Solve the equation on the interval [0, 2\small \pi). Show all work. Do not use a calculator - use your unit circle!

Given:

We are given the x(t) vs time curve.

To find:

Speed of particle at t = 4

Step by step solution:

We know that the slope of x-t curve represents the speed of the particle.

To calculate the speed of the particle at t = 4, We will calculate the slope of the curve at t = 4

From here we can say that the slope of the curve between x = 0 and x = 6 is equal to 5.

So the value of speed is also 5 units, Which is equal to option A.

Answer:

{2,4}

Explanation:

Given sets A and B defined below:

The set A Π B is the set of elements common to sets A and B.

Remember that the formual for the area of a circle is:

And the formula for the circumference is:

Using this formulas and the data given,

The cookie has an area of 78.54 square inches and a circumference of 31.42 inches

Answer:

The number will lie between -3 and 11

Step-by-step explanation:

Let the number be 'x'

According to the question,

-15 < 4x - 3 < 41

-12 < 4x < 44 (Adding 3)

-3 < x < 11 (Dividing by 4)

ANSWER

EXPLANATION

We have that the graph of y is:

It is first reflected about the x axis.

A reflection about the x axis is represented as:

y = -f(x)

which means that we find the negative of the function:

Then, it is translated 3 units up (vertical shift) and 4 units right (horizontal shift).

A translation is represented as:

y = f(x - a) + b

where a = horizontal shift; b = vertical shift

So, we have to find:

y = f(x - 4) + 3

That is:

Therefore, that is the equation of the transformed graph.

The variables are:

x: cost of each bag of soil

y: cost of each bag of fertilizer

He bought 15 bags of soil and 3 bags of fertilizer for $282.72, that is,

15x + 3y = 282.72 (eq. 1)

He bought another 5 bags of soil and 2 bags of fertilizer for $107.23, that is,

5x + 2y = 107.23 (eq. 2)

Multiplying equation 2 by 3, we get:

3(5x + 2y) = 3(107.23)

3(5x) + 3(2y) = 3(107.23)

15x + 6y = 321.69 (eq. 3)

Subtracting equation 3 to equation 1, we get:

15x + 3y = 282.72

-

15x + 6y = 321.69

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

-3y = -38.97

y = -38.97/-3

y = 12.99

Replacing this result into the first equation,

15x + 3(12.99) = 282.72

15x + 38.97 = 282.72

15x = 282.72 - 38.97

15x = 243.75

x = 243.75/15

x = 16.25

D. Each bag of fertilizer was $12.99, and each bag of soil was $16.25.

Solution

- The question would like us to convert the number 4527 to scientific notation.

- In order to write a number to its scientific notation, we need to follow these steps:

1. Move the decimal place to the right of the first digit of the number. Make sure you count each step as you move the decimal point from right to left or left to right.

2. The number of steps corresponds to the exponent of 10 that multiplies the decimal form of the original number.

- We can apply these steps to solve the question given as follows:

- Thus, we have that the scientific notation of the number 4527 is

Final Answer

The scientific notation of the number 4527 is

Given:

The per day earning $50

The function is

Find-:

The maximum value of earning

Explanation-:

The function is

Where,

The students work for a whole week.

So the maximum value is

The maximum earning is $350

Slope is a measure of its steepness

Mathematically,

Slope = Rise / Run

Rise = y2 - y1

Run = x2 - x1

Slope = y2 - y1 / x2 - x1

Answer:

Suppose a linear equation describes something (say, population growth). The slope is the rate (say, of growth) and the y-intercept gives the starting value.

Step-by-step explanation:

We will have the following:

First: We dilate by a factor of 2, then we would have:

Second: We rotate by 180°:

Given:

The coordinates of the triangle are A(-3,4), B(-1,2), and C(-5,0).

Required:

We need to translate the given triangle to <4,2> 4 units right and 2 units up.

Explanation:

The image of the point can be written as follows.

Consider point A(-3,4).

Consider point B(-1,2).

Consider point C(-5,0).

Final answer:

A'(1, 6), B'(3, 4) and C'(-1, 2).

Starting with the expression:

Substract the numbers to find the value of y:

Answer:

if y = 75-29 the we subtract 29 from 15

75-29=46

y=46

y=(5/3)x+4

I am aware that the slope is "big," m = - 5 /3, and that the yy-intercept is "left(0, 4), right" (0,4). The final graph of the line should be declining when viewed from left to right because the slope is negative.

y = mx+c

how to draw this graph?

step 1: Plot the given equation's yy-intercept, which is left(0,4right), first (0,4).

On the xy axis, the position (0,4) .

step2: Use the slope largem = -5 /3

m= 5/3

to locate a different point using the y-intercept b as a guide. The slope instructs us to move 3 units to the right after dropping down 5 units.

To find the opposite spot, start at (0,4) and go 5 units down and 3 units to the right.

Step 3: Make a line that goes through all of the points.

Create a line that joins the coordinates (0,4) and (3,5)

To learn more about y-intercept b refer to:

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Nora needs to order some new supplies for the restaurant where she works. The

restaurant needs at least 478 forks. There are currently 286 forks. If each set on sale

contains 12 forks, write and solve an inequality which can be used to determine s, the

number of sets of forks Nora could buy for the restaurant to have enough forks.

Let

s -----> the number of sets of forks Nora could buy for the restaurant to have enough forks

so

the inequality that represent this situation is

solve for s

According to the information given in the exercise, you know that he cycled a total of of 16 kilometers by making 4 trips to work.

