The function f is graphed below. Determine the intervals on which f is increasing and decreasing.

The coordinates of the receiver are (x, y) = (10, 5), and the standard form of the hyperbola is x² - 20x + 212.5 = 0.

A hyperbola is the location of all the points on a plane whose distances from two fixed points in the plane differ by an amount that is always constant. The centre, represented by O in the above diagram as the centre of an ellipse, is where two foci are connected by a line segment when they are united by a line segment. The transverse axis of the hyperbola is the line segment that passes across both foci.

From the given situation we have,

The length of the transverse axis is 180/2 = 90 miles.

Using the distance formula between the two transmitters we have:

d1 = √((x - 5)² + y²)

d2 = √((x + 5)² + y²)

Now, the equation of d is:

|d1 - d2| = 90

Simplifying and squaring both sides, we get:

(d1 - d2)² = 8100

Substituting the expressions for d1 and d2 and expanding, we get:

[(x - 5)² + y² - (x + 5)² - y²]² = 8100

-40x² + 800x - 400 = 8100

-40x² + 800x - 8500 = 0

Dividing by -40, we get:

x² - 20x + 212.5 = 0

d1 = √((x - 5)² + y²) = √((7.5)² + y²)

d2 = √((x + 5)² + y²) = √((2.5)² + y²)

Substituting d1 - d2 = 90/2 = 45 and simplifying, we get:

y² - 50y + 450 = 0

Solving for y:

We get y = 5 or y = 45.

Since the receiver is in the first quadrant, we take y = 5.

Therefore, the coordinates of the receiver are (x, y) = (10, 5), and the standard form of the hyperbola is x² - 20x + 212.5 = 0.

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Answer:

Step-by-step explanation:

Let's call the distance from the tower's base to the end of the wire "d". According to the problem, the height of the tower is 8 feet greater than "d". We can write this as:

height of tower = d + 8

We also know that the wire is 40 feet long. The wire stretches from the ground to the top of the tower, so we can use the Pythagorean theorem to relate the distance "d", the height of the tower, and the length of the wire:

d^2 + (d + 8)^2 = 40^2

Expanding and simplifying this equation gives:

2d^2 + 16d - 960 = 0

Dividing both sides by 2 gives:

d^2 + 8d - 480 = 0

We can solve this quadratic equation using the quadratic formula:

d = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = 8, and c = -480. Substituting these values and simplifying, we get:

d = (-8 ± sqrt(8^2 + 4(480))) / 2

d = (-8 ± sqrt(2080)) / 2

d ≈ -25.73 or d ≈ 17.73

Since "d" represents a distance, it cannot be negative. Therefore, we choose the positive solution:

d ≈ 17.73

Now we can use the equation we derived earlier to find the height of the tower:

height of tower = d + 8

height of tower ≈ 17.73 + 8

height of tower ≈ 25.73

So the distance from the tower's base to the end of the wire is approximately 17.73 feet, and the height of the tower is approximately 25.73 feet.

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

[tex]y=\stackrel{\stackrel{m}{\downarrow }}{4}x-1\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

so we're really looking fo the equation of a line whose slope is 4 and it passes through (-3 , 2)

[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{2})\hspace{10em} \stackrel{slope}{m} ~=~ 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{ 4}(x-\stackrel{x_1}{(-3)}) \implies y -2= 4 (x +3) \\\\\\ y-2=4x+12\implies {\Large \begin{array}{llll} y=4x+14 \end{array}}[/tex]

480 m³ is the volume of the given solid.

What is Volume?

The space that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

The dimensions of the trapezoidal prism are given in the diagram.

The dimensions of the cuboidal cavity are also given.

Volume of the solid = Volume of trapezoidal prism - Volume of cuboidal cavity

Volume of trapezoidal prism = (1/2)[Sum of parallel sides][h]×length

= (1/2)×[13+8]×[5]×10

= 525 m³

Volume of cuboidal cavity = l×b×h

= 10×3×1.5

= 45 m³

Volume of the solid = 525 - 45 m³

= 480 m³

The volume of the solid is 480 m³.

