Find the equation for the line parallel to the given line and passing through the given point.
3y = -12x + 4; (1,1)

The distance between point (12,6) and the line y = x - 14 is given as follows:

5.6 feet.

The standard equation of a line is given by the rule presented as follows:

ax + by + c = 0.

The coordinates of the point which we want to find the distance from the line are given as follows:

(x0,y0).

The equation that obtains the shortest distance of the point (x0, y0) to the line ax + by + c = 0 is presented as follows:

[tex]D = \frac{|a(x_0) + b(y_0) + c|}{\sqrt{a^2+b^2}}[/tex]

The line for this problem is given by the rule presented as follows:

y = x - 14.

In standard notation, it is defined by the rule presented as follows:

x - y - 14 = 0.

Hence the coefficients are presented as follows:

a = 1, b = -1, c = -14.

The point has the coordinates given as follows:

(12,6).

Hence:

x0 = 12, y0 = 6.

Thus the distance from the point to the line is obtained as follows:

[tex]D = \frac{|a(x_0) + b(y_0) + c|}{\sqrt{a^2+b^2}}[/tex]

D = |1(12) -1(6) - 14|/sqrt(1²+(-1)).

D = 8/sqrt(2)

D = 5.6 feet.

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16 boxed lunch cost $187.2.

Given that a company orders 20 boxed lunches from a deli for $234.00.

Each boxed lunch costs the same amount.

20 boxed lunches from a deli for $234

1 boxed lunches from a deli for $234/20 = $11.7

Hence the cost of 16 boxed lunch is = $11.7*16 = $187.2

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Answer: x = -2, y = 3

Step-by-step explanation:

Given that,

-9x+2y = 24..................................(i)

x = 10-4y.......................................(ii)

From equation (i)

-9(10-4y) + 2y = 24  [as x = 10-4y]

=> -90 +36y + 2y = 24

=> 38y = 90 + 24

=> 38y = 114

=> y = 114/38

Therefore, y = 3

Again,

x = 10 - 4(3)  [as y = 3]

=> x = 10-12

Therefore, x = -2

Here, x = -2 and y = 3

Answer:

it would be $3.02

Step-by-step explanation:

you pretty much do $6.04/2 Ib

therefore, your answer would be $3.02

Answer:

Step-by-step explanation:

6.04 divded by 2= 3.02 per pound

Answer: Freddy

Step-by-step explanation:

Choose a common denominator for all the fractions.  Let's use 140.  

Christian:  3/7 = 60/140

Freddy:  3/10 = 42/140

Skyler:  3/4 = 105/140

The least value is 42/140

The proportionality constant is the ratio that connects two given values in a proportional relationship. The constant of proportionality is also known as the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.

When two or more parameters are directly or indirectly proportional to one another, their relationship is expressed as a = kb or a = k/b, where k indicates the nature of the relationship between the two variables. This k is referred to as the proportionality constant.

For example, the number of apples in a crop is proportional to the number of trees in an orchard, with the ratio of proportionality being the average number of apples per tree.

This can be illustrated as:

Let's say y = 4

Let's say x = 2

y = kx

4 = 2k

Divide

k = 4/2

k = 2

The constant is 2.

Note that an overview was given as the information is incomplete.

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350mL will be administered in a week.

No,  the slope of a horizontal line y=6 is,  zero not negative.

What is a Slope?

In Mathematics, a slope of a line is the change in y coordinate with respect to the change in x coordinate.

The net change in y-coordinate is represented by Δy and the net change in x-coordinate is represented by Δx.

Hence, the change in y-coordinate with respect to the change in x-coordinate is given by,

m = change in y/change in x = Δy/Δx

Where “m” is the slope of a line.

Generally, the slope of a line gives the measure of its steepness and direction. The slope of a straight line between two points says (x1,y1) and (x2,y2) can be easily determined by finding the difference between the coordinates of the points. The slope is usually represented by the letter ‘m’.

Slope Formula

If P(x1,y1) and Q(x2,y2) are the two points on a straight line, then the slope formula is given by:

Slope, m = Change in y-coordinates/Change in x-coordinates = Δy/Δx

m = (y2 – y1)/(x2 – x1)

In the given equation of line y=6 .

The line crosses the y-axis at 6, as the line is always at that value. As it is a horizontal line, the slope is zero.

The equation y = 6 means for each and every value of x, y will be equal to 6.

This is the definition of a horizontal line.

By definition, the slope of a horizontal line is m = 0

When x = 0 then y = 6

Therefore, the y-intercept is: (0, 6).

