A rock is dropped from a height of 10 feet. The height of the rock is modeled by the graph shown.Part AWhat is the height of the rock 0.5 seconds after being dropped? The height of the rock 0.5 seconds after being dropped is ........... feet Part BTo the nearest tenth of a second, how many seconds after being dropped does the rock hit the ground? The rock hits the ground approximately ...............................seconds after being dropped.

Answer:

[tex]\textsf{Slope}: \quad \dfrac{1}{3}[/tex]

[tex]\textsf{Point-slope form}: \quad y-8=\dfrac{1}{3}(x-9)[/tex]

[tex]\textsf{Slope-intercept form}: \quad y=\dfrac{1}{3}x+5[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Slope formula}\\\\slope ($m$) $=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ \\are two points on the line.\end{minipage}}[/tex]

Define the given points:

Substitute the defined points into the slope formula:

[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{4-8}{-3-9}=\dfrac{-4}{-12}=\dfrac{1}{3}[/tex]

[tex]\boxed{\begin{minipage}{4.6 cm}\underline{Point-slope formula}\\\\$y-y_1=m(x-x_1)$\\\\where $m$ is the slope and\\ $(x_1,y_1)$ is a point on the line.\end{minipage}}[/tex]

Substitute point (9, 8) and the found slope into the point-slope formula:

[tex]\implies y-8=\dfrac{1}{3}(x-9)[/tex]

[tex]\boxed{\begin{minipage}{3.8 cm}\underline{Slope-intercept formula}\\\\$y=mx+b$\\\\where $m$ is the slope\\ and $b$ is the $y$-intercept.\end{minipage}}[/tex]

To write the equation of the line in slope-intercept form, rearrange the point-slope formula:

[tex]\implies y-8=\dfrac{1}{3}(x-9)[/tex]

[tex]\implies y-8=\dfrac{1}{3}x-3[/tex]

[tex]\implies y-8+8=\dfrac{1}{3}x-3+8[/tex]

[tex]\implies y=\dfrac{1}{3}x+5[/tex]

Reflection and rotation preserve length , so the perimeter of ΔABC is equal to the perimeter of ΔXYZ. A possible set of values for AB, BC and AC is  7,9 and 10 units.

A rotation is a transformation that occurs when a figure is turned a preset number of degrees around a fixed point (referred to as the center of rotation).

The given figure is a triangle ABC such that it is transformed by a rotation of 90 °and reflection about y=-5.

The image thus formed will be congruent to the object and will have same sides and perimeter.

Hence the perimeter will be 26 units and the possible length of AB,BC and AC will be 7,9 and 10 units which is the only possible option as a triangle cannot have sides 2 , 14  and 10.(2+10<14)

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Answer:

4 outfits

Step-by-step explanation:

So to find out how much he has left after all his purchases to buy new biking outfits we can add:

9.54 x 3 = 28.62

22.01 + 28.62 + 322.09 = 372.72

Now we subtract his budget by how much he has already spent:

620 - 372.72 = 247.28

He has $247.28 left for outfits so we can divide 247.28 by $61.82 (the amount per outfit) to find how many he can buy:

247.28 / 61.82 = 4

Adrian can buy 4 outfits.

Answer:

Step-by-step explanation:

-588

Answer:

70°

Step-by-step explanation:

The sum of the interior angles is 180.  Subtract the 40 that you know about and you have 140.  Since the two sides are equal, the angles opposite them are equal.  140/2 = 70

The formula for q will be q = p*logm/(logK - logt)

Logarithm

A logarithm is defined as the power to which a number must be raised to get some other values. It is the most convenient way to express large numbers. A logarithm has various important properties that prove multiplication and division of logarithms can also be written in the form of logarithm of addition and subtraction.

Given equation:

[tex]K=tm^{(\frac{p}{q} )}[/tex]

We have to find a formula for q.