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(a) Mean x = 245.63636363636

(b) Median x = 245

(c) Mode = 207, 255

(d) The mid-range = 252

(e) The results are not likely to be representative because the championship team may not be representative of the entire league.

The median is the value that splits the mathematical numbers or expressions in the half. The median value is the middle number of data points. to find the median first arrange the data points in ascending order.

(a) Mean x = 245.63636363636

(b) Median x = 245

(c) Mode = 207, 255

A. The modes are 201 and 255.

B. There are two modes.

Range = 90

Minimum = 207

Maximum = 297

Count = 11

Sum = 2702

Quartiles Quartiles:

Q1 --> 217

Q2 --> 245

Q3 --> 255

Interquartile Range IQR = 38

Outliers = none

(d) The mid-range = 252

(e) The results are not likely to be representative because the championship team may not be representative of the entire league.

Therefore, all the required values are given above.

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Answer:

34

Step-by-step explanation:

34 trees will be left after 11 years

Where the graphs intersect or touch, the supplied statement is true, and that is the solution to any system.

One or two variables make up a linear equation. Neither the numerator nor the denominator of a fraction can be a variable in a linear equation raised to a power higher than 1. The lines that connect all the points on a coordinate grid when you identify the values that make a linear equation true are congruent.

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. The above is sometimes referred to as "linear equation of two variables," where y and x are the variables.

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Answer:

The perimeter of the shape is 41

Step-by-step explanation:

You have to add 12 plus 9 plus 7 plus 8 plus 2 plus 3, which equals forty one. I got the two and three from the little corner which isn’t labeled. I got it by subtracting 8 from 12, and 7 from 9.

2 times the square root of 48 minus the square root of 3 simplified is 7√3.

what is square root?

The square root of a number is a value that, when multiplied by itself, gives the original number. In other words, it is the inverse operation of squaring a number. For example, the square root of 16 is 4 because 4 multiplied by itself (4 x 4) equals 16.

The symbol used to represent the square root is √. So, the square root of 16 is written as √16.

To simplify this expression, we can first simplify the square root of 48.

We know that 48 can be written as 16 x 3, and since 16 is a perfect square, we can simplify the square root of 48 as follows:

√48 = √(16 x 3) = √16 x √3 = 4√3

Now we can substitute this value into the expression:

2(4√3) - √3 = 8√3 - √3 = 7√3

Therefore, 2 times the square root of 48 minus the square root of 3 simplified is 7√3.

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(5[tex]\sqrt{3}[/tex])^2

= (25 x 3)

= 75

(2[tex]\sqrt{5}[/tex])^2

= (4 x 5)

= 20

Answer:

Step-by-step explanation:

Let's simplify - 4 - (-5):-

[tex]\tt -4 - (-5)[/tex]

[tex]\tt -4+5[/tex]

[tex]\tt 1[/tex]

Now, let's see which expression has the same value:-

F. -4 + (-5)

[tex]\tt -4 + (-5)[/tex]

[tex]\tt -4-5[/tex]

[tex]\boxed{\tt -9}[/tex]

________________

G. -4 +5

[tex]\tt -4 +5[/tex]

[tex]\boxed{\tt 1}[/tex]

_________________

H. -5 + (-4)

[tex]\tt -5 + (-4)[/tex]

[tex]\tt -5-4[/tex]

[tex]\boxed{\tt -9}[/tex]

_________________

J. -5-(-4)

[tex]\tt -5-(-4)[/tex]

[tex]\tt -5+4[/tex]

[tex]\boxed{-1}[/tex]

Therefore, we can say that G. -4 +5 has a similar value as

-4 - (-5).

________________________

Hope this helps! :)

As a result, the vertical asymptotes of the function's curve will be at x=-5 and x=1 of quadratic equation .

A function in mathematics is a formula that associates each element from a set (referred to as the domain) with a single element from another set (called the range). A machine that generates an outcome from an input (the independent variable) can be compared to a function (the dependent variable). Algebraic expressions or equations are frequently used to describe functions, such as f(x) = x2 + 3x - 2. In a coordinate plane, where the x-axis denotes the input values and the y-axis denotes the output values, they can also be graphically depicted as a curve or line.

given

Since division by zero is undefined, we must search for the values of x that cause the denominator of the function to equal zero in order to determine the vertical asymptote of a rational function.