Hence , the the slope of a horizontal line , m = 0.

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Answer: gavin scored 465 points

Step-by-step explanation:

point a and point e are the two points representing extreme points on graph

The equation of the horizontal line passing through the point (2, -6) is :

y = -6

and the equation of the vertical line passing through the point (2, -6):

x = 2

We need to write equations for the horizontal and vertical lines passing through the point (2, -6)

For a vertical line the value of x will never change. This will be true for any value of y.

So, the equation for a vertical line passing through this point is:

x = 2

Similarly, for a horizontal line the value of y will never change. This is true for any value of x.

So, the equation for a horizontal line passing through this point is:

y = -6

Therefore, the equation of the horizontal line passing through the point (2, -6) is y = -6

and the equation of the vertical line passing through the point (2, -6) is x = 2

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Answer:

feeling good

Step-by-step explanation:

I am just happy

Using theoretical probability, the probability of selecting green ball is 3/11, not selecting green ball is 8/11, selecting orange ball is 6/11 and not selecting orange ball is 5/11.

In the given question,

A bag has 2 red, 3 green, and 6 orange balls.

So total number of balls = 2+3+6 = 11

We have to find the theoretical probability.

(a) We have to find the theoretical probability of selecting green ball.

P(G) = Total number of green balls/Total number of balls

P(G) = 3/11

Hence, the probability of selecting green ball is 3/11.

(b) Now we have to find the theoretical probability of not selecting green ball.

Except green ball there is having red and orange i.e.

Total remaining balls except green = 2+6 = 8

P(G) = Total number of balls except green balls/Total number of balls

P(G) = 8/11

Hence, the probability of not selecting green ball is 8/11.

(c) Now we have to find the theoretical probability of selecting orange ball.

P(G) = Total number of orange balls/Total number of balls

P(G) = 6/11

Hence, the probability of selecting green ball is 6/11.

(d) Now we have to find the theoretical probability of not selecting orange ball.

Except orange ball there is having red and green balls i.e.

Total remaining balls except orange = 2+3 = 5

P(G) = Total number of balls except orange balls/Total number of balls

P(G) = 5/11

Hence, the probability of not selecting orange ball is 5/11.

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Answer:

Annie's new job pays more an hour.

Step-by-step explanation:

They tell us that her new job pays $7.25 per hour. So to determine which job pays her more, we need to find how much she earns in her current job.

There are a few ways to find this (none of them are hard.) But this is the easiest way in my opinion.

The chart tells you that Annie earns $13 in 2 hours. We need to find how much she earns in 1 hour. All you need to do is divide $13 by two.

13/2 = 6.5

6.5 = $6.50

If her current job pays her $6.50 an hour and her new job pays $7.25 an hour, she should consider higher paying jobs.

But, yes, the new job pays her more an hour.

Using Laws of exponents, the solution to the expression √(3p⁹q⁷r⁶)/(16x⁶y¹²) is;  (p⁴q³r³/(x³y⁶))√(3pq/16)

The different laws of exponents are;

1) Product With the Same Bases; a^m × a^n = a^(m+n)

where;

m and n are real numbers.

2) Quotient with Same Bases;

a^m/a^n = a^(m-n)

where;

a is a non-zero term and m and n are integers.

3) Power Raised to a Power; (a^m)^n = a^(mn)

where;

a is a non-zero term and m and n are integers.

4) Product to a Power; a^n * b^n = (ab)^(n)

where;

a is a non-zero term and n is the integer.

5) Quotient to a Power; It states that the fraction of two different bases with the same power is represented as; a^n/b^n = (a/b)^n

where;

a and b are non-zero terms and n is an integer.

6) Zero Power; When the power of any integer is zero, then it means that its' value is equal to 1, such that;

a⁰ = 1

where;

a is any non-zero term.

7) Negative Exponent Rule; a^(-m) = 1/(a^m)

We are given the expression as;

√(3p⁹q⁷r⁶)/(16x⁶y¹²)

Applying the laws of exponents, we will have;

√(3p⁹q⁷r⁶)/(16x⁶y¹²) = (p⁴q³r³/(x³y⁶))√(3pq/16)

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The prediction of the wind chill for the wind speed 4 mi/h is 14 degrees

Here, we have the following parameters:

Equation of the trend line: y = 0.36x + 12.6

Where

x = Wind speed

y = Wind chill

Also, we have

x = 4 mi/h i.e. the wind speed

Substitute x = 4  in the equation y = 0.36x + 12.6

So, we have

y = 0.36 x 4 + 12.6

Evaluate the equation

y = 14.04

Approximate

y = 14

Hence, the wind chill  is 14 degrees

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By using the graphing method, a solution to the given system of equations is equal to -6 and -6.

