Find the slope of the following lines

Explain how you got the answer

The equation which correctly models the decreasing supply of helium as described in the task content is; y = 35 - 0.21x.

It follows from the task content that the equation which correctly models the decreasing supply of helium according to the description is to be determined.

Let, y = amount of helium remaining.

Let x = no of years since 2018.

First, one must convert 210 million to billion cubic feets as follows;

210 million = (210/1000) billion.

= 0.21 billion cubic meters per year.

The number above represents the rate of change of the linear model, otherwise termed the slope.

On this note, since the starting deposit of helium in 2018 was; 35 billion.

This insinuates that the y-coordinate of the y-intercept of the required model is; 35.

Hence, the required decreasing Linear model for the supply of helium is;

y = 35 - 0.21x.

The equation above follows from the slope-intercept form of a linear equation.

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The sentence can be represented as 2x+10=-5, with x = -7.5

Given that twice the value of  x plus 10 is equals to -5

Mathematical symbols are used to perform various operations. The symbols make it easier to refer Mathematical quantities. It is interesting to note that Mathematics is completely based on numbers and symbols. The math symbols not only refer to different quantities but also represent the relationship between two quantities. All mathematical symbols are mainly used to perform mathematical operations under various concepts.

• Helps in denoting quantities

• Establishes relationships between quantities

• Helps to identify the type of operation

2(x)+10=-5

2(x)=-15

x=-15/2

x=-7.5

Hence, The sentence can be represented as 2x+10=-5, with x = -7.5

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The sums of series using Polya's four-step problem-solving strategy in (a), (b) and (c) are 79800, 150975, and 1560 respectively.

a sequence is, more or less speaking, a description of the operation of adding infinitely many quantities, one after the opposite, to a given starting quantity. The examine of series is a chief part of calculus and its generalization, mathematical evaluation. series are utilized in maximum areas of mathematics, even for reading finite structures (which includes in combinatorics) thru producing features.

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If Benjamin's credit card has an APR of 19%, calculated on the previous monthly balance, and a minimum payment of 2%, starting the month after the first purchase. the total amount that Benjamin has made in payments over the 7 months is: $285.01.

To determine the  total amount that Benjamin has made in payments over the 7 months we would need to add up or sum up all the Payment Finance received charges for the first six months.

Now let calculate the total amount that Benjamin made in payment.

Hence,

Total amount made in payment=$48.00+$47.80+$47.60+$47.40+$47.20+$47.01

Total amount made in payment =$285.01

Therefore if Benjamin's credit card has an APR of 19%, calculated on the previous monthly balance, and a minimum payment of 2%, starting the month after the first purchase. the total amount that Benjamin has made in payments over the 7 months is: $285.01.

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The quadratic function is defined as follows:

- 2 / 3 x² + 7 / 3 x + 8

The quadratic function has the following sets of values below:

(0,8) (2,10) (3,1).

The quadratic function is represented as follows:

f(x) = ax² + bx + c

using  (0,8)

8 = a(0)² + b(0) + c

8 = c

Therefore, using (2, 10)(3 , 1).

f(x) = ax² + bx + c

10 = a(2)² + b(2) + 8

10 - 8 = 4a + 2b

2 = 4a + 2b

1 = 2a + b

1 = a(3)² + b(3) + 8

1 = 9a + 3b

Hence, combine the equations,

2a + b = 1

9a + 3b = 1

multiply equation(i) by 3

6a + 3b = 3

9a + 3b = 1

3a = - 2

a = - 2 / 3

Therefore,

9a + 3b = 1

9(- 2  / 3) + 3b = 1

-6 + 3b = 1

3b = 7

b = 7 / 3

Therefore, the quadratic function is defined as follows:

- 2 / 3 x² + 7 / 3 x + 8

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option (A) ( - 4 , 3 ) is the correct option to represent the coordinate of point P at ( negative 4, 3 ).

We are given the coordinate of the point as:

(negative 4, 3)

the negative means a minus ( - ) sign.

So, the coordinate of point P can also be written as:

( - 4 , 3 )

So, we get that:

Option (A) ( - 4 , 3 ) is the correct option.

