Find the equation (in terms of xx ) of the line through the points (-4,1) and (5,-3)

The membership of the gym after 7 years is 1385 .

In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable ). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.

Given: The function : M(x)= 180x + 125

where x is the number of years so in this case we have to find the value of M when x= 7 years

Thus the given function on substituting the value becomes

M (7)= 180× 7 + 125

= 1385.

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The difference between expression (-3x²-xy-3y²) - (6x²-4xy+y²) is  

(-9x²+3xy-4y²).

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

Numbers and arithmetic operators make into a mathematical numerical expression. There are no symbols for undefined variables, equality, or inequality.

Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.

= (-3x²-xy-3y²) - (6x²-4xy+y²)

=  -3x²-xy-3y² - 6x²+4xy-y²

= (-9x²+3xy-4y²)

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1) An equation that models the problem is x = 30,600 - 1,440t, where x is the value after t years.

2) After 8 years of straight-line depreciation, the car's value will be $19,080.

Depreciation is an accounting term that refers to the periodic expensing of the cost of a long-term asset.

Using depreciation, a reporting entity annually recognizes the cost of an asset used for many years.

Intangible long-term assets use amortization or depletion instead of depreciation to describe the same meaning.

Price of an automobile in 2003 = $30,600

Annual depreciation = $1,440

The car's value after t years = $19,080.

Value after t years = 30,600 - 1,440t

If 19,080 = 30,600 - 1,440t

1,440t = 30,600 - 19,080

1,440t = 11,520

t = 8 (11,520/1,440)

t = 8

= 8 years

Check:

x = 30,600 - 1,440t

x = 30,600 - 1,440(8)

x = 30,600 - 11,520

x = 19,080

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Step-by-step explanation:

On a horizontal number line, -43 is located to the left of -35. TRUE because -43 is farther away (to the left) from 0 than -35.

29) 3[tex]e^{2i}[/tex] = – 1.248 + 2.728 i (conversion from polar form to rectangular a+bi form of complex number)

3[tex]e^{2i}[/tex] = 3 (cos[tex]2^{c}[/tex] + i sin[tex]2^{c}[/tex]) = 3 ( – 0.416 + i 0.909) = – 1.248 + 2.728 i

33) 3[tex]e^{\frac{5\pi i}{4} }[/tex] = – 2.12 + 2.12 i (conversion from polar form to rectangular a+bi form of complex number)

3[tex]e^{\frac{5\pi i}{4} }[/tex] = 3 (cos[tex](\frac{5\pi }{4})^{c}[/tex][tex]\frac{5\pi }{4}^{c}[/tex] + i sin[tex](\frac{5\pi }{4})^{c}[/tex] ) = 3 ( – 0.707 + i 0.707) = – 2.12 + 2.12 i

37) – 4 i =  4[tex]e^{\frac{3\pi}{2}i}[/tex] (conversion from rectangular a+bi form to polar form of complex number)

– 4 i =   0 – 4 i = [tex]\sqrt{0^{2}+(-4)^{2}}[/tex][tex]e^{i tan^{-1}\frac{-4}{0} }[/tex] =  4[tex]e^{\frac{3\pi}{2}i}[/tex]

41) – 3 + 4 i = 5 [tex]e^{2.214i}[/tex] (conversion from rectangular a+bi form to polar form of complex number)

– 3 + 4 i = [tex]\sqrt{(-3)^{2}+(4)^{2}}[/tex][tex]e^{tan^{-1}\frac{4}{-3}i}[/tex] = 5 [tex]e^{(\pi - 0.927)i}[/tex] = 5 [tex]e^{2.214i}[/tex]

49) 5 – i = [tex]\sqrt{26}e^{-0.197i}[/tex] (conversion from rectangular a+bi form to polar form of complex number)

5 - i = [tex]\sqrt{5^{2}+1^{2}}e^{tan^{-1}(\frac{-1}{5})i}[/tex]  = [tex]\sqrt{26}e^{-0.197i}[/tex]

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By using algebra resolution methods for systems of linear equations, we find that the equation of the form f(x) = a · x² + b · x + c that passes through the three points is equal to f(x) = (5 / 2) · x² + (3 / 2) · x.

