What is the range of this relation?

The slope, y-intercept, and x-intercept of the graph of the linear function are 2, 4 and -2 respectively

The general equation of a straight line is:

y = mx + c,

where m is the slope of the line and c is the y-intercept

Given that: the linear function f models a relationship in which the dependent variable decreases 6 units for every 3 units the independent variable decreases. This implies:

slope (m) = (-6)/(-3) = 2

And that the value of the function at 0 is 4. This implies:

y-intercept (c) = 4

Substitute m = 2 and c = 4 into the general equation:

y = mx + c

y = 2x + 4   (This is the linear function)

To plot the graph:

Using y = 2x + 4

find y when x = 0:

y = 2(0) + 4

y = 4

=> x = 0, y = 4

Also, find x when y = 0:

0 = 2x + 4

2x = -4

x = -4/2 = -2

=> x = -2, y = 0

Thus, graph x = 0, y = 4 and x = -2, y = 0 as shown in the image attached

Therefore, the slope, y-intercept, and x-intercept of the graph are 2, 4 and -2 respectively

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Answer:

Area of triangle = ½ × b × h

Step-by-step explanation:

Now we have to,

→ write formula of area of triangle.

Formula we use,

→ A = ½ × b × h

Hence, this is the formula.

Answer: Use the formula

Step-by-step explanation:

Answer: $13.10

Step-by-step explanation: 4 small packages, 4*2.50 is $10. Add one large  package which is $3.10 and you'll have your answer, it costs $13.10.

Answer:

It will cost him $13.10 to send 4 small packages and 1 large package.

Step-by-step explanation:

1. Cost of sending 4 small packages = 4 * $2.5 = 4 * $2.50 = $10

2. Cost of sending 1 large package = 1 * 3.1 = $3.1

Total cost of sending 4 small and 1 large packages = $10 + $3.10 = $13.10

Answer:

$0.80

Step-by-step explanation:

Given:

To find the unit price in dollars per centimeter, divide the total amount by the number of centimeters:

[tex]\implies \dfrac{16.40}{20.5}=\dfrac{164}{205}=\dfrac{41 \times 4}{41 \times 5}=\dfrac{4}{5}=0.8[/tex]

Therefore, the unit price in dollars per centimeter is $0.80.

Answer:

Uhmmm You Didn't Say The Formula...

Answer:

DC = 38 ; CM = 19

Step-by-step explanation:

DC = 2/3 DM

DC = 2/3 * 57

DC = 2 * 19

DC = 38

CM = 57 - 38 = 19

The balance of Accounts Payable at the end of March is $83,900.

According to question;

Balance in the beginning Accounts payable account =$77,300

Add: Purchases made during the month on account  = $43,500                                                                          

Less: Cash already paid on account payable balance =$36,900

Balance at the end of march in Accounts payable  = $83,900

Therefore, balance left at the end of march is $83900.

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Answer:

37.5

Step-by-step explanation:

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The original amount of the bill exists $ 90.

What is the Gratuity amount?

A gratuity exists as a totality of money customarily provided by a customer to specific service sector workers such as hospitality for the service they have executed, in addition to the basic expense of the service.

Gratuity on a restaurant bill = $18 and tip = 20%.

To find the original amount of the bill.

The tip exists directly proportional to the total cost = $ 90

18/(20%)

=(18/(20/100))

=$90

Therefore, the original amount of the bill exists as $ 90.

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Answer: 12

Step-by-step explanation:  7 1/2 divided by 5/8 equals 12.

Answer:

12

Step-by-step explanation:

7 1/2 = 15/2

15/2 divided by 5/8 = 12

Hope this helps

After t=1 or t=4 seconds, the ball will reach 20 meters high.

The ball will go up to 31.25 meters high.

After 4.5 seconds, the ball will be at a height of 11.25 meters.

What is a quadratic equation?

A quadratic equation is any equation in algebra that can be rearranged in standard form as ax²+bx+c=0, where x is an unknown value and a, b, and c are known numbers.

For 19)

The given equation is h = 25t - 5t²

Now the height of the ball is 20 meters, so put h = 20, so the equation will become,

               20 = 25t - 5t²

         ⇒ 5t² -25t + 20 = 0

         ⇒ t² - 5t + 4 = 0

       finding factors, we get

              t² - 4t - t + 4 = 0

              t (t - 4) - 1(t - 4) = 0

                    (t - 4)(t - 1) = 0

                t = 4 seconds  (or) t = 1 second.

For 20)

To find the maximum height, we have to differentiate the given function with respect to the 't'

so differentiating 'h' with respect to 't', we get

 dh/dt = 25 - 10t

dh/dt = velocity.

  v = 25 - 10t,

The maximum height will attain at v = 0,

  25 - 10t = 0

   ⇒ t = 2.5 seconds

so at t = 2.5 seconds, the ball will achieve its maximum height.

put t = 2.5 in the given function, we get

         h = 25(2.5) - 5(2.5)²

         h = 62.5 - 31.25

         h = 31.25 meters.

