Find the domain and range og tje ff. Rational function f(x) = 2/x+1

The measure of the exterior angle as shown in the triangle is 140°.

Exterior angle is the angle between a side of a polygon and an extended adjacent side.

Exterior angle theorem: The exterior angle of a triangle is equal to the sum of the two opposite interior angles.

From the diagram below, applying the theorem above,

Hence, the exterior angle is 140°.

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Answer:b=2/3 if u don't need an answer that is not a fraction or decimal u can write 17. as a whole number.

Step-by-step explanation:

The common ratio, r = -0.75, 20th term = -18.9056, exact sum of the infinite sequence = 1750.

a.

common ratio r = a2/a1

= -3360/4480

= -0.75.

r = a3/a2

= 2520/-3360

= -0.75

b.

[tex]a_{n}[/tex] = a*r^(n-1)

here a = 4480 and r = -0.75.

= 4480(-0.75)^(20-1)

= 4480(-0.75)^19

= 4480*(-0.00422)

[tex]a_{20}[/tex] = -18.9056.

c.

[tex]s_{n}[/tex] = a*((1-r^n)/(1-r))

= 4480*((1--0.75^4)/(1--0.75))

= 4480*((1-0.31640625)/(1--0.75))

= 4480*(0.68359375/1.75)

= 4480*0.390625

= 1750

Therefore the common ratio, r = -0.75, 20th term = -18.9056, exact sum of the infinite sequence = 1750.

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The original amount of nuts, x, in the recipe is 103

The equation for the original amount is 2x + 2x = 412

An algebraic expression can be defined as an expression made up of terms, factors, constants, coefficients, and variables.

These expressions are also known to be made up of mathematical operations such as;

From the information given, we have that;

Beverly doubles the amount of nuts and peanut butter chips

Total number = 412

This is represented as;

2x + 2x = 412

collect like terms

4x = 412

Make 'x' the subject of formula

x = 412/ 4

x = 103

Hence, the value is 103

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She needs to complete 20 laps for a total distance of 0.5 kilometer.

1 kilometers = 1000 meters

0.5 kilometers = 500 meters

Length of swimming pool = 25 meters

That means, she covers 25 meters in 1 lap.

Laps to cover 500 meters = 500/25

                                            = 20

Hence, she needs to do 20 laps.

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The equation of the absolute value function graph is: y = |x - 3| + 5.

The equation, y = a|x – h| + k, represents the equation of an absolute value function in the vertex form, where:

We are given the following from the graph:

Vertex (h, k) = (3, 5)

Plug in the values of h and k into the equation, y = a|x – h| + k:

y = a|x - 3| + 5

A point on the graph is (5, 7). Find the value of a by substituting (x, y) = (5, 7) into y = a|x - 3| + 5:

7 = a|5 - 3| + 5

7 = a|2| + 5

7 = 2a + 5

7 - 5 = 2a

2 = 2a

2/2 = 2a/2

1 = a

a = 1

Write the equation of the absolute function graph by substituting a = 1 into y = a|x - 3| + 5:

y = |x - 3| + 5

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Answer:

-3

Step-by-step explanation:

You can use  to find the slope of a line going through  and .

I like to line up the points and subtract vertically. Then put 2nd difference over 1st difference.

(6,h)

minus

(7,-10)

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

-1     h-(-10)

This also said to be equal to -7:

Multiply -1 on both sides:

Subtract 10 on both sides:

[texh=-3[/tex]

So if h=-3 then the slope of the line going through (6,h) and (7,-10) is -7.

Let's test it:

(6,-3)

minus

(7,-10)

----------

-1  7

So the slope is 7/-1=-7. This is the intended goal.

The check is good.

The x-intercept of the equation is 13 and its interpretation in the context of the problem is the number of time in hours for which Lily left her house.

In Mathematics, the x-intercept can be defined as the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" is equal to zero (0).

