The length (L) of a rectangle of fixed area varies inversely as the width (W). If the
length of the rectangle is 6 feet when the width is 12 feet, find the length of the
rectangle when the width is 4 feet.

Answer: Slope of [tex](-3, -2)[/tex] and [tex](-1, -5)[/tex] is [tex]-1.5[/tex].

Step-by-step explanation:

The slope of a line is given by, [tex]m=\frac{y_2-y_1{} }{x_2-x_1}[/tex]

Here we have,

[tex](x_{1}, y_{1}) = (-3, -2)[/tex] and [tex](x_{2}, y_{2}) = (-1, -5)[/tex]

Now put the known values in the slope formula we get,

[tex]m=\frac{(-5) -(-2) {} }{(-1) -(-3)}[/tex]

   [tex]m=\frac{(-3) {} }{2}[/tex]

Slope (m) = 1.5

To learn more about Slope,

https://brainly.com/question/18636573

The correct statement regarding the linear function y = 3x + 5 is given as follows:

The line passes through the ordered pair (0,5) and has a slope of 3.

The slope-intercept definition of a linear function is presented as follows:

y = mx + b.

The slope and the intercept are given as follows:

In this problem, the function is defined as follows:

y = 3x + 5.

Hence the coefficients have the values given as follows:

m = 3, b = 5.

The statements are given by the image shown at the end of the answer.

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

Answer:

In general, the dividend income on W number of shares of XYZ stock will be W * Y dollars if XYZ distributes a $Y per share dividend.

Step-by-step explanation:

The dividend income on W number of shares of XYZ stock will be W * Y dollars if XYZ distributes a $Y per share dividend. This is because the dividend income is calculated by multiplying the number of shares that an investor owns by the amount of the dividend per share.

For example, if an investor owns W = 100 shares of XYZ stock and XYZ distributes a $Y = 5 per share dividend, then the investor's dividend income will be 100 * 5 = 500 dollars.

In general, the dividend income on W number of shares of XYZ stock will be W * Y dollars if XYZ distributes a $Y per share dividend.

Answer:

Step-by-step explanation:

0.69

Answer: x= (−∞,∞)

Step-by-step explanation:

3+8x+6 = 5(x+2) + 3x-1

9+ 8x = 5x +10 + 3x -1

9 + 8x = 8x +9

Subtract nine on both sides

8x= 8x

 x = Any number!

On #9:

Slope-intercept form is y = mx + b

Based on the graph, the slope is -4/3 and the y-intercept is (0,0).

The answer is y = –4/3 x.

You could add "+0" at the end to have y = –4/3 x +0, but since adding 0 doesn't change it, it's usually left off.

Answer:

y = -4/3x + 0 or just y = -4/3

Step-by-step explanation:

you just find the slope by doing rise over run, and find the y-intercept by looking at what number the line hits on the y-axis.

Answer:

see explanation

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

(a)

given the equation of L1 is

2x - y = 3 ( subtract 2x from both sides )

- y = - 2x + 3 ( multiply through by - 1 )

y = 2x - 3 ← in slope- intercept form

with slope m = 2

• Parallel lines have equal slopes

then slope of L2 is m = 2

given the equation of L2 is

kx + 2y = 3 ( subtract kx from both sides )

2y = - kx + 3 ( divide through by 2 )

y = - [tex]\frac{k}{2}[/tex] + [tex]\frac{3}{2}[/tex] ← in slope- intercept form

with slope m = - [tex]\frac{k}{2}[/tex]

since slope of L1 and L2 are equal, both 2 , then

- [tex]\frac{k}{2}[/tex] = 2 ( multiply both sides by 2 to clear the fraction )

- k = 4 ( multiply both sides by - 1 )

k = - 4

----------------------------------------------

(b)

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

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{2}[/tex]

Then

for L2 to be perpendicular to L1

- [tex]\frac{k}{2}[/tex] = - [tex]\frac{1}{2}[/tex] ( multiply both sides by - 1 )

[tex]\frac{k}{2}[/tex] = [tex]\frac{1}{2}[/tex] , thus

k = 1

The triangles are similar by Angle-Angle similarity since they are congruent.