For 21)

        Put t = 4.5 seconds,

         h = 25(4.5) - 5(4.5)²

         h = 112.5 - 101.25

         h = 11.25 meters.

Hence,

After t=1 or t=4 seconds, the ball will reach 20 meters high.

The ball will go up to 31.25 meters high.

After 4.5 seconds, the ball will be at a height of 11.25 meters.

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Answer:3200 m²

Step-by-step explanation: length times width so 80*40

Answer: 3,200 meters

Step-by-step explanation:

Area of a rectangle = length times width

A=lw

A=80(40)

A=3,200 meters

There would be 150 students enrolled in the school, according to estimates, in 2001.

468 students are projected to be enrolled in the school in the academic year 2018

We have the equation as

[tex]y = 123.1(1.069)^x[/tex]

where we have x to be the difference in the number of years

2001 - 1998 = 3

y = 123.1(1.069)³

y = 123.1 * 1.2216115

y = 150.4

The estimated number of persons that would be studying in the school in the year 2001 would be 150.

b. 2018

We have to take the difference

x = 2018 - 1998 = 20

y = 123.1(1.069)²⁰

y = 123.1 * 3.798

y = 467.5

y ~ 468

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The equation to model the population is P = [tex]\frac{1}{40}[/tex] [tex]e^{0.05t}[/tex] + 30

Here the population P of a small town, measured in hundreds, is modeled by the inverse of the function,P−1(t) = 20ln(40t − 1200)

where t is measured in years.

We need to find an equation to model the population.

let y = [tex]p^{-1}[/tex](t)

where t is measured in years.

We need to find an equation to model the population.

20[tex]ln[/tex](40y - 1200) = t

[tex]ln[/tex](40y - 1200) = t/20

[tex]e^{ln(40y - 1200)}[/tex] = [tex]e^{0.05t}[/tex]

(40y - 1200) = [tex]e^{0.05t}[/tex]

40y = [tex]e^{0.05t}[/tex] + 1200

y = [tex]\frac{1}{40}[/tex] [tex]e^{0.05t}[/tex] + 30

Now, we determine the initial value.

P(0) = [tex]\frac{1}{40}[/tex] + 30

P(0) = 30

The equation to model the population is P = [tex]\frac{1}{40}[/tex] [tex]e^{0.05t}[/tex] + 30

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For given function when f(x) = -20 then x = 2

In this question, f(x) varies inversely with x

We have been given f(x) = -8 when x = 5

We need to find x when f(x) = -20

So, we get an equation,

-20/5 = -8/x

-4 = -8/x

x = (-8)/(-4)

x = 2

Therefore, for given function when f(x) = -20 then x = 2

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Answer:

77.6 m

Step-by-step explanation:

Angle of Depression

If a person stands at a point and looks down at an object, the angle between their horizontal line of sight and the object is called the angle of depression.

To find how far the bridge is from the front of the boat, model as a right triangle and solve using the tan trigonometric ratio.

Tan trigonometric ratio

[tex]\sf \tan(\theta)=\dfrac{O}{A}[/tex]

where:

Given information:

As the teenagers' line of sight is 1.8 m above the bridge, the side of the right triangle opposite the angle of depression is:

Therefore:

[tex]\implies \sf \tan21^{\circ}=\dfrac{29.8}{A}[/tex]

[tex]\implies \sf A=\dfrac{29.8}{\tan21^{\circ}}[/tex]

[tex]\implies \sf A=77.6\;m\;\;(nearest\;tenth)[/tex]

To make a profit of 20% the article should be sold for $12.1

The new selling price will be solved by comparing the percentage increment with the old selling price

The selling price is $10.8 and the profit is 8%

The cost of the item is gotten from the profit percent as below

10.8 * 0.08 = 0.864 (profit)

cost price + profit = selling price

cost price = selling price - profit

cost price = 10.8 - 0.864

cost price = 9.936

comparing the percentages

8% profit is 0.864, 20% profit will be

8 = 0.864

20 = ?

cross multiplying

8 * ? = 20 * 0.864

? = 2.16

The new selling price

= cost price + profit

= 9.936 + 2.16

= 12.096 approximately $12.1

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Answer:

3000 dollars per year

Step-by-step explanation:

hope this helped :)

The engagement score in 4 months ago would be 7.69.

Future worth is the value of an asset in the future. It estimates the nominal amount of money that a certain quantity of money will be "worth" at a specified moment in the future under the assumption of a particular interest rate and is calculated by multiplying the present value by the accumulation function.

In four months, we must determine the future value of the engagement score.

The formula for calculating future value:

FV = P (1 + r)^n

FV = Future value  

P = Present value = 4.89  

R = rate of increase = 12%

N = number of months = 4

4.89 ( 1.12)^4 = 7.69

Therefore the engagement score in 4 months ago would be 7.69.