Therefore, we get that, option (A) ( - 4 , 3 ) is the correct option to represent the coordinate of point P at ( negative 4, 3 ).

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Answer:

y = ± 11

Step-by-step explanation:

y² = 121 ( take square root of both sides )

[tex]\sqrt{y^2}[/tex] = ± [tex]\sqrt{121}[/tex]

y = ± 11

Answer: 3x^3 +13x^2 -4x +2 +0/(x+2)

Step-by-step explanation:

-2: 3 19 22 -6 4=

       -6 -26 8 -4

    3 13 -4  2   0 ==> 3x^3 +13x^2 -4x +2 +0/(x+2)

Quotient: 3x^3 +13x^2 -4x +2

Remainder: 0

Answer:  

10/100= 0.1

100/10= 10

Step-by-step explanation:

Answer:

10 OR 100. Read the explanation for details.

Step-by-step explanation:

If Martin scored 10%, and this represents 10 points, that means that martin scored 10 points. If he is talking about ALL the points in total then there are 100 points because 10% is 1/10, and if each 1/10th is 10 points, if you multiply that by 10 you get

100.

Answer:110degrees

Step-by-step explanation:

the angles of the inside of a triangle always add up to 180
180-30-40=a
a is unknown angle
180-30-40=110

Answer: done

x + 3 = 0

subtract 3 on both sides

x = -3

x +4 = -3

subtract 4 on both sides

x = -7

3x = 0

divide 3 on both sides

x = 0

5x = 2

divide 5 on both sides

x = 2/5

x - 4 = 0

add 4 on both sides

x = 4

5x - 4 = 0

add 4 on both sides then divide both sides by 5

x = 4/5

2x + 4 = 5

subtract both sides by 4 then divide both sides by 2

x = 1/2

2x^2 = 9

square root both sides then divide both sides by 2

x = 3/2

5x - 1 = 2

add both sides by 1 then divide both sides by 5

x = 3/5

x + 3 = 65

subtract both sides by 3

x = 62

The quotient will have 2 significant figures.

The digits in the number , that contribute to the degree of accuracy can be defined as Significant Figures.

For Example ; 2.096 has 4 significant Figures

0.069 has 2 significant figures.

Rule Of Significant for Multiplication & Division :

Rule says in multiplication or division , the final result should retain as many significant figures as there are in the original number with the least significant figures.

In the given question

4.0286 × 10⁹   = 5 significant figures

3.1 × 10⁻⁴  = 2 significant figures

The quotient on dividing the numbers is 1.2995 x 10¹³  will have 2 significant figures as the least significant from 5 and 2 is 2.

Therefore , the quotient will have 2 significant figures.

The given question is incomplete , the complete question is

You are solving a measurement problem where the numbers 4.0286×10⁹ and 3.1×10⁻⁴ are divided. How many significant digits should the quotient have?

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The range of the function is {-11, -9, -7, -5}.

The given function is g(x)=x−13.

We need to find the range of g(x).

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

Now, put x=2,4,6,8 in the given function and find the range of function.

So, g(2)=2−13=-11

g(4)=4−13=-9

g(6)=6−13=-7

g(8)=8−13=-5

Therefore, the range of the function is {-11, -9, -7, -5}.

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Answer:

when x=-3 then from the graph the value of y is -2

1 - there will be increase of  233.33 %  ,  2 - there will be increase of 122.22 % , 3 - there will be decrease of 15 % , 4 - there will be decrease of 55.56 % , 5 - there will be increase of 100%

% is a relative number that is used to represent hundredths of any quantity. Since one percent (1%) equals one tenth of something, 100 percent denotes the entire amount, and 200 percent denotes twice the amount mentioned percentage.

