Find the distance from the line to the given point.
y=1/6x+6,(-6,5)

The dimensions of the sticker are 6 centimeters and 9 centimeters, respectively.

According to the statement, we find a rectangular sticker whose perimeter and area are known. By the perimeter and area formulas of the rectangle we have the following system of equations:

x · y = 54                      (1)

2 · (x + y) = 30              (2)

By (2):

2 · x + 2 · y = 30

2 · x = 30 - 2 · y

x = 15 - y

(2) in (1):

(15 - y) · y = 54

15 · y - y² = 54

y² - 15 · y + 54 = 0

(y - 9) · (y - 6) = 0

The solutions are y₁ = 9 and y₂ = 6, respectively.

By (2):

x₁ = 15 - y₁

x₁ = 15 - 9

x₁ = 6

x₂ = 15 - y₂

x₂ = 15 - 6

x₂ = 9

The solutions are x₁ = 6 and x₂ = 9, respectively.

The dimensions of the sticker are 6 centimeters and 9 centimeters, respectively.

To learn more on algebraic equations: https://brainly.com/question/24875240

#SPJ1

Answer:

i think 10 is in between -8 and

Step-by-step explanation:

hope this

The equation of the line which is perpendicular to 2x - y = 4 and passing through (4, 1) will be y = (-1/2)x + 3

Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.

The equation of the line is given below.

2x - y = 4

Then the slope of the perpendicular line will be

y = 2x - 4

m = 2

Then the equation of line will be

y = -(1/2)x + d

Then the line is passing through (4, 1), then we have

1 = -(1/2)4 + d

3 = d

The equation of the line which is perpendicular to 2x - y = 4 and passing through (4, 1) will be y = (-1/2)x + 3

More about the equation of a perpendicular line link is given below.

https://brainly.com/question/14200719

#SPJ1

Answer:

C° = K-273.15

Step-by-step explanation:

The goal is to get C by itself, so subtract 273.15 from both sides.

Comparing the functions f(x) = ln (x) and [tex]f^{-1}(x) = e^x[/tex], we can conclude that the domain of [tex]f^{-1}(x)[/tex] is all real numbers and the range is all real numbers greater than 0.

Given function is the logarithmic function f(x) = ln(x).

Now, f(x) has a domain(D) of all real numbers greater than zero and a range(R) of all real numbers.

i.e., f : D → R defined by f(x) = ln(x)

So if an inverse exist for f(x), then, [tex]f^{-1}(x)[/tex] will have R as its domain and D as its range.

i.e.,  [tex]f^{-1}[/tex] : R → D defined by [tex]f^{-1}(x) = e^x[/tex].

Because f( [tex]f^{-1}(x)[/tex] ) = ln([tex]e^x[/tex]) = x, that is the identity function.

So [tex]e^x[/tex] is the inverse of ln(x).

Also, the domain of [tex]f^{-1}(x)[/tex] is all real numbers and the range is all real numbers greater than 0.

Learn more about inverse functions at https://brainly.com/question/3831584

#SPJ4

Answer:

Step-by-step explanation:

A logarithm is a power that requires a number to be raised to another power.

The logarithmic equation given in the question can be written as

log2(16) =x

We will rewrite this equation in the exponential form by considering the definition of logarithm.

The definition states that,

If x and b are two positive real numbers and the value of b is not equal to 1, then the log of

log b (x)=y is equivalent to by=x

We will convert the given equation according to the above definition,

2x=16

The bases of all the values involved must be identical. So, we will create equivalent expressions in the equation that all have equal bases.

2x=24

Now we have the same bases; the two expressions can only be said equal if the exponents are also equal.

x=4

The variable x is equal to 4.

4

More similar problems are solved in the given link below.

https://brainly.com/question/28596588?referrer=searchResults

#SPJ4

Answer:

-10.08

Step-by-step explanation:

Using order of operations:

[tex] - 17 + (\frac{ - 2.3 + 8.12}{6} ) \times {4}^{2} - 8.6[/tex]

[tex] - 17 + \frac{5.82}{6} \times 16 - 8.6[/tex]

[tex] - 17 + .97 \times 16 - 8.6[/tex]

[tex] - 17 + 15.52 - 8.6[/tex]

[tex] - 10.08[/tex]

The value of the expression ( 1/2 )x + ( 1/2 )x + x + 1 is 2x + 1.

A variable, a number, or a mix of numbers, operations, and numbers symbols make up an expression. Two expressions joined by an equal sign form an equation.

A formula called an equation uses the equals symbol (=) to denote the equality of two expressions.

