A company's revenue can be modeled by r=2t^2-23t+77, where r is the revenue (in millions of dollars) for the year that is t years since 2005. Predict when the revenue was or will be at 14 million

Geometry (like any other branch of math) starts from a set of statements that we assume to be true, which we call axioms.

Then, we declare some rules that allow us to deduce true things from true things. For example, syllogism is one of this rules. So, if we know that [tex]A[/tex] is true, and it is also true that [tex]A\implies B[/tex], then we're allowed to deduce that [tex]B[/tex] is true as well.

So, the purpose of a proof is to show that a certain statement is true.

In its structure, you'll always start from some true facts, and you'll deduce new true facts by using allowed deductive methods.

In Geometry, a proof is used to demonstrate the validity of a statement or theorem. A proof consists of a statement, diagram, given conditions, logical reasoning, and a conclusion. It provides a convincing and rigorous argument.

Purpose of a proof in Geometry

In Geometry, a proof is used to demonstrate the truth or validity of a statement or theorem. It provides a logical and systematic argument, using previously established statements (called axioms or postulates) and mathematical reasoning, to support the conclusion.

The main purpose of a proof is to build a convincing and rigorous argument, ensuring that the result can be trusted and applied in various mathematical contexts.

Structure of a proof in Geometry

A proof in Geometry typically consists of several components:

Answer:

1. Carissa must scoop out of the sink 125 cups of water with the first cup to empty it.

2. Carissa must scoop out of the sink 31 cups of water with the second cup to empty it.

Step-by-step explanation:

1. Let's calculate the volume of the first cup, this way:

d = 4 ⇒ r =2

Volume of the first cup = π * r² * h /3

Volume of the first cup = π * 2² * 8 /3

Volume of the first cup = 32/3π in³

2. Let's calculate the volume of the second cup, this way:

d = 8 ⇒ r = 4

Volume of the second cup = π * r² * h /3

Volume of the second cup = π * 4² * 8 /3

Volume of the second cup = 128/3π in³

3. Now let's calculate the number of cups of water Carissa must scoop out of the sink with the first cup to empty it, as follows:

Number of cups = Volume of the sink/Volume of the first cup

Number of cups = (4000π/3)/(32π/3)

Number of cups = 4,000π/3 * 3/32π (multiplying by the reciprocal)

We eliminated 3 and π in the numerator and denominator

Number of cups = 4,000/32 = 125

4. Now let's calculate the number of cups of water Carissa must scoop out of the sink with the second cup to empty it, as follows:

Number of cups = Volume of the sink/Volume of the second cup

Number of cups = (4000π/3)/(128π/3)

Number of cups = 4,000π/3 * 3/128π (multiplying by the reciprocal)

Number of cups = 4,000/128 = 31.25

We eliminated 3 and π in the numerator and denominator

Number of cups = 31 (rounding to the next whole)

Answer:

Step-by-step explanation:

Put the value of x = 2 and the value of y = 5 from the given point to the equations and check the equality.

x + 3 = y

2 + 3 = 5

5 = 5          CORRECT

7 - x = y

7 - 2 = 5

5 = 5           CORRECT

4 + x = y

4 + 2 = 5

6 = 5        FALSE

y = 2x

5 = 2(2)

5 = 4             FALSE

Answer:

y 2x

Step-by-step explanation:

Answer:

it would be the the third one an=-17+4(n-1)

Step-by-step explanation:

i don't know the step by step explanation but if you were to like plug in, it checks.

Answer: an = - 17 + 4(n - 1)

Step-by-step explanation:

In an arithmetic sequence, the consecutive terms differ by a common difference.

The formula for determining the nth term of an arithmetic sequence is expressed as

an = a + d(n - 1)

Where

a represents the first term of the sequence.

d represents the common difference.

n represents the number of terms in the sequence.

