What is the slope of the function?

–3
–2
3
4

The amount of fuel used per mile (m) = unit rate = 5.2 gallons per mile.

Initial amount (b) = 0 gallon.

A proportional relationship can be represented as an equation of the form y = mx, where x and y are variables and m is the constant of proportionality, also known as the unit rate

Unit rate (m) = amount of fuel used per mile = 156/30 or 312/60 = 5.2 gallons per mile.

Initial amount (b) = starting value or y-intercept = 0 gallon.

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Answer: Area of path = 1492 m^2 Area of "no path" = 123508 m^2

Step-by-step explanation:

Probably wrong

All 4 helpers will be at the clinic on the same day 7 times in 12 weeks.

What is Prime Factorization?

"Prime Factorization" is the process of determining which prime numbers multiply together to get the original number.

To find the number of times in 12 weeks that all 4 helpers will be at the clinic on the same day, we need to find the least common multiple (LCM) of the numbers 4, 6, 2, and 3.

First, we can find the prime factorization of each number:

4 = 2 x 2

6 = 2 x 3

2 = 2

3 = 3

Next, we can find the LCM by taking the highest power of each prime factor that appears in the factorizations:

LCM = 2 x 2 x 3 = 12

Therefore, all 4 helpers will be at the clinic on the same day every 12 days. Since 12 weeks is equivalent to 84 days, we can divide 84 by 12 to get the number of times:

84 ÷ 12 = 7

So, all 4 helpers will be at the clinic on the same day 7 times in 12 weeks.

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Simpson's 1/3rd rule is a method of numerical integration that is used to approximate the value of a definite integral.

It is based on the idea of approximating the area under a curve by dividing it into a series of trapezoids and calculating the area of each trapezoid. The formula for Simpson's 1/3rd rule is:

∫abf(x)dx ≈ (b-a)/6 [f(a) + 4f((a+b)/2) + f(b)]

In this formula, a and b are the limits of integration, and f(x) is the function being integrated. The rule is called the "1/3rd rule" because the coefficient of the middle term is 4/3, which is equal to 1/3 when multiplied by the 3 in the denominator.

To use Simpson's 1/3rd rule, you first need to divide the interval [a,b] into an even number of subintervals. Then, you can apply the formula to each subinterval to get an approximation of the integral over that subinterval. Finally, you can add up the approximations for each subinterval to get an approximation of the integral over the entire interval.

Simpson's 1/3rd rule is a more accurate method of numerical integration than the trapezoidal rule, but it is still an approximation. The accuracy of the approximation depends on the number of subintervals used and the smoothness of the function being integrated.

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Divisions of the rectangle will be equal apart from the color Inga assign.

A rectangle is a two-dimensional shape that has four sides and four right angles. The opposite sides are parallel and equal in length. The area of a rectangle can be calculated by multiplying the length of the rectangle by its width.

Here,
Since the rectangles are identical, they would have the same area and thus, the same divided parts. Therefore, the areas of the colored parts would also be equal.

Thus, divisions of the rectangle will be equal apart from the color Inga assign.

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Answer:

If the Esteban's car continues to decrease 20%, by five years the car will be worthless.

20 x 5 is 100. This means that 100%  of the car will have lost its value and will be worthless.

I hope this helps & Good luck <3 !!!

The solution of AB = BC  for A, assuming that A,B and C are square matrices and B is invertible is [tex]A = BCB^{-1}[/tex]

We have to solve the equation

AB = BC , given that these all are square matrices and B is invertible.

Write the required Equation:

 AB = BC

Multiply both sides by inverse of B

The multiplicative inverse of a matrix is the matrix that gives you the identity matrix when multiplied by the original matrix.

Matrix multiplied by an identity matrix, the result is always the same original non-identity (non-unit) matrix, and thus, as explained before, the identity matrix gets the nickname of "unit matrix"

[tex]ABB^{-1} = BCB^{-1}\\AI = BCB^{-1}\\A = BCB^{-1}[/tex]

so the solution of AB = BC is [tex]A = BCB^{-1}[/tex]

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The ratio of SR and ML and ratio of ST , MN are equal ,so they are similar triangles .

What is triangle ?

Triangle can be defined in which it consists of three sides , three angles and sum of three angles is always 180 degrees.

In given two triangles,

RST and NLM

In the triangle RST ,

The sum of angles is 180

so,

44  + 15 + S = 180

S =   180 - 59

S = 121

And similarly in the triangle NLM,

N + 121 + 44 = 180

N = 180 - 165

N = 15

Therefore, The values of given angles S and N are 121 , 15 respectively

SR / ML  = 3.61 / 5.415 = 0.667
ST / MN = 9.71 / 14.565 = 0.667

Hence, The ratio of SR and ML and ratio of ST , MN are equal ,so they are similar triangles .