Consider the expression,

1/2x + 1/2x + x + 1

Taking common out,

( 1/2 )x + ( 1/2 )x + x + 1 = ( 1/2) × [ x + x ] + x + 1

( 1/2 )x + ( 1/2 )x + x + 1 = (1/2x) × 2 + x + 1

( 1/2 )x + ( 1/2 )x + x + 1 = x + x + 1

( 1/2 )x + ( 1/2 )x + x + 1 = 2x + 1

Therefore, the value of ( 1/2 )x + ( 1/2 )x + x + 1 is 2x + 1.

Learn more about expression here:

https://brainly.com/question/1718606

#SPJ9

The quantities X and Y are proportional as y = rx  then the constant of proportionality r is 1/9.

Firstly, there is proportional relationship.

Two values x  and  y are said to be in a proportional relationship if x=ky, where x and y are variables and k is a constant.

The constant k is called constant of proportionality.

WE have been given quantities X and Y are proportional

y = rx

Where r is constant of proportionality.

Then x = 45 and y = 5

Thus,

y = rx

5 = 45r

Now divide by 45 on both side;

r = 5/45

r = 1/9

Therefore, the constant of proportionality r is 1/9.

Learn more about directly inversely proportional relationship variable here:

https://brainly.com/question/13082482

#SPJ1

Answer:

The area of this section of pavement is 800 square feet

Step-by-step explanation:

10 ft times 80 ft = 800 square feet

Give me brainliest if that helped :)

Step-by-step explanation:

Given that

To find

So, according to the question

From figure we can say that there is present five rectangle of same size.

So far finding the area of this irregular figure we have to find the area of this single rectangle and multiply it by 5 so from that process we can calculate the area of this irregular figure.

Now first we have to learn about the area,

The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina.

So, we know

The area of one rectangle = l x w

Now, putting the values = 3 x 2 = 6

So,

The area of this irregular figure = 5 ( The area of one rectangle )

                                                   = 5 x 6

                                                   = 30

Answer:

To learn more about area, please click on the link:

https://brainly.com/question/27683633

#SPJ9

The quetient is 2x - 5 with no remainder.

Step-by-step explanation:

The give polynomial is   2x² + x - 15

And the given divisor is  (x + 3)

Now, Using divide rule of polynomials

x + 3 ) 2x² + x - 15 ( 2x - 5

         2x² + 6x

        -       -    

____________________

         - 5x - 15

         - 5x - 15

        +       +

__________________

                0

Hence, we get the quotient is 2x - 5 and the remainder is 0

Therefore, The correct answer 2x - 5 with no remainder.

To know more about polynomial remainder theorem, visit:https://brainly.com/question/9160275

#SPJ9

Answer:

m=3/19

Step-by-step explanation:

Answer:

m = 3/19

Step-by-step explanation:

Let's solve your equation step-by-step.

19m = 3

Step 1: Divide both sides by 19.

19m/19 = 3/19

- You might be wondering, why do we need to divide both sides by 19? -

Well, to find m, you need to get it by itself. So by dividing 19m by 19, m stands alone. But again, what we do to one side, we need to do to the other. So 3 must also be divided by 19.

Answer:

m = 3/19

Place value is defined as the value of a digit in a number which depends on its position in the number. On the other hand, Total value is the product of a digit and its place value.

Rounding off entails changing a number into an approximation such that it has fewer significant numbers. To change the digit 5 in this question to 0, we will need to round off the given numbers to the most appropriate place value.

a. 478 578

We round off to the nearest thousands, this becomes 479 000

b. 353 897

We round off to the nearest tens of thousands, this becomes 400 000

c. 294 025

We round off to the nearest ones, this becomes 294 030

d. 500 000

The 5 in this value cannot be converted to 0 since 5 is the largest place value in the number.

Read more: https://brainly.com/question/14631150?referrer=searchResults

#SPJ4

a. The dot plot that represents the situation is shown in the diagram attached below.

b. The typical number = 8.

-To create a dot plot, the frequency of each data point of the data distribution is represented by a "dot". The number of "dots" on a data point determines the number of times that data point appears in the data distribution.

Given the data for the number of eggs produced: 6,7,7,7,8,8,8,8,9,10,10,11,12,12,13, we have the following data points and their frequency:

6 - 1 dot

7 - 3 dots

8 - 4 dots

9 - 1 dot

10 - 2 dots

11 - 1 dot

12 - 2 dots

13 - 1 dot

a. The dot plot that represents the situation is shown in the diagram attached below.

b. The typical number of eggs is: 8.

