consider the function rpresented by 9x + 3y = 12 with x as the independant variable. How can this function be writte using function notation? f(y) = - 1/3y + 4/3, f(x) = -3x + 4, f(x) = - 1/3 x + 4/3 f(y), = - 3y + 4

Answer:

a = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

since (2, - 3 ) lies on the graph then it makes the equation true.

substitute x = 2 and y = - 3 into the equation and solve for a

2(- 3) = a(2) - 7 , that is

- 6 = 2a - 7 ( add 7 to both sides )

1 = 2a ( divide both sides by 2 )

[tex]\frac{1}{2}[/tex] = a

The augmented matrices for each system are given as follows:

1.

[ -9 4 | 1 ]

[ 7 0 | 14]

2.

[ -5 6 | 1 ]

[ 5 -2 | 9]

For a system of n variables, the first n columns of the matrix are composed by the coefficients of the variable of the system.

The two systems in this problem have variables x and y, hence:

Then the last column is composed by the values on the right side of the equations, that is, the results of the operations.

The second equation of the first system is:

7x - 9 = 5 -> 7x + 0y = 14 (this format is needed to build the augment matrix.

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Hello!

What is the standard form of the parabola:

 [tex]\hookrightarrow y=(x-h)^2+k[/tex]

          => h: x-coordinate of vertex

          => k: y-coordinate of vertex

Since our vertex is (1,-8)

 [tex]\hookrightarrow \text{Our equation is }y=(x-1)^2}-8[/tex]  <== Answer

Hope that helps!

A solution set exists the set of values that satisfy a given set of equations or inequalities.

Its position must be 1600 then It takes 10s to get to the ground.

A solution set exists the set of values that satisfy a given set of equations or inequalities. For instance, for a set of polynomials over a ring , the solution set exists the subset of on which the polynomials all vanish (evaluate to 0), formally.

The formula,

h = 16t²

where h is height and t is time.

You want to see how long it will take an object to fall 1600 feet down to the ground. These means its position must be 1600.

By setting the equation equal to this value,

we get:

1600 = 16t²

To estimate the value of t.  

First, divide both side by 16, getting:

100 = t²  

Now taking the square root of both sides, we get:

√(100) = 10 seconds.

It takes 10s to get to the ground.

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The height of the pyramid = BC = 14 units

It is a three-dimensional shape that has a polygonal base and flat triangular faces which joins at the apex at the top of the pyramid.

We have,

Base edge length = 14 units

From the figure below,

The base of a solid oblique pyramid is an equilateral triangle with a base edge length of 14 units so,

We get,

AC = CD = AD = 14 units _____(1)

All sides in an equilateral triangle are equal.

In the right triangle ABC,

tan 45° = BC / AC

tan 45° = 1

1 = BC / AC _____(2)

From (1) and (2) we get,

1 = BC / 14

BC = 14 units

The height of the pyramid = BC = 14 units

Thus,

The height of the pyramid is 14 units.

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Answer: C 14 UNITS

Step-by-step explanation:

Answer:

2, 9, 12

Step-by-step explanation:

We know that the first number is ten less than the third number and that the third number is one more than the first number and second number combined. Because of this, our third number has to be one away than the combination of the first two numbers. Now, we just have to see the numbers of the first two values and the first number is 10 less than the third number. You can mostly guess the numbers once you understand. I hope that this didn't confuse you more. Hope this helps!

Answer:

Find the slope by putting your rise over your run. Make sure to label your points.

Step-by-step explanation:

Carly needs to perform 33 additional sales to earn 100 this week.

Firstly forming the expression as per the weekly earning and individual payment on extra sale. Writing the expression -

Amount earned = 35 + 2×number of sales

Keep the value of amount earned in mentioned formula to find the number of sales.

100 = 35 + 2×number of sales

2×Number of sales = 100 - 35

Performing subtraction on Right Hand Side of the equation

2×Number of sales = 65

Shifting 2 to Right Hand Side of the equation

Number of sales = 65/2

Performing division on Right Hand Side of the equation

Number of sales = 32.5

Round off the number

Number of sales = 33

Therefore, she needs to make 33 additional sales.