1 - Start : 3 end : 10

  formula for finding percentage increase is = [tex]\frac{end - start }{start } * 100[/tex]

so substituting value in the formula ;

       that is equal to = [tex]\frac{10-3}{3} * 100[/tex]

                                 = [tex]\frac{7}{3} * 100[/tex]

                                 = 233.33% increase

2 - Start : 9  End : 20

      directly substituting the values in the above mentioned formula

                                            = [tex]\frac{20-9}{9} * 100[/tex]

                                            = [tex]\frac{11}{9} * 100[/tex]

                                            = 122.22% increase

3 - Start : 100 end : 85

             plugging in the values = [tex]\frac{85-100}{100}*100[/tex]

                                                   = [tex]\frac{-15}{100} * 100[/tex]

                                                   = -15% i.e. decrease of 15%

4 -  Start : 45 end : 20

             putting in the values = [tex]\frac{20-45}{45} * 100[/tex]

                                                = [tex]\frac{-25}{45}*100[/tex]

                                                = -55.56% i.e. decrease of 55.56 %

5 - Start : 30 end : 60

                  putting in the values = [tex]\frac{60-30}{30}* 100[/tex]

                                                       = [tex]\frac{30}{30} * 100[/tex]

                                                       = 100%  increase

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Answer: 1/2

Step-by-step explanation: 2/4 = 0.5

1/2 = 0.5

Hello and Good Morning/Afternoon

Let's take this problem step-by-step:

The sum of all angles in a triangle is equal to 180 degrees:

 [tex]\hookrightarrow x + 120 +20 = 180\\\hookrightarrow x + 140 = 180\\\hookrightarrow x =180-140=40[/tex]

∠y and ∠x are on a flat line ⇒ total angle measured between is 180°

[tex]\hookrightarrow x + y = 180\\\hookrightarrow 40 + y = 180\\\hookrightarrow y = 180-40=140[/tex]

Answer: y = 140°

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Answer:

If there is divide sign between (2x+20) and y, then the answer is 8 but if there's multiplication sign between (2x+20) and y, then the answer is 200.

Answer:

y=

Step-by-step explanation:

The ordered pair for the greatest amount he can buy is (3.2, 12)

He  has $12 to put gas in his car. The gas costs $3.75 per gallon.

Therefore,

Hence, the total amount he has to spend is 12 dollars.

Therefore,

y = 3.75x

where

y = 12 dollars

Therefore,

12 = 3.75x

divide both sides by 3.75

12 / 3.75 = 3.75x / 3.75

x = 3.2

Therefore, the ordered pair for the greatest amount he can buy is (3.2, 12)

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Answer: 108 liters

Step-by-step explanation: There are 86,400 seconds in a 24-hour day. If 25 mL leak every 20 seconds, divide 86,400 by 20 (4,320), then multiply by 25 (108,000). There is 1,000 mL for every liter, so divide 108,000 by 1,000, and you will get 108 liters.

Expression -4/-9 equals fraction numerator 9 minus 4 in math.

Fraction definition:

It has two negative numbers, hence the result will be the same because of the rule, which is why it is equivalent (minus times minus is equal to zero)

4/9= -4/-9

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Answer:

Step-by-step explanation:

Answer:

A. {-6,0,9} but in order of domain it's {9,0,-6}

Step-by-step explanation:

There's two ways of finding the range;

Way #1: The traditional method

Way #2: The graphing calculator method

hi

A = 6x^(2)+4x+3*y + 6y + y^(2)

A= 6x²+y²+4x+9y

Using relations in a right triangle, it is found that

The height of the tree is of 91.6 meters.

The graph for this problem is given at the end of the answer.

The relations in a right triangle are given as follows:

From the diagram graphed, we can build two relations involving the tangent of the angles, as follows:

From the smaller right triangle:

tan(43º) = h/x

0.9325 = h/x

x = (1/0.9325)h.

x = 1.0724h (we want to find h, hence we write x as a function of h).

From the larger right triangle:

tan(38º) = h/(x + 19).

tan(38º) = h/(1.0724h + 19).

0.7813 = h/(1.0724h + 19).

Applying cross multiplication:

h = 0.7813(1.0724h + 19).

h = 0.8379h + 14.8447.

0.1621h = 14.8447

h = 14.8447/0.1621

h = 91.6 meters.

The height of the tree is of 91.6 meters.

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