se the drawing tool(s) to form the correct answers on the provided graph.
Consider the given function.

Plot the x-intercept(s), y-intercept, vertex, and axis of symmetry of the function.

Drawing Tools
Click on a tool to begin drawing.

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Answer: 601 meters

Step-by-step explanation:

First, let's find the midpoint between the "Falcon Flyer" and the "Sprinter".

The x-coordinate of the midpoint is (50 + 400)/2 = 225.

The y-coordinate of the midpoint is (300 + 550)/2 = 425.

So the midpoint is (225, 425).

Now we need to find the distance between the midpoint and the "Air Rider". Using the distance formula:

d = sqrt[(800 - 225)^2 + (250 - 425)^2]

d = sqrt[(575)^2 + (-175)^2]

d = sqrt[330625 + 30625]

d = sqrt(361250)

d ≈ 601.041

So the distance you will walk on this shortcut is approximately 601 meters.

Answer:

The equation of function g after horizontal compression by a factor of 3 is:

g(x) = 7(3x) + 1 = 21x + 1

To substitute a numerical value for k into the function equation, we need to know the value of k. It is not given in the question, so we cannot provide a numerical answer.

Step-by-step explanation:

When a function is horizontally compressed by a factor of k, we divide the input (x) by k to obtain the new input for the transformed function.

The equation for the horizontally compressed function is:

g(x) = f(x/k)

Substituting f(x) = 7x + 1, we get:

g(x) = 7(x/k) + 1

Simplifying, we get:

g(x) = (7/k)x + 1

Thus, the equation for the transformed function g is obtained by replacing k with the given compression factor.

For example, if the compression factor is 3, then:

g(x) = (7/3)x + 1

And to substitute a numerical value for k, we need to know the value of k. If k = 2, for example, then:

g(x) = (7/2)x + 1

Answer: i. y = 60÷5

Step-by-step explanation: If he has 60 sheets of paper and 5 notebooks, it would only make sense to divide the number of sheets by the number of notebooks to get the sum. Which is 12 btw! <33

Rates of first and second mechanics are 75 and 60 per hour respectively.

A mathematical statement or relation between two or more numeric values, variable and mathematical operations via equal sign is called an Equation.

Elimination method is a kind of method to solve simultaneous equations in two variables. In elimination method we compare coefficient of one of two variables and in next step we eliminate that variable using addition or subtraction and form another relation with only one variable and find the value for that one variable and then substituting that value initial equation we can get the value of another variable.

Let the rate of first mechanic and second mechanic be x and y per hour respectively.

Sum of the two rates is 135 per hour. So the suitable equation will be,

x+y = 135 ............... (i)

Since they charged together 1650 after working 10 hours by first and 15 hours by second mechanics. So the suitable equation this time will be,

10x+15y = 1650

5(2x+3y) = 1650

2x+3y = 1650/5

2x+3y = 330 ............... (ii)

Multiplying 2 with equation (i) and then subtracting it from equation (ii) we get,

(2x+3y) - 2(x+y) = 330 - 2*135

2x+3y-2x-2y = 330-270

y = 60

Substituting y=60 in equation (i) we get,

x+60 = 135

x = 135-60 = 75

Hence, the rates charged per hour are 75 and 60 per hour respectively.

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Answer:

7

Step-by-step explanation:

part a:

Henry should take a route that bypasses the park on the way to school and on the way home from school in order to ride the least possible distance.

He should take Route C on his way to school and Route B on his back.

part b: no values were given to calculate the distance.

Distance is described as a numerical or occasionally qualitative measurement of how far apart objects or points are.

Since the park near Henry's house is closed before school, so he cannot ride through the park on his way to school, he should take Route C on his way to school and Route B on his back.