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For given angle of elevation equals to 66 degree and distance to kite is 303feet and hand is 4 feet above the ground then kite is 280.8feet high.

As given,

Shown in diagram attached,

Angle of elevation ∠AEB=66°

Distance to the kite AE=303 feet

Hand above the ground DE=4feet

DE=BC

BC=4feet

Let 'h' be height of AB

Height of the kite=(h +4)feet

In ΔABE,

sin66°=h/303

⇒h=sin66° ×303

     =0.9135 ×303

      =276.7905

      ≈276.8 feet

Height of kite=(h +4) feet

                             =276.8 +4

                             =280.8 feet

Therefore, for given angle of elevation equals to 66 degree and distance to kite is 303feet and hand is 4 feet above the ground then kite is 280.8feet high.

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Inequality is 32.50x + $10.50 ≤ $160 and 4 people can go to the amusement park.

inequality, A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.

Given that,

$160 = Amount of money they have

$10.50 = Parking Cost

$32.50 = Cost of tickets per person

Because they only have $160, they can't spend more than that amount.

Therefore, the inequality would be the ticket cost per person, times the amount of people being payed for (x) plus the parking cost is less than or equal to the amount of money they have to spend. Hence the inequality:

32.50x + $10.50 ≤ $160

Solve the equation

$160 - $10.50 = $149.50 (149.50 is how much is left for tickets after subtracting the parking cost)

$32.50 x 4 = $130 (4 tickets can be bought for the price of $32.50)

$149.50 - $130 = $19.50 (19.50 isn't enough for another person)

So, the solution to the inequality is 4 people can go to the amusement park.
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Answer:37.5

Step-by-step explanation:

so basically a square has four sides so 150 divided by 4

Answer:

Let the length be x. The breadth be y Area=xy. On reducing breadth by 4 new breadth will be (y-4). X(y-4)=xy-240. Xy-4x=xy-240. -4x=-240. X=60. Hence rectangle is 60cm long

Step-by-step explanation:

hope it will help

Answer:

y = 3

Step-by-step explanation:

y = -5(-4) - 17
multiply first

y = (-5*-4) - 17

y = +20 -17

y = 3

Solutions are given below:

1. (14x^(5))/(5y^(2))=(2x^(4))/(10y) → x=y/14

2. ((x)/(y))((4y)/(3x))=((6y^(2))/(8x^(3))) → [tex]x=\frac{\sqrt[3]{36y^{2} } }{4}[/tex]

3. (5(y+6))/(2(xy-3))]=((y+6)/(4(xy-3))) → (-∞,∞)

4. ((x^(2)-4)/(x^(2)+5x+4))=((x+2)/(x+1)) → x=-2

What is a solution?

Solutions are given below:

1. (14x^(5))/(5y^(2))=(2x^(4))/(10y) → x=y/14

2. ((x)/(y))((4y)/(3x))=((6y^(2))/(8x^(3))) → [tex]x=\frac{\sqrt[3]{36y^{2} } }{4}[/tex]

3. (5(y+6))/(2(xy-3))]=((y+6)/(4(xy-3))) → (-∞,∞)

4. ((x^(2)-4)/(x^(2)+5x+4))=((x+2)/(x+1)) → x=-2

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Step-by-step explanation:

it is a bit difficult to read the handwriting (and even the printed original texts) in this diffuse picture.

let's go through the 3 problems as I could decipher them.

1)

from what I can see you made a calculation mistake for y.

but you were right with your approaches.

12x - 8 = 15x - 23

15 = 3x

x = 5

therefore,

12x - 8 = 12×5 - 8 = 60 - 8 = 52°

and the large angle up there is

52 + 70 = 122°

and now

6y + 96 = (12x - 8) + 70 = 122

6y = 26

y = 26/6 = 13/3

by the way, x and y are not angles (and degrees). they are just factors in the expressions to calculate some angles.

12, 15 and 6 are not ° either. all are calculation factors or terms, that then together define the ° of angles.

2)

you made a mistake with the identification of what angles the linear pair is.