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The exponential equation that coordinate points formed is y = -(3)^x

Given the coordinate points (0 -1) and (1 -3), we need to determine the equivalent in the form y=a(b)^x

The equivalent simultaneous equation is:

-1 = ab^0 .......... 1

-3 = ab^1 ............ 2

From equation 1;

-1 = a(1)

a = -1

Substitute a = -1 into equation 2

-3 = (-1)b
b = 3

The required exponential equation is y = -1(3)^x

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Answer:7/12

Step-by-step explanation:

Answer:

7/12

Step-by-step explanation:

The slope in both equations shows the rate of their savings per week, is Adma saves 3$ per week while Shane saves $4 per week.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees. And also it is defined as the rate of change of a function.

Here,
Adam and Shane are competing to see who can save the most money in one month. From the graph, Adam's linear function of saving is given as by slope-intercept form of equation as,
y = 3x + 3

While the linear function for Shane is not given, so we assume the function as y = 4x.

The slope in both equations shows the rate of their savings per week, is Adma saves 3$ per week while Shane saves $4 per week.

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The amount of State withholding tax is, $20.65 and the amount of Federal withholding tax is, $17.7.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Assuming the State withholding tax to be 7% and the Federal withholding tax to be 6%.

Given, A  person made $295 last week.

Therefore, The amount of Federal withholding tax is,

= $(6/100)×295.

= $17.7.

And, The amount of State withholding tax is,

= (7/100)×295.

= $20.65

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Find the difference between the starting and ending values:

    72 - 60 = 12

Divide that difference by the starting value:

    12 ÷ 60 = 0.2

Convert that to a percent:

   0.2 = 20%

The number of teachers increased by 20%.

The key is to divide the difference by the original number, not the ending number.

Answer:

              An equation to represent the given geometric sequence would be [tex]a(x)=5*3^{x-1}[/tex], and a(8) of the geometric sequence will be 10,935.

Step-by-step explanation:

              In order to write an equation for a geometric sequence, first we must analyze the sequence to find its starting value and its constant ratio. The starting value is simply the first term in the sequence, which is 5. As for the constant ratio, it is the rate of change that the equation uses. In this sequence, the constant ratio is 3. Now, we can write out an equation for this geometric sequence.

              We know the first term of the sequence is 5, and the common ratio is 3, so we can write out a function for the geometric sequence, which will be [tex]a(n)=5*3^{n-1}[/tex]. NOTE that the exponential power is n - 1, and not n. This is because the first term of the sequence is 5, and not the "0th" term, therefore we must subtract 1 from n (the term number) to have the right sequence.

              Lastly, we can use the equation [tex]a(n)=5*3^{n-1}[/tex] to find the 8th term of the sequence by replacing n with 8. So [tex]a(x)=5*3^{n-1}[/tex] would become [tex]a(8)=5*3^{8-1}[/tex], and you will get [tex]a(8)=5*3^{8-1}[/tex] ⇒ [tex]a(8)=5*3^{7}[/tex] ⇒ [tex]a(8)=5*2187[/tex] ⇒ [tex]a(8)=10,935[/tex]. Therefore, the equation for the nth term of the geometric sequence would be [tex]a(n)=5*3^{n-1}[/tex], and the 8th term of the sequence is 10,935.

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An expression that is used to represent the number of pennies is; 2n - 7

Algebraic word problems are defined as questions that require translating sentences to equations, then solving those equations. The equations we need to write will only involve basic arithmetic operations.

Now, we are told that;

Number of pennies  is 7 less than twice the number of nickels.

Thus. if n represents the number of nickels, then we can say that;

Number of Pennies = 2n - 7

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Function transformation rules are a set of rules that can be applied to a basic function in order to transform or modify its graph. These rules include:

1. Vertical translation: adding or subtracting a constant to the function. This shifts the graph up or down without changing its shape.

2. Horizontal translation: replacing x with x + c. This shifts the graph left or right without changing its shape.

3. Vertical scaling: multiplying the function by a constant. This stretches or compresses the graph vertically.

4. Horizontal scaling: replacing x with kx. This stretches or compresses the graph horizontally.

5. Reflection: reflecting the graph across the x-axis or y-axis. This changes the orientation of the graph.

6. Composition: combining two or more functions to create a new function.

These rules allow mathematicians to manipulate and analyze functions in order to better understand their properties and behavior. By applying these rules to a basic function, mathematicians can create a variety of related functions with different features and behaviors.

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The process in which a number is changed, such as by adding, subtracting, dividing or multiplying is called mathematical operation.

A mathematical operation is a process that changes a number in some way. The most common mathematical operations are:

Addition is adding two or more numbers together to find their sum.

Subtraction is finding the difference between two numbers by subtracting one from the other.

Multiplication is finding the product of two or more numbers by multiplying them together.

Division is finding the quotient of two numbers by dividing one by the other.

In addition to these basic operations, there are also other mathematical operations such as modulo, exponentiation, and square roots.

These operations are used to perform various mathematical calculations and are fundamental to many areas of mathematics, including algebra, calculus, and geometry. They are also used in many real-world applications, such as in finance, engineering, and science.