Raising the whole equation to the power of q, we get

[tex]K^q=t^qm^{p}[/tex]

We can rewrite it as,

[tex]\frac{K^q}{t^q}=m^p[/tex]

[tex](\frac{K}{t})^q=m^p[/tex]

Operating with logarithm on both sides, we get,

q*log(K/t) = p*logm

q = p*logm/log(K/t) = p*logm/(logK - logt)

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The number of phone calls on the first evening is 16. The number of phone calls on the second evening is 26. The number of phone calls on the third evening is 32.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Over the last 3 evenings, Maria received a total of 74 phone calls at the call centre. The second evening, she received 10 more calls than the first evening. On the third evening, she received 2 times as many calls as the second evening.

The number of phone calls on the first evening:- x

The  number of phone calls on the second evening:- x + 10

The number of phone calls on the third evening:- 2x

x + x + 10 + 2x = 74

4x = 74 - 10

4x = 64

x = 16

The number of phone calls on the second evening:-

x + 10

16 + 10 = 26

The number of phone calls on the third evening:-

2x = 2 x 16 = 32

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To find:

The midpoint of the line segment with the endpoints P1(11/2,3/8) and P2 (-7/2,5/8).

Solution:

The midpoint formula is:

Put the values:

Thus, the midpoint is (1, 1/2).

Answer:

Communitave Property

Step-by-step explanation:

Hope this helps!<3°

The most appropriate choice for linear equation will be given by -

Length of the rectangle is 80 inches

What is linear equation?

At first it is important to know about equation

Equation shows the equality between two algebraic expressions by connecting the two algerbraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Here,

Let the length of the pegboard be l inches

Width of the pegboard = [tex]\frac{1}{2}l - 8[/tex]

Perimeter =

                   [tex]2(l + \frac{1}{2}l - 8 )\\2(\frac{3l}{2} - 8)\\[/tex]

                    [tex](3l - 16)[/tex] inches

But the problem,

[tex]3l - 16 = 224\\3l = 224 +16\\3l = 240\\l = \frac{240}{3}\\[/tex]

[tex]l = 80[/tex] inches

The length of the rectangle is 80 inches.

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Answer: Is 17 a prime number? Yes, 17 is a prime number because it only has two factors, 1 and 17.

The value of the limit of piece wise function is 2k.

For the given question;

The piece wise function is defined as a;

f(x) = (x² - k²)/(x - k) , x ≠ k

f(x) = 4 - k , x = k

For the value of lim (x → k⁻) f(x);

Use function for  x ≠ k, as the left hand limit of the functions is to be evaluated.

=  lim (x → k⁻) f(x)

Let x = k - h, put in the function.

=  lim (h → 0)  ((k-h)² - k²)/(k - h - k)

= lim (h → 0) h(h - 2k)/-h

=  lim (h → 0) 2k - h

Pu h = 0

= 2k

Thus, the  value of the limit of piece wise function is 2k.

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Rational fraction is a fraction where a and/or b are fractions and b is not equal to 0.

Any function that can be expressed mathematically as a rational fraction—an algebraic fraction in which both the numerator and the denominator are polynomials—is referred to as a rational function. The polynomials' coefficients don't have to be rational numbers; they can be found in any field K. Any function that can be expressed as a polynomial divided by a polynomial is said to be rational. The domain of a rational function is the set of all numbers except the zeros of the denominator since polynomials are defined everywhere.

Given Data

a_____________ is a fraction where a and/or b are fractions and b is not equal to 0.

A rational fraction is a fraction where a and/or b are fractions and b is not equal to 0.

Example 1. f(x) =[tex]\frac{x}{x-3}[/tex]

The denominator has only one zero, x = 3.

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Answer:

137°

Step-by-step explanation:

Given: ∠2 = 43°

Find: ∠1 = ?

Solution:

∠1 + ∠2 = 180°

∠1 = 180° - ∠2

∠1 = 180° - 43°

∠1 = 137°

The values of interior angle is 63°,  46°,  71°

Angles inside a polygon are referred to as interior angles. A triangle, for instance, has three interior angles. Interior angles are sometimes defined as "angles enclosed in the interior region of two parallel lines when they are intersected by a transversal."