From the information given,

a = - 17

d = - 13 - - 17 = - 9 - - 13 = 4

Therefore, the equation for the nth term of the arithmetic sequence is

an = - 17 + 4(n - 1)

Answer:

3.75 minutes

Step-by-step explanation:

For every 2/3 minutes, Aaron's Tire loses 8/9 of a liter of air

Total Volume of Air in the Tyre = 5 liters

Now, we divide the total volume by volume of air lost every stated interval to know how many air loss it will take the Tyre to be empty

[tex]\dfrac{5}{8/9} =\dfrac{5X9}{8} =\dfrac{45}{8}[/tex]

Then, to get when the tire will be completely flat in:

[tex](\frac{2}{3}X\frac{45}{8}) minutes[/tex]=3.75 minutes=3 minutes 45 seconds

The tyre will be empty in 3 minutes 45 seconds

Answer:

x^3-6x^2+18x-10

Step-by-step explanation:

(f-g) (x) =f(x) - g(x) =

x^3-2x^2+12x-6-(4x^2 - 6x+4)=

x^3-2x^2+12x-6-4x^2+6x-4=

x^3-6x^2+18x-10

Answer:

Solution given:

f(x)=x3−2x2+12x−6

g(x)=4x2−6x+4

now

(f-g)(x)=f(x)-f(g)=x3−2x2+12x−6-4x²+6x-4

=x³-6x²+18x-10

Answer:

¼

Step-by-step explanation:

BBBB

GGGG

BBBG

BBGB

BGBB

GBBB

GGGB

GGBG

GBGG

BGGG

BBGG

GGBB

GBGB

BGBG

GBBG

BGGB

3G and 1B

4/16 = 1/4

Using probability and sample space concepts, it is found that there is a 0.25 = 25% probability of getting three girls and one boy (in any order ).

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

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

For 4 children, the sample space is given by:

B - B - B - B

B - B - B - G

B - B - G - B

B - B - G - G

B - G - B - B

B - G - B - G

B - G - G - B

B - G - G - G

G - B - B - B

G - B - B - G

G - B - G - B

G - B - G - G

G - G - B - B

G - G - B - G

G - G - G - B

G - G - G - G

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

Thus:

[tex]p = \frac{D}{T} = \frac{4}{16} = 0.25[/tex]

0.25 = 25% probability of getting three girls and one boy (in any order ).

A similar problem is given at https://brainly.com/question/16256175

[tex](2x+1)(x-2) = 0[/tex]

Multiplying the factors we obtain:

[tex]2x\cdot x+2x\cdot (-2)+1\cdot x+1\cdot (-2)=0[/tex]

[tex]2x^2-4x+x-2=0[/tex]

[tex]2x^2-3x-2=0[/tex]

The general form of quadratic equation is:

[tex]ax^2+bx+c=0[/tex]

Therefore,

[tex]a=2[/tex]

[tex]b=-3[/tex]

[tex]c=-2[/tex]

The correct answer is the first one.

Answer:

Step-by-step explanation:

Use the given equation, and use your understanding of quadratic functions to reason about the solution.

  R = xp

  R = (1500 -100p)p . . . . . substitute the given expression for x

This is q quadratic function in p. It has zeros where p=0 and p=15. (These are the values that make the factors be zero.) We know this function has a maximum (because we're told to find it, and because p^2 has a negative coefficient). That maximum is the vertex of the parabola, which is located on the line of symmetry, halfway between the zeros.

The maximum revenue is obtained when p = (0+15)/2 = 7.5. That value of revenue is R = (1500 -100·7.5)(7.5) = 5625.

The price $7.50 will yield the maximum revenue, $5625.

To find the price that will bring in the maximum revenue, substitute the given equation for x into the revenue equation. Use calculus to find the value of p that yields the maximum revenue. Substitute the value of p into the revenue equation to find the maximum revenue.

