The** slope-intercept **form of a function f(x) = mx + c therefore,f(x) = -3x + 4 is the correct **notation **of the function 9x + 3y = 12 so option (B) is correct.

The **function **is a relationship between variables, and the **nature **of the **relationship **defines the function for example y = sinx and y = x +6 like that.

The **machine **will only accept specified **inputs**, described as the function's domain, and will potentially produce one **output **for each input.

As per the given **function**,

9x + 3y = 12

**Subtract **9x both sides,

9x - 9x + 3y = 12 - 9x

3y = 12 - 9x

**Divide **by 3 into both sides,

y = 12/3 - 9x/3

y = -3x + 4

Since,y = f(x)

f(x) = -3x + 4 .Here -3 is the **slope **while 4 is the y-intercept.

Hence "The** slope-intercept **form of a function f(x) = mx + c therefore,f(x) = -3x + 4 is the correct **notation **of the function 9x + 3y = 12".

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The perimeter of the flag is 2260 ft Determine the flag's width and length if the length is 350 ft greater than the width.

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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The value of y varies directly with x. If y = 8, when x = 4, what is y when x = 48?

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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What is the equation of the parabola with the vertex of (1,-8) that passes through (2,-6)

Hello!

What is the standard form of the parabola:

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

(h,k): vertex's coordinate=> 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!

y=-5(-4)-17

please add an explanation

**Answer:**

y = 3

**Step-by-step explanation:**

y = -5(-4) - 17

multiply first

y = (-5*-4) - 17

y = +20 -17

y = 3

The formula h 16t² describes the time t in seconds that it takes for an object to fall from a height of h feet. An object is dropped from

height of 1,600 feet. How many seconds does it take to reach the ground?

seconds

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 mass of two bodies are attracted with a force of 745N.if their distance of separation is 70.3m, find the mass of one the bodies, if the mass of the other is 2050kg (G=6.7by 10^-11Nm^2kg^2

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]

What is mass ?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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carly has a job that pays 35 a week plus 2 for each sale she makes. how many sales dose she need to make to earn more than 100 this week?

Carly needs to perform **3****3**** **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 of****f**** **the number

Number of sales = 33

Therefore, she needs to make **33** **additional** **sales**.

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A (2,-4), B (3, 3) and C (-1,5) are the vertices of ΔABC . Find the equation of the altitude of the triangle through C.

**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

Sara hiked up a mountain on a steep 3-mile trail. Then she hiked downhill on a less

steep 5-mile trail. She hiked 0.5 mph faster downhill than uphill.

If Sara hiked uphill at a rate of r mph, how fast was she hiking downhill?

**Answer:**

wait, its r + 0.5

**Step-by-step explanation:**

Apply the Strategy Solve each problem by making a table. 5. 1. A page from Dana's album is shown. Dana puts the same number of stickers on each page. She has 30 pages of stickers. How many stickers does she have in all? Dana has stickers in all. MOPPOPPG-BUDG

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**

The area of a square is 150 square feet. What is the side length of the square?

**Answer:37.5**

**Step-by-step explanation:**

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

Round 2.629 to the nearest tenth.

**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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1. Write a matrix to represent the following system.

[tex]\left \{ {{-9x+4y =1} \atop {7x-9=5}} \right.[/tex]

Complete the matrix below.

[ _ _ | _ ]

[ _ _ | _ ]

[ _ _ | _ ]

2. Write a matrix to represent the following system.

[tex]\left \{ {{-5x+6y=1} \atop {5x-2y=9}} \right.[/tex]

Complete the matrix below.

[ _ _ | _ ]

[ _ _ | _ ]

[ _ _ | _ ]

The **augmented matrices **for each system are given as follows:

**1.**

[ -9 4 | 1 ]

[ 7 0 | 14]

**2.**

[ -5 6 | 1 ]

[ 5 -2 | 9]

How to build the augmented matrix of a system of equations?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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Jamal is constructing the bisector of angle ABC. He has a list of steps for the construction, but they are not in

order.

