A line passes through the point (-2, 6) and has a slope of 6.
Write an equation in point-slope form for this line.

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Work Shown:

|3x+12| = 18

3x+12 = 18 or 3x+12 = -18

3x = 18-12 or 3x = -18-12

3x = 6 or 3x = -30

x = 6/3 or x = -30/3

x = 2 or x = -10

The rule used in step 2 is the idea that if |x| = k, for some positive number k, then x = k or x = -k. One equation breaks into two separate ones. From there we solve each equation for x as normal. Follow PEMDAS in reverse, undoing each operation, to isolate x.

If you're curious why the absolute value breaks into two parts, consider something like |x| = 7. This means x is 7 units away from zero on a number line. There are two possible locations where x could be: 7 and -7. This is one example showing why we get two different results. The same applies to our equation as well, just it's a bit more complicated.

Answer:

Yes, because the ratios will always be the same between them, and it is a straight line

Hope this helps! :)

Answer:

yes, see explanation below...

Step-by-step explanation:

1). A graph that represents a proportional relationship means that as [tex]x[/tex] increases, [tex]y[/tex] increases.

2). The graph is a straight line through the origin.

Answer: 1.8

Step-by-step explanation:

(-18-(-9))/(12-7)=-9/5

Answer:

70

Step-by-step explanation:

triangle xbc is an isosceles triangle.

there are 180 degrees in a triangle.

angle xbc=55.

so that means angle xcb is also 55.

55+55=110

180-110=70

hope this helps

Answer:

(for the second one)

y = 4x + 10

solution:

so first you have to find the slope, there is an equation for it. it is y2 - y1/ x2 - x1 or just y1 - y2/ x1 - x2 . so input the easiest points. id say f(0) and f(1)

so it will look like

2 - 6/0 - 1

-4/-1

4

so you can now write the equation as

y = 4x + b

now you have to find the y-intercept so input a point. i dont think you should input a point you used to find the slope because you could have made a mistake calculating so lets input f(2)

sooo

18 = 4(2) + b

18 = 8 + b

b = 10

so the function for the second one is y = 4x + 10

[tex]\begin{gathered}\boxed{\begin{array}{c|c}\boxed{\bf x} &\boxed{\bf y} \\ \sf -1 &\sf 1.5 \\ \sf 0 &\sf 3\\ 1 &\sf 6 \\ \sf 2 &12\end{array}}\end{gathered}[/tex]

Plug in x values in the equation y = 3(2)^x

Graph plotted below:

Answer:

Five multiplied by a number increased by seven.

Two multiplied by a number increased my three.

Step-by-step explanation:

Answer:

x= 1.6

Step-by-step explanation:

The total remaining bank balance in the account of Omar after reducing all the debit and adding paycheck is $761.25

The money which is paid from an account is called the debit amount and the money which is paid into an account is called the credit amount.

To know the remaining balance of account, all the debit amount is subtracted from it and all the credit amount is added into it.

The table for the Omar's transaction is attached below. The data given in the table is,

The initial balance is $219.80, and a pay check of $1015.50 is credited in his account. Thus, the total balance in his account without any debit is,

[tex]A_i=1015.50+219.80\\A_i=1253.30[/tex]

The total amount debited from the account of Omar is,

[tex]A_d=15.20+425.00+22.30+26.70\\A_d=474.05[/tex]

Thus, the total remaining amount in his account is,

[tex]A=1253.3-474.05\\A=761.25[/tex]

Hence, the total remaining bank balance in the account of Omar after reducing all the debit and adding paycheck is $761.25

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Answer:

$761.25

Step-by-step explanation:

took the quiz on edge

Here's your answer, folks:

Without substitution, yes, here? No.

The value of the substituted numbers is essential to finding the correct answer in algebra.

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

5 x 3 = 15

15 squared or cubed = 15 x 15 || 15 x 15 x 15

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

In that case, 15 times a number could not possibly be equal to 5 x 3 unless x was actually 1, which we do not know.

Answer:

NO

Step-by-step explanation:

5*3^x[tex]\neq[/tex]15x

because 3 is raised to the x power not multiplied by it, so it is not equal

Answer: one CD cost $12 and  one DVD cost $15 .  

Step-by-step explanation:

In this situation we will represent the cost o one CD by x and the number of  one DVD by y.  Four CDs  plus five DVDs cost 123  so we will represent it by the equation  4x + 5y = 123  

The same or the second part of the statement. 2 CDs plus 4 DVDs cost $84  so we will also represent that by the equation , 2x + 4y = 84

Since we have two equations we will use it to solve or x and y using the elimination method.

4x + 5y = 123

2x + 4y = 84         Multiply the down equation by -2 to eliminate the x variable.