3x = 5x - 20

20 = 2x

x = 10 (again, not °, just a number)

3x = 3×10 = 30° (this is then an angle)

= 5x - 20

for y we could then use 2 different approaches

a) your linear pair approach.

4y is one angle, true, but the other is (2y + 3x) !

so,

4y + 2y + 30 = 180

6y = 150

y = 25 (again, not °, just a number)

2y = 50°

4y = 100°

3)

I hope you are right with (11x + 19) and (12y - 24). I would have read this in the picture as (11x + 18). and it could be (12y + 24).

assuming you are right :

11x + 19 = 7x + 47

4x = 28

x = 7 (again, not °, just a number)

11x + 19 = 7x + 47 = 96°

7z + 17 = 87

7z = 70

z = 10 (again, not °, just a number)

and yes, for y we are using the linear pair again. the two combining angles are (12y - 24) and (11x + 19).

(12y - 24) + (11x + 19) = 12y - 24 + 96 = 180

12y + 72 = 180

12y = 108

y = 9 (again, not °, just a number)

12y - 24 = 12×9 - 24 = 108 - 24 = 84°

Answer:

x + 7y = 34

Step-by-step explanation:

the altitude through C meets the opposite side AB at right angles

calculate the slope of AB using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = A (2, - 4 ) and (x₂, y₂ ) = B (3, 3 )

[tex]m_{AB}[/tex] = [tex]\frac{3-(-4)}{3-2}[/tex] = [tex]\frac{3+4}{1}[/tex] = [tex]\frac{7}{1}[/tex] = 7

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{7}[/tex] , then

y = - [tex]\frac{1}{7}[/tex] x + c ← partial equation of the altitude

to find c substitute C (- 1, 5 ) into the partial equation

5 = [tex]\frac{1}{7}[/tex] + c ⇒ c = 5 - [tex]\frac{1}{7}[/tex] = [tex]\frac{35}{7}[/tex] - [tex]\frac{1}{7}[/tex] = [tex]\frac{34}{7}[/tex]

y = - [tex]\frac{1}{7}[/tex] x + [tex]\frac{34}{7}[/tex] ( multiply through by 7 )

7y = - x + 34 ( add x to both sides )

x + 7y = 34 ← equation of altitude in standard form

A function is defined as a relation between a set of inputs having one output each.

The value of y when x = 48 is 96.

A function is defined as a relation between a set of inputs having one output each.

The inputs are called the domain of the function.

The outputs are called the range of the function.

We have,

The value of y varies directly with x.

y = 8, when x = 4.

Domain = input = 4

Range = output = 8

Now,

We can say that y is a function.

i.e y = 2x.

Where x = input = domain and y = range = output.

The value of y when x = 48:

y = 2x

y = 2 x 48

y = 96

Thus,

The value of y when x = 48 is 96.

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The length is 780 feet and the width is 430 feet.

Distance is measured in length.

The dimension of distance is a property of length in the International System of Quantities.

Let the length be x

Width = x - 350

Perimeter = 2260 feet

Now : 2(x + x +350) = 2260

or, 2 x + 700 = 2260

or, 2x = 1560

or, x = 780 feet

So length is 780 feet

Width = 780 -350 = 430 feet

Therefore the length is 780 feet and the width is 430 feet.

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13 + √85/3 is the perimeter of triangle .

Explain what a triangle is.

The points P ( - 3 , -8 ) Q ( - 3, - 1) R ( -9,-8)

Distance between PQ = [tex]\sqrt{( x_{2} - x_{1})^{2} + ( y_{2} - y_{1})^{2} }[/tex]

                                      = [tex]\sqrt{( - 1 + 8)^{2} + ( -3 + 3)^{2} }[/tex]

                                      = [tex]\sqrt{( -7 )^{2} +0 }[/tex]

                                       = √49  ⇒ 7

Distance between QR = [tex]\sqrt{( x_{2} - x_{1})^{2} + ( y_{2} - y_{1})^{2} }[/tex]

                                     = [tex]\sqrt{( -9 + 3 )^{2} + ( -8 + 1)^{2} }[/tex]

                                     = [tex]\sqrt{(- 6)^{2} + ( - 7)^{2} }[/tex]