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The result of the carrying out the operation, Add -4(row 1) to row 3, on the given matrix is:

[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\0&-9&2&12\end{array}\right][/tex]

From the question, we are to perform the given row operation on the given matrix

The given matrix is:

[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\4&-1&6&-8\end{array}\right][/tex]

The operation we are to carry out is:

Add -4(row 1) to row 3

This essentially means we should multiply the first row (row 1) by -4. Then, we will add each of the elements from the results to the corresponding elements on the third row

Multiplying by -4

-4 × [ 1     2    1   | -5

      -4   -8   -4  | 20

Now, we will add the result from the multiplication to the corresponding elements in row 3

    4    -1     6  |  -8

+  -4   -8   -4  | 20

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

    0    -9    2  |  12

Hence,

The resulting matrix becomes

[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\0&-9&2&12\end{array}\right][/tex]

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The new mixture contains 34% peanuts.

The correct option is A

We have,

Jenny mixed 4 kg of mixed nuts containing 16% peanuts with 12 kg of mixed nuts containing 40% peanuts.

First, Total weight = 4 kg + 12 kg = 16 kg

Now, Total weight in kilograms is =  (4 kg) (0.16) + (12 kg) (0.40)

= 0.64 kg + 4.80 kg

= 5.44 kg.

Now, the Percent of peanuts

= (Total amount of peanuts / Total weight) x 100%

= (5.44 kg / 16 kg) x 100

= 34%

Thus, the new mixture contains 34% peanuts.

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The required unit rate is 0.333 products per minute.

What is a product's utilisation rate?

A measurement of how much of a product a user consumes in a certain amount of time; users can be classified as heavy, moderate, or light.

Given that a factory worker can make 15 products in 45 minutes.

We are to find the unit rate.

We will be using the unitary method to solve the given problem.

In 45 minutes, the number of products made by the worker = 15

Therefore, in 1 minute, the number of products made by the worker is given by

= Number of products / Amount of time taken

= 15/45

= 0.333

Thus, the required unit rate is 0.333 products per minute.

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the correct response to the question is: Yes, No, Yes, No and Yes.

We can determine if each set of numbers can be the lengths of the sides of a right triangle by evaluating each set.

Evaluating each set :

#1 :

5, 12, 13

5² + 12² = 13²

25 + 144 = 169

169 = 169

It is a Yes

#2 :

12, 35, 20

12² + 35² = (20√3)²

144 + 1225 = 400*3

1369 ≠ 1200

It is a No

#3 :

5, 10, 5√5

5² + 10² = (5√5)²

25 + 100 = 25(5)

125 = 125

It is a Yes

#4 :

8, 12, 15

8² + 12² = 15²

64 + 144 = 225

208 ≠ 225

It is a No

#5 :

20, 99, 101

20² + 99² = 101²

400 + 9801 = 10201

10201 = 10201

It is a Yes

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The question lacks some details, see complete question in the attached image.

second square

add up all the inches and youll see second had bigger number leading to the answer b

The pair of the functions that are inverse is

The inverse of the function is solved by the operations as follows

f(x) = x - 4 let y = f(x)

y = x - 4

solving for x

x = y + 4

interchanging the variables

y = x + 4  (this is the inverse)

the inverse x + 4 is equal to g(x) hence they are inverse functions

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The ice rink is 14.42 units away from the origin and other solutions are added below

First, we have the library at (7,8), which is 7 units to the right of the origin and 8 units up from the origin.

Next, we have the market at (3,6), which is 4 units to the left of the library (7-4=3) and 2 units down from the library (8-2=6).

Then, we have the bank at (3,8), which has the same x-coordinate as the market (3) and a y-coordinate of 8.

We have the school at (10,8), which has the same y-coordinate as the bank (8) and an x-coordinate of 10.

The pool is located at (7,3), which is 5 units down from the school (8-5=3) and 3 units to the left from the school (10-3=7).

Finally, the park is located at (7,1), which has the same x-coordinate as the pool (7) and a y-coordinate of 1.

