2. Consider the following graph of a quadratic function.
Part A: Define the domain.
Part B: Define the range.
Part C: Where is the graph increasing?
Part D: Where is the graph decreasing
Part E: Identify any relative maximums.
Part F: Identify any relative minimums

Answer:

Credit to Desmos :D (Great online graphing program)

Step-by-step explanation:

Answer:

50,800

Step-by-step explanation:

Answer:

volume of cuboid = lbh = 8.2 ft x 9.4 ft x 10.7 ft

= 824.8 ft^3

Answer:  see below

Step-by-step explanation:

f(x) = x(19 - x)

     = 19x - x²

A) f(x+h) = (x + h)[19 - (x + h)]

             = (x + h)(19 - x - h)

             = 19x - x² - 2xh + 19h - h²

B) f(x+h) - f(x) = (19x - x² - 2xh + 19h - h²) - (19x - x²)

                     = - 2xh + 19h - h²

                     = h(-2x + 19 - h)

C) [f(x+h) - f(x)]/h = [h(-2x + 19 - h)]/h

                           = -2x + 19 - h

As h → 0:           = -2x + 19

The function will be equal to -2x + 19.

A function is defined as the expression that set up the relationship between the dependent variable and independent variable.

f(x) = x(19 - x)

    = 19x - x²

f(x+h) = (x + h)[19 - (x + h)]

               = (x + h)(19 - x - h)        

               = 19x - x² - 2xh + 19h - h²

f(x+h) - f(x) = (19x - x² - 2xh + 19h - h²) - (19x - x²)

                    = - 2xh + 19h - h²

                    = h(-2x + 19 - h)

[f(x+h) - f(x)]/h = [h(-2x + 19 - h)]/h

                          = -2x + 19 - h

As h → 0:            = -2x + 19

Therefore, the function will be equal to -2x + 19.

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Answer:

3/8

Step-by-step explanation:

\( \frac{p}{q} = \frac{ \frac{3}{4} }{ \frac{2}{1} } \\ \frac{p}{q} = \frac{3}{8} \)

\( \frac{p}{r} = \frac{ \frac{1}{3} }{ \frac{1}{2} } \\ \frac{p}{r} = \frac{2}{3} \)

\( \frac{ \frac{p}{q} }{r} = \frac{ \frac{3}{8} }{ \frac{2}{3} } \\ \frac{ \frac{p}{q} }{r} = \frac{9}{16} = \frac{3}{8} \)

Answer:

y = -7x + 2

Step-by-step explanation:

Use the slope-intercept form y = mx + b.

Substitute -7 for m, 0 for x and 2 for y.  Then

2 = (-7)(0) + b, so b must be 2.

The desired equation is y = -7x + 2.

Answer:

38,500 pounds

Step-by-step explanation:

1 ton = 2000 pounds

The profit function is P(x) = -500.523x^2 + 600x - 200.

To find the profit function, P(x), we need to subtract the cost function, C(a), from the revenue function, R(x).

Given:

Cost function: C(a) = 500x^2 + 300

Revenue function: R(x) = -0.523x^2 + 600x - 200 + 300

Profit function, P(x), is obtained by subtracting the cost function from the revenue function:

P(x) = R(x) - C(a)

P(x) = (-0.523x^2 + 600x - 200 + 300) - (500x^2 + 300)

Simplifying the expression:

P(x) = -0.523x^2 + 600x - 200 + 300 - 500x^2 - 300

P(x) = -500x^2 - 0.523x^2 + 600x + 300 - 200 - 300

P(x) = -500x^2 - 0.523x^2 + 600x - 200

Combining like terms:

P(x) = (-500 - 0.523)x^2 + 600x - 200

Simplifying further:

P(x) = -500.523x^2 + 600x - 200

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The perimeter of the figure is 58 m.

To find the perimeter of the given figure we can divide the figure in three rectangles.

Rectangle 1:

Perimeter= 2 (l + w)

= 2(5 + 2)

= 2 x 7

= 14 m

Rectangle 2:

Perimeter= 2 (l + w)

= 2(5 + 1)

= 2 x 6

= 12 m

Rectangle 3:

Perimeter= 2 (l + w)

= 2(14 + 2)

= 2 x 16

= 32 m

So, the perimeter of the figure is

= 14 + 12 + 32

= 58 m

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Answer:

mostly. trees and most plants arent

EXPLANATION

As Megan scored 117 points by collecting 3 coins, we need to divide the points by the number of coins and apply the unitary method in order to get the number of points that Megan will get.

In conclusion, Megan will score 468 points.

Part A: There are 28 green beans in the garden. Part B: There are 80 plants that are either pumpkin or tomato. Part C: There are 52 more corn plants than cucumber plants.

