RECTANGLE ABCD has vertices A(-5,2) B(-5,4) C(4,4) D(4,2) calculate the area.

Answer:

Step-by-step explanation:

Recall that we use the first derivative to discover where a function is increasing or decreasing; it's increasing where the first derivative is + and decreasing where the first derivative is -.

The derivative of y = x^4 - 8x^2 + 16 is  dy/dx = 4x^3 - 16x, or 4x(x^2 - 4).

This can be factored further:  4x(x - 2)(x + 2).

Set this equal to zero and solve for the three critical values:

{-2, 0, 2}.

Set up a total of four intervals:  (-∞, -2), (-2, 0), (0, 2), (2, ∞).

Now choose a test point within each interval:  {-3, -1, 1, 3}.

Evaluate the first derivative, dy/dx, at each of these four test points.  Rule:  if the first derivative is +, we know the function is increasing on that interval; if -, the function is decreasing.

At x = -3, dy/dx = 4x(x - 2)(x + 2) becomes (-)(-)(-), which is -, so we know that the function is decreasing on interval (∞, -2).

At x = -1, dy/dx is (-)(-)(+), which is +, so we know that the function is increasing on (-2, 0).

At x = 1, dy/dx is (+)(-)(+), which is -, so we know that the function is decreasing on (0, 2).

Finally:  at x = 3, dy/dx is (+)(+)(+), so we know that the function is increasing on (2, ∞ ).

To find the best fit model for the given data, draw a scatterplot and fit the models given. For each model, calculate the regression equation and R-squared value. Compare the R-squared values, the model with the highest value is the best fit.

To construct a scatterplot and identify the mathematical model that fits the data, first plot the points of weight and gallons of juice on a graph, with weight as the x-coordinate (independent variable) and juice as the y-coordinate (dependent variable). Next, try to draw each of the models given (linear, exponential, power and logarithmic) through the data points.

For each model, you'll need to calculate the regression equation and the R-squared value. The R-squared value is a statistical measure that shows the proportion of variance for a dependent variable that's explained by an independent variable. It ranges from 0 to 1, with 1 indicating a perfect fit.

After this, you should compare the R-squared values of different models. The model giving the highest R-squared value would be the best fit for your data. This model's regression equation will be the most accurate for the prediction of the dependent variable over the scope of your data.

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The best mathematical model that fits the given data is a linear model. The regression equation is y = -13.07 + 0.079x

To find the regression equation of the best model, we need to compare the values of R2 for different models. Let's start by constructing a scatterplot using the given data:

To solve this, you need to input the data points of the x (pounds of oranges) and the y (gallons of orange juice) into a calculator or statistics software to calculate the best regression model fit. The data points are 4321, 5012, 5239, 5366, 8978, 25413 for x and 341.3, 391.5, 399.6, 417.2, 656.1, 1927.3 for y.

From the scatterplot, we can see that the data points form a linear pattern. Therefore, the best mathematical model that fits the data is a linear model. Using a calculator or computer, we can find the regression equation:

y = -13.07 + 0.079x

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Answer:

-6

Step-by-step explanation:

You are finding the dot product of vectors <2, 4> and <1, -2>.  Recall that the dot product is a SCALAR.  In this case  <2, 4> · <1, -2> = 2(1) + 4(-2)>, or

2 - 8, or -6.  

Answer:

D

Step-by-step explanation:

The roots are where the curve crosses the x-axis.  So that's x=-3 and x=4.

Answer D.

Answer:

D

Step-by-step explanation:

The roots are the points on the x- axis where the function has a value of zero. That is where the graph crosses the x- axis

The graph crosses the x- axis at x = - 3 and x = 4, hence

Roots of the quadratic function are x = -3, 4 → D

Answer:

87 million tickets are sold every year.

Step-by-step explanation:

Number of Americans attending classical music concerts:

30 million

Average number of times a spectator attends a concert in a year

2.9 times

Then the amount of tickets sold "x" for concerts of classical music in a year, will be equal to the number of people attending for the number of times they attend. So:

[tex]x= 30 * 2.9[/tex]

Where "x" is given in units of millions.

[tex]x = 87[/tex]

It is 5/3 because it going up by 5 over by 3 hope this helps.

Answer:

The logarithmic function modeled by the table would be

[tex]f(x)=log_{2} x[/tex]

So it would seem to be answer B.

Hello There!

-What We Know-

Erin made 66 deviled eggs for a party.

After an hour 8 eggs were left.

X amount of eggs were eaten within the first hour.

——————————————————————————

We subtract 8 eggs how many were left after the hour

From how many eggs we had in total.