-2(2x + 4y ) = -2(84)

-4x -8y = -168    

We will now have the new equations ,

4x + 5y = 123

-4x - 8y = -168    Add both equations to      

      -3y = -45  

        y= 15  

This means each DVD cost $15 .

Now we will now have to solve for x by plotting in the value of y into the equation .

4x + 5(15) = 123

4x + 75 = 123

      -75     -75

4x = 48  

x = 12        

This also means that  one CD cost $12.

Answer:

Here,

We know that,

Sum of interior angles of a heptagon=900°

So,

b+120+110+140+135+160+100=900

or, b+765= 900

or, b=900-765

Therefore, b= 135°

Answer:

135

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

If you perform the vertical line test, each row where there is a point only gets hit once, if it got hit twice it would not be a function.

Answer:

b

Step-by-step explanation:

The answer is A. 1,512 cm^2

[tex]\\ \sf\longmapsto P(x,y)=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)[/tex]

[tex]\\ \sf\longmapsto P(x,y)=\left(\dfrac{(1)(-14)+(4)(-3)}{1+4},\dfrac{(1)(7)+(4)(6)}{1+4}\right)[/tex]

[tex]\\ \sf\longmapsto P(x,y)=\left(\dfrac{-26}{5},\dfrac{31}{5}\right)[/tex]

Answer:

x = 4

Step-by-step explanation:

it's important to keep in mind that you can do anything to an equation as long as you do it to both sides, and it will still be equal.

2x + 5 = 13

subtract 5 from both sides of the equation

2x + 5 -5 = 13 - 5

2x = 13 -5

2x = 8

divide both sides of the equation by 2

2x/2 = 8/2

x = 4

The value of x for the equation 2x + 5 = 13 is x = 4.

Given that:

There is an equation in x which is given as,

2x + 5 = 13

It is required to find the value of x.

That is, solve the equation.

It is required to get the equation in such a way that x is on one side and a constant on the other side.

2x + 5 = 13

Subtract both sides by 5.

2x = 8

Divide both sides by 2.

x = 4

Hence the value of x is 4.

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d = log₂p represents a logarithmic function, The expression log₂(10) tells us when the population reaches 10,000 and the equation 7 = log₂(128) tells us that the population reaches 128,000 in 7 days.

An exponential function is in the form:

y = abˣ

Where a is the initial value of y and b is the multiplication factor.

Let p represent the bacteria population in thousand after d days.

Since each day, the bacteria population grows by a factor of 2, hence:

[tex]p=2^d[/tex]

Hence, d = log₂p represents a logarithmic function

The expression log₂(10) tells us when the population reaches 10,000 and the equation 7 = log₂(128) tells us that the population reaches 128,000 in 7 days.

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Answer:

-509

Step-by-step explanation:

h(t) = -16t² + 38t + 9

h(7) = - 16(49) + 38(7) + 9

h(7) = -784 + 266 + 9

h(7) = -509

Solution:

It should be noted:

To find h(7), let's find "t" by comparing h(7) and h(t).

Compare h(7) and h(t):

Now, find h(7) by substituting the value of t into the equation.

Substitute the value of t into the equation:

Thus, h(7) is -509.

Answer:

60 km/hr.

Step-by-step explanation:

When Dad caught up the the time he had been  driving was 4 hours and the time Mom had been driving was 1 + 4 = 5 hours.

They both drove the same distance, d km.

For Dad:

speed = d / time

75 = d / 4

d = 75 * 4 = 300 km.

Mom took 5 hours to travel this distance, so

Mom's speed was 300 / 5 = 60 km/hr.

Step-by-step explanation:

Answer:

a solid 50 km/hour

Step-by-step explanation:

Answer:

8-8/8+8

Step-by-step explanation:

answer = 8-8/8+8

            = 8-1+8

            = 7+8

            = 15

Answer: The cost of a single group lesson is $5 and a single private lesson is $25

Step-by-step explanation:

Let the cost of a single group lesson be y.

Let the cost of a single private lesson be z.

A karate school offers a package of 12 group lessons and 2 private lessons for $110. This can be written as:

12y + 2z = 110 ..... equation i

It also offers a package of 10 group lessons and 3 private lessons for $125. This can be written as:

10y + 3z = 125 ...... equation ii

Combining equation i and ii

12y + 2z = 110 ..... equation i

10y + 3z = 125 ...... equation ii

12y + 2z = 110 × (3)

10y + 3z = 125 × (2)

36y + 6z = 330 ....... equation iii

20y + 6z = 250 ...... equation iv

Subtract equation iv from iii

16y = 80

y = 80/16

y = 5

From equation ii

10y + 3z = 125

10(5) + 3z = 125

50 + 3z = 125

3z = 125 - 50

3z = 75

z = 75/3

z = 25

The cost of a single group lesson is $5 and a single private lesson is $25

A group lesson costs = $5.

A private lesson costs = $25.

