Susan has a rectangle and a right triangle.
• The length of the rectangle is 4 more than its width, w.
.
• The length of the shorter leg of the triangle is equal to the rectangle's
width.
• The length of the longer leg of the triangle is twice the length of the
rectangle.

Answer:

Y=7x+67

Step-by-step explanation:

Answer: Let x be the number of $13 books that Auggie bought and y be the number of $24 books. Then we can represent the given information in the following system of linear equations:

x + y = 8 (the total number of books Auggie bought is 8)

13x + 24y = 159 (the total amount of money Auggie spent is $159)

This system of linear equations represents the given situation. We can use this system to find out how many books Auggie bought of each price by solving the system of equations.

The equation (1) represents the number of books that Auggie bought is 8, and equation (2) represents the amount of money he spent $159. This system of equations is a valid representation of the given situation because the values of x and y that satisfy the system of equations will be the number of $13 books and the number of $24 books that Auggie bought.

Step-by-step explanation:

The three ways of finding the x-intercept are:

By looking at the equation, we may determine the y-intercept when the equation is expressed in the slope-intercept form (y=mx+b). The y-intercept is the value of b. This is due to the fact that the y-intercept occurs when the x value is 0. Y = B when x = 0, since mx = 0 at this point.

We set y = 0 and solve the equation for x to determine the x-intercept. This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = mx + b, we can still solve for the intercepts by substituting 0 where necessary and then solving for the final variable.

The formula for the x-intercept is y = 0: The x-intercept(s) can be determined by factoring or by employing the quadratic formula because ax2 + bx + c=0.

To learn more about intercept :

https://brainly.com/question/24990033

#SPJ4

The values of k are 3 and −1.

Note: The equation taken here is 4x^2 −2(k+1)x+(k+1)=0

Given: Equation 4X^2−2(k+1)x+(k+1)=0 has real and equal roots i.e., its discriminant is zero.

⇒b2−4ac=0

[An expression that can be produced from the square of a binomial equation is a perfect square trinomial. A perfect square trinomial is a formula that has the elements ax^2 + bx + c and satisfies the condition b^2 = 4ac. The roots of the quadratic equation ax2 + bx + c = 0 are real and equivalent if the discriminant is equal to zero (b2 - 4ac = 0), a, b, and c are real values, and a0.]

For given equation, a=4,  b=2(k+1),c=(k+1)

(2(k+1))^2 −4.4(k+1)=0

⇒(2k+2)^2−16(k+1)=0

⇒4k2+8k+4−16k−16=0

⇒4k2−8k−12=0

⇒4(k2−2k−3)=0

⇒k2−2k−3=0

⇒k2−3k+k−3=0

⇒k(k−3)+1(k−3)=0

⇒(k−3)(k+1)=0

⇒k−3=0   and   k+1=0

⇒k=3   and  k=−1

So, the values of k are 3 and −1.

To know more about Quadratic equation here:

https://brainly.com/question/29011747#

#SPJ4

(x - 3) is a factor of the polynomial f(x) = x³ - 3x² + 4x - 12 since f(3) = 0.

To solve the problem, recall the factor theorem.

Factor Theorem states that if we have a polynomial f(x) and if (x - a) is a factor of f(x), then f(a) = 0

The given function is:

f(x) = x³ - 3x² + 4x - 12

To see whether x - 3 is a factor of f(x) = x³ - 3x² + 4x - 12, we need to find f(3).

Substitute x = 3 into f(x):

f(3) =3³ - 3(3)² + 4(3) - 12

f(3) = 27 - 27 + 12 - 12

f(3) = 0

Since f(3) = 0, then x -3 is a factor of  x³ - 3x² + 4x - 12

Your question is incomplete, but most probably your question was:

Is x - 3 a factor of the polynomial  x³ - 3x² + 4x - 12?

Learn more about factor here:

https://brainly.com/question/24380382

#SPJ4

Ramona’s mistake was she just substituted the 8.5 for the wrong variable.