In this problem we must determine the coefficients of a quadratic equation that passes through the points (x₁, y₁) = (1, 4), (x₂, y₂) = (2, 13) and (x₃, y₃) = (4, 46). First, we need to create a system of linear equations by substituting on y and x thrice:

(x₁, y₁) = (1, 4)

a · 1² + b · 1 + c = 4

a + b + c = 4

(x₂, y₂) = (2, 13)

a · 2² + b · 2 + c = 13

4 · a + 2 · b + c = 13

(x₃, y₃) = (4, 46)

a · 4² + b · 4 + c = 46

16 · a + 4 · b + c = 46

Then, we find a system of three linear equations with three variables that offers an unique solution:

a + b + c = 4                             (1)

4 · a + 2 · b + c = 13                 (2)

16 · a + 4 · b + c = 46               (3)

There are different methods to find the solution to this system, we proceed to use algebraic substitution:

By (1):

c = 4 - a - b

(1) in (2) and (3):

4 · a + 2 · b + (4 - a - b) = 13

3 · a + b = 9                          (2b)

16 · a + 4 · b + (4 - a - b) = 46

15 · a + 3 · b = 42                  (3b)

By (2b):

b = 9 - 3 · a

(2b) in (3b):

15 · a + 3 · (9 - 3 · a) = 42

15 · a + 27 - 9 · a = 42

6 · a = 15

a = 15 / 6

a = 5 / 2

By (2b):

b = 9 - 3 · (5 / 2)

b = 9 - 15 / 2

b = 18 / 2 - 15 / 2

b = 3 / 2

By (1):

c = 4 - 5 / 2 - 3 / 2

c = 4 - 8 / 2

c = 4 - 4

c = 0

The coefficients of the quadratic equation are (a, b, c) = (5 / 2, 3 / 2, 0).

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The number of high-quality version downloads is 300.

Given:

Size of the standard version = 2.8 megabytes (MB).

Size of the high-quality version = 4.5 MB.

Total number of downloads = 870

Total download size = 2946 MB

Let the number of high-quality version downloads be x.

Then the number of standard version downloads will be 870 - x.

Now the sum of the number of downloads of each type multiplied by their sizes equals 2946 MB.

So the equation is,

4.5x + 2.8(870 - x) = 2946

4.5x + 2436 - 2.8x = 2946

1.7x = 2946 - 2436

1.7x = 510

x = 510/1.7

x = 300

Therefore, the number of high-quality version downloads is 300.

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Kanesha is making scented candles to sell at the craft fair. She buys a 5-pound package of candle wax, a package of 12 small candle tins that each have a volume of 4 ounces and the package of 12 medium candle tins that each have a volume of 6 oz. Kanesha knows that 1 lb of candle wax will fill 20 oz in volume.

Assuming Kanesha sells all of the scented candles she makes how many candle tins of each size should she use in order to maximize the amount of money she will earn at the craft fair...



____ small 4 oz candles

____ medium 6 oz candles



what is the maximum amount of money she will earn in the craft fair?​

________________________________________

1 lb of candle wax will fill 20 oz

She buys a 5-pound package, therefore, she will fill 20*5= 100 oz

Tin size S small (4 oz ) and M medium (6 oz)

S*4 + M*6 = 100

S*7.5 + M*9 = amount of money

_____________________

S*4 + M*6 = 100

4 S = 100 - 6M

S= 100/4 -6/4M

S= 25 -3/2M

Replacing

(25 -3/2M )*7.5 + M*9 = amount of money

187.5 - 11.25M + 9M = amount of money

187.5 - 2.25M = amount of money

According to the expression, the fewer medians sell, the higher the income will be.

Reviewing the candle values by ounces used.

7.5/ 4 = 1.875 sale price / oz

9.0/6 = 1.5 sale price / oz

_____________________________

Therefore, in order to maximize the profit, it would be necessary to make as many small ones as possible, that is, 12.

12* 4 oz = 48

100- 48 = 52

what is left after using the 4 oz tins can be used in the medium candles

52/ 6 = 8

___________________________________

Answer

Assuming Kanesha sells all of the scented candles she makes how many candle tins of each size should she use in order to maximize the amount of money she will earn at the craft fair...



__12__ small 4 oz candles

___8_ medium 6 oz candles

Step-by-step explanation:

Simplifying

6a + -9b = 0

Solving

6a + -9b = 0

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '9b' to each side of the equation.

