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Step-by-step explanation:

The volume of paint used, V liters, is directly proportional to the area, A square feet, that the paint can cover.

This is written as:

\begin{gathered}V \propto A\\V=kA,$ where k is the constant of proportionality\end{gathered}

(a)5 liters of paint can cover a wall with an area of 75 square feet.

V=5 liters, A=75 square feet.

Substitution into V=kA

5=75k

k=5/75

\text{Constant of proportionality, k}=\dfrac{1}{15}Constant of proportionality, k=151

(b)Substitution of k=\dfrac{1}{15}k=151 into V=kA

The equation relating V and A is:

V=\frac{1}{15}AV=151A

(c)If A=180 Square feet

Volume of paint needed,

\begin{gathered}V=\frac{1}{15} X 180\\=12$ liters\end{gathered}

Answer:

53.

Step-by-step explanation:

DE = CD = 6 ( as triangle ACE is isosceles so AD is the perpendicular bisector of CE.

Therefore CE = 12.

AB + BC + AC = 41 (given perimeter of ABC)

AB + BC + AE + 12 =   perimeter of ABE.

But AE = AC   ( given), so

AB + BC + AC + 12 = perimeter of ABE

Now we know that AB + BC + AC = 41 , so

41+ 12 = perimeter of ABE.

Answer:

circle tttdonuts

Step-by-step explanation:

d crystal

Answer:

[tex]25 \times \frac{60}{100} = 15[/tex]

Step-by-step explanation:

Multiply 25 by 60%

Answer:

B.  y = -2x-25 These lines will intersect

Step-by-step explanation:

y = 2x+25  Which line has one solution to this equation:

A.  y = 2x+25   [This is the same line!  The solutions are infinite.]

B.  y = -2x-25 [These lines will intersect.  They'll meet at the corner of -12.5th and Zero streets (-12.5,0)]

C.  y = 2x-25  [Same slope, 2.  They, also, will never meet.  Pity]

D.  y = 2x [OMG.  Didn't parallel lines ever get the message.  Get with the slope and focus on the bliss of intersection.]

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

[Extra Credit]

y = 2x + 25

y = –2x – 25

-----------

y = 2x + 25

y = -2x - 25

2y =  0

y = 0

--

y = 2x + 25

0 = 2x + 25

2x = -25

x = -12.5

The single solution is (-12.5,0)

If system of two linear equations has one solution. One of the equations is y = 2x + 25 then y = –2x – 25 is the other equation.

Two or more expressions with an Equal sign is called as Equation.

A system of two linear equations has one solution.

One of the equations is y = 2x + 25

We need to find the other equation which has one solution

y = 2x+25  

This is the same line

The solutions are infinite.

y = -2x-25

These lines will intersect.

The other equation is y = –2x – 25 because this equation is interacting with y = 2x + 25

Hence, if system of two linear equations has one solution. One of the equations is y = 2x + 25 then y = –2x – 25 is the other equation.

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Answer:

7.) y=10x

8.) $140 in 14 months, $60 in 6 months

9.) He will have saved $100 in 10 months and $175 in 17.5 months

10.) The rate of change is 10

11.) Knowing the rate of change helps you in answering this problem because it tells you how much money he saves per month.

12.)

0- $0

1- $10

2-$20

3-$30

4-$40

Step-by-step explanation:

7.) The standard form of a linear equation is y=mx+b

The starting balance is 0 so there is no point to adding b. M is the amount of money he deposits each month so that is 10. You plug in the values and you get y=10x (+0)

8.) y=10(14)

$140

y=10(6)

$60

9.) 100=10x

100/10= 10

10 months

175=10x

175/10=17.5

17.5 months

10.) The rate in change is m so 10.

Hope I explained this in simple enough terms. Have a good day!

Answer:A

Step-by-step explanation:i mean that sound logiclity correct

2022 EDGE ASSIGNMENT

Modeling Functions Using Finite Differences

1. C

2. A, E

3. B

4. B, D

5. D

6. A

7. B, F

Answer:

The mean

Step-by-step explanation:

The mean would allow you to make an average aka the inference about the price of houses whilst if you take the median, you're just taking the middle number from a  list of numbers and not the average.

Answer: Median

Step-by-step explanation:

Median, because there is an outlier that affects the mean.

Step-by-step explanation:

The outlier is 1,110,000

As you have learned in the lesson, outliers affect means, meaning that you should not use them.

Hope this helped! ❤

Therefore, you will pay $42 after a year.

Hoped this helped.