In Mathematics, a graph can be defined as a type of chart that is typically used to graphically represent data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate respectively.

Next, we would simplify the equation as follows:

4u = 2v - 12

Dividing both sides of the equation by 4, we have:

4u/4 = (2v - 12)/4

u = v/2 - 3

By critically observing the graph of this system of equations, we can logically deduce that the point of intersection is at (-6, -6).

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Answer:

225

Step-by-step explanation:

a1 = 1

a15 = 29

sum = n/2 ( a1 + a15) =  (15/2) ( 1 + 29) = 225

Answer:

36

48

60

Reason:

Since it is multiples of twelve, we can find out and multiply

12*3= 36

12*4= 48

12*5= 60

I hope this helps!

Answer: 36, 48, and 60.

Step-by-step explanation:

36, 48, and 60 are the only numbers that can be divided by 12 into a whole number.

36/12 = 3

48/12 = 4

60/12 = 5

The economy's nominal GDP in 2006 and real GDP in 2010 is option B)  Nominal GDP in 2006 $1,000, Real GDP in 2010 = $2,000.

What does GDP Price Index mean?

Nominal GDP in 2006=$1,000;

Real GDP in 2010=$2,000

Price index = (nominal GDP/real GDP) ×100

thus, nominal GDP in 2006=(price index × real GDP)/100

= (100×$1,000)/100

=$1,000

Real GDP in 2010= (nominal GDP/price index) ×100

= ($2,200/110) ×100

=$2,000.

Hence, the economy's nominal GDP in 2006 and real GDP in 2010 is option B)  Nominal GDP in 2006 $1,000, Real GDP in 2010 = $2,000.

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Answer:

She will pay the same amount at both

Step-by-step explanation:

For Life Studio,

the initial sign up fee + $30 each month

= $30 = 30 × 6 = $180

Hence, $60 + $180 = $240

For Yoga Mind,

$40 each month for 6 months

= $40 × 6

$40 × 6= $240

Therefore, she will pay the same amount at both

Answer:

Slope = -5/2

Y-intercept = -9

Step-by-step explanation:

Hello!

The equation is given in Slope-Intercept Form: y= mx + b

Since the slope is the coefficient of the x-term, the slope of this equation is -5/2, or -2.5

The y-intercept is the numerical constant, which is given the by the integer -9.

Answer:

Step-by-step explanation:

Slope: 6/3 = -2

since the line is going from left to right, it is a negative slope

Answer:

-7/3 or 2.3333333333333

Step-by-step explanation:

X= -1 – -4 = 3

Y= -4 – 3 = -7

y = -2.3333333333333x – 6.3333333333333

or

y = -7/3 x - 19/3

So when y= -6.33 that will mean x= -2.71

Using the trigonometry relation, the value of sin2x=4√2/9, cos2x=7/9 and tan2x=4√2/7.

In the given question, we have to find the value of sin(2x), cos(2x) and tan(2x).

The given value of six=1/3, x in quadrant first.

We firstly finding the value of cosx.

cosx = √1-(sinx)^2

Now putting the value of sinx

cosx = √1-(1/3)^2

cosx = √1 -1/9

cosx = √(9-1)/9

cosx = √8/9

cosx = 2√2/3

We know that;

sin2x=2sinxcosx

sin2x=2* 1/3 * 2√2/3

sin2x=4√2/9

Now finding the value of cos2x

We know that;

cos2x=1-2(sinx)^2

cos2x=1-2(1/3)^2

cos2x=1 -2/9

cos2x=(9-2)/9

cos2x=7/9

Now finding the value of tan2x

As we know that

tan2x=sin2x/cos2x

tan2x=(4√2/9)/(7/9)

tan2x=4√2/7

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x = - 8 is not a root of √(x + 12) - 6 = x, since it is an extraneous solution.

In this question we have a radical equation that offer two possible roots. A root is an extraneous solutions when it brings out an absurd (i.e. 1 = 4) when the expression is evaluated. First, write the radical equation:

√(x + 12) - 6 = x

Second, use algebra properties to find the possible roots of the radical equation:

√(x + 12) - 6 = x

√(x + 12) = x + 6

x + 12 = x² + 12 · x + 36

x² + 11 · x + 24 = 0

(x + 3) · (x + 8) = 0

x = - 3 or x = - 8

Third, evaluate the radical equation at each root:

√(- 3 + 12) - 6 = - 3

√9 - 6 = - 3

3 - 6 = - 3

- 3 = - 3 (TRUE)

√(- 8 + 12) - 6 = - 8

√4 - 6 = - 8

2 - 6 = - 8

- 4 = - 8 (FALSE)

x = - 8 is an extraneous solution.

