Draw a graph of Lin’s distance as a function of time for this situation:



Lin walked a half-mile to school at a constant rate. Five minutes after arriving at school, Lin realized that she had left her permission slip at home. Lin began sprinting home, but when she was halfway there she got tired and walked the rest of the way.

The compositions between functions f(x) = 3 · x - 2 and g(x) = x + 1 are f[g(x)] = 3 · x + 1 and g[f(x)] = 3 · x - 1, respectively.

Let be f(x) and g(x) functions, there is a composition of the form f[g(x)], when the independent variable of function f is substituted by function g. That is to say:

f ° g(x) = f [g(x)]

First, define functions f(x) and g(x):

f(x) = 3 · x - 2

g(x) = x + 1

Second, perform the required compositions and simplify the expressions:

f[g(x)] = 3 · (x + 1) - 2

f[g(x)] = 3 · x + 1

g[f(x)] = (3 · x - 2) + 1

g[f(x)] = 3 · x - 1

To learn more on composition of functions: https://brainly.com/question/14626983

#SPJ1

An infinite solution has both sides equal.

What number has an unlimited number of answers?

There are infinitely many possible solutions to some equations. In these equations, the equation is true regardless of the value given to the variable.

             If you attempt to solve an equation and it yields a variable or value that is equal to itself, then the equation has an endless number of solutions. 2x and 2x should be combined.

Are all possible solutions parallel?

There are no answers when the lines are parallel, and occasionally the two equations will graph as the same line, in which case there are an endless number of solutions. These kinds of systems are occasionally described using specific words.

Learn more about infinitely many solutions

brainly.com/question/29093214

#SPJ4

Answer:

Below

Step-by-step explanation:

When it reaches the ground h = 0

h =     0 = -16t^2+676

            16t^2 = 676

             t^2 = 42.25       t = 6.5 s

(x+5)(x - 1) is a factor of p(x) = x² - 4x - 5

We can see that by applying polynomial long division or by applying synthetic division, both of these methods will give the same result.

x² - 4x - 5 = (x + 5)(x - 1)q(x) + r(x)

where q(x) and r(x) are the quotient and remainder of the polynomial division respectively. Since r(x) = 0, it means (x + 5)(x - 1) is a factor of p(x) = x² - 4x - 5.

Answer:

a = -6

Step-by-step explanation:

9+a/6=8 1. -9 both sides

(6)a/6= -1(6)    2. multiply 6 on both sides

a = -6

Out of the 500 homes, 226 Type A forms were sent while 274 Type B forms were sent.

To determine the number of forms sent, we can begin by identifying how much Jeannie spent on mailing each of the questionnaires. The sum of $0.19 and $0.23 is $0.42. Now, we will find out how much of these were the total cost as follows:

Type A:

$0.19 / $0.42 ×  $106.20

= $48.

Type B:

$0.23 / $0.42 ×  $106.20

= $58.2

Next, we will determine how much of these went into the 500 homes as follows:

Type A:

$48 / 106.2 × 500

= 225. 9 ≈ 226 homes

Type B:

$58.2 / $106.2 × 500

= 274 homes

So, while Type A was sent to 226 homes, Type B was sent to 274 homes.

Learn more about surveys here:

https://brainly.com/question/14610641

#SPJ1

The store that sells strawberries at a cheaper unit price is Fine Foods.

In Mathematics, a proportional relationship can be defined as a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

In order to have a proportional relationship and equivalent ratios, the variables x and y must have the same constant of proportionality.

Next, we would determine the constant of proportionality (k) as follows:

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 2/1 = 6/3 = 10/5 = 14/7

Constant of proportionality (k) = 2.

Therefore, an equation for the price of strawberries at Fine Foods is y = 2x and as such, it sells strawberries at a cheaper unit price.

Read more on proportional relationship here: brainly.com/question/20167968

#SPJ1

Answer: Well for a family of 6 we spend around 200-300$, so a family of 4-5 if older like teens, or 6-7 for young toddlers.

Answer:

2x² + x + 3

Step-by-step explanation:

2x² + x + 3

2x² + (5/2)x + 3

As per the given ratio, the number of roses is 45 and the number of tulips is 27

The term ratio also known as proportion is defined as an ordered pair of numbers a and b, written a / b where b does not equal 0

Here we have given that the ratio of roses to tulips is 5: 3.