6a + -9b + 9b = 0 + 9b

Combine like terms: -9b + 9b = 0

6a + 0 = 0 + 9b

6a = 0 + 9b

Remove the zero:

6a = 9b

Divide each side by '6'.

a = 1.5b

Simplifying

a = 1.5b

Answer:

[tex]a=22\\b=6\\c=14\\d=8[/tex]

Step-by-step explanation:

So (Didn't even know what it was until now), is a square where all rows, columns, and diagonals sum up to the same number.

So, from the diagonal of 7, 15, and 23, but adding them up, we can tell that each row, column, and diagonal should sum up to 45.

If we know that, you can solve it either arithmetically or algebraically (I'm going to sovle them algebraically)

Here are the equations I used to solve for each:

[tex]7+16+a=45\\23+a=45\\a=22\\\\24+15+b=45\\39+b=45\\b=6\\\\15+16+c=45\\31+c=45\\c=14\\\\14+23+d=45\\37+d=45\\d=8[/tex]

Any further questions? Just leave a comment.

the probability of winning a lottery game out of all the games played is 0.16.

We are given that:

In a lottery game, the chances of win are = 4 in 25

So, this means that:

if a person plays 25 games of lottery, then he will probably win 4 games out of them.

So, we get that:

Total games = 25

Win games = 4

Probability = win games / total games

Substituting the values, we get that:

Probability = 4 / 25

P = 0.16

Therefore, we get that, the probability of winning a lottery game out of all the games played is 0.16.

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How many pounds of Virginia peanuts does Sergio use?

Assume he is making 10 lb of the $3.40 mixture

Let x = no. of pounds of the Virginia ($3.50) peanuts

Then (10-x) = no. of pounds of the Spanish ($3) peanuts

The Equation:

3.5x + 3(10-x) = 3.4(10)

3.5x + 30 - 3x = 34

.5x = 34 - 30

x = 4/.5

x = 8 pounds of Virginia peanuts

:

(b)How many pounds Spanish peanuts does Sergio use?

Spanish peanuts must be 2 pounds since the total is 10 pounds

:

Check:

3.5(8) + 3(2) = 3.4(10)

28 + 6 = 34

6 possible values of squares that she can move.

What is possibility or probability?

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it.

it is already known that Oris has to move 7 squares (because 3 + 4 = 7), yet she has another 6 sets of possibilities because a dice has 6 facets.

Hence she has 6 different possible numbers of squares she can move.

The possibilities are:

-8 squares (if she rolls a 1)

-9 squares (if she rolls a 2)

-10 squares (if she rolls a 3)

-11 squares (if she rolls a 4)

-12 squares (if she rolls a 5)

-13 squares (if she rolls a 6)

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The net image of a figure is a visual representation of the original figure.

From the given net image, the solid that has the net image can be said to be a traingular

Answer: 71%

Explanation:

100% - total earth surface

29% - earth surface uncovered by water

100 - 29 = 71% of surface covered by water

First, we find the value of r:

Then r is calculated as follows:

Multiplying

Simplify

Apply exponential properties

Applying the limit, the solution is

So, r = 0.4 and since r is less than 1, the series converges.

Answer: From the ratio test, r = 0.4. The series converges.

Given the figure of an object consists of a cylinder and a rectangular prism.

We will find the volume of the cylinder using the following formula:

As shown, the diameter of the base = d = 3 ft

So, the radius = r = d/2 = 3/2 = 1.5 ft

And the height = h = 4 ft

Use π = 3

so, the volume of the cylinder will be as follows:

Now, we will find the volume of the rectangular prism using the following formula:

As shown, the length = l = 7 ft

The width = w = 4 ft

The height = h = 4 ft

So, the volume of the rectangular prism will be as follows:

So, the total volume of the object will be =

So, the answer will be V = 139 ft³

Answer:

F (-3) = -8

Step-by-step explanation:

We start by substituting x = -3 into F (x) = 2x - 2

That gets us to: F ( -3) = 2 * (-3) - 2

Then we calculate the equation, bringing us to:

F (-3) = -6 - 2

When we add -6 + -2 we get: F (-3) = -8

[tex]\vec{a}[/tex] and [tex]\vec{b}[/tex]  are two unit vectors. If [tex]\vec{5a} + \vec{3b}[/tex] and [tex]\vec {a} - \vec {b}[/tex] are perpendicular to each other, then the angle between a and b is ( 2n + 1)π/2.