A circle graph, often called a pie chart, is a circular graph with sectors on it, each representing a particular category or set of data. Each sector's area or angle is proportionate to the amount it stands for. In data visualisation, circle graphs are frequently used to show the relative sizes or proportions of several categories or groups within a dataset. They can instantly convey the distribution of data without the need for laborious numerical calculations, which makes them effective for presenting data that is divided into discrete groups. However, if the data is not presented in a clear and simple manner or if the sectors are not precisely drawn to scale, circle graphs may be deceiving.

Part A: The percentage of green beans in the circle graph is 14%.

14% of 200 = 0.14 x 200 = 28

Part B: The circle graph shows:

pumpkin plants and tomato plants is 20% + 20% = 40%.

40% of 200 = 0.40 x 200 = 80

Part C: The corn plants is 36% and the percentage of cucumber plants is 10%.

36% of 200 - 10% of 200 = (0.36 x 200) - (0.10 x 200) = 72 - 20 = 52

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Answer:

300

Step-by-step explanation:

A=wl=10·30=300

multiply the length of the rectangle by the width of the rectangle.

The area is measurement of the surface of a shape. To find the area of a rectangle or a square you need to multiply the length and the width of a rectangle or a square. Area, A, is x times y.

Answer:

Area = 378.5 ft²

Step-by-step explanation:

The figure is having two semi circles and one rectangle.

\({ \sf{area = area \: of \: semicircles + area \: of \: rectangle}} \\ \\ { \sf{area = 2( \frac{1}{2} \pi {r}^{2}) + (l \times w) }} \\ \\ { \sf{area = \pi {r}^{2} + (l \times w) }} \\ \\ { \sf{area = 3.14 \times {5}^{2} + (30 \times 10)}} \\ \\ { \sf{area = 378.5 \: {ft}^{2} }}\)

Answer:

67

Step-by-step explanation:

This is the right answer

This means that she made a 20% return on the money she invested in the property. For every dollar she invested, she earned 20 cents in profit.

To calculate Jennifer Aniston's return on investment (ROI), we can use the formula:

ROI = (Net Profit / Initial Investment) * 100

First, let's calculate the net profit. The net profit is the selling price minus the initial investment:

Net Profit = Selling Price - Initial Investment

Net Profit = $2,200,000 - $2,000,000

Net Profit = $200,000

Next, we calculate the ROI:

ROI = (Net Profit / Initial Investment) * 100

ROI = ($200,000 / $1,000,000) * 100

ROI = 0.2 * 100

ROI = 20%

Jennifer Aniston's return on investment for this property is 20%.

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The term "isometric" has the Greek roots "isos," which means "same," and "metron," which means "measure." The definition of an isometric transformation is one in which the original figure and its transformed equivalent have the same shape, size, and orientation.

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Answer:

1.the slope is 1/2 and the y int is -4

2.the slope is -3 and the y int is 6

Answer:

0.5 (any number between 0 and 1)

Step-by-step explanation:

34 * 0.5 = 17

34 > 17 > 0

92 adult tickets were sold

230 child tickets were sold

Explanation

Step 1

set the equations

let x represents the number of adult tickets sold

let y represents the number of child tickets sold

cost of adult ticket: 12

cost for child ticket : 5

so

a)On the first day of the fair, 322 tickets were sold

so

b)total of $2,254

Step 2

Solve the equations:

a) isolate x in equation (1) and then replace in eqaution(2)

replace in equation (2)

b) now, replace the y value in equation (1) and solve for x

therefore

92 adult tickets were sold

230 child tickets were sold

I hope this helps you

Answer:

To solve this problem, we need to subtract the cost of the book and the total amount donated to charities from the total amount of cash Katye received for her birthday. Here are the steps:

Add up the value of the gifts Katye received:

Total value of gifts = (value of gift 1) + (value of gift 2) + ... + (value of gift 15)

Add up the value of the cash Katye received:

Total cash = $100

Subtract the cost of the book from the total cash:

Cash remaining after buying the book = $100 - $23

Determine the maximum number of $10 donations that Katye can make:

Maximum number of $10 donations = (cash remaining after buying the book) / $10

Multiply the maximum number of donations by $10 to get the total amount donated:

Total amount donated = (maximum number of $10 donations) x $10

Subtract the cost of the book and the total amount donated from the total cash:

Cash remaining = $100 - $23 - (total amount donated)

The final answer will be the cash remaining after these calculations

y=1/4x-2 is a perpendicular line and y=-4x+3 is a parallel line.

The equation y= -2 -4x in the form of slope intercept form y=mx+b is y=-4x-2.