[tex]-BrainaicUser1357-[/tex]

Answer:

42

Step-by-step explanation:

3.5*12=42

Answer:

12

Step-by-step explanation:

g(−3)=2

g(0) = 3g(0)=3

Step-by-step explanation:

Given

The attached graph

Required

Determine

g(-3)g(−3)

g(x) = 3g(x)=3

Since a graph has been provided, the question will be solved graphically;

Solving g(-3)

This implies that;

x = -3

And the interpretation is to solve for the y value when x = -3

From the attached graph;

When x = -3; y = 2

Hence;

g(-3) = 2g(−3)=2

Solving g(x) = 3

This implies that;

y = 3

And the interpretation is to solve for the x value when y = 3

From the attached graph;

When y = 3; x = 0

Answer:

5

Step-by-step explanation:

So lets do this slowley

3x3=9

9x3=27

27x3=81

81x3=243

It took 5 threes or 3x3x3x3x3 to get 243

Answer:

y=81, try that for answer

Answer:

207

Step-by-step explanation:

Answer:

  a) x = {-2 2/3, -2}

  b) x = {-8, 3}

  c) x = {-1, 23}

Step-by-step explanation:

If all you want are solutions, a graphing calculator can give them to you easily. The attachment shows the solutions as x-intercepts when the equation is rearranged to the form f(x) = 0.

__

In general, it can be convenient to write the equation in standard form with integer coefficients. Common factors among the coefficients should be removed.

  3(x+4)^2 = 10x +32 . . . . . given

  3(x^2 +8x +16) -10x -32 = 0

  3x^2 +14x +16 = 0

To factor this, we're looking for factors of 3·16 that total 14.

  48 = 1·48 = 2·24 = 3·16 = 4·12 = 6·8

The last pair of factors has a total of 14, so we can rewrite the equation as ...

  (3x +6)(3x +8)/3 = 0

  (x +2)(3x +8) = 0

The solutions are the values of x that make the factors zero:

  x = -2, x = -8/3

__

  (x +4)^2 = 3x +40 . . . . . . . . given

  x^2 +8x +16 -3x -40 = 0 . . . . subtract the right side

  x^2 +5x -24 = 0 . . . . . . . . simplify

  (x +8)(x -3) = 0 . . . . . . factor

The solutions are the values of x that make the factors zero:

  x = -8, x = 3

__

  (x^2 -1)/2 -11x = 11 . . . . . given

  x^2 -1 -22x -22 = 0 . . . . . . multiply by 2, subtract the right side

  x^2 -22x -23 = 0 . . . . . . simplify

  (x -23)(x +1) = 0 . . . . . . factor

  x = 23, x = -1

_____

Additional comment

Factoring often gets to the solution with the least fuss when the solutions are rational. There are several ways factoring can be done when the leading coefficient is not 1. One of them is illustrated in (a) above. We will show two other methods that give the same result.

factoring by pairs

We have identified the factors of 3·16 = 48 that have a total of 14. We can use those factors to rewrite the 14x term in the equation.

  3x^2 +6x +8x +16 = 0

Now, we can group the terms in pairs, and factor each pair. It does not matter which of the factors (6 or 8) you write first. You will end with the same result.

  (3x^2 +6x) +(8x +16) = 0

  3x(x +2) +8(x +2) = 0

  (3x +8)(x +2) = 0   ⇒   x = -8/3, x = -2

__

factoring using the X method

This method is usually shown using a large graphic X. In the top quadrant is written the product of the leading coefficient and the constant: 3·16 = 48.

In the bottom quadrant is written the coefficient of the x-term: 14.

If one or the other, or both, of these top/bottom values is negative, be sure to keep the sign.

The side quadrants are then filled with values that have a product equal to the top number, and a sum equal to the bottom number. (Pay attention to the signs.) Further, in each of those quadrants, the number written is divided by the leading coefficient, and the fraction reduced to lowest terms.

Here, we would have 6/3 = 2 on one side, and 8/3 on the other side. Now the factors are written as (bx+a), where the reduced fraction on either side is a/b. In our example, the factors are (x+2) and (3x+8)

__

alternate X method

This starts off in the same way the X method does, as described above. However, the factors on either side of the X are not divided by the leading coefficient (a). If those side values are 'p' and 'q', the quadratic is written in factored form as ...

  (ax +p)(ax +q)/a = 0

You will notice we used this form above: (3x +6)(3x +8)/3 = 0.

Now, the divisor 'a' can be used to reduce either or both of the numerator factors. Here, the entire factor of 3 can be removed from (3x+6) to make the factorization be ...