According to the Angle-Angle Similarity Theorem, if two angles in one triangle are equal to two angles in another triangle, the triangles are similar. The triangles are similar if two pairs of corresponding angles in a pair of triangles are congruent. We know this because if two angle pairs are equal, then the third pair must be equal as well.

Two triangles with two angles, starting with Triangle 1, one measuring 47 degrees and the other measuring 53 degrees, are congruent to two angles in Triangle 2. Following the AA similarity theorem, it is assumed that Triangle 1 is similar to Triangle 2.

In this case, angle MNP = angle QPL (corresponding angles, //lines) (A)

angle QLP is common angle (A)

By AA, the 2 triangles are similar.

Learn more about triangles on:

https://brainly.com/question/17335144

#SPJ1

The measure of the acute angles in the right triangle are 10 and 80 degrees.

A right angle triangle is a triangle that has one of its angles as 90 degrees.  The sides of a right angle triangle can be named base on the position of the angles. The sides includes hypotenuse side, opposite side and adjacent side.

The sum of angles in a right angle triangle is 180 degrees.  

The other measures of the right triangle are acute angles.

Any angle that measures greater than 0° and less than 90° is called an acute angle.

Hence, let's find the measure of the acute angles

let

x = measure of one acute angle

Hence,

x + 8x + 90 = 180

9x = 180 - 90

9x = 90

x = 90 / 9

x = 10

Therefore, the measure of the acute angles are 10 and 80 degrees.

learn more on right angle triangle here: brainly.com/question/13737075

#SPJ1

Answer:

d=189 when c=4725

Step-by-step explanation:

c:d

125:5

divide by 5 to find the value of c when d=1

25:1

multiply by 6 to find the value of c when d=6

150:6

4725:?

4725/25=189

189*1=189

The slope of the line that connects (10,4) and (5,13) is -9/5.

Here given,

The two points are (10,4) and (5,13).

We have to find the slope that passes through the given points,

The formula to find slope(m) is,

The slope of the line that passes through (x1 , y1) and (x2,y2) is,

Slope(m) = y2 - y1 / x2 - x1

By substituting the values in x and y

Slope = 13 - 4 / 5 - 10

          = 9 / -5

Slope = -9/5

          = -1.8

Therefore the slope of line that passes through (10,4) and (5,13) is -9/5.

To learn more about slope refer to :

https://brainly.com/question/16949303

#SPJ1

Answer:

0.00000797

Step-by-step explanation:

Answer:

[tex]\frac{16}{6561}[/tex]

Step-by-step explanation:

[tex]\frac{2x2x2x2}{9x9x9x9}[/tex] = [tex]\frac{16}{6561}[/tex]

yes 38/53 is the simplest form

Step-by-step explanation:

The fraction is already reduced.

The required given Co-ordinates are plotted in graph below.

The numbers on a direction lattice are utilized to find focuses. Each point can be recognized by an arranged sets of numbers; that is, a number on the x-axis  called a x-coordinate, and a number on the y-hub called a y-coordinate. Requested matches are written in enclosures (x-coordinate, y-coordinate).

Graph is characterized as to make an outline that shows a connection between at least two things. An illustration of diagram is to make a progression of bars on charting paper

coordinates plane so that the x-axis extends from -9 to 9 and the y-axis

extends from -6 to 6

Plotted points on the graph are shown in image below.

To know more about Graphs visit:

brainly.com/question/17267403

#SPJ1

To isolate a certain variable in an equation, we must perform inverse operations on both sides of the equal sign to cancel out values.

[tex]S=-qtr[/tex]

⇒ Right now, r is being multiplied by q and t. Divide both sides by qt to cancel these values out:

[tex]\dfrac{S}{qt}=\dfrac{-qtr}{qt}\\\\\dfrac{S}{qt}=-r[/tex]

⇒ Now, to remove the negative symbol, multiply both sides by -1:

[tex]r=-\dfrac{S}{qt}[/tex]

[tex]r=-\dfrac{S}{qt}[/tex]

As domain x approaches positive infinity, S(x) approaches positive infinity. Option B is correct.