66-8=58.

58 eggs were eaten within the hour.

Answer:

58 eggs

Step-by-step explanation:

Answer:

Other answer.

Step-by-step explanation:

[tex]f(x) = 3(x-1)^4\\ f(-x) = 3(-x-1)^4 = 3\big(-(x+1)\big)^4 = 3(x+1)^4 \\ \\ f(-x)\neq f(x) \\ f(-x)\neq -f(x)\\ \\ \Rightarrow \text{The function is neither odd or even}[/tex]

Answer:

The function is neither even nor odd.    

Step-by-step explanation:

Given : Function [tex]f(x)=3(x-1)^4[/tex]

To find : Determine whether the function is even or odd ?

Solution :

Rules to determine the function is even or odd :

If f(x)=f(-x) then the function is even.

If f(x)=-f(x) then the function is odd.

Now, Test for even function

[tex]f(x)=3(x-1)^4[/tex]

[tex]f(-x)=3(-x-1)^4[/tex]

[tex]f(-x)=3(-(x+1)^4[/tex]

[tex]f(-x)=3(x+1)^4[/tex]

[tex]f(x)\neq f(-x)[/tex] so function is not even.

Test for odd function,

[tex]f(x)=3(x-1)^4[/tex]

[tex]-f(x)=-3(x-1)^4[/tex]

[tex]f(x)\neq -f(x)[/tex] so function is not odd.

So, The function is neither even nor odd.

The fundamental identity used in the second step of the proof is sin^2(θ) + cos^2(θ) = 1

An identity is true for general case, and not only for special cases. The proof for given statement is derived by using Pythagorean identity.

[tex]sin^2(\theta) + cos^2(\theta) = 1\\\\1 + tan^2(\theta) = sec^2(\theta)\\\\1 + cot^2(\theta) = csc^2(\theta)[/tex]

Given statement is [tex]\sin^2\theta - \cos^2\theta\sin^2\theta =\sin^4\theta\\\\[/tex]

Taking its left side:

[tex]\begin{aligned}\sin^2\theta(1 - cos^2\theta) &= \sin^2\theta \times sin^2\theta \\&= sin^4\theta \end{aligned}[/tex]

(from first Pythagorean identity).

Thus, the given statement is proved using Pythagorean identity (first) that [tex]sin^2\theta + cos^2\theta = 1\\[/tex]

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[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{5\% of 50000}}{\left( \cfrac{5}{100} \right)50000}\implies 500[/tex]

The realtor receives a 5% commission from the sale of a property. For a property sold at $50,000, the realtor's commission would be $2,500, calculated by multiplying the sale price by the commission rate.

To calculate the amount the realtor receives from the sale of a property when they earn a commission of 5%, you can use the following formula:

Commission = Sale Price * Commission Rate

In this case, the sale price of the property is $50,000 and the commission rate is 5%, which is 0.05 when expressed as a decimal.

Thus, the commission the realtor earns is calculated as follows:

Commission = $50,000 * 0.05

Commission = $2,500

Therefore, the realtor would receive $2,500 from the sale of a property that sells for $50,000.

Answer: the height would be 15

Step-by-step explanation:

v= pi*radius^2*height

1215pi mm= pi*9^2*height

1215pi mm= pi*81*height

(divide by pi on both sides, which isolates pi on both sides)

1215 mm= 81*height

(divide by 81 on both sides, which would isolate 81 on the right side of the equation)

1215/81= 15= height

The height of the cylinder is 15 mm.

To find the height of a cylinder, we can use the formula for the volume of a cylinder, which is V = πr²h, where V is the volume, r is the radius, and h is the height.

Given that the volume is 1215π mm and the radius is 9 mm, we can plug these values into the formula and solve for h.

1215π = π(9)²h

Simplifying the equation, we have:

1215 = 81h

Dividing both sides by 81, we find:

h = 15 mm

Therefore, the height of the cylinder is 15 mm.

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Answer:

Part 1) The value of w is 13.3 units

Part 2) The value of x is 10.3 units

The answer is the option

w=13.3, x=10.3

Step-by-step explanation:

see the attached figure with letters to better understand the problem

Part 1) Find the value of w

we know that

In the right triangle ABD

tan(42°)=12/w

Solve for w

w=12/tan(42°)=13.3 units

Part 2) Find the value of x

In the right triangle ABC

tan(27°)=12/(w+x)

(w+x)=12/tan(27°)=23.6 units

(w+x)=23.6 units

Solve for x

x=23.6-w

substitute the value of w

x=23.6-13.3=10.3 units

The measure of side lengths w and w are 13.3 and 10.3 units respectively.

