To rent a stereo for a
party you pay a one-
time fee of $75 plus
$10 per day.

Answer:

\(y-2=3(x-4)\)

Step-by-step explanation:

We are given a line contains the point (4, 2).

We also know that the line is parallel to y= 3x - 7.

We want to write the equation of this line.

Parallel lines have the same slopes.

First, let's find the slope of y = 3x - 7.

3 is in the place of where m (the slope) is, so that means it is the slope of that line.

It is also the slope of the line whose equation we want to write.

The equation of the line can be written in three ways:

All of these ways are valid, but for this problem, let's write the equation in point-slope form, as it is the easiest.

Substitute 3 as m in \(y-y_1=m(x-x_1)\).

\(y-y_1=3(x-x_1)\)

Now, substitute 4 as \(x_1\) and 2 as \(y_1\).

\(y-2=3(x-4)\)

Topic: parallel and perpendicular lines

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Hey there! I'm happy to help!

All the sides of a square are the same. This means that you multiply one of the sides by itself to get the area, which is conveniently called squaring. To go backwards, you find the square root. We already know that 144 is 12×12, but if you didn't know you could do √144 on your calculator and get 12.

Since each side is 12, we multiply 12 by 4, giving us 48 feet as our perimeter.

Have a wonderful day! :D

9514 1404 393

Answer:

  additive inverse

Step-by-step explanation:

The equation shows that the sum of a number and its additive inverse is zero. This is the additive inverse property.

_____

Additional comments

This property is used, together with the identity property of addition, to solve equations by making terms disappear where you don't want them.

Example:

  x + 1 = 3

We would like to remove the +1 in order to find the value of x. Using the additive inverse property, we add the additive inverse of +1 to both sides of the equation.

  x +1 -1 = 3 -1

The additive inverse property tells us the sum of +1 and -1 is zero, so this becomes ...

  x +0 = 2

The additive identity property tells us the sum of x and 0 is simply x, so ...

  x = 2

The result of the synthetic division is the final row. In this case, the result is -3, 5, -15, 18.

A polynomial is an expression consisting of variable and coefficient and are used to model real world situation it is an equation of degree greater than one where the exponents of the variables can be any non-negative integer for example the polynomial equation x 2 + 3x + 2 represent a parable of windcraft polynomial are used in name variety of field such as mathematics and physics.

The process of synthetic division is used to divide polynomials of the form ax^n + bx^n-1 + ... + c, where a is the coefficient of the highest power of the variable x.

To divide -3 into the polynomial 1 8 9 -18 0, the following steps should be taken:

Step 1: Line up the divisor, -3, to the left of the polynomial, as shown below:

-3 | 1 8 9 -18 0

Step 2: Bring down the first coefficient in the polynomial, which is 1, and place it directly below the -3.

-3 | 1 8 9 -18 0
  -3

Step 3: Multiply the -3 by the first coefficient and place the result in the next row, directly below the 8.

-3 | 1 8 9 -18 0
  -3
 -3

Step 4: Add the result to the 8, and place the new result in the next row.

-3 | 1 8 9 -18 0
  -3
 -3
  5

Step 5: Repeat steps 3 and 4 for each coefficient in the polynomial.

-3 | 1 8 9 -18 0
  -3
 -3
  5
 -15
-15
 18

Step 6: The result of the synthetic division is the final row. In this case, the result is -3, 5, -15, 18.
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Complete questions as follows-
Divide Using Synthetic Division
-3|1 8 9 -18 0

Answer:

=,<,<

Step-by-step explanation:

good luck!!

Answer:

nine hundred eighty-two < 800 + 90 +2

Four hundreds and six ones <  431

5 tens + 3 ones < 501

Answer:

0.5

Step-by-step explanation:

its hard to explian how to do it but you can find a video im sure

Answer:

x=6,36

Step-by-step explanation:

step 1 : cross multiply

x-3=3.36

x=3.36+3

x=6.36

Answer: 2

Step-by-step explanation:

Answer:

To find the value of x, add 5 to each side.

x - 5 = 13

+5 +5

x = 18

:)

Answer: 180 gallons needed

Step-by-step explanation:

Zykeith,

Assume x gallons of 50% antifreeze is needed

Final mixture is x + 60 gallons

Amount of antifreeze in mixture is 0.4*(x+60)

Amount of antifreeze added is .5x + .1*60 = .5x + 6

so .5x + 6 = .4(x + 60)

.5x -.4x = 24 -6

.1x = 18

x = 180

Let x be the number of gallons of the 50% antifreeze solution needed. We know that the resulting mixture will be 70 + x gallons. To get a 40% antifreeze mixture, we can set up the following equation:

\({\implies 0.5x + 0.1(70) = 0.4(70 + x)}\)

Simplifying the equation:

\(\qquad\implies 0.5x + 7 = 28 + 0.4x\)

\(\qquad\quad\implies 0.1x = 21\)

\(\qquad\qquad\implies \bold{x = 210}\)

\(\therefore\) We need 210 gallons of the 50% antifreeze solution to mix with 70 gallons of 10% antifreeze to get a mixture that is 40% antifreeze.