Let a group lesson costs = $x

A private lesson costs = $y.

According to the question:

12x + 2y = 110

10x + 3y = 125

Solving them we get x = 5, y = 25

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Answer:

where are the graphs?

Step-by-step explanation:

Answer:

C. a rotation 180° clockwise about the origin followed by a reflection across the line y = x

Step-by-step explanation:

Let us assume that the coordinate of A in triangle ABC is A(x, y)

A) If there is a reflection across line y = x, the new coordinate is at A'(y, x).

If a reflection across the line y = -x is then followed, the new coordinate is at A"(-x, -y)

B) If there is a reflection across line x axis, the new coordinate is at A'(x, -y).

If a reflection across the line y axis is then done, the new coordinate is at

A"(-x, -y)

C) If there is a rotation 180° clockwise about the origin, the new coordinate is at A'(-x, -y).

If a reflection across the line y = x is then followed, the new coordinate is at A"(-y, -x)

D) B) If there is a reflection across line y axis, the new coordinate is at A'(-x, y).

If a reflection across the line x axis is then done, the new coordinate is at

A"(-x, -y)

Since only option C has a different result from the remaining options, hence option C would not five triangle A'B'C'

Answer:

C. a rotation 180° clockwise about the origin followed by a reflection across the line y = x

Step-by-step explanation:

Let us assume that the coordinate of A in triangle ABC is A(x, y)

A) If there is a reflection across line y = x, the new coordinate is at A'(y, x).

If a reflection across the line y = -x is then followed, the new coordinate is at A"(-x, -y)

B) If there is a reflection across line x axis, the new coordinate is at A'(x, -y).

If a reflection across the line y axis is then done, the new coordinate is at

A"(-x, -y)

C) If there is a rotation 180° clockwise about the origin, the new coordinate is at A'(-x, -y).

If a reflection across the line y = x is then followed, the new coordinate is at A"(-y, -x)

D) B) If there is a reflection across line y axis, the new coordinate is at A'(-x, y).

If a reflection across the line x axis is then done, the new coordinate is at

A"(-x, -y)

Since only option C has a different result from the remaining options, hence option C would not five triangle A'B'C'

Answer:

  see attached

Step-by-step explanation:

A graphing calculator can graph your function nicely. See the attachment.

__

Additional comment

A spreadsheet can do this, too. However, that generally requires you compute a number of points on the graph.

Answer:

28

Step-by-step explanation:

its ans may be 28 hope you will know

Answer:

28

Step-by-step explanation:

The order of magnitude as long as the mite is to the gecko is 9.9999

A measurement unit is a standard quantity used to express a physical quantity.

The dust mite measures 10⁻³ millimetres in length.

The wall gecko measures 10 centimetres in length.

The orders of magnitude as long as the mite is the gecko is as follows;

1 mm = 0.1 cm

10⁻³ mm (0.001 mm)= ?

length(cm) = 0.0001 / 1 = 0.0001 cm

length of mite = 0.0001 cm

The order of magnitude as long as the mite is to the gecko is 10  - 0.0001  = 9.9999

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Answer: $34.50

Step-by-step explanation:

If 3 bags of cat food cost $17.50 this means that 6 will be double that or $34.50.

Answer:

Step-by-step explanation:

B

The set that represents a Pythagorean triple  is B: 33, 44, 55

A Pythagorean triple consists of three positive integers such that the square of the larger one of them is equal to the sum of the squares of the other two .

Let (a, b, c) represents a Pythagorean triple where a, b, c  are positive integer and a is the larger one  then a² = b² + c²

For A: 27 ,38, 42

Let a = 42 , b= 38 ,c= 27

⇒a² = 42² = 1764

and b² + c² =  38² + 27² = 1444 + 729 = 2173

∴a² ≠ b² + c²

Thus , A: 27 ,38, 42 is not a Pythagorean triple

For B: 33 ,44, 55

Let a = 55 , b= 33 ,c= 44

⇒a² = 55² = 3025

and b² + c² =  33² + 44² = 1089 + 1936 = 3025

∴a² = b² + c²

Thus , B: 33 ,44, 55  is a Pythagorean triple

For C: 35 ,38, 42

Let a = 42 , b= 35 , c= 38

⇒a² = 42² = 1764

and b² + c² =  35² + 38² = 1225 + 1444 = 2669

∴a² ≠ b² + c²

Thus ,   C: 35 ,38, 42 is not a Pythagorean triple

For D: 68 ,72, 81

Let a = 81 , b= 68 , c= 72

⇒a² = 81² = 6561

and b² + c² =  68² + 72² = 4624 + 5184 = 9808

∴a² ≠ b² + c²

Thus ,  D: 68 ,72, 81  is not a Pythagorean triple

Therefore, Only set B: 33, 44, 55 represents a Pythagorean triple.

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