Next, we would determine the number of time for which Lily has left her house since in the morning by substituting the value of B with zero (0) as follows:

B = -4t + 52

0 = -4t + 52

4t = 52

Time, t = 52/4

Time, t = 13 hours.

Therefore, the x-intercept of the given equation is (0, 13).

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Answer:

I believe it's 4.5 seconds

Tower B is 14.9 miles away from the fire.

What is the law of sines?

According to the law of sine, or sine law, the ratio of a triangle's side length to the sine of the opposing angle remains constant for all three sides. The sine rule is another name for it.

Here,

According to the law of sines

BC/sin A = AC/sin B = AB/sin C

∠A = 43°, ∠B = 31°, ∠C = 180° - ∠A - ∠B = 106°

AB = 21 miles

So, BC = (AB/SinC)×SinA

BC = 14.9 miles

Hence, Tower B is 14.9 miles away from the fire.

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The partners are assigned in the form of (1, 15) (2, 14) (3, 13) (4, 12) (5, 11) (6, 10)  (18, 7) (17, 8), and (16, 9).

A square number, also known as a perfect square, is an integer that is the square root of another integer, or the result of multiplying another integer by itself.

For example:

Square of 2 = 4

Square of 3 = 9

Square of 4 = 16

Here we have  

A science class is pretty small

There are just 18 students in the class.

The teacher gave each of them numbers from 1 through 18 on lab days

Start from 1 and find by adding which number we will get a square number

Here  1 + 15 = 16

2 + 14 = 16

3 + 13 = 16

4 + 12 = 16

5 + 11 = 16

6 + 10 =16

After the above combinations, the remaining numbers are

7, 8, 9, 16, 17, 18          

which can be added as given below to get square number 25  

=>  18+7=25

=>  17+8=25

=>  16+9=25  

Therefore,

The partners are assigned in the form of (1, 15) (2, 14) (3, 13) (4, 12) (5, 11) (6, 10)  (18, 7) (17, 8), and (16, 9)  

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Answer:

After 8 minutes ; altitude = 22,400 feet

Step-by-step explanation:

s1 = 2800t

s2 = -3200t + 48 000

2800t = -3200t + 48 000

28t = -32t + 480

7t = -8t + 120

7t + 8t = 120

15t = 120

15/15 t = 120/15

t = 8 minutes

s = 8 * (2800)  =   22400 feet

Answer:

============

Since both points have same y-coordinate, the distance between the points is the difference of x-coordinates:

11.5 and 15 are the values that are part of the solution set of the inequality.

Inequality is defined as relationship between non-equal numbers or expressions. The solution of an inequality is the set of values that satisfies the given inequality.

To determine the solution set of the given inequality, isolate the variable to one side and simplify.

-4x + 24 < -2x + 2

-4x + 2x < -24 + 2

-2x < -22

22 < 2x

11 < x

Hence, the solution set of the given inequality is the set of numbers greater than 11. Among the given choices, 11.5 and 15 are both greater than 11.

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The equation in the given question is answered in main body.

What is equation?

In arithmetic , an equation may be a formula that expresses the equality of 2 expressions, by connecting them with the sign =

Main body:

according to question :

A) equation for Saturday sale = 84c +157d = 2640

equation for Sunday sale = 67c +134d = 2211

when subtracted we will get, 17c +23d = 429

This equation shows the difference in sales of these 2 days in terms of ticket sold and collection.

B) According to second part solution are c= 9 , d= 12.

equation given : 17c+23d = 429

now substituting value of c and d.

⇒17(9) + 23(12)

⇒153+276

⇒429 = R.H.S

Hence equation satisfies.

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The  line with a slope of –5 that passes through the points (7,–2) and (8,q) has q as -7.

The equation of a line can be described as follows:

y = mx + b

where

Therefore, the line passes through  (7, –2) and (8, q) with a slope of - 5.