The completed table is:

Point Ordered Pair (x, y)

Library (7,8)

Market (3,6)

Bank (3,8)

School (10,8)

Pool (7,3)

Park (7,1)

Bao's new location can be found by moving 5 blocks down from his current location of (3,13) and then 2 blocks right.

This gives us the new coordinates of (5,8) for Boo.

The new location is 5 units right and 8 units up of the origin

To get to the baseball diamond, he traveled 3 blocks to the right from his starting point (3 - 3 = 0) and 8 blocks down (15 - 8 = 7), which gives us the new coordinates of (3, 15) for the baseball diamond.

Bao's starting point was (0, 7).

Bao's starting point can be found by moving 5 blocks to the left from his current location of (14, 13) and then 10 blocks down.

This gives us the new coordinates of (9,3) for Bao's starting point.

The distance between the ice rink and the origin can be found using the distance formula:

d = √((x2 - x1)^2 + (y2 - y1)^2)

In this case, we have:

d = √((12 - 0)^2 + (8 - 0)^2) = √(144 + 64) = √(208) ≈ 14.42

So the ice rink is approximately 14.42 units away from the origin.

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Step-by-step explanation:

sin (pi/4)  = sqrt(2) / 2 = .707

  you either just know this after a time or you can use a calculator (in RADIAN mode)

Answer:

sin(π/4) = sin(45°) = 0.707106781186548 ≈ 0.707 (rounded to 3 decimal places)

Step-by-step explanation:

here are the steps:

Convert π/4 to degrees: π/4 * (180/π) = 45°

sin(45°) = opposite/hypotenuse

sin(45°) = opposite/hypotenuse = adjacent/hypotenuse = 1/√2

sin(45°) = 1/√2 * √2/√2 = √2/2

Therefore, sin(π/4) = sin(45°) = √2/2 ≈ 0.707 (rounded to 3 decimal places).

those attending the party ate 4 1/2 pounds of candy in total.

How to solve the question?

To solve this problem using an array model on graph paper, we can draw a rectangular array with 2 1/4 rows and 3 1/2 columns. Each cell in the array represents a 1/4 pound of candy. The total number of cells in the array will give us the total amount of candy eaten.

To start, we can divide each row into four equal parts to represent 1/4 pound of candy. We can also divide each column into two equal parts to represent 1/2 pound of candy. Then, we can shade in the cells that represent the amount of candy eaten.

Starting with the first row, we shade in two full rows and an additional half row, representing 2 1/2 bags of candy. Then, in the second row, we shade in two full columns and an additional half column, representing 2 1/4 bags of candy.

When we count the total number of shaded cells in the array, we see that there are 18 cells shaded. Each cell represents 1/4 pound of candy, so we can multiply 18 by 1/4 to get the total amount of candy eaten:

18 * 1/4 = 4 1/2 pounds

Therefore, those attending the party ate 4 1/2 pounds of candy in total.

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The direct write-off method and the allowance method are two different ways of accounting for uncollectible accounts receivable.

The direct write-off method is a simple method of accounting for bad debts, where the uncollectible accounts receivable are written off as an expense at the time they are deemed uncollectible.

In contrast, the allowance method is a more complex method of accounting for bad debts, where the company estimates the amount of bad debt expense that it expects to incur over time and creates an allowance account to record this estimate.

The main difference between the two methods is the timing of the recognition of bad debt expense. Under the direct write-off method, bad debt expense is recognized only when an account is written off, whereas under the allowance method, bad debt expense is recognized in advance based on an estimate of the amount of bad debts.

The direct write-off method is not considered to follow generally accepted accounting principles (GAAP) because it violates the matching principle, which requires that expenses be matched with the revenues they generate in the same accounting period.

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The length of AB can be found to be 9. 85 units .