Here we also know that the shop has 72 tulips on Friday morning.

And then let us consider that if the florist uses up half of each type of flower to fill an order, then the ratio of roses to tulips in the shop change is calculated as,

=> 5x + 3x = 72

=> 8x = 72

Then the value of x is calculated as,

=> x = 9

Therefore, the number of roses is

=> 5(9) = 45

And the number of tulips is written as,

=> 3(9) = 27

To know more about Ratio here

https://brainly.com/question/13419413

#SPJ4

a) The monthly payment for a loan of $38,000 borrowed by Fred for 5 years at 4% APR is $699.83.

b) The total payment to be made is $41,989.80.

c) The finance charge is $3,989.80.

The finance charge is the difference between the sum of the monthly payments and the loan amount.

The monthly payments, total payment, and finance charge can be computed using an online finance calculator as follows:

N (# of periods) = 60 months (5 years x 12)

I/Y (Interest per year) = 4%

PV (Present Value) = $38,000

FV (Future Value) = $0

Results:

PMT (Monthly Payments) = $699.83

Sum of all periodic payments (Total Payment) = $41,989.80

Total Interest (Finance Charge) = $3,989.80

Learn more about the finance charge at https://brainly.com/question/3436429

#SPJ1

Answer:

3/4 : 1 1/2    1 2/4 : 3.  5 : 10

Step-by-step explanation:

When graphing polynomials, we can determine the end behavior by the degree of the polynomial and the coefficient of the leading term.

The degree of a polynomial is the highest exponent of the variable found in the equation. The coefficient of the leading term is the number that is multiplied by the variable in the leading term. The end behavior of a polynomial can be determined by examining the sign of the coefficient and the degree of the polynomial.

For example, let's consider the polynomial equation y = x^3 - 2x^2 + 5x + 7. The degree of this polynomial is 3, and the coefficient of the leading term is 1. This means that the end behavior of this polynomial equation will be increasing, since the coefficient and degree are both positive. To confirm this, we can calculate the limit of the polynomial as x approaches positive and negative infinity. As x approaches positive infinity, the limit of y is positive infinity (∞), and as x approaches negative infinity, the limit of y is also positive infinity (∞). This confirms that the end behavior of this polynomial equation is increasing.

Learn more about polynomial here:

https://brainly.com/question/11536910

#SPJ4

The statement which is correct about the Area of the rectangle in discuss as required is that the area decreased by; Choice C; 33.(3)%.

As evident in the task content; the length of a rectangle increases 2 times and the width decreses 3 times;

Since the initial length can be said to be; l and the initial width can be said to be; w and Area A = l × w.

However, when the length and width change as described; the area of the rectangle is;

Area = 2l × ( w / 3 )

Area = ( 2/3 ) × lw

On this note, the new Area of the rectangle is two-third the initial area.

On this note, the area of the rectangle has decreased by one-third which is equivalent to; Choice C; 33.(3)%.

Read more on area of rectangle;

https://brainly.com/question/16239445

#SPJ1

Answer: 562.50

Step-by-step explanation:

The Atlantis water slide measures 70.69 feet in length when the slide's base is 37 feet from the pool and it is 60 feet tall.

The Pythagorean Theorem, often known as the Mathematicians, is the fundamental Euclidean geometry relation between the three sides of a right triangle. The area of a cube with the velocity vector side equals the sum of the areas of polygons with the other two sides, according to this rule. The Pythagorean Theorem says that the square that spans a right triangle's hypotenuse opposite the perfect distance equals a sum of the squares that span its sides. It is sometimes written as the basic algebra notation a2 + b2 = c2.

given

According to Pythagoras's Theorem, which states that

c2 = a2 + b2

c2 = 3600 + 1369

c2 = 4969

c = 70.49, the water slide in Atlantis is 60 feet high and has a base that is 37 feet from the pool.

The Atlantis water slide measures 70.69 feet in length when the slide's base is 37 feet from the pool and it is 60 feet tall.

To know more about Pythagorean theorem visit:

https://brainly.com/question/14930619

#SPJ1

Answer:

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

Given system:

We can solve it by elimination.

Multiply the first equation by 6 and add up to get:

Without solving for x we can see there is one solution.

The last answer choice is the correct one.

Answer:

The given system of equations has exactly one solution (1, ⁴/₃).