The function is undefined at x=-5 and x=1 because the denominator of f(x) = (x-2)/(x2+4x-5) is a quadratic equation that can be factored as (x+5)(x-1).

As a result, the vertical asymptotes of the function's curve will be at x=-5 and x=1 of quadratic equation .

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Answer:

<1 and <2 - Add to 180

<1 and <3 - Equal

<3 and <4 - Add to 180

<2 and <4 - Equal

Step-by-step explanation:

No such step-by-step explanation, but we can reason with theorems.

The Vertical Angle theorem states: the opposing angles of two intersecting lines must be congruent, or identical in value.

The Linear Pair theorem states: If two angles form a linear pair, then the measures of the angles add up to 180°.

<1 and <2

<3 and <4

These angle pairs criteria make them apply to the Linear Pair theorem. Therefore, when a pair of angles are a linear pair, they add up to 180.

<1 and <3

<2 and <4

These angle pairs' criteria make them apply to the Vertical Angle Theorem. Therefore, when a pair of angles are vertical angles, they will be congruent (equal, have the same measure).

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The area under the curve of function f on [a, b] is the limit of both LRAMn f and RRAMn f as n approaches infinity.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The Left Riemann Sum (LRAM) and Right Riemann Sum (RRAM) of a non-negative, increasing function f on the interval [a, b] are defined as follows -

LRAMn f = (b - a)/n × [ f(a) + f(a + (b-a)/n) + f(a + 2(b-a)/n) + ... + f(a + (n-1)(b-a)/n) ]

RRAMn f = (b - a)/n × [ f(a + (b-a)/n) + f(a + 2(b-a)/n) + ... + f(a + n(b-a)/n) ]

As f is an increasing, non-negative function on [a, b], both LRAMn f and RRAMn f will be non-negative, and the area under the curve of f will also be non-negative.

Since f is increasing on [a, b], we have -

f(a) ≤ f(a + (b-a)/n) ≤ f(a + 2(b-a)/n) ≤ ... ≤ f(a + (n-1)(b-a)/n) ≤ f(b)

Therefore, LRAMn f will be less than or equal to the area under the curve of f on [a, b], which is less than or equal to RRAMn f.

That is -

LRAMn f ≤ Area under curve of f on [a, b] ≤ RRAMn f

So we can conclude that the area under the curve of f on [a, b] is bounded between LRAMn f and RRAMn f.

Therefore, as n increases, both LRAMn f and RRAMn f converge to the area under the curve of f on [a, b].

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Answer:

To find the integer that describes the change in temperature, we can divide the total temperature drop by the number of hours:

32 ÷ 4 = 8

Therefore, the temperature dropped by 8 degrees Fahrenheit each hour. The integer that describes the change is -8, since the temperature decreased.

Answer: To find the integer that describes the change in temperature, we need to divide the total change in temperature (32° F) by the number of hours over which the temperature dropped (4 hours). This will give us the amount that the temperature dropped by each hour.

So, dividing 32 by 4, we get:

32 ÷ 4 = 8

Therefore, the temperature dropped by 8 degrees Fahrenheit each hour.

Step-by-step explanation:

The solution is, the capacity of the largest container that can fill the tanks an exact number of times is, 44 litres.

In mathematics, the greatest common divisor of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers x, y, the greatest common divisor of x and y is denoted {\displaystyle \gcd}.

here, we have,

We subtract the remainders from the amounts.

447 - 7 = 440

577 - 5 = 572

669 - 9 = 660

Now we need the GCF of 440, 572, 660

440 = 2³ × 5 × 11

572 = 2² × 11 × 13

660 = 2² × 3 × 5 × 11

GCF = 2² × 11 = 44

The greatest common factor is 44.