\(\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}\)

Answer:

y = x/3

Step-by-step explanation:

y = 3x

x = 3y

3y = x

y = x/3

⊱_____________________________________________________⊱

Answer:

Step-by-step explanation:

\(\large\displaystyle\begin{gathered} \rm{To \ find \ the \ inverse, \ switch \ the \ places \ of \ x \ and \ y} \\ \sf{ y=3x} \\ \sf{x=3y} \\ \rm{Now \ solve \ for y} \\ \sf{x/3=y} \\ \sf{\dfrac{x}{3}=y \end{gathered}\)

done !!

⊰______________________________________________________⊱

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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Answer:

f−1(x)=√6(x+4)6,−√6(x+4)6

Plz let me know if im wrong!!!

Answer:

are u sure this is written correctly?

Answer:

Your coordinates would be (4,2) and you would be in Quadrant 4

Step-by-step explanation:

-3+7 is 4 since going to the right goes towards the positive numbers while left is negative

Step-by-step explanation:

new Coordinates =(4,2)

You are in first quadrant

Answer:

7.14 in²

Step-by-step explanation:

A = LW

A = 2 x 2 = 4

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

A = 3.14r²

A = 3.14 (1²)

A = 3.14 (1)

A = 3.14

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

3.14 + 4 = 7.14

Answer:

2 and -8

Step-by-step explanation:

\(x^2+6x-6=10 \\\\x^2+6x-16=0 \\\\(x+8)(x-2)=0 \\\\x=2, -8\)

Hope this helps!

Research Report:

Title: The Number of Coins Carried by Teachers

Introduction:

This research report aims to investigate the number of coins carried by teachers. The study seeks to understand the reasons behind carrying coins and whether there are any patterns or correlations between the number of coins and certain factors such as age, gender, and occupation.

The data was collected through a survey distributed among teachers from various educational institutions. The findings of this study provide insights into teachers' habits and preferences when it comes to carrying coins.

Results and Analysis:

A total of 300 teachers participated in the survey. The data revealed that the majority of teachers (60%) carry less than 5 coins, while 25% carry between 5 and 10 coins. Only a small percentage (15%) reported carrying more than 10 coins.

Further analysis based on demographic factors indicated that age and occupation had a significant influence on the number of coins carried. Older teachers were more likely to carry fewer coins, with 70% of teachers above the age of 50 carrying less than 5 coins.

Additionally, primary school teachers tended to carry more coins compared to secondary school teachers.

Discussion and Interpretation:

The findings suggest that the number of coins carried by teachers is influenced by various factors.

Teachers may carry coins for a range of reasons, such as purchasing small items, providing change for students, or utilizing vending machines.

The lower number of coins carried by older teachers could be attributed to a shift towards digital payment methods or a preference for carrying minimal cash.

The discrepancy between primary and secondary school teachers could be due to differences in daily activities and responsibilities.

This research provides valuable insights into the habits and preferences of teachers regarding the number of coins they carry.

Understanding these patterns can assist in designing more efficient payment systems within educational institutions and potentially guide the development of tailored financial solutions for teachers.

Further research could explore the reasons behind carrying coins in more depth and investigate how the digitalization of payments affects teachers' behavior in different educational contexts.

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Answer:

Step-by-step explanation:

The graph tells you the zeros of the function are x=-3/4 and x=4.

The y-intercept is the constant in the function: 12.

The maximum is 22.5625 at x = 1.625.

Answer:  -1/2 is the correct answer

Step-by-step explanation:

(-5/8)+(1/8)

=((-5+1)/8)

= -4/8

=-1/2

Answer:

18

Step-by-step explanation:

13.5 × 100 ÷ 75

Answer:

Rotate 90 clockwise wxyz

Step-by-step explanation:

Answer:

10/21

Step-by-step explanation:

I) Get common denominators:

5 1/3 = 5 7/21 (x7)

4 6/7 = 4 18/21 (x3)

II) Subtract:

5 7/21 - 4 18/21 = 10/21

Answer:

Step-by-step explanation:

If you meant " | ", as in |x|, that's "absolute value."  The domain of this function is "all real numbers," and the range is "all real numbers zero or greater."

-27.58%

Answer:

Solution given:

Percent change of 87 to 63

is difference/(initial value)*100%

here

difference=63-87=-24

initial value=87

now

substituting value we get

percentage change=\(\frac{-24}{87}*100\)%

=-24/87*100

=-27.58%

87 ==> 63

Soo :

24/150 × 100%

= 24/15 × 10%

= 240%/15

= 16%✔

Answer:

6 times.

Step-by-step explanation:

There is a 1/9 chance you pick the orange one. If you pick 54 times, you can expect to pick the orange marble 6 times.

Answer:

One ticket cost $10.90.

Step-by-step explanation:

The total spent was $98.50--food, drinks, admission--everything.

$44.00 was for food and drinks.

We can take the 44 away from the total.

98.50 - 44.00

= 54.50

They spent 54.50 on 5 tickets to get in. Divide to find the cost of one tickets. This assumes that all 5 tickets were the same price.

54.50 ÷ 5 = 10.90



The price of one ticket was $10.90

To make this look like algebra class...

let x = the price of one ticket

5x = the price of 5 tickets

5x + 44 = 98.50

subtract 44

5x = 54.50

divide by 5

x = 10.90

Answer:

86

Step-by-step explanation:

33+61=94

180-94=86

Answer:

(a) 1/6. One out of six sides will give you the desired result.

(b) 3/6. 3 out of 6 sides will give you the desired result.

(c) 2/3. 4 out of 6 sides will give you the desired result.