Put all the values equal to 180°,

=> (2x+5) + (x+17) + (3x-16) = 180°

Now, solve this equation and find x,

=> 6x + 22 - 16 = 180

=> 6x = 180 - 6

=> x = 174 / 6

=> x = 29°

Put x = 29° in the 2x + 5, x + 17, 3x - 16

2x + 15                |   x + 17          |   3x - 16      

2 * 29 + 15          |  29 + 17        |   3 * 29 - 16

63°                      |   46°             |   71°

Therefore, the  values of interior angle is 63°,  46°,  71°

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There are 28 ways in which a couple can choose the name of the baby for its name.

If we need to choose objects from two groups of x and n objects so that one object from each group is chosen, we can do so by calculating the combinations possible by:  

= ˣC₁  ×  ⁿC₁

Let 'x' be the set of first name = 7

Let 'n' be the set of second name = 4

Putting the values in formula;

= ⁷C₁ × ⁴C₁

= 7 × 4

= 28

Thus, there are 28 ways in which a couple can choose the name of the baby for its name.

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The complete question is-

A couple has narrowed down the choices of a name for their new baby to 7 first names and 4 second names.

How many different first- and second-name arrangements are possible?

Answer:

28

Step-by-step explanation:

J(x) = 3x^2 + 2x - 5

they have asked us to find J(3), therefore substitute x with 3 throughout the equation.

j(3) = 3*3^2 + 2*3 - 5

J(3) = 3*9 + 6 - 5

J(3) = 27 + 6 - 5
J(3) = 33 - 5 = 28

The nth term in the Fibonacci series is printed at the conclusion of the program.

So, until a condition is satisfied, recursions involve calling a function from within a function.

The necessary function, which uses comments to describe each line, is as follows:

//This defines the function

public static int fibonacci(int n) {

//The function returns -1, if n is negative

if(n<0){

return -1;}

//The function returns the value of n, if n is 0 or 1

if(n==0||n==1){

return n;}

//If otherwise

else{

//The function returns the nth term of the Fibonacci series

return fibonacci(n-1)+fibonacci(n-2);

}

}

Therefore, the nth term in the Fibonacci series is printed at the conclusion of the program.

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The correct question is given below:

The Fibonacci sequence begins with 0 and then 1 follows. All subsequent values are the sum of the previous two, for example: 0, 1, 1, 2, 3, 5, 8, 13. Complete the fibonacci() method, which takes in an index, n, and returns the nth value in the sequence. Any negative index values should return -1.

Ex: If the input is: 7

the out put is :fibonacci(7) is 13

Note: Use recursion and DO NOT use any loops. // is this mean i don't have to use loops? for (int i = 1; i<= n; ++i)

import java.util.Scanner;

public class LabProgram {

public static int fibonacci(int n) {

/* Type your code here. */

public static void main(String[] args) {

Scanner scnr = new Scanner(System.in);

int startNum;

System.out.println("Enter your number: ");

startNum = scnr.nextInt();

System.out.println("fibonnaci(" + startNum + ") is " + fibonacci(startNum));

}

}

Answer: Let's be honest, no one knows the answer. Unless you want to pay coursehero $9.95/mo for an answer and step-by-step explanation, you're toast.

Some of my answers are absolutely amazing, and actually helpful. But some of my answers are not.

A lot of the time, Brainly's "Expert Verified Answers" are very incorrect, and even if you report it, Brainly does not care.

So, if Brainly ITSELF can't answer a question properly, well,

Simply put, your grade is toast.

And if Brainly deletes this absolutely wonderful fantastic answer, that just means that they are acknowledging that these "Expert Verified Answers" are not as "expert" as they may think they are.

:|

The appropriate choice of ratio  will be given by

She will need 6 cups of orange juice to keep the ratio in a full punch bowl the same.

What is ratio?

Ratio determines the comparision among many quantities with the same unit.

Here,

Let the number of cups of Cranberry juice be 4x,

Number of cups of lemon lime soda be x

Number of cups of orange juice be 2x,

Number of cups of pineapple juice be 2x

Total = 4x + x  + 2x + 2x = 9x cups

By the problem,

                          9x = 27

                            x = [tex]\frac{27}{9}[/tex]

                            x = 3

Number of cups of orange juice = 2 * 3 = 6 cups

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Answer:

Use the distributive property to solve this.