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If Robert bought a used car for $10,332 with an added sales tax of 2.5%. Then the original price of the car would be around $10,080.

Option (B) is correct.

What is a percentage?

A percentage is a relative value that represents the hundredth part of any quantity. One percent (symbolized 1%) is the one-hundredth part; thus, 100 percent represents the entire amount and 200 percent specifies twice the given amount.

Robert bought a used car for $10,332 with an added sales tax of 2.5%.

so the additional amount would be = 10,332 * 2.5%

                                                           = 10332 * 0.025

                                                           = $258.3

So the original price of the car would be = 10332 - 258.3

                                                                    ≈ $10,080.

Hence, If Robert bought a used car for $10,332 with an added sales tax of 2.5%. Then the original price of the car would be around $10,080.

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Answer:

a) Consecutive interior angles.

b) Alternate exterior angles.

c) Corresponding angles.

d) Alternate interior angles.

e) Corresponding angles.

f) None.

g) Alternate exterior angles.

h) Consecutive interior angles.

i) None.

j) Corresponding angles.

k) Corresponding angles.

l) Alternate exterior angles.

m) Alternate interior angles.

n) Consecutive interior angles.

Step-by-step explanation:

Transversal

A line that crosses two other lines in the same plane at two distinct points.

Corresponding angles

A pair of angles that are in the same position relative to both lines crossed by the transversal.

Alternate interior angles

A pair of angles on the inner side of the two lines that the transversal crosses, but on opposite sides of the transversal.

Alternate exterior angles

A pair of  angles on the outer side of the two lines that the transversal crosses, but on opposite sides of the transversal.

Consecutive interior angles

A pair of angles on the inner side of the two lines that the transversal crosses, and are on the same side of the transversal.

a) Lines p and q are crossed by transversal line s.

Therefore, ∠4 and ∠7 are consecutive interior angles as they are on the inner side of lines p and q, and are on the same side of the transversal s.

b) Lines r and s are crossed by transversal line p.

Therefore, ∠2 and ∠11 are alternate exterior angles as they are on the outer side of lines r and s, but on opposite sides of the transversal p.

c) Lines p and q are crossed by transversal line s.

Therefore, ∠12 and ∠16 are corresponding angles as they are in the same position relative to lines p and q crossed by the transversal s.

d) Lines r and s are crossed by transversal line q.

Therefore, ∠8 and ∠13 are alternate interior angles as they are on the inner side of lines r and s, but on opposite sides of the transversal q.

e) Lines p and q are crossed by transversal line s.

Therefore, ∠11 and ∠15 are corresponding angles as they are in the same position relative to lines p and q crossed by the transversal s.

f) ∠7 and ∠10 have no relationship.

g) Lines p and q are crossed by transversal line r.

Therefore, ∠1 and ∠14 are alternate exterior angles as they are on the outer side of lines p and q, but on opposite sides of the transversal r.

h) Lines p and q are crossed by transversal line s.

Therefore, ∠12 and ∠15 are consecutive interior angles as they are on the inner side of lines p and q, and are on the same side of the transversal s.

i) ∠6 and ∠7 have no relationship

j) Lines r and s are crossed by transversal line p.

Therefore, ∠1 and ∠3 are corresponding angles as they are in the same position relative to lines r and s crossed by the transversal p.

k) Lines r and s are crossed by transversal line q.

Therefore, ∠14 and ∠16 are corresponding angles as they are in the same position relative to lines r and s crossed by the transversal q.

l) Lines r and s are crossed by transversal line q.

Therefore, ∠6 and ∠15 are alternate exterior angles as they are on the outer side of lines r and s, but on opposite sides of the transversal q.

m) Lines p and q are crossed by transversal line r

Therefore, ∠5 and ∠10 are alternate interior angles as they are on the inner side of lines p and q, but on opposite sides of the transversal r.

n) Lines r and s are crossed by transversal line q.

Therefore, ∠8 and ∠14 are consecutive interior angles as they are on the inner side of lines r and s, and are on the same side of the transversal q.

Answer:

2⁵ that is my answer for the question

Answer: 2^5

Step-by-step explanation:

3^3 = 27

1^10 = 1

2^5 = 32

5^2 = 25