A road descends a vertical distance of 2000 feet over a distance of 3.5 miles as shown in the diagram.
Find the approximate measure of , the angle shown in the diagram. Give your answer to the nearest thousandth of a degree. Show or explain how you found your answer. (Use 1 mile = 5280 feet.)

The predicted interval for the given function is, f(x) ≥ 0 over the interval [-1,1]. So Option C is correct

Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).

Vertical line test:-

Whenever we want to check whether a given expression is a function or not we can apply a vertical line test, in this test we check for a single image of x , we are getting a single image or more.

If we get more images then it will not be a function.

For example, let us take, y² = 4ax

y = ±√4ax

For single value of x we get two values of y

Hence, it will not be a function.

Given that,

The ordered pairs of the given function

(-3,15), (-2,-5), (-1,0), (0,5), and (1,0).

It can be observed from the values of f(x) with respect to x, that the function reaches zero at x = -1, then then reach up to 5 at x = 0 and then again reaches zero at x = 1

Hence, the value of f(x) remains positive within the interval of [-1,1].

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1. [tex]m\angle BOC=45^{\circ}[/tex] since angles on a straight line add to [tex]180^{\circ}[/tex]

2. [tex]m\angle DOE=60^{\circ}[/tex] because vertical angles are congruent

3. [tex]m\angle AOE=120^{\circ}[/tex] because vertical angles are congruent

Answer:1. y=2x+3

             2. y=-1x-2  

             3. y=-3x+4

             4= y=3x+0

The function at its maximum value will be at point (9,2) and its value is 51 which can be derived keeping in mind the constraints that have been given.

The maximum value of any kind of a function is the place where the said function reaches its highest point, or vertex, on a graph. If your kind of quadratic equation has something as a negative of a term, it will also have a maximum value.

There are a bit of three ways to find that maximum, depending on which form of a quadratic function you have got.

here, we have,

Herein we can find the closed region ABC from the three equations or constraints given

and can mark the points as

A = (2,2)

B = (5, 2)

C = (9, 2)

if we put up the values of the points, we get

at (9, 2) ,

z=5x+3y

 =45+6

  =51 that is the maximum value amongst the three.

Thus, the maximum point of the function can be calculated as (9,2)

How do you extract out the maximum or minimum value of a function?

We will at first set out the first derivative of the function to absolute zero and then solve for x to get the exact critical point.

If we then take the second derivative or f’’(x), there in we can find out whether this point will be a maximum or minimum. If the second derivative is seen as positive, it will be a minimum value

What is the maximum value of a function called?

The maximum or minimum value that is calculated over the entire function is called an “Absolute” or “Global” maximum or minimum of the function.

There is presence of only one global maximum (and only one global minimum) but there can be several that is more than one local maximum or minimum

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The value of the functions for the condition is,

1. f(x + h) = 3(x + h)² - (x + h) + 5,

2. (fog)(x) =  27x² -33x + 15,

3. f(g(h(-1))) = 16,060.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input.

Given f(x) = 3x² - x + 5

g(x) = -3x + 2

h(x) = -5x³

1. Find f(x + h),

so  f(x) = 3x² - x + 5

substitute x = x+ h

f(x + h) = 3(x + h)² - (x + h) + 5

2. (fog)(x),

f(g(x))

g(x) = -3x + 2

f(-3x + 2)  = 3(-3x + 2)² - (-3x + 2) + 5

f(g(x)) = 3(9x² + 4 - 12x) - 2 + 3x + 5

f(g(x)) = 27x² + 12 - 36x - 2 + 3x + 5

f(g(x)) = 27x² -33x + 15

3. Find f(g(h(-1)),

h(x) = -5x³

g(x) = -3x + 2

g(h(x)) = -3(-5x³)² + 2

g(h(x)) = -75x⁶ + 2

f(x) = 3x² - x + 5

f(g(h(x))) = 3(-75x⁶ + 2)² - (-75x⁶ + 2) + 5

f(g(h(x))) = 3(5625x¹² + 4 - 300x⁶) + 75x⁶ - 2 + 5

f(g(h(x))) = 16875x¹² + 12 - 900x⁶ + 75x⁶ -2 + 5

f(g(h(x))) = 16875x¹² - 825x⁶ + 10

substitute x = -1,

f(g(h(-1))) = 16875(-1)¹² - 825(-1)⁶ + 10

f(g(h(-1))) = 16,060

Hence  f(x + h) = 3(x + h)² - (x + h) + 5,

2.f(g(x)) = 27x² -33x + 15,

3. f(g(h(-1))) = 16,060.