(3x²-5x+7)(2x²+x-2)

= 6x⁴+3x³-6x²-10x³-5x²+10x+14x²+7x-14

= 6x⁴-7x³+3x²+17x-14

Answer:

Step-by-step explanation:

Answer:

Option 1

Step-by-step explanation:

[tex]|x-2|<14 \\ \\ x-2<-14, x-2>14 \\ \\ x<-12, x>16[/tex]

The value of c in the equation 7c - cy = 10x will give a line with slope +5 is -2.

We can rewrite the equation as:-

-cy = 10x - 7c

y = (-10/c) x + 7

Now the equation is in slope-intercept form which is given by:-

y = mx + b

Where,

m represents the slope of the line

b represents the y-intercept of the line

(x,y) represents ordered pair of each point of the line

Comparing both the equations, we get

m = -10/c

b = 7  

We have to get m = +5

Hence, equating both the values of m, we get

5 = -10/c

c = -10/5

c = -2

Hence, the value of c is -2.

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The average rate of change from week 1 to week 4 is 3 animals per week.

It should be noted that a mean simply refers to the average set of numbers that are given.

This will be illustrated as thus:

The total number of rate of change animals from week 1 to week 4 will be:

= (73 - 62) + (78 - 73) + (86 - 78)

= 11 + 5 + 8.

= 24

Therefore, the average will be:

= Total changes / Number of weeks

= 24 / 8.

= 3

Therefore, there's an average of 3 animals added every week.

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Answer:

y = √25 - x

y = -√25 - x

Step-by-step explanation:

x + y² = 25

-x                -x

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

y² = -x + 25

√y² = √-x + 25

y = √25 - x

y = -√25 - x

I hope this helps!

Missing value of the table is 9.

When we compare two ratios, they are said to be equivalent. To determine whether two or more ratios are equivalent, they can be compared to one another. For instance, the ratios 1:2 and 2:4 are equivalent. If two or more ratios have the same value when reduced to their most basic form, they are said to be equal. For instance, the ratios 1:2, 2:4, and 4:8 are identical. When reduced to their most basic form, all three ratios have the same value, or 1:2. We can multiply or divide the words by a natural number to get analogous ratios to a given ratio. When two words are co-prime (have just one other common factor), we multiply them by any natural number instead of performing the division procedure.

Given Data

Violins

Cellos

8  24

3

Let missing number be x

[tex]\frac{8}{24}[/tex] = [tex]\frac{3}{x}[/tex]

When we compare two ratios, they are said to be equivalent.

If two or more ratios have the same value when reduced to their most basic form, they are said to be equal

simplifying, [tex]\frac{8}{24}[/tex]

[tex]\frac{1}{3}[/tex]

[tex]\frac{3}{x}[/tex] =[tex]\frac{3}{9}[/tex]

Missing value of the table is 9.

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The rate at which the x-coordinate is changing is 3√3 units per second .

In the question ,

it is given that

the equation of the particle moving in the circular orbit is x²+y²=16

given the y coordinate decreases at 3units per second

So, dy/dt = -3.

to find the rate at which the x-coordinate is changing , we will differentiate the given equation.

Differentiating the equation  x²+y²=16 with respect to t , we get

d/dt(x²+y²) = d/dt(16)

2x(dx/dt) + 2y(dy/dt) = 0

2x(dx/dt) =  -2y(dy/dt)

Dividing both sides by 2 ,

we get ,

x(dx/dt) =  -y(dy/dt)

[tex]\frac{dx}{dt} =\frac{-y(\frac{dy}{dt}) }{x}[/tex]

As the particle is passing through the point (2,2√3) , So, the point will satisfy the equation.

Substituting the value of x=2 , y=2√3 and dy/dt= -3 ,

we get ,

dx/dt = ((-2√3)*(-3))/2

= (6√3)/2

= 3√3

Therefore , the rate at which the x-coordinate is changing is 3√3 units per second .

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