^^^^^^^^^^^^^^^^^^^^^^^^^^^

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

A solid oblique pyramid has an equilateral triangle base with a base edge length of 14 units. The base triangle is triangle A C D. The apex is point B. The angles formed with the lateral sides are 45 degrees.

What is BC, the height of the pyramid?

7 units

7StartRoot 2 EndRoot units

14 units

14StartRoot 2 EndRoot units

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:**

Miranda is making bracelets. She already has 15 and she can make 3

per day. Determine the slope and the y-intercept.

**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

(d^2+4)b=g

Solve for b

**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]

Starting with the number 0, build a sequence of 5 numbers.

**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 sum of three numbers is 23. The third number one more than the sum of the first and second numbers. The first number is ten less than the third number. Find the numbers.

**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!

You are holding a kite string in your hand. The angle of elevation from your hand to the kite is 66 degree and the distance to the kite is 303 feet. Your hand is 4 feet above the ground. How high is the kite? Round your answer to the nearest tenth of a foot.

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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A group of friends wants to go to the amusement park. They have no more than $160 to spend on parking and admission. Parking is $10.50, and tickets cost $32.50 per person, including tax. Write and solve an inequality which can be used to determine x, the number of people who can go to the amusement park.

**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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If the point (2, – 3) lies on the graph of the equation 2y = ax – 7, then the value of a is

**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

If the breadth of a rectangle is reduced by 4cm it's are would be reduced by 240 cm². How long is the rectangle?

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

How do I find the slope?

**Answer:**

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

**Step-by-step explanation:**

You find the slope by using rise/over run. Rise=y run=x. If you go down on the y axis that is negative slope. If you go left on the x axis that is negative as well. Up y axis=+ right x axis=+. Look for a point on the graph that will make your equation true

Need help finding the perimeter

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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I’m failing geometry pls help. Why did my teacher mark me wrong on this problem and what are the correct answers?

**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°

Please help. The problem is attatched!

The equation is **15 + 0.5x = 25 + 0.25x **and number of miles is **4****0****.**** **

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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Anyone please help me this all and have solutions

**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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Which relation represents a function?

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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Solve for y 10x -5y=30

**Answer:**

y=2(x−3)

**Step-by-step explanation:**

What is the six day creation according to Christianity? Thanks
Purchases of streamed music can be modeled by f (t) = 3.7 + 0.84 ln(t +1), where f (t) is measured in billions of dollars and t is measured in years, with t=0 corresponding to 2012.a. What was the amount spent by consumers on streamed music in 2014? Use the correct units.b. How fast was the amount spent by consumers on streamed music changing in 2014?Use the correct units.
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Based on "The Patient Cat" as a whole, what type of character is the protagonist? Direct Dynamic Indirect Static
poker hand is defined as drawing 5 cards at random without replacement from a deck of 52 playing cards. find the probability of each of the following poker hands: (a) four of a kind (four cards of equal face value and one card of a different value). (b) full house (one pair and one triple of cards with equal face value). (c) three of a kind (three equal face values plus two cards of different values). (d) two pairs (two pairs of equal face value plus one card of a different value). (e) one pair (one pair of equal face value plus three cards of different values)
Which equations represent the conservation of matter? (choose 2)ResponsesA A + B ABA + B , , ABB A + B CA + B , , CC A + B + C BC + DA + B + C , , BC + DD AB + CD AC + BBAB + CD , , AC + BBE AB + C AC + B
in a blank , members of the channel pursue their own goals and maximize their own profits, regardless of the effect on other channel members. multiple choice question. corporate vertical marketing system conventional marketing channel strategic relationship jit system
y = 3x 5 y=-x-5Parallel, perpendicular or neither ?
1 point2. Consider the inequality below. Which value of x is a solution to theinequality?*2x + 39O x=-10+13x = -60 x = 0O x = 6
a nursing student is preparing to administer the drug bethanechol to a client with urinary retention. after researching the drugs actions and uses, the student demonstrates understanding of the drug by identifying it as which type of medication? select all that apply.