Where m represents the slope and y intercept is -2.

The slope of a line perpendicular to another line is the negative reciprocal of the slope of the given line.

The negative reciprocal of -4 is 1/4.

Therefore, the slope of the perpendicular line is 1/4.

The perpendicular line is y=1/4x-2.

We know that the parallel lines have same slope.

y=-4x+3

Hence, y=1/4x-2 is a perpendicular line and y=-4x+3 is a parallel line.

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Answer:

I) ∠2 and ∠5

Step-by-step explanation:

Answer:

• from first principles rule:

\({ \boxed{ \bf{ \frac{ \delta y}{ \delta x} = {}^{lim _{x} } _{h \dashrightarrow0} \: \frac{f(x + h) - f(x)}{h} }}}\)

• f(x) → (csc x)^½

• f(x + h) → {csc (x + h)}^½

\({ \rm{ \frac{ \delta y}{ \delta x} = {}^{lim _{x} } _{h \dashrightarrow0} \: \frac{ \{\csc(x + h) \} {}^{ \frac{1}{2} } - (\csc x ) {}^{ \frac{1}{2} } }{h} }} \\ \\ \hookrightarrow \: { \tt{rationalise : }} \\ \\ = { \rm{{}^{lim _{x} } _{h \dashrightarrow0} \: \frac{ \csc(x + h) - \csc x }{h \{ \{\csc(x + h) \} {}^{ \frac{1}{2} } + ( \csc x) {}^{ \frac{1}{2} } \} } }} \\ \\ = { \rm{{}^{lim _{x} } _{h \dashrightarrow0} \: \frac{1 - (\sin (x + h))( \csc x)}{h \{ \sin(x + h) \} \{ \csc(x + h) \} {}^{ \frac{1}{2} } \{ \csc x \} {}^{ \frac{1}{2} } }}} \\ \\ = { \rm{ = { \rm{{}^{lim _{x} } _{h \dashrightarrow0} \: \frac{1 - ( \sin(x) \cos(h) + \cos(x) \sin(h)) \csc x }{h \{ \sin(x + h) \} \{ \csc(x + h) \} {}^{ \frac{1}{2} } \{ \csc x \} {}^{ \frac{1}{2} } }}} }} \\ \\ = { \rm{ = { \rm{{}^{lim _{x} } _{h \dashrightarrow0} \: \frac{1 - \cos(h) + \cot(x) \sin(h) }{h \{ \sin(x + h) \} \{ \csc(x + h) \} {}^{ \frac{1}{2} } \{ \csc x \} {}^{ \frac{1}{2} } }}} }} \\ \\ { \tt{but : \sin(h) \approx h}} \\ { \tt{ : \cos(h) \approx 1 }} \\ \\ = { \rm{{{}^{lim _{x} } _{h \dashrightarrow0 \: } \: \frac{h \cot(x) }{h \{ \sin(x + h) \} \{ \csc(x + h) \} {}^{ \frac{1}{2} } \{ \csc x \} {}^{ \frac{1}{2} } } }}} \\ \\ { \tt{h \: tends \: to \: 0}} \\ \\ { \boxed{ \rm{ \frac{dy}{dx} = - \frac{1}{2 \sqrt{ \cot(x) \csc(x) } } }}}\)

The value of 4 Superscript negative 4 is negative StartFraction 1 Over 4 Superscript negative 4 EndFraction.

In the given table, Tasha observed a pattern in the powers of 4. When the exponent decreases by 1, the previous value is divided by 4. Using this pattern, she determined the values for 4 squared, 4 Superscript 1, 4 Superscript 0, 4 Superscript negative 1, and 4 Superscript negative 2.

To find the value of 4 Superscript negative 3, she divided the previous value (StartFraction 1 Over 16 EndFraction) by 4, resulting in StartFraction 1 Over 64 EndFraction.

Similarly, for 4 Superscript negative 4, she divided the previous value (StartFraction 1 Over 64 EndFraction) by 4, yielding StartFraction 1 Over 256 EndFraction.

Finally, to rewrite the value for 4 Superscript negative 4, she expressed it as negative StartFraction 1 Over 4 Superscript negative 4 EndFraction.

Therefore, the value of 4 Superscript negative 4 is negative StartFraction 1 Over 4 Superscript negative 4 EndFraction, which simplifies to StartFraction 1 Over 256 EndFraction

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Answer:

The volume is: \(V = \frac{\pi}{3}\) cubic units

Step-by-step explanation:

Volume of a solid:

The volume of a solid, given by the function f(x), over an interval between a and b, is given by:

\(V = \pi \int_{a}^{b} (f(x))^2 dx\)

y = x, y =1, x = 0

This means that the upper function is y = 1, and the lower function is y = x. So

\(f(x) = (1 - x)\)

The lower limit of integration is x = 0.