To find the length of AB, we can use the distance formula which is:

d = √ ( ( x2 - x1) ^ 2 + ( y2 - y1) ^2 )

The vertices for AB are:

A - ( 1, 7 )

B - ( 10, 3 )

When the values are plugged into the formula, we get :

d = √ ( ( x2 - x1) ^ 2 + ( y2 - y1) ^2 )

d = √ ( ( 10 - 1 )^ 2 + ( 3  - 7) ^2 )

d = √ ( 81 + 16 )

d = √ 97

d = 9. 85 units

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If the vector is drawn from (0,0) to (5, -1), the outcome or the required vector is drawn.

A mathematical concept known as a vector has both a magnitude and a direction. Physical quantities like force, velocity, and acceleration are represented by it. In the physical sciences, engineering, and computer graphics, vectors are frequently employed. They can also be used to represent abstract concepts like magnitude, directions, and other things.

Here in the question,

(0, 0) is the beginning position. There should be an arrow above each vector name listed below.

Ink a line beginning at (3, -1). A vector has an origin of (0,0) and a destination of (3, -1).

Put a line through points (2,2). The vector B has a start point of (0, 0) and an end point of (2, 2).

These two vectors add up to: a + b = (3-1) + (2,2) = (5,1) when combined.

Whatever order they are in, b + a = (2,2) + (3, -1) = (5,1) regardless.

Either way, the same conclusion is reached.

The terminal point of A + B is at (5, 1).

If the vector is drawn from (0,0) to (5, -1), the outcome vector is drawn.

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1. the APR for this loan is 6%.

2.  the unearned interest is $118.83.

3.  the monthly payment necessary to amortize the $80,000 mortgage at 6% annual interest for 25 years is $506.69.

APR = (finance charge / loan amount) / number of years * 100%

In this scenario, the loan amount is $2400 and the finance charge is $288. Since it's a two-year loan, the number of years is 2

APR = (288 / 2400) / 2 * 100%

APR = 0.06 * 100%

APR = 6%

b.

Number of payments = 4 years * 12 months/year = 48

If the loan is paid off in 3 years instead of 4 years, the number of payments made is:

Number of payments made = 3 years * 12 months/year = 36

Substituting these values into the formula, we get:

Unearned interest = (1426 / 48) * (48 - 36)

Unearned interest = $118.83

3.

To find the monthly payment necessary to amortize a mortgage, we need to use the formula:

M = P * (r / (1 - (1 + r)^(-n)))

where M is the monthly payment, P is the principal (loan amount), r is the monthly interest rate, and n is the total number of payments (in months).

In this scenario, the loan amount is $80,000, the annual interest rate is 6%, and the loan term is 25 years. To find the monthly interest rate, we divide the annual interest rate by 12 (since there are 12 months in a year):

Monthly interest rate = 6% / 12 = 0.005

To find the total number of payments, we multiply the number of years by 12:

Number of payments = 25 years * 12 months/year = 300

Substituting these values into the formula, we get:

M = 80000 * (0.005 / (1 - (1 + 0.005)^(-300)))

M ≈ $506.69

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There are four significant digits in the number 9.15 x 10⁴.

The digits that provide the number with useful information are known as the important digits.

As they add to the value of the number in this instance, the numbers 9, 1, and 5 are all important.

The exponent, 4, just instructs us on how many places to relocate the decimal point, therefore it has no bearing on the number of significant digits.

Therefore, the number 9.15 x 10⁴ has four significant digits.

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The slope-intercept form of the equation is y = 18x.

To find the function in slope-intercept form, we have to write the general form below as;

y = mx + c

m = slope

c = y-intercept

To find the slope, we need to take two points from the table given;

slope (m) = y2 - y1 / x2 - x1

m = 720 - 450 / 40- 25

m = 18

The slope of the line is 18

we can use this with any point to find the y - intercept

y = mx + c

720 = 18(40) + c

720 = 720 + c

c = 720 - 720

c = 0

The equation of the line in slope-intercept form is y = 18x

b. To determine how far he travelled with 55 gallons of gas

y = 18x

y = 18(55)

y = 990 miles

c. How many gallons will be required to cover 630 miles

y = 18x

630 = 18x

x = 630 / 18

x = 35 gallons

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A function relating these variables is D(x) = 10 + 2x,

D(9) = 28, meaning after 9 hours of snowfall,

An independent variable is a variable that is manipulated or controlled by the researcher in an experiment to observe its effect on the dependent variable. It is the variable that is changed deliberately to see how it affects the outcome of the experiment.