The correct option is A) w = 13.3; x = 10.3

The figures in the image are those of two right triangles.

To solve for the measure of side length w and x, we use the trigonometric ratio:

First, we solve for side length w:

Angle θ = 42 degrees

Opposite to angle θ = 12

Adjacent to angle θ = w

tan(θ) = opposite / adjacent

tan( 42 ) = 12 / w

w = 12 / tan( 42 )

w = 13.3

Now we solve for side length x:

Angle θ = 27 degrees

Opposite to angle θ = 12

Adjacent to angle θ = ( w + x )

tan(θ) = opposite / adjacent

tan( 27 ) = 12 / ( w + x )

( w + x ) = 12 / tan( 27 )

( w + x ) = 23.55

Plug in w = 13.3

13.3 + x = 23.55

x = 23.55 - 13.3

x = 10.3

Therefore, the value of x is 10.3 units

Option A) w = 13.3 and x = 10.3 is the correct answer.

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ANSWER

20 units.

EXPLANATION

We want to find the distance between (-8,-8) and (4,8).

We use the distance formula:

[tex]d = \sqrt{ {(x_2-x_1)}^{2} + {(y_2-y_1)}^{2} } [/tex]

We substitute the points into the formula to get:

[tex]d = \sqrt{ {(4 - - 8)}^{2} + {(8 - - 8)}^{2} } [/tex]

We simplify to get;

[tex]d = \sqrt{ {(12)}^{2} + {(16)}^{2} } [/tex]

[tex]d = \sqrt{144+ 256} [/tex]

[tex]d = \sqrt{400} [/tex]

[tex]d = 20[/tex]

The distance between the two points is 20 units.

Answer:

Distance = 20 units

Step-by-step explanation:

Points to remember

Distance formula

Length of a line segment with end points (x1, y1) and (x2, y2) is given by,

Distance = √[(x2 - x1)² + (y2 - y1)²]

To find the distance between give 2 points

Here (x1, y1) = (-8, -8)  and (x2, y2) = (4, 8)

Distance = √[(x2 - x1)² + (y2 - y1)²]

 = √[(4 - -8)² + (8 - -8)²]

 = √[(4 + 8)² + (8 + 8)²]

 = √[12² + 16²] =  √[144 + 256)

  =  √400 = 20

Therefore distance = 20 units

Answer:-(√3)/2, (√2)/2, -√3, and undefined

Step-by-step explanation:

There are two ways you can solve this.  One is with the Pythagorean identity:

sin²θ + cos²θ = 1

The other way is by knowing your unit circle.

1. From the unit circle, we know that cos θ = 1/2 at θ = π/3 and θ = 5π/3.  Since θ is in Quadrant IV, then θ = 5π/3.  sin (5π/3) = -(√3)/2.

We can check our answer using the Pythagorean identity:

sin²θ + cos²θ = 1

sin²θ + (1/2)² = 1

sin²θ + 1/4 = 1

sin²θ = 3/4

sin θ = ±(√3)/2

Since sine is negative in Quadrant IV, sin θ = -(√3)/2.

We can repeat these steps for the other questions.

2. sin θ = (√2)/2 at θ = π/4 and θ = 3π/4.  Since θ is in Quadrant I, θ = π/4.  Therefore, cos θ = (√2)/2.

3. cos θ = -1/2 at θ = 2π/3 and θ = 4π/3.  Since θ is in Quadrant II, θ = 2π/3.  Therefore, sin θ = (√3)/2, and tan θ = sin θ / cos θ = -√3.

4. sin θ = -1 at θ = 3π/2.  Therefore, cos θ = 0.  tan θ = sin θ / cos θ, so tan θ is undefined.

1. sinθ = √3/2, 2. cosθ = √2/2, 3. tanθ = -√3, 4. tanθ is undefined.

1. Given that cosθ=1/2 and θ terminates in Quadrant IV, we can use the Pythagorean identity sin^2θ + cos^2θ = 1 to find sinθ. Substitute the value of cosθ into the equation: sin^2θ + (1/2)^2 = 1. Solve for sinθ: sinθ = ± √(1 - (1/4)) = ± √(3/4) = ± √3/2. Since θ terminates in Quadrant IV, sinθ is positive. Therefore, sinθ = √3/2.

2. Given sinθ=(√2)/2 and θ terminates in Quadrant I, we can again use the Pythagorean identity sin^2θ + cos^2θ = 1 to find cosθ. Substitute the value of sinθ into the equation: (√2/2)^2 + cos^2θ = 1. Solve for cosθ: cosθ = ± √(1 - (1/2)). Since θ terminates in Quadrant I, cosθ is positive. Therefore, cosθ = √(1 - (1/2)) = √(1/2) = 1/√2 = √2/2.

