WHAT IS THE NAME OF THIS FORMULA????

The equation of the line in point slope form that passes through  the point (2, 6) and has a slope of 5 is y - 6 = 5(x - 2) .

The equation of a line can be represented in different form such as standard form, general form, point slope form and slope intercept form.

Therefore,

y - y₁ = m(x - x₁)

where

The line passes through (2, 6) and has a slope of 5.

Hence,

m = 5

The equation of the line in point slope form is as follows;

y - 6 = 5(x - 2)

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Answer:

  3.36 km

Step-by-step explanation:

You want the distance P east of a refinery so that the cost of laying pipe from the refinery 1 km north of a river and under a 3 km wide river to storage on the south bank is minimized. The cost of under-river pipe is double the cost of overland pipe.

Let p represent the distance east of the refinery where the river crossing starts. Then the distance in km from the refinery to the river crossing is ...

  d1 = √(1² +p²)

The storage facility is 5 km east of the refinery, so is (5-p) km east of the north-bank point where the river crossing starts. The length of the pipe under the 3 km-wide river is ...

  d2 = √(3² +(5-p)²) = √(p² -10p +34)

The cost is the sum of costs of laying pipe for each segment. The cost for each unit of distance is double for the under-river pipe, so the total cost can be described by ...

  c ∝ d1 + 2×d2

  c ∝ √(1² +p²) +2√(p² -10p +34)

The cost is minimize for the value of p that makes dc/dp = 0. The implicit derivative is ...

  c' = p/√(p² +1) +(2p -10)/√(p² -10p +34) = 0

Subtracting the second term and squaring gives ...

  p²/(p² +1) = (4p² -40p +100)/(p² -10p +34)

Cross-multiplying gives the 4th-degee equation ...

  p⁴ -10p³ +34p² = 4p⁴ -40p³ +104p² -40p +100

In standard form, this is ...

  3p⁴ -30p³ +70p² -40p +100 = 0

The only positive real solution in the domain (0, 5) is p ≈ 3.362.

P should be located about 3.36 km downriver from the refinery.

__

Additional comment

This problem does not ask for the cost, so we only need to know the relative cost of two routes.

The solution of the quartic equation is found using a graphing calculator in the first attachment.

The same graphing calculator can find the minimum of 'c' without bothering with differentiation and reducing the equation to a polynomial. This is shown in the second attachment. Note that graph also shows the cost in units of $300,000. That is, the cost of the pipeline will be about $3.1 million.

The greatest common factor, GCF, of 8y, -12x, and 4xy is 4

From the question, we are to determine the greatest common factor of the given expressions.

The given expressions are 8y, -12x, and 4xy

To determine the greatest common factor, we will express each of the expressions as a product of their factors.

8y = 2 × 2 × 2 × y

-12x = 2 × 2 × 3 × -x

4xy = 2 × 2 × x × y

From above, we can observe that the greatest common factor is

2 × 2

= 4

Hence, the greatest common factor is 4

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Answer:

-40

Step-by-step explanation:

The y-intercept occurs when x is equal to 0. In order to find the y-coordinate, you would just plug in x with 0:

2(5x² − 2)(x − 5) (4x² − 2)

2(5[0]^2 - 2)(0 - 5)(4[0]^2 - 2)

2(-2)(-5)(-2)

-40

The identification of the length of the missing section of each line, assuming that the lines are equally divided, is as follows:

a) The missing section is 24 units.

b) The missing section is 18 units.

c) The missing section is 10 units.

The missing sections can be computed using the mathematical operations of division and multiplication.

The product (quotient) of a division operation involves applying the divisor on the dividend using a division operand (÷).

The product of a multiplication operation applies the multiplier on the multiplicand using the multiplication operand (×).

a) The total units = 36

Division parts = 3

The units of each division = 12 (36/3)

The missing section = 24 (12 x 2)

b) The total units = 36

Division parts = 4

The units of each division = 9 (36/4)

The missing section = 18 (9 x 2)

c) The total units = 16

Division parts = 8

The units of each division = 2 (16/8)

The missing section = 10 (2 x 5)

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The equation of the line that has a slope of -2 and x-intercept of -1 in point slope form is y = -2(x + 1).

Linear equations can be represented in different form such as point slope form, slope intercept form, general form and standard form.

Therefore, let's represent the equation of the line in point slope form.

Using point slope form,

y - y₁ = m(x - x₁)

where

Therefore, the equation of the line has a slope of -2 and an x-intercept of -1.

The slope of a line is the change in the dependent variable with respect to the change in the independent variable.

The x-intercept is where a line crosses the x-axis. The x-intercept is the value of x when y = 0.

hence,

m = -2 and (-1, 0)

x₁ = -1

y₁ = 0

Therefore,

y - 0 = -2(x + 1)

y = -2(x + 1)

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Answer:804,000,000,000 & 8.0e+11

Step-by-step explanation:

logic

Answer:

Step-by-step explanation:

The equation of the line will be y = 12x -3 and the graph of the line with the given y-intercept and slope is shown below.

First, let us understand the slope intercept form of a line:

The equation of the line is written in the slope-intercept form, which is: y = mx + b, where m represents the slope and b represents the y-intercept.

We are given:

(0, −3), m = 12.

We need to determine the graph of the line with the given y-intercept and slope.

To find the value of b;

substitute the given values in the equation of the line, we will get;

y = mx + b

-3 = 12 *0  + b

b = -3

So, the equation of the line will be:

y = 12x -3

Thus, the equation of the line will be y = 12x -3 and the graph of the line with the given y-intercept and slope is shown below.

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Step-by-step explanation:

The total price of sneakers including tax will be equal to $20.75.

The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from. Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.