Let be "d" the total amount of kilometers Mr. Santos will have cycled after 5 trips to work.

Based on the above, you can set up the following proportion:

Finally, you must solve for the variable "d" in order to find its value. This is:

Therefore, the answer is:

First we can find the slope. The standard form of the equation of a line is:

Where a is the slope and b is the intercept.

When 2 lines are perpendicular, the slopes are reciprocal and opposite to each other. If we write the given equation of the perpendicular line in the standard form we have:

So you got the slope right, it's 5/6.

Now, with the given point we find the intercept. The point is x = -6 and y = -7, so we replace these values into the expression we have until now:

And solve for b

So the equation of the line is:

The first step to solve this problem is to solve the substraction between the first two fractions:

We are given the following exponential function.

The function h(x) is always increasing as can be seen in the given graph.

The y-intercept of a graph is the point where the function intersects/crosses the y-axis.

As you can see from the graph, the graph intersects the y-axis at the point (0, 5)

Therefore, the function's y-intercept is located at (0, 5)

The x-intercept of a graph is the point where the function intersects/crosses the x-axis.

As you can see from the graph, the graph does not intersect the x-axis at any point.

Therefore, there is no x-intercept.

Notice that the graph of the function h(x) is always positive for all values of x.

Answer:

Step-by-step explanation:

Given:

the population size P(1) after t hours is given by the following exponential function:

Find the initial population size?

The initial size = 2000

Does the function represent growth or decay?

Growth, Because the initial value multiplied by a factor > 1

By what percent does the population size change each hour?

The factor of change = 1.09 - 1 = 0.09

So, the bacteria is increasing by a factor of 9% each hour

Let N be the total amount of whole ounces that are mailed.

Since mailing the first ounce has a cost of $0.39, then there will be N-1 ounces charged for $0.22 each.

The total cost of mailing N ounces will be:

If that cost cannot exceed $7.24, then:

Solve the inequality for N:

Since N must be a whole number, the maximum value of N that satisfies the inequality is 32.

Therefore, the maximum number of whole ounces that can be mailed for $7.24 is:

The explicit and recursive equations of the sequence 2, 12, 72, 432 are f(n) = 2 · 6ⁿ⁻¹ and f(n) = 6 · f(n - 1).

In this problem we find an example of a geometric progression, whose explicit and recursive forms are defined below:

Explicit form

f(n) = a · rⁿ⁻¹

Recursive form

f(1) = 2, f(n) = r · f(n - 1)

Where:

If we know that a = 2 and r = 6, then we find the explicit and recursive equations below:

Explicit form

f(n) = 2 · 6ⁿ⁻¹

Recursive form

f(n) = 6 · f(n - 1)

The first four elements of the sequence are 2, 12, 72, 432.

To learn more on geometric sequences: https://brainly.com/question/11266123

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Given:

The distance travelled by Tracy till she stopped to smell roses, x=90 feet.

The distance from roses to the friend, y=200 yards.

The distance travelled by Tracy one side,

(1 yard=3 feet).

Now, the total distance travelled byTracy both sides is,

Therefore, Tracy walk was 1380 feet long.

To determine the amount that will be on the account after 4 years you have to apply the given exponential function that models the amount of money on the account with respect to the time.

Where

a represents the initial amount

r represents the interest rate expressed as a decimal value

t is the time period in years

The initial amount on the account is a= $600

The time period is t= 4 years

The interest rate is r=5%, divide it by 100 to express it as a decimal value:

Using this information, you can calculate the final amount:

After 4 years there will be $732.84 on the account. The correct option is B.

3x + 8y = -18 -----------------------(1)

6x + 16 y = - 54 ---------------------------(2)

Using elimination method,

multiply equation (1) by 6 and equation (2) by 3

18x + 48y = -108 -----------------(3)

18 x + 48y = 162 -------------------(4)

From this, we can deduce that there is no solution to the system of equations

The equation is

n + 2 = - 16 - 5n

By collecting like terms, we have

n + 5n = - 16 - 2

6n = - 18

Dividing both sides of the equation by 6, we have

6n/6 = - 18/6

n = - 3

It has only one solution

Since it is a cube, all its three dimensions must be equal.

Also the term 'unit cube' is used which suggests that the volume of the cube should be 1 units.

Consider that the 2nd and 5th options are incorrect as the dimensions are note equal.

Consider the third dimension, note that before analyzing the numeric part we should make sure that the units are same for all three dimensions.

Here, the units are different, and we know that,

So the third option is also incorrect.

Consider that the options 1st and 4th consist all three dimensions same. Also their product yields 1 in the same cubic units.

So they both represent a unit cube.

Therefore, options 1st and 4th are the correct choices.

We can model each savings account balance in function of time as a linear function.

Andre starts with $100 and he adds $5 per week. If t is the number of weeks, we can write this as:

In the same way, as Elena starts with $10 and saves $20 each week, we can write her balance as:

We can evaluate their savings after 4 weeks (t=4) as:

After 4 weeks, Andre will have $120 and Elena will have $90.

We can calculate at which week their savings will be the same by writing A(t)=E(t) and calculating for t:

In 6 weeks, their savings will be the same. We know it beca

Statement | Reason

Points M and N are on AB | Given

AM ≅ NB | Given

AM + MN ≅ NB + MN | Addition Property of Equality

AM + MN = AN | Segment Addition Postulate

NB + MN = MB | Segment Addition Postulate

AN ≅ MB | Substitution Property of Equality