To find the price that will bring in the maximum revenue, we need to determine the value of p that maximizes the revenue function R = xp. We can substitute the expression for x into the revenue function to get R = (1500 - 100p)p. To find the p that yields the maximum revenue, we can use calculus by finding the critical points of the revenue function. Taking the derivative and setting it equal to zero, we can solve for p. After finding the value of p, we can substitute it back into the revenue function to find the maximum revenue.

https://brainly.com/question/31336205

#SPJ3

Answer:

1. Exponential

Step-by-step explanation:

The simplest RC-Circuit, that is, a capacitor and a resistor in a series configuration can be modeled by using Ohm's Law and Kirchhoff's Circuit Laws:

[tex]C \cdot \frac{dV}{dt} + \frac{V}{R} = 0[/tex]

By rearranging the formula, an homogeneous linear first-order differential equation is found:

[tex]\frac{dV}{dt} + \frac{1}{R \cdot C} \cdot V = 0[/tex]

Whose solution has the form of a exponential model:

[tex]V(t) = V_{o} \cdot e^{-\frac{t}{R \cdot C} }[/tex]

Since [tex]\alpha[/tex] lies in quadrant II and [tex]\beta[/tex] lies in quadrant IV, we expect [tex]\sin\alpha>0[/tex], [tex]\cos\alpha<0[/tex], and [tex]\sin\beta<0[/tex].

Recall the Pythagorean identities,

[tex]\sin^2x+\cos^2x=1\iff1+\cot^2x=\csc^2x\iff\tan^2x+1=\sec^2x[/tex]

It follows that

[tex]\sec\alpha=\dfrac1{\cos\alpha}=-\sqrt{\tan^2\alpha+1}=-\dfrac{13}5\implies\cos\alpha=-\dfrac5{13}[/tex]

[tex]\sin\alpha=\sqrt{1-\cos^2\alpha}=\dfrac{12}{13}[/tex]

[tex]\sin\beta=-\sqrt{1-\cos^2\beta}=-\dfrac45[/tex]

Recall the angle sum identity for sine:

[tex]\sin(\alpha+\beta)=\sin\alpha\cos\beta+\sin\beta\cos\alpha[/tex]

So we have

[tex]\sin(\alpha+\beta)=\dfrac{12}{13}\dfrac35+\left(-\dfrac45\right)\left(-\dfrac5{13}\right)=\boxed{\dfrac{56}{65}}[/tex]

The value of sin(α+β) is 56/65

Given the following parameters

tan α = -12/5 = opposite/adjacent

Determine the hypotenuse using Pythagoras theorem:

hyp² = 12² + 5²

hyp² = 144 + 25

hyp² = 169

hyp = 13

Determine the value of  sin α and cos α

sin α = opp/hyp

sin α = 12/13

cos α = adj/hyp = -5/13

Similarly if cosβ=3/5 = adj/hyp

opp^2 = 5^2 - 3^2

opp^2 = 16
opp = 4

sin β = opp/hyp = -4/5

Determine the value of sin(α+β)

sin(α+β) = sinαcosβ + cosαsinβ

sin(α+β) = 12/13(3/5) + (-5/13)(-4/5)

sin(α+β) = 56/65

Hence the value of sin(α+β) is 56/65

Learn more on trigonometry here: https://brainly.com/question/24349828

Answer:

16

Step-by-step explanation:

Let x and y be two numbers other than 12.

We have been given that the average (arithmetic mean) of three positive numbers is 10. We can represent this information in an equation as:

[tex]\frac{x+y+12}{3}=10[/tex]

We are also told that the product of the other two numbers is 32. We can represent this information in an equation as:

[tex]x\cdot y=32...(2)[/tex]

[tex]x=\frac{32}{y}[/tex]

Upon substituting this value in above equation, we will get:

[tex]\frac{\frac{32}{y}+y+12}{3}=10[/tex]

[tex]\frac{\frac{32}{y}\cdot y+y\cdot y+12\cdot y}{3}=10\cdot y[/tex]

[tex]\frac{32+y^2+12y}{3}=10y[/tex]

[tex]\frac{32+y^2+12y}{3}\cdot 3=10y\cdot 3[/tex]

[tex]32+y^2+12y=30y[/tex]

[tex]y^2+12y-30y+32=30y-30y[/tex]

[tex]y^2-18y+32=0[/tex]

[tex]y^2-16y+2y+32=0[/tex]

[tex]y(y-16)-2(y-16)=0[/tex]

[tex](y-16)(y-2)=0[/tex]

[tex]y=2, 16[/tex]

Since product of 2 and 16 is 32, therefore, the greatest of the three numbers would be 16.