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Answer: it is B

Step-by-step explanation:

hope this helps!!

Answer:

it hi

Step-by-step explanation:

The answer to the given question is Yes, we can. We can conclude that there are two distinct subsets of the 14 3-digit numbers in the list which have the same sum.

There are [tex]2^{14}[/tex] = 16384 subsets. Since each number goes in the range from 0 through 999 and there are at most 14 3-digit numbers in a subset, the sum of any subset of the numbers will be in the range from 0 through 14 x 1000.

So, there are at most 14001 possible values for the sum of a subset of the 3-digit numbers. Since 16384 > 14001, if each subset is plotted to the value of its sum, then there need to be at least two different subsets which are plotted on to the same value.

For that reason, there are at least two different subsets whose numbers sum to the same value.

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In the word hawks, it is possible to rearrange the letters if none repeat and the letter w must go last as follows,

In the word “HAWKS” there are 24 possible ways to rearrange the letters so that no letter can be repeated and letter ‘w’ must go last.

It can be solved using Factorial concept.

Given word = “HAWKS”

Number of letters in Hawks = 5

There is a condition that W must be the last letter. So according to that we are now left with the 4 letters that we have to place so that no letter should be repeated.

By using the Factorial concept, (solve the numbers of letters left)! which is 4!

4! = 4x3x2x1

    = 24

By this way we can say that there are 24 possible ways to rearrange the letters of “Hawks” by fulfilling all the conditions.

Hence there are 24 possible ways to rearrange the letters of Hawks.

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The equation of the parabola is y = -1/3 ([tex]x^2[/tex]+4x).

What is parabola ?

  A bowl-shaped object forms a curve when the surface of the cone intersects a plane perpendicular to a straight line. Another curve is created when the moving point is moved such that the distance from the fixed point is equal to the distance from the fixed line. A parabola is a U-shaped curve representing the graph of a quadratic function. Graph of the equation y=x2,

Here the equation of the parabola is

=> y= a[tex]x^2[/tex]+bx+c.

Now pt given points to find value of a, b, c .

=> y = a(x-p)(x-q)

=> y = a(x+2-2)(x+2+2)

=> y = a(x)(x+4)

Here the line passes through the point ,

(x,y) = (-1,1)

=> 1 = a(-1)(-1+4)

=> 1 = a (-3)

=> a = -1/3.

Now the equation is ,

y = a (x)(x+4)

=> y = -1/3 ([tex]x^2[/tex]+4x)

Therefore the equation of the parabola is y = -1/3 ([tex]x^2[/tex]+4x).

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The number of different possible selections for the lottery is of:

25,872,165.

First we decide which formula is used, as follows:

It is stated in this problem that the order of the numbers is not important, hence the combination formula is used.

The number of different combinations of x objects from a set of n elements is obtained with the formula presented as follows, using factorials.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem, 6 numbers are selected from a set of 54, hence the number of different combinations is of:

[tex]C_{54,6} = \frac{54!}{6!48!} = 25,872,165[/tex]

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An amount of $ 23,479.45 after a period of 5 years.

In this problem we find the case of an amount that increases itself by the effect of compound interest, that is, that the money deposited is increased accumulatively. The compound interest model is described below:

C' = C · (1 + r / 100)ⁿ

Where:

Please notice that four quarters equals a year.

If we know that C = 13,000, r = 3 and n = 20, then the final amount of the money deposited in the account after a period of 5 years is:

C' = 13,000 · (1 + 3 / 100)²⁰

C' = 23,479.45

The final amount of the money deposited is $ 23,479.45.

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Answer:

  ∆APQ is isosceles, so sides AP, AQ are congruent

Step-by-step explanation:

You want to show that AP≅AQ in the given figure.

The Angles of Intersecting Chords Theorem tells you that the angle where chords cross is half the sum of the intercepted arcs. Here, that means ...

  ∠APY = (arc BX +arc AY)/2

  ∠AQX = (arc AX +arc CY)/2

Given that arc AX ≅ arc BX, and arc AY ≅ arc CY, we can substitute for BX and CY to get ...

  ∠APY = (arc AX +arc AY)/2

  ∠AQX = (arc AX +arc AY)/2

Two angles equal to the same thing are equal (substitution property), so ...

  ∠APY ≅ ∠AQX

These are base angles in the isosceles triangle APQ, so their opposite sides, AQ and AP, respectively, are congruent.

  AP ≅ AQ

Hence, the blue paper will she need to cover all area of the bulletin board is 3.12.

The rectangle's characteristics are listed below:

Here, the length and width are different. So the bulletin board will be rectangle.

Given :

Length = 2.6 ; Width = 1.2

Area of rectangular bulletin board = Length * Width

= 2.6 * 1.2

= 3.12

Hence, the blue paper will she need to cover all area of the bulletin board is 3.12.

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