From given conditions:

Ramona used the regression equation y = 444x - 21.29,  

where x represents height and y represents shoe size,

According to Romana her answer is incorrect as a man who is -17.52 inches tall does not predict the approximate height of a man.

The 8.5 refer to shoes size, not height.

So substituting 8.5 for the x-variable is wrong, because x refers to height and y represents shoe size.

Therefore, Ramon just substituted the 8.5 for the wrong variable. She must replace 8.5 for y-variable, because that's the right one for shoe size.

Learn more about an equation here:

https://brainly.com/question/649785

#SPJ4

Answer:

2

Step-by-step explanation:

look at where it intersects the line that goes straight up

By solving the given factorial question we get a+b=2538.

In mathematics, the term "factorial" refers to the sum of all positive integers that are less than or equal to a specific positive integer, which is followed by an exclamation point. Thus, factorial seven is denoted by the symbol 7!, which stands for 1 2 3 4 5 6 7. Factorial 0 is equal to 1 by definition.

Solution:-

1! + 2! = 1! ( 1 + 2 )

2! + 3! = 2! ( 1+ 3 )

3! + 4! = 3! ( 1 + 4 )

4! + 5! = 4! ( 1 + 5 )

5! + 6! = 5! ( 1 + 6 )

6! + 7! = 6! ( 1 + 7 )

7! + 8! = 7! ( 1 + 8 )

8! + 9! = 8! ( 1 + 9 )

Once again:

1! + 2! = 1! ( 3 )

2! + 3! = 2! ( 4 )

3! + 4! = 3! ( 5 )

4! + 5! = 4! ( 6 )

5! + 6! = 5! ( 7 )

6! + 7! = 6! ( 8 )

7! + 8! = 7! ( 9 )

8! + 9! = 8! ( 10 )

The LCM of 1!, 2!, 3!, ... , 8! is 8!

The LCM of 3, 4, 5, ... , 10 is 2520

The LCM is 2520 * 8!

a = 2520

b = 8

a + b = 2528

To know more about factorial visit:-

brainly.com/question/1483309

#SPJ4

The probability that Mr. Espinoza will select the middle toll booth on Monday and Tuesday is 8%.

Probability refers to the odds of Mr. Espinoza selecting the middle toll booth on Monday and Tuesday when he could have selected toll booths 1, 2, 4, or 5.

The chances of selecting one out of five toll booths = 1/5 or 0.2

The likelihood of Monday and Tuesday out of the five working days = 2/5 or 0.4

The probability of selecting the middle toll booth on Monday and Tuesday = 1/5 x 2/5

= 0.2 x 0.4

= 0.08

= 8%

Learn more about probabilities at https://brainly.com/question/25839839

#SPJ1

The temperature at midnight as required to ve determined in the task content is; 14°C.

According to the task content; the temperature was 11.2°C at 2 : 00am.

However, since the temperature dropped 1.4 °c each hour; we have that;

In the two hours between midnight and 2:00am, the total temperature drop is; 2 × 1.4°C = 2.8°C.

On this note, the temperature at midnight can be evaluated as; 11.2°C + 2.8°C = 14°C.

Read more on temperature;

https://brainly.com/question/24313700

#SPJ1

There are two steps of solving the equation -3(2x+6)=12.

The steps are given below.

Two algebraic expressions having same value and symbol '=' in between are called as an equation.

Given equation:

-3(2x+6)=12

The first step:

Solving the parenthesis first,

-6x -18 = 12

Adding 18 to both sides,

-6x = 30

Divide by -6,

x = -5

The alternate step:

-3(2x+6)=12

Divide by -3,

2x + 6 = -4

2x = -10

x = -5

Therefore, x = -5 is the solution of the equation.

To learn more about the equation;

https://brainly.com/question/12788590

#SPJ1

The function’s average rate of change over the interval from x = 1 to x = 2 is: -2. The correct option b.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

We have the interval from x = 1 to x = 2.