Hence, let's find q.

y = - 5x + b

Let's find y-intercept

-2 = -5(7) + b

b = -2  + 35

b = 33

Therefore,

y = -5x + 33

Hence, let's find q.

y = -5(8) + 33

q = -40 + 33

q = -7

Therefore, q = - 7

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Answer:

x = 9/5 y - 4/5

Step-by-step explanation:

Make x the subject:

9y - 5x =4

Subtract 9y from each side

9y-9y - 5x =-9y+4

-5x = -9y +4

Divide each side by -5

-5x/-5 = -9y/-5 + 4/-5

x = 9/5 y - 4/5

Answer:

x = (9/5)y - (4/5)

Step-by-step explanation:

Given equation,

→ 9y - 5x = 4

Solving for the required value of x,

→ 9y - 5x = 4

→ -5x = -9y + 4

→ x = (-9y + 4)/-5

→ [ x = (9/5)y - (4/5) ]

Hence, value of x = (9/5)y - (4/5).

Read the left colum top to bottom then the right column top to bottom, hope this helps

Answer:

g(10)=-33, x=3

Step-by-step explanation:

g(x)=-4x+7. --------(1)

a) g(10)=?

since we know function x = -4x+7 to find function g(10) we will just place 10 whenever we see x

g(10)=-4(10)+7

g(10)=-40+7

g(10)= -33

b.)find x if g(x)=-5. ---------(ii)

g(x)=-4x+7. we will place (I) in (ii)

g(x)=-5

-4x+7=-5

-4x=-5-7

-4x=-12

cancel the minus(-) sign in both sides

4x=12

x=12/4

x=3

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The length of the shortest ladder is 16.64 ft.

In triangle ABC, using Pythagoras theorem

[tex]AC^{2} = AB^{2} + BC^{2}[/tex]  OR

[tex]L^{2} = h^{2} + (x+4)^{2}[/tex]       .....(1)

We also have similar triangles if we consider:

△ABC and △DEC

Which gives us the proportional relationship:

AB:DE = BC:EC

or    h/8 = (4+x) / x

h = 8( 4+x) /x      

Substituting this last expression for h into Eq [1] we get:

[tex]L^{2} = \frac{(8(x+4))^{2} }{x^{2} } + (x+4)^{2}[/tex]

Our aim is to now minimize L wrt x, and this involves looking for critical points of the derivative, so differentiation wrt x we get:

[tex]2L\frac{dL}{dx} = 2( 8 + \frac{32}{x} ) (-\frac{32}{x^{2} } ) + 2(x+4)[/tex]

At a critical point the derivative is zero and so we have the equation:

         =  [tex]2 (x + 4) ( 1 - \frac{256}{x^{3} } ) = 0[/tex]

From here we can find the value x :

x + 4 = 0                                                            1 - [tex]\frac{256}{x^{3} }[/tex]  = 0

x = -4                                                                 x  = [tex]\sqrt[3]{256}[/tex]

We require x > 0 so we neglect the -ve solution and only take +ve solution

therefore the minimum height of the ladder can be given by putting the value of x in eqn 1.

[tex]L^{2} = ( 8 + \frac{32}{\sqrt[3]{256} } )^{2} + ( \sqrt[3]{256} +4) ^{2}[/tex]

L² = 277.14

L = 16.64 ft

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The equation of the line perpendicular to y = - (1 / 2) · x - 2 and that passes through the point (x, y) = (- 3, - 5) is y = 2 · x + 1.

In this problem we must determine the equation of a line perpendicular to another line, provided that the equation of a line and a point of intersection are given. According to analytical geometry, two lines are perpendicular if and only if the product of the two slopes equals - 1.

The equations of the line are defined by functions of the form:

y = m · x + b

Where:

And the slope relationship between two perpendicular line:

m · m' = - 1

Where:

First, derive the equation of the line in slope-intercept form:

x + 2 · y = - 4

2 · y = - x - 4

y = - (1 / 2) · x - 2

Second, calculate the slope of the perpendicular line by the slope relationship:

m' = - 1 / (- 1 / 2)

m' = 2

Third, find the y-intercept of the perpendicular line by the equation of line, the slope and the coordinates of the given point:

b = y - m · x

b = - 5 - 2 · (- 3)

b = - 5 + 6

b = 1

Then, obtain the equation of the line in slope-intercept form:

y = 2 · x + 1

The equation of the line is y = 2 · x + 1.