The independent variable, x, represents the number of hours since snow began falling,

and the dependent variable is the total amount of snow on Jace's lawn because the amount of snow depends on the number of hours since it began to snow.

A function relating these variables is D(x) = 10 + 2x, where D(x) is the total amount of snow on Jace's lawn in inches after x hours of snowfall.

So, D(9) = 28, meaning after 9 hours of snowfall, Jace will have a total of 28 inches of snow on his lawn.

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The vertical component of the particle's location, when its horizontal component is 2, is:

y = -1.25

To find the vertical component of the particle's location when its horizontal component is 2, we need to first find the value of t when x = 2.

Given the equation:

x = 3sin(t)

Substitute x with 2:

2 = 3sin(t)

Now, isolate t by dividing both sides by 3:

sin(t) = 2/3

Take the inverse sine (arcsin) of both sides:

t = arcsin(2/3)

Now, plug the value of t back into the y equation:

y = t - 4cos(t) + 1

y = arcsin(2/3) - 4cos(arcsin(2/3)) + 1

Using a calculator to find the approximate value of y, we get:

y ≈ -1.25

Therefore, the vertical component of the particle's location when its horizontal component is 2 is:

y = -1.25

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If the loan is a total of $8,465 at 5.9% compounded monthly. at the end of the 12-month repayment period, the student will owe a total of $9246.35 on the loan.

   First, calculate the monthly interest rate by dividing the annual interest rate by 12:

Monthly interest rate = 5.9% / 12 = 0.004917

   Next, calculate the number of months in the repayment period, including the grace period:

Total repayment period = 12 + 6 = 18 months

   Use the formula for calculating the future value of a loan to find the total amount owed at the end of the repayment period:

   FV = PV x (1 + r)^n

   where:

   PV = the present value of the loan (i.e. the amount borrowed)

   r = the monthly interest rate

   n = the number of months in the repayment period

   Plugging in the numbers, we get:

FV = $8,465 x (1 + 0.004917)^18

FV = $9246.35

Therefore, the student will owe a total of $9246.35 on the loan.

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The possible values of a are 3 and -3.

We know that the coefficient of x⁷ in the given expression is 1215, the expression is:

[tex]x^3(ax + 3)^5[/tex]

The term with x⁷ will be:

[tex]5*(3x^7*a^4) = (15a^4)*x^7[/tex]

Then we need to solve the equation:

15a⁴ = 1215

a⁴ = 1215/15

a⁴ = 81

a = ⁴√81 = ± 3

These are the possible values of a.

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The possible values for the perimeter of Rebecca’s garage door are 48 feet or 48 inches

What is meant by perimeter?

Perimeter is the total length of the boundary of a two-dimensional shape. It is the sum of the lengths of all sides of the shape. The perimeter is commonly used to measure the distance around an object or figure and is often used in geometry to calculate the area of a shape.

According to the given information

The perimeter of a rectangle is calculated by adding the four sides of the rectangle. The formula for the perimeter of a rectangle is given as P = 2 (Length + Width) 12.

Therefore, the possible values for the perimeter of Rebecca’s garage door are 48 feet or 48 inches

Complete question is

Rebecca found the length and width of the 6. garage door. She used the measurements to find the perimeter of the garage door. Which of the following could be the perimeter of Rebecca's garage door? F 48 square feet /G 48 square inches/ H 48 feet/ J 48 cubic feet​

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