To find the function’s average rate of change over the interval from x = 1 to x = 2 is:

We interpreted the interval in the coordinate form.

The curve from (1, 2) to (2, 0) is a straight line.

And the slope of the line is the average rate of change of the function.

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

m = (0-2) / (2-1)

m = -2/1

m = -2

Therefore, the average rate of change is -2.

To learn more about the slope;

brainly.com/question/3605446

#SPJ1

Answer:c/π=d

Step-by-step explanation: the d and π was multiply with the d and if we want separate with it, we need to use the opposite way to get it.

The tasks that Keith can delegate to the assistant are List the account balances from the general ledger in the Trial Balance columns of the end-of-period spreadsheet, Add the Debit and Credit columns of the trial balance and Type the formal financial statements using the data from the Income Statement and Balance Sheet columns of the spreadsheet.

List the account balances from the general ledger in the Trial Balance columns of the end-of-period spreadsheet: Keith should delegate this task to his assistant. This is a relatively straightforward task that does not require a deep understanding of accounting principles. The assistant can be provided with clear instructions on how to pull the account balances from the general ledger and list them in the trial balance columns of the spreadsheet.

Add the Debit and Credit columns of the trial balance: Keith should delegate this task to his assistant. This is a simple arithmetic task that the assistant can perform with clear instructions.

Make the adjusting entries on the spreadsheet: Keith should retain this task. Adjusting entries involve more complex accounting knowledge and require a deeper understanding of accounting principles. It would be difficult for the assistant to complete this task without proper training.

Complete the spreadsheet: Keith should retain this task. This task requires a deep understanding of accounting principles and an understanding of how the various accounts and transactions relate to each other. It would be difficult for the assistant to complete this task without proper training.

Type the formal financial statements using the data from the Income Statement and Balance Sheet columns of the spreadsheet: Keith should delegate this task to his assistant. The assistant can be provided with clear instructions on how to organize the data from the spreadsheet into formal financial statements. It does not require a deep understanding of accounting principles.

Journalize and post the adjusting entries: Keith should retain this task. This task requires a deep understanding of accounting principles and an understanding of how the various accounts and transactions relate to each other. It would be difficult for the assistant to complete this task without proper training.

--The question is incomplete, answering to the question below--

"Keith Martin is the controller for Daniels Printing Service. Keith has been putting in a lot of overtime; therefore, Mr. Daniels has allowed Keith to hire an assistant. Keith's assistant is a bright, high school graduate, but he has never taken an accounting class. Keith is trying to decide which accounting activities could be delegated to his assistant. Keith is willing to give the assistant a few simple instructions on how to complete each task, but he doesn't have the time to teach the assistant to be an accountant.

For each task listed, state whether Keith should continue to do the work or delegate the task to his assistant. Explain each answer.

1. List the account balances from the general ledger in the Trial Balance columns of the work sheet.

2. Add the Debit and Credit columns of the trial balance.

3. Make the adjusting entries on the work sheet.

4. Complete the work sheet.

5. Type the formal financial statements using the data from the Income Statement and Balance Sheet columns of the work sheet.

6. Journalize and post the adjusting entries."

To know more on accounting tasks

https://brainly.com/question/6356744

#SPJ4

Answer:

C. 2%

Step-by-step explanation:

(6500-5000) / 15 / 5000 x 100% = 1500 / 15 / 5000 x 100% = 100 / 5000 x 100% = 0.02 x 100% = 2%

Answer:

240

Step-by-step explanation:

The total overall profit of all the weekdays is 1200. The question asks for the average. 1200 divided by 5 is 240. the average is 240 dollars per weekday

Answer:

278

Step-by-step explanation:

average = sum/count

count = 7 (7 days)

monday = 150

tuesday = 250

wednesday = 200

thursday = 250

friday = 350

saturday = 450

sunday = 300

sum = 150 + 250 + 200 + 250 + 350 + 450 + 300 = 1950

mean = 1950/7 = 278.571428571 ≈ 278

16<x+y<19,60<xy<84,10/7<y/x<12/6,3<y-x<6

smallest with the smallest biggest with the biggest, biggest with smallest, smallest with biggest

The function in the attached graph is nonlinear

The function is negative where x < 0 and where x > 0.