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}-x+6y=7\\6x-30y=-34\end{cases}[/tex]

To solve the given system of equations, multiply all terms of the first equation by 5:

[tex]\implies -x \cdot 5+6y \cdot 5=7 \cdot 5[/tex]

[tex]\implies -5x+30y=35[/tex]

Add this to the second equation to eliminate the term in y:

[tex]\begin{array}{crcccl}&6x & - & 30y & = &-34\\\vphantom{\dfrac12}+ & (-5x & + & 30y & = & \;\;\:35)\\\cline{2-6}\vphantom{\dfrac12}&x&&&=&\;\;\;\;\:1\\\cline{2-6}\end{array}[/tex]

Therefore, x = 1.

Substitute the found value of x into the first equation and solve for y:

[tex]\implies -(1)+6y=7[/tex]

[tex]\implies 6y=8[/tex]

[tex]\implies y=\dfrac{8}{6}[/tex]

[tex]\implies y=\dfrac{4}{3}[/tex]

Therefore, the given system of equations has exactly one solution (1, ⁴/₃).

As per the unitary method, the number of care is 9 and the number of additional method is 2.

The term unitary in set theory is defined as the way to find the value of a single unit and then multiply the value of a single unit to the number of units to get the necessary value.

Here we have given that the total number of units is 56.

And here we also know that the number of units in each care is 6.

Now, we have to find the total number of care, that can be obtained by dividing the total care by the units in each care,

then it can be written as,

=> 56/6

When we divide the term then we get the quotient as 9 and the remainder as 2.

Therefore, while looking into these we have identified that there are 9 cares and 2 additional units are in the group.

To know more about Unitary method here,

https://brainly.com/question/28276953

#SPJ4

The midpoint method is a numerical integration technique used to approximate the definite integral of a function over a given interval. It is a Riemann sum method.

The line that connects these two places is split in half equally at the halfway. In addition, the halfway is reached if a line is drawn to divide the line that connects these two places. When we know the coordinates of two points, we can apply the midpoint formula to get the midpoint between them.

Here,

The midpoint method is used for a few reasons:

Simplicity: The midpoint method is relatively easy to understand and implement, compared to other numerical integration techniques.

Accuracy: The midpoint method is more accurate than some other Riemann sum methods like the left-hand rule or right-hand rule, which evaluate the function at the endpoints of each subinterval.

Efficiency: The midpoint method is more efficient than some other numerical integration techniques, especially for functions that are not smooth or have sharp changes.

Flexibility: The midpoint method can be used for both definite and indefinite integrals, and for functions that are not well-behaved.

Overall, the midpoint method is a simple, accurate, efficient and flexible numerical integration method that can be used to approximate the definite integral of a function over a given interval.

Learn more about midpoint

brainly.com/question/5566419

#SPJ1

the solution of equation  y=x+2 and  y=3x-2 are x= 2 and y=4

y = x+2 ------------ equation 1

y = 3x -2 ------------ equation 2

in the first equation y = x +2

in the second equation y = 3x -2

this mean equation 1 = equation 2

then we can equate the two together to get one of the variable

remember, we have to unknown variables which are x and y, so we need to isolate y to get x

x + 2 = 3x -2

let collect the like terms

x - 3x = -2 -2

let us factorize out x on the right hand side of the equation

x(1 - 3) = -4

x(-2) = -4

-2x = -4

divide both sides by -2

-2x/-2 = -4/-2

x = 2

to find y put x in any of the above equations

let us use equation one

y = 2 + 2

y = 4

complete question

How do you solve, y=x+2 y=3x-2

learn more about of equation here

https://brainly.com/question/29135556

#SPJ4

Answer:235

Step-by-step explanation: its because.......

The parent function of the quadratic family is f(x) = x2. A transformation of the graph of the parent function is represented by the function g(x) = a(x − h)2 + k, where a ≠ 0.

A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero.

A parabola is the shape of a quadratic function's graph. Although the "width" or "steepness" of a parabola can vary as well as its direction of opening, they all share the same fundamental "U" form. The three graphs in the image below are all parabolas.

A quadratic function's graph takes the form of a parabola. The parabola will open upward if the value of the "a" term is positive, and downward if the value is negative

A function can be raised by adding outside of it: f (x) + b raises f (x) by b units. The same principles apply for moving a function down, except instead of subtracting a positive integer, f (x) b represents f (x) moved down b units.