The graph is a demonstration of curves that gives the relationship between the x and y-axis.

Given expression for the attendance of the student is,
S(x) = (x - 50)² + 19

The end behavior of their graph is given as after x = 50 the graph starts heigh increasing gradient and it keeps increasing, till x =  infinity, as shown in the graph.

Thus, the curve of the given equation S(x) will increase from x = 50 to x = ∞ .

Learn more about graphs here:

brainly.com/question/16608196

#SPJ1

Answer:

Step-by-step explanation:

(5). ( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )  

y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex] )

~~~~~~~~~~~~~~~~~

( 4 , 8 )

y = [tex]\frac{1}{7}[/tex] x - 5 ; slope m = [tex]\frac{1}{7}[/tex]

Slope of line ⊥ to the given line is opposite reciprocal to [tex]\frac{1}{7}[/tex] and equal to ( - 7)

y - 8 = - 7( x - 4 )

(6).  

( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )

( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )

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

y = mx + b

~~~~~~~~~~~~

( 4 , 3 )

( 5 , 1 )

m = [tex]\frac{1-3}{5-4}[/tex] = - 2

y - 3 = - 2( x - 4 )

y = - 2x + 11

(7). y = - [tex]\frac{1}{2}[/tex] x + 2

The equation of the line that passes through the point (1, 4) and has a slope of -2 is y = -2x + 6

What is slope-intercept form of a line?

The equation of the line in slope-intercept form is given by:

y = mx + c

Here,

(x, y) = Every point on the line

m = Slope of the line

c = y-intercept of the line

According to the given question:

The given line has slope m = -2 and point (1, 4) passes through the line.

By slope-intercept form general equation of line is y = mx + b where b is

y-intercept.

Substituting values of m and point (1, 4) in this equation to get value of b

y = mx + b

4 = -2(1) + b

b = 6

Hence equation of the line is y = -2x + 6

To know more about slope-intercept form visit

https://brainly.com/question/9682526

#SPJ1

Answer:

Step-by-step explanation:

The amount of bacteria that will be there in 100 milliliters of water will be: 1.5 × 10⁸.

A standard notation is a method of writing a given number, equation, or expression in a specific format that adheres to certain rules. 4.5 billion years, for example, is written as 4,500,000,000 years.

The main reason for converting numbers to scientific notation is to make calculations involving unusually large or small numbers easier.

Even though zeros are no longer always seemed to set the decimal point, all digits in a scientific notation number are significant.

Here, it is given that,

The number of bacteria found in  1 milliliter of water = 1,500,000.

So,

The number of bacteria in 100 milliliters of water = 1,500,000 x 100

The number of bacteria in 100 milliliters of water = 15,00,00,000

The number of bacteria in 100 milliliters of water = 1.5 × 10⁸.

Correct option: e

To know more about standard notation refer to:

brainly.com/question/10253124

#SPJ4

Therefore, the solution of this problem is the domain would be

0 < t ≤ 1.61.

A function's domain is the set of possible values that can be entered. This set reflects the values of x in a function like f. (x). Its range refers to the set of possible values that a function can accept. These are the values that are returned by the function when we enter an x value.

Here,

The remaining distance that would result from multiplying the speed by the time t will be added to the 20 miles that make up the total distance. The formula for the equation would be as follows:

120 = 15 + 65t

It would be 0 hours at the very least. When the entire 120-mile distance has been accomplished, the time limit is reached.

t ≤ (120 - 15)/65

t ≤ 1.61 hours

Therefore, the solution is the domain would be 0 < t ≤ 1.61.

To know more about Domain ,visit

https://brainly.com/question/28135761

#SPJ1

Answer: the number is 4

Step-by-step explanation:

5x+5=25 is the equation

solve for x by isolating x

5x+5-5=25-5

5x=20

divide both sides by 5 to isolate x

x=4

Answer: 4

Step-by-step explanation:

5x + 5 = 25 this is what the equation is!