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Step-by-step explanation:

The equivalent expression in the form of a product is:

(8x) * (4x + 6)

To locate the fractions we must divide the unit in the number of the denominator (point A). According to the information, each shell symbol means 2 shells. Mark found 4 fewer shells than Tania. Mark and Carlos found 10 more shells than Mei Ling. Lastly, the numbers are rounded to the nearest number.

To locate the fractions we must divide the unit in the part number that says the denominator of the fraction and locate the fraction in the numerator position as shown in the graph. They all go in the first position.

Based on the information in the graph, it can be established that:

To approximate the numbers we must identify which of the numbers in the graph is closest:

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Answer:

To solve the expression [(4r²t)³]², you need to follow the order of operations (PEMDAS):

Calculate the expression inside the outermost parenthesis first: (4r²t)³ = (4 * r^2 * t)^3, where r and t are variables.

Raise the result to the power of 3: (4 * r^2 * t)^3 = 64 * r^6 * t^3.

Raise the result to the power of 2: (64 * r^6 * t^3)^2 = 4096 * r^12 * t^6.

So, [(4r²t)³]² = 4096 * r^12 * t^6.

Step-by-step explanation:

Answer:

( 0,1)

Step-by-step explanation:

y-4x=1

We want to find the y-intercept ( where it crosses the y-axis).

Let x = 0

y-4*0=1

y = 1

The coordinates of the y-intercept are ( 0,1).

The statement that will not produce a triangle is side lengths of 5.5 ft, 11 ft, and 5.5 ft, the correct option is C.

Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side.

Suppose a, b and c are the three sides of a triangle. Thus according to this theorem,

[tex](a+b) > c\\(b+c) > a\\(c+a) > b[/tex]

Given;

A. angle measures of 47o, 58o, 75o

Here,47o+ 58o,+75o=180

B. angle measures of 61o, 61o, 58o

Here, 61o+61o+58o=180

C. side lengths of 5.5 ft, 11 ft, and 5.5 ft

5.5+5.5 is not equal to 11

D. side lengths of 5 in, 7 in, and 8 in

5+7 is greater than 8

Therefore, the triangle with side lengths of 5.5 ft, 11 ft, and 5.5 ft is not the triangle.

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Answer:

25 is X

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

1+3=4

4+5=9

9+7=16

16+9=25

3+2=5

5+2=7

7+2=9

The size of the total economic surplus in this market is $32.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

Welfare and Efficiency-End of Chapter Problem

Consider the national market for in-home childcare, depicted in the accompanying graph

The size of the total economic surplus in this market,

= (1/2)(18 - 10) 8

= 32

Therefore, the surplus is $32.

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The larger television is Vehicle Viewing, explanation is mentioned below,

The diagonal of a television refers to the length of a line segment connecting two opposite corners of the screen. It is a way of measuring the size of the television screen, rather than its width or height. The diagonal measurement gives a good indication of the overall screen size and is commonly used as a specification for television screens.

Given that,

Two television,

Vehicle Viewing having diagonal 75 inches

Traveling TV Co having diagonal 8.5 inches

larger television =?

Vehicle Viewing, Inc. has the larger television with a diagonal of 75 inches compared to Traveling TV Co.'s diagonal of 8.5 inches.

This can be determined by simply comparing the two diagonal measurements given.

Hence, the larger television is Vehicle Viewing.