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Answer:

I think is 50m.

Step-by-step explanation:

Answer:

X = 2, Y = 0

Step-by-step explanation:

Add the two equations together to cancel out -4y and +4y

leaving you with:

8x = 16

8x = 16

divide both sides of the equation by 8 to get x on its own (8x/8 = x, 16/8 =2)

leaving you with:

x = 2

substitute the value of x back into the equation to calculate y (it can be either equation, top or bottom):

8(2) - 4 y = 16

8 x 2 = 16

leaving you with:

16 - 4y = 16

subtract 16 from both sides to get 4y on its own

leaving you with:

-4y = 0

so y = 0, and x = 2

The slope of the line is 0.393.

Slope is the inclination of a line with respect to the horizontal is measured numerically. The ratio of the vertical to the horizontal distance between any two points on a line, ray, or line segment is known as its slope in analytic geometry ("slope equals rise over run").

Given,

A data set has an r- value of 0.793. If the standard deviation of the x-coordinates is 5.591, and the standard deviation of the y-coordinates is 2.772.

We'll use the following formula for slope if the r- value (or Pearson's coefficient) and the standard deviations of the x and y coordinates are provided:

m = 8ₓ/8ₐ

where m is the slope of the best-fit line.

8ₓ = Standard deviation of the x-coordinates is 5.591,

8ₐ =  the standard deviation of the y-coordinates is 2.772.

Slope is:

m = 8ₐ/8ₓ

m = (0.793)(2.772)/5.591

m = 0.393

The slope of the line is 0.393.

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y = 0.1x + 1 is the linear function for pressure based on the depth in meters

Given that:  At 30 meters in depth the water pressure measures 4 (atm)

At 50 meters in depth under water the pressure is 6 (atm)

We will consider the two given data values as our points 1 and 2 respectively. And that is what we are going to use to create a linear function for pressure

Let the y and x represent the pressure and depth respectively

point 1 (30, 4) and point 2 (50, 6)

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

where  x1 =30, y1 = 4 and x2 = 50, y2 = 6

slope(m) = 6-4 / 50-30 = 2/20 = 1/10

Linear function are of the form y-y1 = m(x-x1). Thus:

y-4 = 1/10 (x-30)

y-4 = 1/10(x) - 3

y = 1/10(x) + 1 = 0.1x + 1

Therefore, the linear function for pressure based on the depth in meters is y = 0.1x + 1

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Answer:

50:75

Step-by-step explanation:

let the ratio of 2:3 be x

now,

125=2+3x

or,5x=125

therefore,x=125/5

                x=25

now,

2x=25*2

   =50

3x=25*3

    =75

They should produce 1091 units each day to yield a minimum cost.

What is the vertex formula?

When the graph crosses its symmetry axes, the vertex formula aids in determining the vertex coordinate of a parabola. The vertex point is often represented by (h, k).

We know that a parabola's conventional equation is y=ax²+bx+c. The vertex in this case should be near the base of the U-shaped curve if the coefficient of x² is positive. The vertex should be at the peak of the U-shaped curve if the coefficient of x² is negative.

We have,

C = 70,000 - 120x + 0.055x²

C = 0.055x² - 120x + 70,000

Hence, for this equation, the graph will be parabola opening upward.

For that, the vertex will be the minimum cost

x = (-b) / 2a

Here, a = 0.055 , b = -120

Now, find and put the values of x.

minimum cost (x) = ( -(-120) ) ÷ ( 2 × 0.055 )

                           = 120 ÷ 0.11

                           = 120 ÷ 0.11

                           = 1090.90  ≈ 1091 units

The minimum cost will be yield for 1091 units.

Therefore, They should produce 1091 units each day to yield a minimum cost.

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