Answer:

The greatest of the three number is 16.            

Step-by-step explanation:

We are given the following in the question:

Let x and y be the two numbers.

[tex]\text{Mean} = \dfrac{12+x+y}{3} = 10\\\\12 + x + y = 30\\x + y = 18[/tex]

Also

[tex]xy = 32[/tex]

Puting values, we get,

[tex]x(18-x) = 32\\-x^2 + 18x - 32 = 0\\x^2 - 18x + 32 = 0\\(x-16)(x-2) = 0\\x = 16, x = 2[/tex]

When x = 16, y = 2

When x = 2, y = 16

Thus, the greatest of the three number is 16.

Answer:

Step-by-step explanation:

This is a parabola.  The only way you could find the actual rate of change at those x values is by finding the instantaneous rate of change at each of those points which requires calculus.  The average rate of change is found when you find the slope of the line between the 2 points (-20, y) and (-15, y).  To find y in each case, sub in the x values and solve for y:

[tex]f(-20)=(-20)^2+7(-20)+10[/tex] and

f(-20) = 270 and the resulting coordinate is (-20, 270).

Likewise for f(-15):

[tex]f(-15)=(-15)^2+7(-15)+10[/tex] and

f(-15) = 130 and the resulting coordinate is (-15, 130)

Applying the slope formula now will find the average rate of change between those 2 points:

[tex]m=\frac{130-270}{-15-(-20)}[/tex] which simplifies to

[tex]m=\frac{-140}{5}[/tex] so

m = -28

Answer:

Step-by-step explanation:

Please look at the 2 photos below, they may be your correct answers.

Answer:

Correct answer:  First answer is true

Step-by-step explanation:

Where x is independently variable and refers to the elapsed time and

( i-d )(x) is a function or dependent variable and shows the number of gallons during that time.

f (x) = ( i-d )₍ₓ₎ = 3 x² + 2 - ( 4 x - 1) = 3 x² - 4 x + 3

( i-d )₍ₓ₎ = 3 x² - 4 x + 3

( i-d ) (3) = 3 · 3² - 4 · 3 + 3 = 27 - 12 + 3 = 18

( i-d ) (3) = 18 gallons after 3 hours in the tank

God is with you!!!

There are 18 gallons of liquid in the tank at t = 3 hours

The liquid tank has both an inlet pipe to add liquid and a drain pipe to drain liquid from the tank.

The modeled function of inlet pipe = i(x) = 3[tex]x^{2}[/tex]+2

The modeled function of drain pipe = d(x) = 4x-1 ,

where the rate is measured in gallons per hour in both functions.

(i-d)(x) = 3[tex]x^{2}[/tex]+2-(4x-1)

⇒ (i-d)(x) =  3[tex]x^{2}[/tex]+2-4x+1

⇒ (i-d)(x) =   3[tex]x^{2}[/tex]-4x+3

⇒ (i-d)(3) = 3×[tex]3^{2}[/tex]-4×3+3

⇒ (i-d)(3) = 27-12+3

⇒ (i-d)(3) = 18

Learn more about tank problem here :

https://brainly.com/question/14975917

#SPJ2

Answer:

The person will feel dizzy.

Answer:

Step-by-step explanation:

The person will feel energetic because the heart rate will increase. ... The heart will pump less blood per beat because the blood vessels will have less blood to circulate.

Answer:

Thus he was able to save 4.438 dollars by paying 30 days before due.

Step-by-step explanation:

given that Mr. Davis borrowed $600 for 60 days at 9% annual interest.

Thus interest payable for 60 days = [tex]\frac{600*60*9}{365*100} \\=8.876[/tex]

Because he paid fully after 30 days his interest would have been only for 60 days

or half of interest for 60 days

So savings of interest = 50% of 8.876

=4.438 dollars

Thus he was able to save 4.438 dollars by paying 30 days before due.