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a. The median of Otter 2 's data is greater than the median of Otter 1's data. b. The variability in the data for Otter 1 is greater than the variability in the data for Otter 2.

c. Liz can conclude that Otter 2 generaily eats more food.

In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution.

The median is the value in the middle of a data set, meaning that 50% of data points have a value smaller or equal to the median and 50% of data points have a value higher or equal to the median.

The median for A is 25.5 and 26 for B. This implies that B has higher median than A.

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Answer:

5 weeks

Step-by-step explanation:

Let factory B produce the same amount of shoes as factory A in w weeks.

then,

70+50w = 120+40w

50w - 40w = 120 - 70

10w = 50

w = 50/10

w = 5

Therefore, in 5 weeks factory B will produce the same amount of shoes as factory A will produce in 5 weeks time.

Answer: You would round down so 9,372,000

Step-by-step explanation: Since you are rounding to the nearest 1,000 it would be Answer: 9,372,000

Please give me branliest

The value of complex number |2 - 3i| will be, 3.605

A complex number is one that has the formula a + bi, where I is the imaginary unit and a and b are real numbers. A and b are the real and imaginary halves of a complex number, respectively.

In order to expand the real number system to include answers to polynomial equations that couldn't be solved with just real numbers, complex numbers were first introduced. Many branches of mathematics and science, such as computer science, physics, and engineering, are based on the idea of a complex number.

The absolute value of a complex number "a + bi" can be calculated as the square root of the sum of the squares of its real and imaginary parts:

|a + bi| = √(a² + b²)

In this case, a = 2 and b = -3, so:

|2 - 3i| = √(2 + (-3)²)

          = √(4 + 9)

          = √(13)

          = approximately 3.6055

So, the value of |2 - 3i| is approximately 3.6055.

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Answer:

[tex]Option\ B[/tex]

Step-by-step explanation:

[tex]The\ explicit\ formula\ given:\\f(n)=3n-8\\Since\ n\ can\ be\ any\ positive\ real\ number\,\\The\ formula\ describes\ an\ AP\ whose\ d=3.\\Also,\ Substituting\ n=1:\\f(n)=3*1-8\\f(n)=-5\\Hence, a_1=-5[/tex]

[tex]However,\\We\ also\ know\ that,\\d=a_n-a_{n-1}\\Hence,\\a_n-a_{n-1}=3\\Or,\\a_n=a_{n-1}+3\\These\ conditions\ are\ appropriately\ specified\ on\ Option\ B.[/tex]

The required, Jim can drive the truck for approximately 221.51 miles.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

We can use algebra to solve this problem. Let x be the number of miles Jim drove the truck. Then the total cost can be represented as:

15.99 + 0.86x = 206.91

To find the number of miles driven, we can subtract the base fee from both sides of the equation:

15.99 + 0.86x - 15.99 = 206.91 - 15.99

0.86x = 190.92

Finally, we can divide both sides of the equation by 0.86 to find x:

x = 221.51 miles

So, Jim drove the truck for approximately 221.51 miles.

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The mathematical expression that shows the number of math problem left for Ernest is 16-p

Linear expressions are expression that it's highest power in of it's variable is 1. Linear expression can have more than one variables.

Some of the examples of linear equations are 2x – 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, 3x – y + z = 3.

Ernest has 16 math problem , he has solved p out of it.

To actually know the remaining math problem left, we subtract the number he has done from the number of original problem

This means the number r of problem left = 16-p

therefore the expression is 16-p

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Answer: search it up

Step-by-step explanation:

The area of the triangle below is 34 Square per units. The Option A is correct.

The area of a triangle is total region that is enclosed by the three sides of any particular triangle.  It is equal to half of the base multiplied by the height.

The area of a triangle is given as: Area of triangle= 1/2 * Base of triangle * Height of Triangle where the height is 4 and base is 17

The calculation of our area:

= 1/2 * 17 * 4.

= 34²

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Torr and mmHg are two units of pressure that are often used interchangeably. In fact, 1 mmHg is equal to 1 torr, which means that they are equivalent units of measurement.

To convert torr to mmHg, you can simply multiply the pressure value in torr by 1, since 1 torr is equivalent to 1 mmHg. For example, if you have a pressure of 760 torr, you can convert it to mmHg as follows:

760 torr x 1 mmHg/torr = 760 mmHg

Therefore, 760 torr is equivalent to 760 mmHg. Alternatively, you can also convert mmHg to torr by dividing the pressure value in mmHg by 1. For example, if you have a pressure of 760 mmHg, you can convert it to torr as follows:

760 mmHg ÷ 1 mmHg/torr = 760 torr

Therefore, 760 mmHg is equivalent to 760 torr.

Torr and mmHg are two units of pressure that are often used interchangeably. In fact, 1 mmHg is equal to 1 torr, which means that they are equivalent units of measurement.

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Answer:

225

Step-by-step explanation:

(x+y)^2, if x=6 and y=9

Put 6 in place of x and 9 in place of y.

(6+9)^2 According to order of operations, add the 6+9 first.

(6+9)^2

= 15^2

= 225