]

[tex]Midpoint=\left(2,-1\right)[/tex]

Therefore, the y-coordinate of the midpoint of line segment YZ is -1.