There is an extrema.

The maximum is located at x = 0.

As the x-value decreases the y-value decreases for x < 0

As the x-value increases the y-value decreases for x > 0

The function is not a straight line graph, because of this, it is a non linear function

The extrema refers to points of maximum or minimum values. The function on the graph has a maximum value at (0, 0)

The end behavior of the function is described as

x ⇒ ∞ f(x) ⇒ - ∞

x ⇒ -∞ f(x) ⇒ -∞

Learn more about end behavior here:

https://brainly.com/question/28954897

#SPJ1

Answer:

Step-by-step explanation:

Based on the fact that Ms. Michaels surveyed her class on whether they preferred free time at the beginning of class or at the end of class and found that students who prefer free time at the end of class are 12 over 19, the thing which the ratio 12 over 19 represents is C. 12 students prefer free time at the beginning of class, and 19 students prefer free time at the end of class.

What is a Ratio?

This refers to the quantitative relation that is used to show the relation between two variables, which shows the number of times one is contained in the other.

Hence, it can be seen that based on the result of the survey by Ms. Michaels about the preference of the students about free time at the beginning of class or at the end of class, the meaning of the ratio is that 12 students prefer free time at the beginning of class, and 19 students prefer free time at the end of class.

Answer:

Step-by-step explanation:

the ratio 13 over 17 represents how many students preferred free time at the beginning of class to how many students preferred free time at the end of class.a little extra: more people want free time at the end of class than at the beginning

The value of x is 14.7224.

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

Sin 60° = x/17 ____(1)

Sin 60° = √3/2 _____(2)

From (1) and (2) we get,

√3/2 = x/17

x = 17√3/2

x = 17 x 1.73205 / 2

x = 14.7224

Thus,

The value of x is 14.7224.

Learn more about trigonometric identities here:

https://brainly.com/question/14746686

#SPJ1

Answer: x = a/b - c

Step-by-step explanation:

First divide by b on each side to get the x by itself.

Then subtract c from both sides to make x the subject of the formula.

Step-by-step explanation:

a = bx + c

the goal is to get to a form with "x = ...".

a - c = bx

(a - c)/b = x

done.

The graph of y is a straight line parallel to the x−axis through the point (0,1)

Now, According to the question:

Let's know:

What is slope and example?

Whenever the equation of a line is written in the form y = mx + b, it is called the slope-intercept form of the equation. The m is the slope of the line. And b is the b in the point that is the y-intercept (0, b). For example, for the equation y = 3x – 7, the slope is 3, and the y-intercept is (0, −7).

The equation is Y = 1

A straight line in slope (m) and intercept (c) form is:

y = mx + c

y is a straight line of slope 0 and y- intercept of 1

y = 0.x + 1

y = 1

Hence, the graph of y is a straight line parallel to the x−axis through the point (0,1)

Learn more about Graph at:

https://brainly.com/question/11591663

#SPJ4

Answer:

N = Pd - 2

Step-by-step explanation:

P = N + 2/d

Pd = N + 2

Pd - 2 = N

N = Pd - 2

Using graphical method, the solution to the system of linear inequality (x, y) are (1, 5)

A mathematical statement called a linear inequality depicts the relationship between two different variables, typically on a graph. A line or border that divides the area of all the points that fulfill the inequality from the areas of the points that do not constitutes the graph of a linear inequality. A set of lines in the coordinate plane that represent the equations of a system of linear inequalities is called a graph. The region of the coordinate plane where each of the inequalities holds can be seen by joining these lines to create a graph.