Learn more about the dot plot on:

https://brainly.com/question/25957672

#SPJ1

The runner completes a 10 miles race in 16 minutes.

According to the question we have been given that,

Runner takes 8 minutes to complete = 5 miles race

We need to find that if the runner is in the same pace then how many miles the runner completes in 16 minutes

This multi-step problem can be solved using the unitary method. That is,

              8 minutes = 5 miles

              1 minute = 5/8 miles          

             16 minutes = 5/8*16 miles

                                  = 5*2 miles

                                  = 10 miles

Hence runner completes a 10miles race in 16 minutes

Learn more about unitary method here : https://brainly.com/question/8083231

#SPJ9

Step-by-step explanation:

(a+b)² = (a+b) × (a+b)

= a(a+b) × b(a+b)

= a² +ab + ba + b²

= a² + b² + 2ab

103² = (100 + 3)²

= 100² + 3² + (2×100×3)

= 10000 + 9 + 600

= 10609

The location of S will be at 9 and ₋19 .

When speaking of a straight line in mathematics, the term "number line" refers to the placement of numbers along some or all of the breadth. Any direction can be used to postpone a number line, which is frequently displayed horizontally.

Given, on a number line R and S are points on the number line.

RS = 5 and R is located at 14.

S is located at = ?

Let x be the coordinate of the point S. Then we have:

14 ₋ x = ±5

x = ± 5 ₋ 14

x = 5 ₋ 14 or ₋5₋14

x = 9 or ₋19

Then the location of point S will be at 9 and -19.

Learn more about the number line here:

brainly.com/question/13189025

#SPJ9

The standard form is 3/2x + y +2 = 0 for line perpendicular to -2 x+3 y=9 through (-1,-3)

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

In an equation, parallel lines have the opposite reciprocal slope. In other words, if a line's slope is a positive fraction, its reciprocal slope is negative.

Here given that  -2 x+3 y=9

can also be written as

y = 2/3x + 3

Here -2/3 is the slope and 3is the y-intercept

To find a parallel line to the following equation, use the opposite reciprocal slope and point, then solve using the point-slope formula.

y - y₁ = m(x - x₁)

We have, m = -3/2 x₁ = -1 and y₁ = -3

y - (-3) = -3/2(x - (-1))

y + 3= -3/2x +1

3/2x + y +2 = 0

We have the standard form 3/2x + y +2 = 0 of a line  perpendicular to y = (2/3)x - 1 through (0,6)

Learn more about  linear equations

brainly.com/question/14323743

#SPJ4

x<=-4 or x>=-1

A compound inequality is a sentence with two inequality statements joined either by the word “or” or by the word “and.”

“And” indicates that both statements of the compound sentence are true at the same time. It is the overlap or intersection of the solution sets for the individual statements.

“Or” indicates that, as long as either statement is true, the entire compound sentence is true. It is the combination or union of the solution sets for the individual statements. A compound inequality that uses the word “and” is known as a conjunction.

By seeing the graph we can see that there are 2 inequalities. We have to solve them separately

Final answer: x<=-4 or x>=-1

To learn more about compound inequality visit: https://brainly.com/question/17957246

#SPJ9

Based on the number of candy pieces that Mack ate on the first and net day, the number of pieces of candy that he collected on Halloween night was 78 pieces of candy

The total pieces of candy that Mack had left on the next day was:

Number of candy pieces collected - 7 pieces of candy - (10% x Number of candy pieces collected) = 63

To find the number of candy pieces collected:

x - 7 - 10% × x = 63

x - 7 - 0.1x = 63

x - 0.1x = 63 + 7

0.9x = 70

x = 70 / 0.9

x = 77.7

= 78 pieces of candy

Find out more on candy remaining at https://brainly.com/question/16014529

#SPJ1

The equation of the line in slope-intercept form is: y = -4/5x - 8/5.

Using two points on the line, say, (-2, 0) and (3, -4), follow the steps below to find the equation of the line:

Step 1: Find the slope of the line

Slope (m) = (-4 - 0)/(3 -(-2))

Slope (m) = -4/5

Step 2: Find the y-intercept (b)

Substitute m = -4/5 and (x, y) = (-2, 0) into y = mx + b

0 = -4/5(-2) + b

0 = 8/5 + b

0 - 8/5 = b

b = -8/5

Step 3: Substitute m = -4/5 and b = -8/5 into y = m + b

y = -4/5x - 8/5

Thus, the equation of the line in slope-intercept form is: y = -4/5x - 8/5.