3. Given cosθ=-1/2 and θ terminates in Quadrant II, we can find sinθ using the Pythagorean identity sin^2θ + cos^2θ = 1. Substitute the value of cosθ into the equation: sin^2θ + (-1/2)^2 = 1. Solve for sinθ: sinθ = ± √(1 - (1/4)) = ± √(3/4) = ± √3/2. Since θ terminates in Quadrant II, sinθ is positive. Therefore, sinθ = √3/2. Now, we can find tanθ using the relationship tanθ = sinθ / cosθ. Substitute the values of sinθ and cosθ into the equation: tanθ = (√3/2) / (-1/2) = -√3.

4. Given sinθ=-1 and 0≤θ<2π radians, we can find cosθ using the Pythagorean identity sin^2θ + cos^2θ = 1. Substitute the value of sinθ into the equation: (-1)^2 + cos^2θ = 1. Solve for cosθ: cos^2θ = 1 - 1 = 0. Since 0^2 = 0, cosθ = 0. Now, we can find tanθ using the relationship tanθ = sinθ / cosθ. Substitute the values of sinθ and cosθ into the equation: tanθ = -1 / 0 = undefined.

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ANSWER

(-12,8)

EXPLANATION

The equation of the parabola is given as:

[tex]y = - \frac{1}{12} {x}^{2} - 2x - 1[/tex]

We can rewrite this in the vertex form as:

[tex] {(x + 12)}^{2} = - 12(y - 11)[/tex]

This implies that

[tex]4p = 12[/tex]

p=3

The vertex of this parabola is (-12,11)

The focus is

(-12,11-3)

=(-12,8)

Answer: -12, 8

Step-by-step explanation:

Separate the shape into two figures, a semi circle and a rectangle. Find the area of each and add.

See attached picture:

Answer:  The area of the figure is 29.13 sq. units.

Step-by-step explanation:  We are given to find the area of he figure shown in the graph.

The figure is made up of a triangle and a semi-circle.

Let us divide the figure into two parts, triangle ABC with base BC and altitude AD and the circle with diameter BC as shown in the attached image below.

From the graph, we note that

AD = 5 units  and  BC = 6 units.

Since BC is the diameter of the semicircle, so its radius will be

[tex]r=\dfrac{1}{2}\times BC=\drac{1}{2}\times6=3~\textup{units}.[/tex]

So, the area of the semicircle is given by

[tex]A_{sc}=\dfrac{\pi r^2}{2}=3.14\times \dfrac{3^2}{2}=3.14\times 4.5=14.13~\textup{sq. units}.[/tex]

Also, the area of the triangle ABC is given by

[tex]A_t=\dfrac{1}{2}\times AD\times BC=\dfrac{1}{2}\times5\times6=15~\textup{sq. units}.[/tex]

Therefore, the total area of the figure will be

[tex]A=A_{sc}+A_t=14.13+15=29.13~\textup{sq. units}.[/tex]

Thus, the area of the figure is 29.13 sq. units.

Answer:

D

Step-by-step explanation:

When a number is listed outside the function it is a vertical movement. So negative is down, positive is up!

Inside the function would be left/right. This would have been found in your exponent.

D. The graph of [tex]f(x)[/tex]  is shifted three units down from the graph of g(x).

f(x) = [tex]-4^{5x} -3[/tex] and g(x) = [tex]-4^{5x}[/tex]

In general, replacing x with x – h in a mathematical sentence translates its graph h units horizontally. Similarly, replacing y with y – k in a sentence translates its graph k units vertically.

For example, your sketch of Group B should show that the graph of y = x2 + 3 is 3 units above the graph of y = x2.

Using the slope-intercept form, the slope is 4 . All lines that are parallel to y=4x−6 y = 4 x - 6 have the same slope of 4 .

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Answer:

A

Step-by-step explanation:

The geometric mean of 2 values a and b is [tex]\sqrt{ab}[/tex]

The 7 th term is the geometric mean of the 6 th and 8 th terms

Hence

[tex]a_{7}[/tex] = [tex]\sqrt{6(216)}[/tex] = 36 → A

Hello There!

X=9

If we substitute X in this equation, it would say 3*9 which equals 27 subtract 6 and you get 21 which is true.

the value of x that satisfies the equation 3x - 6 = 21 is x = 9.

To find the value of x in the equation 3x - 6 = 21, we need to isolate the variable x on one side of the equation. We can do this by performing inverse operations.