The inequality given are;

This can be solved using a graphing calculator;

The point of intersection shows the solution to the graph

The solution to the linear inequalities (x, y) are (1, 5)

The broken lines in the graph is from the greater than inequality, while then straight unbroken lines is the inequality with greater than or equal to sign.

Learn more on graph of system of linear inequality here;

https://brainly.com/question/23093488

#SPJ1

The correct equation which represent an identity will be;

⇒ 4(5x+2) = 20x+8

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

All the equations are,

1) 2x + 1 = 3x + 4

2) 4x - 3 = 2(2x + 7)

3) 6x + 3 = 2x + 10

4) 4(5x + 2) = 20x + 8

Now,

Solve each equation and find an identity as;

1) 2x + 1 = 3x + 4

⇒ 1 - 4 = 3x - 2x

⇒ - 3 = x

⇒ x = -3

Thus, It is not represent an identity.

2) 4x - 3 = 2(2x + 7)

⇒ 4x - 3 = 4x + 14

⇒ - 3 ≠ 14

Thus, It shows no solution.

3) 6x + 3 = 2x + 10

⇒ 6x - 2x = 10 - 3

⇒ 4x = 7

⇒ x = 7/4

Thus, It is not represent an identity.

4) 4(5x + 2) = 20x + 8

⇒ 20x + 8 = 20x + 8

⇒ 20x - 20x = 8 - 8

⇒ 0 = 0

Clearly, '0' is an additive identity.

Thus, This equation shows an identity.

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1

The length of the field for the missing width is 350 ft. and the function (w) to represent the length of the field is w = (l-50)

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given that a table for showing the relation between length and width of a field;

                Width (w)                                     Length (l)

                       0                                                   50

                     100                                                 150

                     200                                                250

                     300                                                350

We see, that, width is 50 less than the length.

Therefore, the function (w) to represent the length of the field will be =

w = l-50

Hence, the length of the field for the missing width is 350 ft. and the function (w) to represent the length of the field is w = (l-50)

For more references on functions, click;

https://brainly.com/question/21145944

#SPJ1

The solution of the equations are x = √1 = ± 1

Now, According to the question:

The given equation is [tex]9x^4 - 2x^2 - 7 = 0[/tex]

Using the substitution rule we put [tex]x^{2}[/tex] = u .

The given equation now changes to

[tex]9u^2 - 2u - 7 = 0[/tex]--- (1)

Equation(1) is a simple quadratic equation which can be solved by factorization as follows:

[tex]9u^2 - 2u - 7 = 0[/tex]

(9u + 7)(u - 1) = 0

Therefore

9u + 7 = 0 → u = -7/9

u -1 = 0→ u = 1

Since u = [tex]x^{2}[/tex] implies

x = √-7/9 = ± i√7/9

x = √1 = ± 1

Learn more about Equation at:

https://brainly.com/question/29657983

#SPJ4

The complete question is this:

What are the solutions of the equation [tex]9x^4 - 2x^2 - 7 = 0[/tex]? use u-substitution to solve.

Answer:I know why your father never came back

Step-by-step explanation: So when he got the milk he got stuck in traffic for a long time which caused the milk to expire and so he went back to grab new milk and on his way home he was stuck in traffic again and the milk got expired so he repeats the process and the same thing happens over and over and over, so hes stuck in an infinite loop until he passes away.

the distance it will cover before coming to rest is 75m. Solved using the concept of velocity.

Simply said, velocity is the rate of movement in a certain direction. such as the speed of a car driving north on a highway or the pace at which a rocket takes off.

Due to the fact that it includes both magnitude and direction, velocity is a vector quantity. Since acceleration is only the rate at which velocity changes, acceleration is likewise a vector quantity.

Given that,

initial velocity (u) = 30 m/s

acceleration (a) = - 6 m/s²

As we know,

v² = u² + 2as

or, 0 = (30)² + 2 × (-6) × s

or, s = 75 m

Hence, the distance it will cover before coming to rest is 75m

To know more about velocity refer to:

https://brainly.com/question/25749514

#SPJ4