Learn more about the equation of a line on:

https://brainly.com/question/13763238

#SPJ1

The equation of point slope form of (4,6) and (10,30) is -4x + y + 10 = 0.

A straight line is represented using its slope and a point on the line using point slope form. In other words, the point slope form is used to determine the equation of a line whose slope is "m" and passes through the point (x1, y1).

given that

the coordinates points are (4, 6) and (10, 30)

(x1,y1) = (4,6)

(x2, y2) = (10,30)

The formula of point-slope is

(y - y1) = m(x - x1)

Here,

x1 = 4 and y1 = 6 but we don't know the value of

m.

now,find the value of m using the following formula

[tex] m = \frac{(y2 - y1)}{(x2 - x1)}[/tex]

now, substitute the values, we get

[tex]m = \frac{(30 - 6)}{(10 - 4)}[/tex]

[tex]m = \frac{24}{6}[/tex]

m = 4

so, the value of m is 4.

substitute these values into the point-slope formula

(y - 6) = 4(x - 4)

y-6 = 4x - 16

y = 4x -16 + 6

y = 4x - 10

-4x + y + 10 =0

Hence, the equation of point slope form of (4,6) and (10,30) is -4x + y + 10 = 0.

Learn more about point-slope from here:

https://brainly.com/question/24907633

#SPJ4

Answer: 41 minutes and 40 seconds

Step-by-step explanation:

1000 meters=1 km

10 km * 1000 meters/1 km=

10 * 1000/1=

10*1000=10000 meters

10000 meters * 1 second/4 meters=

10000 * 1/4=

10000/4=2500 seconds

60 seconds=1 minute

2500 seconds * 1 minute/60 seconds=

2500/60=

(2460+40)/60=

2460/60 + 40/60= 41 minutes and 40 seconds

Answer:

Step-by-step explanation:

So our ratio for this problem is

3/8
Now, to find how many teaspoons per ounce, we divide 3 by 8

3/8=0.375

Hope this helps!^^

To find ounces per teaspoon, we do 8/3

8/3 = 2.666666667

Hope this helps^^

Answer:

4521 is a rational number because it can be expressed as the quotient of two integers: 4521 ÷ 1.

Step-by-step explanation:

Rational Numbers: Any number that can be written as a ratio (or fraction) of two integers is a rational number

Hope this helps

The property of real numbers illustrated by the equation  - [ -(x - 10)] = x-10 is Distributive property.

Distributive Property of real number is represented by the expression

a(b+c)=a*b+a*c.

For Example : 3(2+4)=3*2+3*4

                                  =6+12

                                  =18

In the given question ;

LHS  =-[-(x-10)]

First applying distributive property in side "[ ]".            

=  -[-x-(-10)]

= -[-x+10]   

Again applying distributive property , we get

= -(-x)-(+10)

= x-10  =RHS

Therefore , Distributive Property of Real numbers is illustrated by the equation  - [ -(x - 10)] = x-10.

Learn more about Distributive Property here https://brainly.com/question/11770372

#SPJ4

The remaining scarves he can spend is 4.

A mixture of constants, variables, and operators make up an algebraic expression. Algebraic expressions can be used to accomplish the four fundamental mathematical operations of addition, subtraction, multiplication, and division. Algebraic expression addition and subtraction are quite similar to addition and subtraction of numbers.

Jesse has a total of 47 dollars.

The cost of the new hat is = 19 dollars

The remaining dollars after buying the new hat is 47 dollars - 19 dollars = 28 dollars.

The cost of the scarves is 7 dollars

Thus total scarves for 28 dollars = 28/7 = 4 scarves.

To learn more about Algebraic expressions refer the link:

https://brainly.com/question/15060745

#SPJ1

The simplified value of the expression given as (29x - 3) + (13y - 17) - (15x + 7) is 14x + 13y  -27

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

(29x - 3) + (13y - 17) - (15x + 7)

Open the bracket in the above expression

So, we have

(29x - 3) + (13y - 17) - (15x + 7) = 29x - 3 + 13y - 17 - 15x - 7

Collect the like terms in the above expression

So, we have

(29x - 3) + (13y - 17) - (15x + 7) = 29x - 15x + 13y - 3  - 17  - 7

Evaluate the like terms in the above expression

So, we have

(29x - 3) + (13y - 17) - (15x + 7) = 14x + 13y  -27

Hence, the simplified value of the expression given as (29x - 3) + (13y - 17) - (15x + 7) is 14x + 13y  -27

Read more about expressions at

https://brainly.com/question/4344214

#SPJ1

Complete question

Evaluate the following expression

(29x - 3) + (13y - 17) - (15x + 7)