As per the given information in the question,

Price of sneakers = $20

Tax on sneakers = 3.75%

Then, the amount of tax will be,

(20 × 3.75)/100

= 75/100

= $0.75

Then, the total price of the sneakers will be,

$20 + $0.75

= $20.75

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Answer:

B

Step-by-step explanation:

Since -1 is greater the values given then x is less than -1

h(n) = -17·0.2^(n-1)

Step-by-step explanation:

The explicit formula for a geometric sequence with first term a1 and common ratio r is ...

an = a1·r^(n-1)

Your sequence h has first term a1 = -17 and common ratio r = 0.2. Then the explicit formula is ...

h(n) = -17·0.2^(n-1)

(2,1) because if you graph it, the dot won’t be on the line.

Using easy mathematical operations, we know that the value of x in the given rectangle is 6 cm.

An operation, in mathematics, is a mathematical function that transforms zero or more input values into a precisely defined output value.

The arity of the operation is influenced by the number of operands.

PEMDAS, parenthesis, exponents, multiplication, and division.

So, the value of x will be:

The given two rectangles have similar sides.

2cm is similar to 4cm.

3cm is similar to xcm.

Now, we can calculate x as follows:

2/4 = 3/x

2x = 4×3

2x = 12

x = 12/x

x = 6

Therefore, using easy mathematical operations, we know that the value of x in the given rectangle is 6 cm.

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The value of n in the line segment is - 9 / 4.

The length of a line segment can be found as follows:

Two point of the line segment are 2n + 9 / 2 and 9 / 2. The distance of the line segment is 9 / 2.

Therefore, let's find n as follows:

9 / 2 - (2n + 9 / 2) = 9 / 2

9 / 2 - 2n - 9 / 2 = 9 / 2

9 / 2 - 9 / 2 - 2n = 9 / 2

- 2n = 9 / 2

cross multiply

-2n × 2 = 9

- 4n = 9

divide both sides by -4

n = 9 / -4

n = - 9 / 4

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Answer: you should watch a quick video about it :)

Step-by-step explanation:

46 Days the number of days that the funds were on deposit on Interest rate.

What exactly does "interest rate" mean?

Interest earned = Principal*Interest rate*Time period

155.27 = 20,000 * 0.06 * Time period

Time period = 155.27/(20,000*0.06)

                      = 0.129339 years

                     =(0.129339 * 360)

                     = 46.56204 days

                     = 46 days(Approx)

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Answer:

1.6repeat miles per minute

Step-by-step explanation:

I'm not totally sure, but i just divided 5/3 and that's how I got the answer

Answer:

x = -3

y = 1

Step-by-step explanation:

Desmos is free and it will graph for you.  See picture.

Answer:

7

Step-by-step explanation:

THe answer is 7 because 10-3=7 SOrry if wrong

The original price of purchasing is $825 plus 7% sales tax, then the interest will be $9.20. Hence, option D is correct.

The Latin term "per centum," which signifies "by the hundred," is where the word "percentage" originally came from. With 100 as the denominator, percentages are fractions. To put it another way, it's the relationship here between a component and a whole, in which the value of the whole is always assumed to be 100.

As per the given data in the question,

The original purchase price = $825

The sales tax = 7% of $825 = 825 × 7/100 = $57.75

Total credit = $825 + $57.75 = $882.75

The monthly interest rate = 12.5%/12 = 1.0417%

Interest = $882.75 × 1.0417/100

Interest = $9.20

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Answer:37 number

Step-by-step explanation:

Answer:

[tex]\$320.29[/tex]

Step-by-step explanation:

Determine the formula:

[tex]x - (x \times 0.66) = 108.90[/tex]

Solve for x to get the original price:

[tex]x - (x \times 0.66) = 108.90\\x - 0.66x = 108.90\\x(1-0.66) = 108.90\\x = \frac{108.90}{1-0.66}\\x = \frac{108.90}{0.34}\\x \approx 320.29[/tex]

Answer:

-1    x     120

-2    x     60

-3    x     40

-4    x     30

-5    x     24

-6    x     20

-8    x     15

-10    x     12

1    x     -120

2    x     -60

3    x     -40

4    x     -30

5    x     -24

6    x     -20

8    x     -15

10    x     -12

Answer:

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120.

Step-by-step explanation:

Answer:  

The area of the room is 34*21 = 714 ft^2

the cost of the carpet is $5 per square foot, so the cost to carpet the whole room will be

5*714 = $3570

Step-by-step explanation:

3570 is the cost of the largest circular area rug that will fit in Susie’s dining room.

The area of Rectangle is length times of width.

Given that, Circular area rugs are priced at $5 per foot based on the circumference of the carpet used.

We need to find  the cost of the largest circular area rug that will fit in Susie’s dining room.

The area of the room is 34×21 = 714 ft²

The cost of the largest circular area rug that will fit in Susie’s dining room

$5 per foot based on the circumference of the carpet

Multiply 5 with 714

5×714

3570

Hence, 3570 is the cost of the largest circular area rug that will fit in Susie’s dining room.

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The value of f(-2) in the function f(x) = 3x² + 2x + 4 is 12.

A function is defined as a relation between a set of inputs having one output each. In a simpler term a function relates input and output.

In other words, a function relates each element of a set with exactly one element of another set (possibly the same set).

Therefore, let's solve the function below:

f(x) = 3x² + 2x + 4

Let's find f(-2) as follows;

To solve f(-2), we have to substitute the value of x in the function f(x) = 3x² + 2x + 4 with -2.

Therefore,

f(x) = 3x² + 2x + 4

f(-2) =  3(-2)² + 2(-2) + 4

f(-2) = 3(4)  - 4 + 4

f(-2) = 12 - 4 + 4

f(-2) = 12

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