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The correct equation for the graph include the following: C. y = 2x/3 - 4.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

From the information provided above, we have the following slope and data points on the line:

At point (0, -4), a linear equation of this line can be calculated in point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - (-4) = (0 + 4)/(6 - 0)(x - 0)

y + 4 = 2x/3

y = 2x/3 - 4

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Answer: 67.1 cm

Step-by-step explanation:

Using the Law of Sines:

[tex]\frac{i}{\sin I}=\frac{h}{\sin H}\\\\\frac{i}{\sin 24^{\circ}}=\frac{97}{\sin 144^{\circ}}\\\\i=\frac{97 \sin 24^{\circ}}{\sin 144^{\circ}}\\\\i \approx 67.1 \text{ cm}[/tex]

Answer:  67.1

Step-by-step explanation:

The combined area of the square and rectangle is 3x² + 3x - 3.

The expression 2x² + 6x - 4 represents the area of a square.  The area of a rectangle is represented by x² - 3x + 1.  The combined area of the square and the rectangle is the sum of the area of the square and the area of the rectangle.

Therefore,

area of the square = 2x² + 6x - 4

area of the rectangle = x² - 3x + 1

Let's find the combined area as follows:

combine area of the square and rectangle = 2x² + 6x - 4 + x² - 3x + 1

combine area of the square and rectangle = 2x² + x² + 6x - 3x - 4 + 1

combine area of the square and rectangle = 3x² + 3x - 3

Therefore,

the combined area = 3x² + 3x - 3

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Answer:

In Fig. 12.35, if ATB = 82°, then the angles of ABC would be A = 82°, B = 98°, and C = 180°. This can be determined by using the fact that the sum of the angles in a triangle is 180°.

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

Points   (-3,5)   and   ( 3,1)

distance d can be found using the distance formula ( modified Pyhtagorean theorem)

d^2 = ( x1-x2)^2 + ( y1-y2)^2

d^2 = ( -3 -3)^2  + ( 5-1)^2

d^2 = 36 + 16

d^2 = 52

d = sqrt(52) = 2 sqrt(13)

Note that where Tom Harris is 24 years old and he wishes to purchase a $7,000 value 10-year term insurance, his annual premium will be:  $290.5.

Gross premiums written in the insurance sector are the sum of direct and assumed premiums written before subtracting ceded reinsurance. Direct premiums written are the premiums on all policies issued by the company's insurance subsidiaries throughout the fiscal year.

To compute Tom's insurance premium we must use the information given as well as the table above:

Given:

Tom's Age = 24 years

Value of Insurance Cover Requested = $7,000

Type of Insurance cover requested = 10-Year Term

The rate for the Type of Insurance Cover requested: Since he 24 and wants a 10-year term, the rate applicable from the table is; 4.15%

Thus, his annual premium  = 7000 * 4.15%
= 29050/ 100
= $290.5

Thus, Tom Harris' annual insurance premium is: $290.5

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Answer:

9.818 years after 2008

Step-by-step explanation:

Y_A = 0.35 * X + 9.6

Y_B = 0.9 * X + 6.5

Equal in year X = (Y_B - Y_A) / (0.35 - 0.9) = (6.5 - 9.6) / (-0.55) = 9.818 years after 2008

X = 9.818 + 2008 = 2018.818

Y_A = 0.35 * (2018 - 2008) + 9.6 = 14.3 billion

Y_B = 0.9 * (2018 - 2008) + 6.5 = 15.3 billion

X2 + 7x + 10 = 0 has roots -5 and -2, the answer.

x2 + 7x + 10 = 0 is a mathematical equation.

x2 + 5x + 2x + 10 = 0 [dividing the middle term] is another way to express the aforementioned equation.

After factoring 2 from the second term of the expression, 2x + 10, and x from the first term of the expression, (x2 + 5x), the expression may be broken down into its constituent parts.

We obtain the factorized equation as follows: x (x + 5) + 2 (x + 5) = 0.

Now we can calculate (x + 2) (x + 5) = 0 by utilizing the distributive property.

The result of separately equating both terms with 0 is,

The equation x2 + 7x + 10 = 0 has -5 and -2 as its roots.

The Complete Question is :

How to Find the roots of the equation x2 + 7x + 10 = 0?