Answer: 44

Check:

447/44 = 10 reminder 7

577/44 = 13 remainder 5

669/44 = 15 remainder 9

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Answer:

Step-by-step explanation:

Let's start by finding out what Denniel's weighted average grade is, given the grading system:

Tests: 40% of 70 = 0.4 x 70 = 28

Classwork: ? (we don't know this yet)

Homework: 0 (since he never does homework)

Weighted average grade: 0.4 x 28 + 0.4 x ? + 0.2 x 0 = 0.4 x ?

We know that his overall weighted average grade is 70, so we can set up an equation to solve for his classwork average:

0.4 x ? = 70 - 0.4 x 28 - 0.2 x 0

0.4 x ? = 42

? = 42 / 0.4

? = 105

So Denniel's classwork average is 105.

The cost per foot of redwood is $42.37, and the cost per foot of pine is $90.65.

In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.

Let's use the variables r and p to represent the cost per foot of redwood and pine, respectively.

From the first purchase, we can set up the following system of equations:

50r + 90p = 292 (equation 1)

90r + 70p = 406 (equation 2)

To solve for r and p, we can use the method of substitution. Solving equation 1 for r, we get:

r = (292 - 90p) / 50

Substituting this expression for r into equation 2, we get:

90[(292 - 90p) / 50] + 70p = 406

Multiplying both sides by 50 to clear the fraction, we get:

162 - 27p + 70p = 4060

Combining like terms, we get:

43p = 3898

Dividing both sides by 43, we get:

p = 90.65

So the cost per foot of pine is $90.65.

To find the cost per foot of redwood, we can substitute this value of p into equation 1 and solve for r:

50r + 90(90.65) = 292

50r = 2118.5

r = 42.37

So the cost per foot of redwood is $42.37.

Therefore, the cost per foot of redwood is $42.37, and the cost per foot of pine is $90.65.

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Answer:

Step-by-step explanation:

One possible solution to the linear equation −5x+y=−10 is:

x = 2

y = 0

To check if this solution is valid, we can substitute the values of x and y into the equation and see if it satisfies the equation:

(-5)(2) + (0) = -10

-10 = -10

Since the equation is true, we have found a valid solution.

Maricopa Success invested $140022.5 in stocks, $64000 in bonds, and $36000 in CDs. The total annual income from the investments was $11877.5.

Income is the money that an individual receives in exchange for work, investments, or other activities. It can be earned from employment, from investments such as stocks and bonds, from business activities, and from government programs. Income can also be earned from other sources such as rents, scholarships, tips, and inheritances. Income is an important source of financial security and can be used to pay for basic needs, to save for future expenses, and to invest in other potential income sources.

To calculate the amount of money Maricopa Success invested in each asset type, we can use the following equation:

Stocks + Bonds + CDs = $190000

To solve for Stocks, we can subtract the amounts invested in Bonds and CDs from the $190000:

Stocks = $190000 - $50000 - $ (11877.5/3.7)
Stocks = $140022.5

To solve for Bonds, we can subtract the amounts invested in Stocks and CDs from the $190000:

Bonds = $190000 - $140022.5 - $ (11877.5/2.75)
Bonds = $64000

To solve for CDs, we can subtract the amounts invested in Stocks and Bonds from the $190000:

CDs = $190000 - $140022.5 - $64000
CDs = $36000

Therefore, Maricopa Success invested $140022.5 in stocks, $64000 in bonds, and $36000 in CDs. The total annual income from the investments was $11877.5.

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Answer: H: (7, 1)

Step-by-step explanation: If the endpoints of A and B are (3, 5) and (11, -3), you just have to find the middle of the x and y coordinate for each endpoint. The middle of 3 and 11 is 7, and the middle of -3 and 5 is 1, therefore the middle point would be (7, 1).

Answer: im sorry you got scamed :(  but heres the answer the answer is C! Min: 30, Q1: 44, Median: 60, Q3: 70, Max: 82

Step-by-step explanation:

How do i know this? well if you look at the box plot it shows you that! it shows a tick on 30, 44, 60, 70 and 82 to its corresponding quartiles. and answer C is the only one that shows this. therefore the answer is C!

Answer:

x=65

Step-by-step explanation:

So how I would think the equation would be would be 108 + x = 173. So how I would solve this is subtracting 108 from both sides to get x = 65. There is most likely a different way to set this up but thats what comes to mind with me.