Then we subtract 5 on both side

5x = 20

Then divided by 5 on both side

x= 4

1) The dimension of the base of the pool is; (x + 3) and (x + 8)

2) The volume of the pool when x = 3 ft is;  198 ft³

3) If the volume is 100 ft³ of water, the height x is; 2 ft

4) If the maximum capacity of the pool is 520 ft³, the maximum depth is; 5 ft

We are given that the volume of water in a rectangular, in-ground, swimming pool is; V(x) = x³ + 11x² + 24x

where;

V(x) is the volume in cubic feet when the water is x ft high

1) V(x ) =x³ + 11x³ + 24x

V(x) is the volume in cubic feet when the water is x ft high

Factorizing the polynomial into its' factors gives;

V(x) = x(x² + 11x + 24)

V(x) = x(x + 8)(x + 3)

The water is x ft high and so the dimensions of the base of the pool are (x + 3) and (x + 8)

2) We want to find the volume of the pool when x = 3 ft. Thus;

V(3) = 3(3 + 8)(3 + 3)

V(3) = 3 (11)(6)

V(3) = 198 ft³

3) If the volume is 100 ft³ of water, the height x is calculated as;

x(x + 8)(x + 3) = 100

Solving for x gives us;

x = 2 ft

4) If maximum capacity of the pool is 520 ft³, then the maximum depth is;

x(x + 8)(x + 3) = 520

Solving for x gives us;

x = 5 ft

Read more about Volume of a cuboid at; https://brainly.com/question/46030

#SPJ1

Answer:117

Step-by-step explanation:

I’m good at math

Answer:

117 Roses

Step-by-step explanation:

234 *0.5 = 117

The unit rate in acres of land planned by the workers per day is found is 16/35 acres.

For the mentioned question-

Total acres of land planted = 2/5 acres.

Total time taken = 7/8 days.

Thus, unit rate in acres per day = Total acres of land planted / Total time taken

unit rate in acres per day = (2/5) / (7/8)

unit rate in acres per day = (2*8)/(5*7)

unit rate in acres per day = 16/35

Thus, unit rate in acres of land planned by the workers per day is found is 16/35 acres.

To know more about the rate of doing work, here

https://brainly.com/question/25864308

#SPJ1

The next day Patsy have t choose between cheerleading and play practice is 17th September

To solve the problem of calculating the next day Patsy will have the events of cheerleading and school play same day, we find the lowest common multiple of the intervals of the occurrence of the two events

The interval of the events are:

cheerleading - 4th day

school play - 6th day

The Lowest common multiple of 4 and 6 is calculated to be 12

If the two events occurred on 5th September the next will on

= 5 + 12

= 17

The next time to choose between the two will be on 17th September

Learn more on Lowest common multiple at:

https://brainly.com/question/16054958

#SPJ1

The rate of width changing will be;

⇒ 4 feet/hour

What is mean by Rectangle?

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

The length of a rectangular drainage pond is changing at a rate of 8 ft/hr and the perimeter of the pond is changing at a rate of 24 ft/hr.

Now,

We know that;

⇒ Perimeter of rectangle = 2 (Length + Width)

Substitute al the values, we get;

⇒ 24 = 2 (8 + x)

⇒ 12 = 8 + x

⇒ x = 12 - 8

⇒ x = 4

Thus, The rate of width changing will be;

⇒ 4 feet/hour

Learn more about the perimeter visit:

https://brainly.com/question/7070897

#SPJ1

A linear pair's total angles are always equal to 180°. Hence ∠ HJL is 94°

given

∠HJL and  ∠LJK are linear pair

∠ HJL = ?

∠HJL +  ∠JLK =180

x + x -8 = 180

2x -8 =180

x = 188/ 2 = 94°

To learn more about linear pair's  refer,

https://brainly.com/question/1757859

#SPJ1