As given in the question,

Given two unit vectors are : [tex]\vec{a}[/tex] and [tex]\vec{b}[/tex]

|a| = 1 and |b| = 1

Vectors which are perpendicular to each other are :

[tex]\vec{5a} + \vec{3b}[/tex] and [tex]\vec {a} - \vec {b}[/tex]

( [tex]\vec{5a} + \vec{3b}[/tex] ). ( [tex]\vec {a} - \vec {b}[/tex] ) = 0

⇒ 5|a|² -2a.b - 3|b|² = 0

⇒ 5(1)² - 2a.b - 3(1)² = 0

⇒ 5 -  2a.b - 3 = 0

⇒ 2[tex]\vec{a}[/tex].[tex]\vec{b}[/tex] = 2

⇒  [tex]\vec{a}.\vec{b}[/tex] = 1

Let θ be the angle between two vectors

   |a||b|cosθ = 1

⇒ (1)(1)cosθ = 1

⇒cosθ = 1

⇒θ = (2n+1)π/2

Therefore, [tex]\vec{a}[/tex] and [tex]\vec{b}[/tex]  are two unit vectors. If [tex]\vec{5a} + \vec{3b}[/tex] and [tex]\vec {a} - \vec {b}[/tex] are perpendicular to each other, then the angle between a and b is

( 2n + 1)π/2.

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SOLUTION

(a) From the information given in the question,

We will select a curve with 58 at its center which represents the mean and

41 and 75 at the left and right sides. That is gotten by subtracting and adding the standard deviation of 17.

Hence the answer is Graph D

(b) The region that represents less than 41 is seen in graph B

Hence graph B is the answer

(c) Option A

The probability is 0.1587 that a randomly selected cell phone plan in this population is less than $41 per month

olution

e have the following statement:

If < ABC and < CBD are supplementary angles then m < ABC and m< CBD = 180º represents the definition of:

A) supplementary angles

Answer:

64

Step-by-step explanation:

If x² = 16, x is the square root of 16.

Therefore, x = 4

Now plug x in:

x³ = 4³ = 64

The correct answer is:  
     [A]:  " ∡2 is supplementary to ∡3 " .

___________________

The other answer choices given—which are correct statements—only prove that " a || b " {that is:  "Line A" is parallel to "Line B".}

___________________

Answer: 10/3

Step-by-step explanation:

[tex]\frac{2}{6}=\frac{x}{10}\\\\x=\frac{10}{3}[/tex]

Answer:

11

Step-by-step explanation:

This will form triangle VWX. So we have values for ∠VWX and ∠XVW but we don't have value for ∠WXV.

Since ∠WXV and ∠WXY are supplementary angles

=> ∠WXV + ∠WXY = 180

=> ∠WXV = 180 - ∠WXY

So the angles of triangle VXY

∠VWX + ∠XVW + ∠WXV = 180

(x + 14) + (x + 9) + (180 - (5x - 10)) = 180

x + x - 5x + 14 + 9 + 180 + 10 = 180

-3x + 213 = 180

-3x = - 33

x= 11

Answer:

1. x = 18

2. x = 154

Step-by-step explanation:

 2          12

------- = -------

  3          x

 3 × 12 = 36

2 × x = 2x

36 = 2x

÷2    ÷2

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

x = 18

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

  6         84

------- = -------

  11           x

6 × x = 6x

84 × 11 = 924

6x = 924

÷6     ÷6

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

x = 154

I hope this helps!

The value of x such that f(x) and g(x) have equal values is 3

Linear equations are equations that have constant average rates of change.

Note that the constant average rates of change can also be regarded as the slope or the gradient

From the question, we have

f(x) = -2x + 4

g(x) = 2x - 8

The question implies that the functions have equal values

This means that

f(x) = g(x)

Substitute f(x) = -2x + 4 and g(x) = 2x - 8 in f(x) = g(x)

So, we have the following equation

-2x + 4 = 2x - 8

Collect the like terms

2x + 2x = 8 + 4

Evaluate the like terms

4x = 12

Divide both sides of the equation by 4

x = 3

Hence, the value of x such that the equations are equal is 3

See attachment for the graph of the functions

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Assest

Cash = 39000

Owned land = 460000

Savings land = 207000

Jewerly = 3000

Total assests = 39000+460000+207000+3000

Total assests = 709000

Liabilities

Bank loans = 350000

Student loan debt = 25000

Total liabilities = 350000+25000

Total = 375000

Net worth = Total assets - Liabilities

Net worth = 709000 - 375000

Net worth = $334,000