                                     = [tex]\sqrt{36 + 49}[/tex]

                                   = √85

Distance between RP = [tex]\sqrt{( x_{2} - x_{1})^{2} + ( y_{2} - y_{1})^{2} }[/tex]

                                     = [tex]\sqrt{( - 3 + 9)^{2} + ( -8 + 8)^{2} }[/tex]

                                     = [tex]\sqrt{(6)^{2} }[/tex]

                                     = √36

                                    = 6

perimeter = PQ + QR+RP/3

                = 7 + √85 + 6/3

              = 13 + √85/3

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Answer:

2.6

Step-by-step explanation:

cause it is 2.6299999999

2.629 to the nearest tenth is 2.6.

Decimals are numbers that have two components, a whole number component and a fractional component, which are separated by a decimal point.

Given:

A decimal number,

2.629.

Here, 2 is the whole number component and 0.629 is the fractional component part.

To round the number to the nearest tenth:

The number in tenth place is 6.

And the value right next to 6 is 2.

6 > 2.

So, the number will stay the same.

2.629 = 2.63

Then 2.63 = 2.6 to the nearest tenth.

Therefore, 2.6 is the required decimal.

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Answer:

y=2(x−3)

Step-by-step explanation:

Answer:

b = [tex]\frac{g}{(d^{2}+4) }[/tex]

Step-by-step explanation:

([tex]d^{2}[/tex] + 4)b = g  Divide both sides by ([tex]d^{2}[/tex] + 4)

b = [tex]\frac{g}{(d^{2}+4) }[/tex]

Answer:

wait, its r + 0.5

Step-by-step explanation:

Step 1:

First count the number of stickers on a page

There are 12 stickers in a page

Step 2

There are 30 pages,

Hence, the number of stickers in 30 pages = 30 x 12 = 360

Final answer

Dana has 360 stickers in all

Answer:

How about:

0, 1, 2, 3, 4..............

lol jk here:

0, 66, 132, 198, 264

Step-by-step explanation:

Guess what it is! ;p

The mass of two bodies are attracted with a force of 745N.if their distance of separation is 70.3m, then the mass of one the bodies is

[tex]m_{1} = 1.88(10)^{-7}[/tex]

The amount of matter that makes up every object or body is the greatest way to understand mass. Everything that we can see has mass. Examples of objects with mass include a table, a chair, your bed, a football, a glass, and even air. The mass of a thing determines whether it is light or heavy.

Given that : The mass of two bodies are attracted with a force of 745N.if their distance of separation is 70.3m

F=[tex]G\frac{m_{1} .m_{2} }{r^{2} }[/tex]

[tex]m_{1} =\frac{F.r^{2} }{Gm_{2} }\\ m_{1} =\frac{745.(70.3)^{2} }{6.7(10)^{-11}.2050 }\\\\[/tex]

[tex]m_{1} =\frac{26881.3(10^{7} )}{13735}[/tex]

[tex]m_{1} = 1.88(10)^{-7}[/tex]

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Answer:

y=3x+15

Step-by-step explanation:

she can make 3 a day so 3x and she already has 15 so the line crosses the y-axis  at 15

The equation is 15 + 0.5x = 25 + 0.25x and number of miles is 40.

While writing the equation for green and blue cars, one time fee will be added with cost of driving for miles. Let us assume the number of miles to be x.

Firstly writing the equation for green car -

Cost = 15 + 0.5×x

Now writing the equation for blue car -

Cost = 25 + 0.25×x

The number of miles for same cost will be calculated by equating the expressions.

15 + 0.5x = 25 + 0.25x

0.5x - 0.25x = 25 - 15

Performing subtraction on Left Hand Side and Right Hand Side of the equation

0.25x = 10

Shifting 0.25 to Right Hand Side of the equation

x = 10 ÷ 0.25

Performing division on Right Hand Side of the equation

x = 40

So, if both the cars travel 40 miles, the rental cost will be same. The correct equation for calculation is 15 + 0.5x = 25 + 0.25x.

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In the given relations , the relation (B) represents a function, others are not function. To become a function each input should have only one output. Since others does not satisfy this criteria they are not functions.

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