We have the fοllοwing respοnse after answering the given questiοn: The equatiοn mοnthly payment, rοunded tο the next penny, is $959.49.

In a mathematical equatiοn, the equals sign (=), which cοnnects twο claims and denοtes equality, is utilized. In algebra, an equatiοn is a mathematical statement that prοves the equality οf twο mathematical expressiοns.

Fοr instance, in equatiοn 3x + 5 = 14, the equal sign separates the numbers by a space. Mathematical expressiοns can be used tο describe the relatiοnship between the twο sentences οn either side οf a letter. The lοgο and the particular piece οf sοftware frequently cοrrespοnd. like, fοr instance, 2x - 4 = 2.

[tex]P = \frac{rP}{(1 - (1 + r)^{-n}}[/tex]

where P is the regular mοnthly payment, r is the interest rate each mοnth, n is the number οf payments, and P is the amοunt οf interest that has already been paid in dοllars.

r = 0.027 / 12 = 0.00225

The number οf payments must then be determined. There are 120 mοnthly payments fοr a 10-year mοrtgage.

n = 120

P = 1% * $100,000 = $1,000

Nοw that the data have been entered, we can cοmpute the monthly payment:

[tex]P = (0.00225 \times $99,000 / (1 - (1 + 0.00225)^{(-120)})) + $8.33[/tex]

where $8.33 represents the mοnthly charge fοr the prepaid interest and $99,000 represents the tοtal amοunt bοrrοwed after subtracting the prepaid interest.

If we cοndense this phrase, we get:

P = $959.49

Hence, The mοnthly payment, rοunded tο the next penny, is $959.49.

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Answer:

The quadratic 2x² - 3x - 5 is in the standard form:

ax² + bx + c

Therefore, we can identify the values of a, b, and c from the coefficients of the quadratic:

a = 2

b = -3

c = -5

So, a = 2, b = -3, and c = -5 for the given quadratic equation.

The total area of the exercise room is 160 square feet.

The number of square yards equivalent to this total area is 17. 78 square yards.

Since the rubber flooring is sold in whole square yards, Juan must purchase exactly 18 square yards.

To find the area of the exercise room, you should divide it into two different rectangles and then add up their areas.

Rectangle 1 length = 16 ft

Rectangle 1 width = ( 13 - 6 ) = 7 ft

Rectangle 2 length = ( 16 - 8 ) = 8 ft

Rectangle 2 width = 6 ft

The area is therefore :

= ( 16 x 7 ) + ( 8 x 6 )

= 160 square feet

1 square yard is 9 square foot so 160 square foot is:

= 160 / 9

= 17. 78 square yards

The area of rubber flooring that Juan must purchase would then be the whole number of 18 square yards which is 17.78 rounded up.

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Answer:

the value of b is 10 +151620 but we have; to check

The value of b in the equation is 13/12

From the question, we have the following parameters that can be used in our computation:

x^2/24 - y^2/b^2 = 1

The equation of a hyperbola with center at the origin and semi-axes lengths a and b can be written as:

x^2/a^2 - y^2/b^2 = 1

Comparing this equation with the given equation, we have:

a^2 = 24.

The directrix of the hyperbola is given as

x = 576/26

For a hyperbola with center at the origin, the distance between the center and the directrix is a^2/b.

So, we have:

a^2/b = 576/26

Substituting the value of a^2, we get:

24/b = 576/26

So, we have

b = 13/12

Hence, the value of b is 13/12

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She earned a total of $44 from doing chores for her neighbors.

Amount is a numerical quantity that is used to measure, count, or indicate the size, magnitude, or extent of something. It can be used to refer to a variety of things, including money, people, time, temperature, and even abstract concepts. Amounts are often expressed as a numerical value, but may also be expressed as a word or phrase.

Alice earned $44 doing chores for her neighbors. She spent $15 on a book, leaving her with $29. She then spent half of that, or $14.50, on the necklace, leaving her with $14.50. Therefore, she earned a total of $44 from doing chores for her neighbors.

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