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Answer:

12.10 pm

Step-by-step explanation:

just take the 45 minutes she uses to bake and add to the time she starts

11.25 a.m+45

12.10 pm

The measure of angle 4 is 90 degrees

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

The rectangle

Also, we have

<5 = 12x -3

<6 = 10x + 9

Angles 5 and 6 add up to 90

So, we have

12x - 3 + 10x + 9 = 90

Evaluate the like terms

22x = 84

So, we have

x = 3.82

The angles in a triangle add up to 180

So, we have

<4 + 12 * 3.82 - 3 + 10 * 3.82 + 9 = 180

Evaluate

<4 = 90

Hence, the measure o this angle is 90 degrees

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The amount of compound remaining from a 84-ounce sample after seven weeks is 4.32 ounces.

Given a half-life of 5 days and a sample of 84 ounces, the exponential decay function can be represented as:

A(t) = 84 * (1/2)^(t/5)

Where A(t) represents the amount of the compound remaining after t days.

To find the amount of compound remaining after 7 weeks

7 weeks * 7 days/week = 49 days,

we can substitute t = 49 into the function:

A(49) = 84 * (1/2)^(49/5)

A(49) = 84 * (1/2)^9.8

A(49) ≈ 4.32 ounces

So, the amount of the compound remaining after 7 weeks would be approximately 4.32 ounces.

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Answer: Undifined!

Step-by-step explanation: Division by zero is considered an invalid operation in mathematics because there is no number that can be multiplied by zero to produce the original number. In other words, there is no single valid answer to dividing by zero. Example: You have 0 cookies and you want to share them among 9 friends. There's no way to share, since you don't have cookies haha!

Answer:

Step-by-step explanation:

An expression without a value is referred to as being undefined; it has an indeterminant form. When a number is divided by zero, it usually has no specified meaning. Mathematically, we can't divide by zero because the result is an equation we can't compute.

Step-by-step explanation:

this you solve via the determinant of the matrix.

for a matrix A

a b

c d

the determinant (A) = ad - bc

so, we have here

x² - 5×-4 = 24

x² + 20 = 24

x² = 4

x = ±2

so, as a simple quadratic equation, there are 2 solutions for x.

The correct inequality that represent the dogs could he have walked on Saturday is,

⇒ 100 + 12.50x > 210

A relation by which we can compare two or more mathematical expression is called an inequality.

We have to given that;

On Saturday, Dylan earned $100 for cleaning a local business.

And, He also walked dogs to earn money, charging $12.50 for each dog he walked.

Now, Let number of dogs = x

Then, We get;

The correct inequality that represent the dogs could he have walked on Saturday is,

⇒ 100 + 12.50x > 210

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22% of the population more than 25 years of age have bachelors degree.

percentage, a relative value indicating hundredth parts of any quantity.

Given that the total population is 298957

66722 cincinnati residents over the age of 25 have the bachelors degree.

We have to find the percent of the population more than 25 years of age have bachelors degree.

x/100×298657=66722

2986.6x=66722

Divide both sides by 2986.6

x=22.340

Hence, 22% of the population more than 25 years of age have bachelors degree.

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Answer:1/6 can be represented as a fraction of a whole unit, where the whole unit is divided into 6 equal parts. Each of these parts represents 1/6 of the whole.

1/2, on the other hand, represents half of the whole unit, so it is twice as much as 1/6.

To visualize this, you can think of a ruler divided into 6 equal parts. 1/6 would represent 1 mark on the ruler, while 1/2 would represent 3 marks. To have the same length as 1/2, you need to add up 3 marks, or 3 copies of 1/6.

You can also think of this as converting 1/6 to a common denominator, which in this case is 6. 3 copies of 1/6 is equal to 3/6 or 1/2.

Step-by-step explanation:

1/6 can be represented as a fraction of a whole unit, where the whole unit is divided into 6 equal parts. Each of these parts represents 1/6 of the whole.

1/2, on the other hand, represents half of the whole unit, so it is twice as much as 1/6.

To visualize this, you can think of a ruler divided into 6 equal parts. 1/6 would represent 1 mark on the ruler, while 1/2 would represent 3 marks. To have the same length as 1/2, you need to add up 3 marks, or 3 copies of 1/6.

You can also think of this as converting 1/6 to a common denominator, which in this case is 6. 3 copies of 1/6 is equal to 3/6 or 1/2.