The second matrix [tex]\left[\begin{array}{ccc}-6&3&12\\0&15&-24\end{array}\right][/tex] represents the triangle dilated by a scale factor of 3.

Step-by-step explanation:

Step 1:

To calculate the scale factor for any dilation, we divide the coordinates after dilation by the same coordinated before dilation.

The coordinates of a vertice are represented in the column of the matrix. Since there are three vertices, there are 2 rows with 3 columns. The order of the matrices is 2 × 3.

Step 2:

If we form a matrix with the vertices (-2,0), (1,5), and (4,-8), we get

[tex]\left[\begin{array}{ccc}-2&1&4\\0&5&-8\end{array}\right][/tex]

The scale factor is 3, so if we multiply the above matrix with 3 throughout, we will get the matrix that represents the vertices of the triangle after dilation.

Step 3:

The matrix that represents the triangle after dilation is given by

[tex]3\left[\begin{array}{ccc}-2&1&4\\0&5&-8\end{array}\right] = \left[\begin{array}{ccc}3(-2)&3(1)&3(4)\\3(0)&3(5)&3(-8)\end{array}\right] = \left[\begin{array}{ccc}-6&3&12\\0&15&-24\end{array}\right][/tex]

This is the second option.

The possible length of the third side of a triangle with sides of 27 m and 11 m, as per the Triangle Inequality Theorem, ranges between 16 m and 38 m.

In mathematics, the possible length of the third side of a triangle, given the other two sides, is determined using the Triangle Inequality Theorem. This theorem states that the length of any side of a triangle is less than the sum of the lengths of the other two sides and more than the absolute value of the difference between those two sides.

Given side lengths of 27 m and 11 m, the possible length of the third side (let's call it 's') is between 27 m - 11 m and 27 m + 11 m.

Therefore, s > 16 m and s < 38 m. So, any value between 16 m and 38 m could be the length of the third side of the triangle.

https://brainly.com/question/30956177

#SPJ12

Answer:

Belle's weekly earnings per week in 2008: $245.7

Step-by-step explanation:

The federal minimum wage in the year 2008 was: $6.55

She worked 37.5 hours per week.

She earn each week:

[tex]weekly earnings = 6.55*37.5=245.7[/tex]

Step-by-step explanation:

Below is an attachment containing the solution.

Answer: angle w = 154 degrees

v = 45 degrees

Step-by-step explanation:

Let w represent the measure of angle W.

Let v represent the measure of angle V.

The measure of angle W is 19 degrees more than three times the measure of angle V. This is expressed as

w = 3v + 19

if the sum of the measures of the two angles is 199 degree, it means that v + 3v + 19 = 199

4v = 199 - 19

4v = 80

v = 180/4 = 45

w = 3v + 19 = (3 × 45) + 19

w = 154

Answer:

  ACDBA, $900

Step-by-step explanation:

The cheapest route will be the one with the lowest cost. Of the routes listed, the cost $900 is the lowest, so route ACDBA is the cheapest.

_____

The "Brute Force Method" requires you compute the costs of the possible routes and pick the lowest. The answer choices have done that for you.

The cost of ACDBA is AC +CD +DB +BA = 240 +230 +210 +220 = 900, as shown in the answer selections.

The three routes listed, and their reverses (which are the same cost), are the only possible routes starting and ending at A.

Answer:

Its c because im quad-RAD-ic... PERIOD LUV

Answer:

Step-by-step explanation:

X and y =4 so X+y is gonna be 4 X+y+16= and 16 times 4 is 64 so the answer is 64

Answer:

Step-by-step explanation:

If two variables are directly proportional, it means that an increase in the value of one variable would cause a corresponding increase in the other variable. Also, a decrease in the value of one variable would cause a corresponding decrease in the other variable.

Given that y varies directly with x, if we introduce a constant of proportionality, k, the expression becomes

y = kx

If y = 16 when x = 4, then

16 = 4k

k = 16/4 = 4

Therefore, the direct variation function is

y = 4x

The values of x that make the inequality x > 1/2 true are Choice A (2 1/3) and Choice D (1).