  (x +2)(3x +8) = 0

__

Sometimes, one factor of the divisor will be removed from one term, and the other factor of it will be removed from the other term. An example of this might be ...

  [tex]\dfrac{(6x+3)(6x+2)}{6}=\dfrac{6x+3}{3}\cdot\dfrac{6x+2}{2}=(2x+1)(3x+1)[/tex]

Answer:

A and C

Step-by-step explanation:

Answer:

130⁰

Step-by-step explanation:

Let,

<Q = x

<R = y

So,

In ∆PQR

2x + 2y + 80 = 180(Sum of all angle in a triangle is 180⁰)

2(x + y) = 180 - 80

2(x + y) = 100

x + y = 100/2

x + y = 50

Now,

In ∆QOR

x + y + QOR = 180(Sum of all angle in a triangle is 180⁰)

50 + QOR = 180

QOR = 180 - 50

QOR = 130⁰

Answer:

Adult = $15 pp

Child =  46 pp

Step-by-step explanation:

  Let A and C be the price of Adult and Child's tickets, respectively.

 We can set up equations for each of the two days, Tuesday and Wednesday.  Each equation adds the totals paid for the two ticket levels and set it equal to the total income for that day:

Tues:  8A+9C=174

Wed:   5A+7C=117

We have two equations and two unknowns.  Let's manipulate one of the equations in a way that allows us to eliminate one of the two variables, A or C.  [One can also solve either equation to isolate one of the variables, and then use that in the second equation.]

I chose to multiply the first by 5 and the second by -8, in order to make the coefficients for A the same value in both equations, but opposite in sign:

Tues:   40A+45C   =  870   [Multiply by 5]

Wed:  -40A -56C = -936     [Multiply by -8]

                      -11C = -66      [Add the two equations]

C = 6                                    [Ta Da.  Now use this price for a child's ticket in either of the original equations to find the cost of an adult ticket.]

8A+9C=174

8A+9*(6)=174

8A+54=174

8A   = 120

A  =  15

====

Use these two prices in the original equations to see if they indeed add up to the correct totals for each day.

                                                       Total Sales

Price     Tues     Wed          Tues  Wed    

A   15           8          5              120    75

C    6           9            7               54    42

               174        117              174   117 [The prices are correct]

Adult is $15 and child is $6

Answer:

Answer: 375 adult tickets were sold and 125 children tickets were sold.

Answer:

Iam very confused on this Answer please help me  

Step-by-step explanation:

Answer:

Yes

Domain: 1, -1, 0, -3, 3

Range: 1, -1, 6

Step-by-step explanation:

The domain is in the left oval, the range is in the right oval. To find if its a function you have to make sure the domain (left side) doesn't "cheat". One number in the domain cant have more than one number in the range (right side), BUT (for future reference) the range can cheat. As shown, the right side numbers 1 and 6 have two different arrow pointed at them. As long as the domain doesnt "cheat" it is a function

Answer:

Step-by-step explanation:

The number is 12.

A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words.

here, we have,

-> If you add 12 to my number and then multiply the result by 3, you will get 64 more than two-thirds of my number.

-> n + 12 and then multiply the result by 3, you will get 64 more than two-thirds of my number.

-> 3(n + 12), you will get 64 more than two-thirds of my number.

-> 3(n + 12) = 64 more than

-> 3(n + 12) = 64 + 2n/3

[Given]

3(n + 12) = 64 +  2n/3

[Distribute]

3n + 36 = 64 + 2n/3

[Multiply both sides by 3]

9n + 108 = 192 + 2n

[Subtract 108 and 2n from both sides]

7n = 84

[Divide both sides by 4]

n = 12

hence, The number is 12.

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Answer:

11

Step-by-step explanation:

22x = 2 · 11 · x

33 = 3 · 11

common factor to both is 11

Answer:

[tex]x=0[/tex] and [tex]x=4[/tex]

Step-by-step explanation:

The roots of a function (also known as "x-intercepts" or "zeroes") are defined where y=0. Therefore, we will solve the quadratic:

[tex]2x^2-8x=0[/tex]

[tex]2x(x-4)=0[/tex]

[tex]x=0[/tex] and [tex]x=4[/tex]

Answer:

The triangle must be an isosceles triangle so as to only get one measurement

Step-by-step explanation:

The Pythagorean theorem states that the square of the hight and base is added then square rooted to get the hypotenuse

THE FORMULA: A square+b square=c square