The upper limit is y = x when y = 1, so x = 1.

Then

\(V = \pi \int_{a}^{b} (f(x))^2 dx\)

\(V = \pi \int_{0}^{1} (1-x)^2 dx\)

\(V = \pi \int_{0}^{1} (1-2x+x^2) dx\)

\(V = \pi (x-x^2+\frac{x^3}{3})|_{0}^{1} dx\)

\(V = \pi(1 - (1^2) + \frac{1^3}{3})\)

\(V = \frac{\pi}{3}\)

The monthly PMI Payment for Christina's loan is $37.50.The correct answer is option B.

To determine Christina's monthly PMI (Private Mortgage Insurance) payment, we need to find the corresponding interest rate for her loan-to-value (LTV) ratio. The LTV ratio is calculated by dividing the loan amount by the property value.

The loan amount can be calculated by subtracting the down payment from the property value:

Loan amount = Property value - Down payment

           = $170,000 - $20,000

           = $150,000

Now we can calculate the LTV ratio:

LTV ratio = Loan amount / Property value * 100

         = $150,000 / $170,000 * 100

         = 88.24%

Since Christina is obtaining a 30-year mortgage, we need to look at the interest rates for LTV ratios between 85.01% and 90%. According to the table, the interest rate for this range is 0.30%.

To calculate the PMI payment, we multiply the loan amount by the PMI rate and divide it by 12 months:

PMI payment = (Loan amount * PMI rate) / 12

           = ($150,000 * 0.30%) / 12

           = $450 / 12

           = $37.50

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The Probable question may be:
Christina is buying a $170,000 home with a 30-year mortgage. She makes a $20,000 down payment.

Use the table to find her monthly PMI payment

Base to loan% = 95.01% to 97%,90.01% to 95%,85.01% to 90%,80.01% to 85%.

30-year fixed-rate loan = 0.55%,0.41%,0.30%,0.19%

15-year fixed-rate loan = 0.37%,0.28%,0.19%,0.17%.

A. $51.25

B. $37.50

C. $23.75

D. $42.50

The missing dimensions from the given expression should be completed with the following:

(81.) A) 2

(82.) AD) x

(83.) E) 12

The expression as a product should be written as: DE) 2(x + 12).

In Mathematics and Geometry, a factored form can be defined as a type of quadratic expression that is typically written as the product of two (2) linear factors and a constant.

In this scenario and exercise, we would complete the table above by showing the factored form and expanded form of each of the given expressions as follows;

        x           12

2      2x         24

Note: 2x/2 = x.

         24/2 = 12.

(2x + 24) = 2(x + 12).

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To multiplicate two fractions, you have to multiply their numerator and denominator, like this:

Answer:

\(\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(\frac{x^2}{4}) + c\)

Step-by-step explanation:

Given

\(\int\limits {\frac{x}{x^4 + 16}} \, dx\)

Required

Solve

Let

\(u = \frac{x^2}{4}\)

Differentiate

\(du = 2 * \frac{x^{2-1}}{4}\ dx\)

\(du = 2 * \frac{x}{4}\ dx\)

\(du = \frac{x}{2}\ dx\)

Make dx the subject

\(dx = \frac{2}{x}\ du\)

The given integral becomes:

\(\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{x}{x^4 + 16}} \, * \frac{2}{x}\ du\)

\(\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{1}{x^4 + 16}} \, * \frac{2}{1}\ du\)

\(\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{x^4 + 16}} \,\ du\)

Recall that: \(u = \frac{x^2}{4}\)

Make \(x^2\) the subject

\(x^2= 4u\)

Square both sides

\(x^4= (4u)^2\)

\(x^4= 16u^2\)

Substitute \(16u^2\) for \(x^4\) in \(\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{x^4 + 16}} \,\ du\)

\(\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{16u^2 + 16}} \,\ du\)

Simplify

\(\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{16}* \frac{1}{8u^2 + 8}} \,\ du\)

\(\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{2}{16}\int\limits {\frac{1}{u^2 + 1}} \,\ du\)

\(\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}\int\limits {\frac{1}{u^2 + 1}} \,\ du\)

In standard integration

\(\int\limits {\frac{1}{u^2 + 1}} \,\ du = arctan(u)\)

So, the expression becomes:

\(\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}\int\limits {\frac{1}{u^2 + 1}} \,\ du\)

\(\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(u)\)

Recall that: \(u = \frac{x^2}{4}\)

\(\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(\frac{x^2}{4}) + c\)