The inequality x > 1/2 means that we are looking for any values of x that are greater than 1/2. Looking at our choices, Choice A (2 1/3) and Choice D (1) are correct since these values are greater than 1/2. Choices B (0), C (-1 1/2) and E (-3/4) are all less than 1/2, so they do not make the inequality true.

https://brainly.com/question/30231190

#SPJ12

Answer:

The answer to your question is below

Step-by-step explanation:

Data

                            x² + 3x + 5

Factor

- Solve using the formula

                     x = -b ±[tex]\sqrt{b^{2} -4 ac} / 2a[/tex]

- Substitution

                     x = -3 ± [tex]\sqrt{3^{2} - 4(1)(5)} /2[/tex]

- Simplification

                     x = -3 ± [tex]\sqrt{9 - 20} / 2[/tex]

                     x = -3 ± [tex]\sqrt{-11} / 2[/tex]

- Result

       x₁ = -3+[tex]\sqrt{11} i / 2[/tex]                    x₂ = - 3 - [tex]\sqrt{11} i[/tex] / 2

Answer:

A candy costs $6.75 and a bag of popcorn costs $7.25

Step-by-step explanation:

Let the cost of one 1 candy=$x

Let the cost of one bag of popcorn=$y

Now, Total Cost Per Item=Number of Item Bought X Price Per Unit Item.

If Nathaniel bought 4 candies and 10 bags of popcorn for a total of 99.50 dollars.

4x+10y=99.50

Grant bought 3 candies and 5 bags of popcorn for a total of 56.50 dollars.

3x+5y=56.50

Solving the two equations simultaneously

4x+10y=99.50    (I)

3x+5y=56.50     (II)

Multiply Equation (I) by 3 and Equation (II) by 4 to eliminate x

12x+30y=298.5

12x+20y=226

Subtracting

10y=72.5

y=$7.25

Now, from (II)

3x+5y=56.50

3x+5(7.25)=56.50

3x+36.25=56.50

3x=20.25

x=20.25/3=$6.75

Therefore a candy costs $6.75 and a bag of popcorn costs $7.25

Answer:

candy costs - $6.75

a bag of popcorn costs - $7.25

Step-by-step explanation:

Answer:

Step-by-step explanation:

a) Profit is the difference between revenue and cost.

  P(y) = R(y) -C(y)

  P(y) = (0.005y² +10y) -(20y +1000000) . . . . use the functions for revenue and cost

  P(y) = 0.005y² -10y -1000000 . . . . . profit as a function of y

___

b) Evaluating this function for y=30,000, we get ...

  P(30000) = 0.005(30000)² -10(30000) -1000000

  = 3,200,000

The company will have a profit of 3,200,000 from the sale of 30,000 cars.

Answer:

a = 1

h = -1

k = 2

Vertex: (-1,2)

It's a V-shaped graph completely above the x-axis.

Vertex at (-1,2) and y-intercept at 3

For the function f(x)=|x+1|+2, a = 1, indicating no vertical stretch or compression and upward direction, h = -1 indicating a shift one unit to the left, and k = 2 indicates a shift two units up. The vertex of the function is at point (-1,2).

The function f(x)=|x+1|+2 is a transformation of the base absolute value function |x|. Here, the 'a' refers to the vertical stretch/compression and reflection, 'h' refers to the horizontal shift, and 'k' refers to the vertical shift. The absolute value function is in the form f(x) = a|x-h|+k. For this specific function, a = 1 since the graph opens upward and is not stretched or compressed, h = -1 because the function is shifted 1 unit to the left, and k = 2 because the function is shifted 2 units up. As the vertex of an absolute value function is the point of its highest or lowest value, the vertex in this case is the point (-1,2).

https://brainly.com/question/37849754

#SPJ2

This is a function because each input (x-value) has only one output (y-value). If an input (x-value) has more than one output (y-value) it is not a function. It is still a function if an output has more than one input.

Your answer is A