You can represent a vertical (up, down) shift of the graph of f(x)=x2 by adding or subtracting a constant, k.

f(x)=x2+k

By increasing or decreasing the output or the input, you can change the direction of the function's graph to the right, left, up, or down. A function's output can be increased to move the graph up. The graph is shifted downward when a function's output is subtracted from.

The output has a constant added to it, which causes the vertical shift. For a positive constant, move the graph upward; for a negative constant, move it below. A constant supplied to the input causes a horizontal shift. For a positive constant, move the graph to the left; for a negative one, move it to the right.

You can represent a horizontal (left, right) shift of the graph of f(x)=x2  by adding or subtracting a constant, h, to the variable x, before squaring.

f(x)=(x−h)2

If h>0, the graph shifts toward the right and if  h<0 , the graph shifts to the left.

To know more about Quadratic function refer to:

https://brainly.com/question/19560160

#SPJ1

I've discovered that using the 3:4:5 triangle is the simplest way to determine for sure if an angle is 90 degrees. According to this rule, a triangle is a right triangle if the diagonal between its two points measures 5, even though one of its sides measures 3 and the other measures 4.

Aim for a measuring ratio of 3:4:5, to create an absolutely square corner. To put it another way, you need a length of three feet on the straight line, four feet on the perpendicular line, and five feet crosswise. You will get a corner that is exactly square if all three measurements are accurate.

To know more about triangles:

https://brainly.com/question/3619475

#SPJ4

Yes, (3, 2) is an ordered pair.

The combination of the x coordinate (abscissa) and the y coordinate (ordinate) is called an ordered pair, which has two values written in a fixed order within parentheses.

It can help us to locate a point on the cartesian plane for better visual understanding. The numerical values in an ordered pair can be both integers or fractions. 

In the Cartesian plane, we can define a two-dimensional space with two perpendicular reference lines, the x-axis and the y-axis. The point where the two lines meet is the origin (O).

For example plot the point Q with the coordinates (3, 2)

According to the definition of ordered pair, the point Q will be written as:

Q = (3, 2)

The left number in the ordered pair shows the distance from the “x” axis which is 3

The right number shows the distance from the “y” axis which is 2.

To know more about cartesian plane, here

https://brainly.com/question/28574364

#SPJ4

The degree 3 polynomial equation is  1/2(4 - x)(x - 1)(x - 2).

Here given,

With zeros and a coefficient, the function is:

f(x) = a(x - 4)(x - 1)(x - 2)

Regarding the y-intercept:

f(0) = a(0 - 4)(0 - 1)(0 - 2)

4 = a(-4)(-1)(-2)

4 = -8a

a = -1/2

As a result, the function is:

f(x) = -1/2(x - 4) (x - 1)(x - 2)

= 1/2(4 - x)(x - 1)(x - 2)

To learn more about polynomial function refer to :

https://brainly.com/question/24380382

#SPJ1

Answer: x < -4

Step-by-step explanation: This is a question of an inequality. Here, everything proceeds like a normal equation that we solve. To obtain the value of x, we will divide 32 by 8.

  -8x<32

   x<-32/8

   x<-4  (On dividing -32 by 8)

This means x can take any value less than -4 i.e. -5,-6,-7,......

Read more about it:

https://brainly.com/question/27893282

The proper method of finding a value table has been mentioned and explained below.

Value tables are a part of domain definition. The value table is maintained at the domain level and thus, is also called domain-level validation. Whenever you create a domain, you can enter the required values. Whenever you use this Domain, the system will make it so that you are forced to enter only these values. This is a sort of master check.

This means that if you want to enter values into this table you have to create a development request & transport the same. The system, then, proposes the value table as a check table. The check against the value table only takes place when a foreign key is defined

.

Learn more about Value tables on

https://brainly.com/question/8629807?referrer=searchResults

#SPJ4

Answer: Cosine ratios are exactly the same idea of sine ratios or tangent ratios. The only difference between it and the other two trigonometric ratios is that it is the ratio of the adjacent side to the hypotenuse of a right triangle.

Answer:

[tex]4^{-3}[/tex]

Step-by-step explanation:

[tex]4^{3}[/tex] = 64

Take the reciprocal of both sides.

1/64 = [tex]4^{-3[/tex]