First, we add 6 to both sides of the equation to cancel out the -6 term: 3x - 6 + 6 = 21 + 6, which simplifies to 3x = 27.

Next, we divide both sides of the equation by 3 to isolate x: (3x)/3 = 27/3, resulting in x = 9.

Therefore, the value of x that satisfies the equation 3x - 6 = 21 is x = 9. When we substitute x = 9 back into the equation, we get 3(9) - 6 = 21, which simplifies to 27 - 6 = 21, confirming that x = 9 is indeed the correct solution.

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It should be 40 degrees

Answer:

60 deg

Step-by-step explanation:

The measure of angle LPM is the sum of the measures of arcs LM and KN divided by 2.

m<LPM = (40 + 80)/2 = 60

Answer: m<LPM = 60 deg

Answer:

Answer is B

Step-by-step explanation:

A number that cannot be expressed as a fraction ,where p and q are integers and q is not equal to zero

Answer:

a number that cannot be expressed as a fraction, , where p and q are integers and q is not equal to zero

Answer:

perpendicular lines

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Given the roots are x = - 1 + 4i and x = - 1 - 4i then the factors are

(x - (- 1 + 4i))(x - (- 1 - 4i))

= (x + 1- 4i )(x + 1 + 4i )

= (x + 1)² - 16i² → [ i² = - 1 ]

Expand and simplify

= x² + 2x + 1 + 16

Hence

x² + 2x + 17 = 0 → c

C=2πr

C=πd

A=πr^2

r=C/2π

r=1/2 d

By the way all you do to solve r is:

C=2πr

C/2π=2πr/2π

C/2π=r

r=C/2π

Hope this helps:)

A: 5.50/p

B: 4.20/p

total 602.10

ratio 1:4 =5

602.10 ÷ 5 =120.42

A= 120.42

(B= 120.42×4= 481.86)

120.42÷ 5.50= 21.8945.....

Answer: 27 pounds

Step-by-step explanation:

We know that Coffee A costs $5.50 per pound, Coffee B costs $4.20 per pound and that this month the total cost was $602.10, then:

[tex]5.50A+4.20B=602.10[/tex]  (2)

We know that this month were used used four times as many pounds of type B coffee as type A, then:

[tex]B=4A[/tex]  (1)

So, you need to substitute (1) into (2) and solve for A:

[tex]5.50A+4.20(4A)=602.10\\22.3A=602.10\\A=27[/tex]

Answer:

She needs to buy 8 packages.

Step-by-step explanation:

Divide 44 (cookies) by 6 (cookies in package) to get 7.33 (packages). Since you can't buy 7.33 packages, you will have to buy 8. Hope this helps!

Answer:

13.7 cm²

Step-by-step explanation:

area of yellow region = area of square - area of 4 quarter circles

area of square = 8² = 64

area of 4 congruent quarter circles = area of circle

area of circle with radius = 4

A = π × 4² = 16π

yellow region = 64 - 16π ≈ 13.7 cm²

Answer:

c(x) = –8x^2 + 3x – 5 is a quadratic

Step-by-step explanation:

A quadratic function involves the 2nd power of x:  x^2, and may (or may not) involve the 1st and zeroth power of x.

a(x) = -2x^3 is not a quadratic because of that exponent 3; in a quadratic, the highest power is always 2.

b(x) = 5x^3 + 8x^2 + 3 is not a quadratic for the same reason that a(x) is not a quadratic.

c(x) = –8x^2 + 3x – 5 is a quadratic:  the highest power of x is x^2, the other powers are x^1 and x^0.

The amount of money that can be saved without having a negative actual net income is: $170 can be saved resulting in an actual net income of $0.

Predict how much money can be saved without having a negative actual net income.

Monthly Budget  (is an itemized list of expected income and expenses that helps you to plan how the money will be spent or saved and track of spending habits.)

Budgeted Amount  (is an itemized allotment of funds, time for a given period)

Actual Amount  (is the particular year in which the amount is spent)

Income  (business receives in exchange to provide a good /service /through investing capital )

Wages  (is monetary compensation paid by  employer to employee in exchange for work done)

Savings Interest  (is money the you earn in return for holding your savings in an account.)

$1150

$25

$900

$25

Expenses

Rent

Utilities

Food

Cell Phone

Savings

$400

$100

$250

$75

$200

$400

$80

$200

$75

$____

Net Income

$150

$____

How much money can be saved without having a negative actual net income?

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Answer:

$170 can be saved resulting in an actual net income of $0.

Step-by-step explanation: