A certain field is a rectangle with a perimeter of 870 feet. The length is 191 feet more than the width. Find the width and length of the rectangular field

Answer:

320

80

Step-by-step explanation:

Answer:

[see below]

Step-by-step explanation:

The domain are all the x-values of the relation or function, while the range are all the y-values of the relation.

The x-values of the relation are -6 and 7.

The y-values of the relation are -1, 2, and 9.

Therefore:

Domain: {-6, 7}

Range: {-1, 2, 9}

Hope this helps you.

The group of people who should make up a sample that will best answer her question is the 9th graders in her school. The correct option is C.

Subjects are the different sets of information which is studied.

9th graders in her school will be perfect because the question is specifically asking about the opinions of 9th-grade students in the high school, so it makes sense to sample this group directly.

The other options may provide some insights, but they may not be as accurate or representative of the opinions of the 9th-grade students in the school.

Thus, the correct option is C, 9th graders in her school.

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Answer:

4 1/2

Step-by-step explanation:

6--------1/2

   /\

 4 1/2

Answer:

  x = 31.2

Step-by-step explanation:

You want the solution to the proportion 12/x = 5/13.

You can eliminate the fractions by multiplying this equation by the least common denominator. That value is 13x, the product of these denominators. Multiplying by 13x, we have ...

  \(\dfrac{12}{x}\times13x=\dfrac{5}{13}\times13x\\\\\\12\cdot13=5\cdot x\qquad\text{simplified}\)

Now, the value of x is found by dividing both sides by its coefficient.

  \(\dfrac{12\cdot13}{5}=\dfrac{5x}{5}\\\\\\\dfrac{156}{5}=x\\\\\boxed{31.2=x}\)

__

Additional comment

The first step we did, multiplying by 13x, is also sometimes called "cross multiplication." The result of that step is that each numerator is multiplied by the opposite denominator.

Multiplying both sides of the equation by the same value (13x) is supported by the multiplication property of equality. The term "cross multiplication" is descriptive of the result, but is not a recognized property of equality. It is a good idea to keep the math operations you do grounded in the properties of equality.

You will notice that the steps we did were "multiply by 13x" and "divide by 5". These can be done at once by "multiply by 13x/5". Of course, that operation is done to both sides of the equation.

Any proportion can be written 4 ways:

  \(\dfrac{12}{x}=\dfrac{5}{13}\qquad\dfrac{x}{12}=\dfrac{13}{5}\qquad\dfrac{x}{13}=\dfrac{12}{5}\qquad\dfrac{13}{x}=\dfrac{5}{12}\)

These can be thought of as "upside down" and "sideways." We like the versions with the variable on top of a fraction, because the solution to that is simply multiplication by the variable's denominator.

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The nth term of 11,13,15,17 is,

⇒ T (n) = 9 + 2n

Given that;

The sequence is,

11, 13, 15, 17, ....

Here, Common difference is,

13 - 11 = 2

15 - 13 = 2

Hence, Sequence is in Arithmetic sequence.

So, the nth term of 11,13,15,17 is,

⇒ T (n) = a + (n - 1)d

⇒ T (n) = 11 + (n - 1) 2

⇒ T (n) = 11 + 2n - 2

⇒ T (n) = 9 + 2n

Thus, The nth term of 11,13,15,17 is,

⇒ T (n) = 9 + 2n

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By performing subtraction we know that the farmer sold 4.2 kilograms of apples in the market.

One of the four operations used in mathematics, along with addition, multiplication, and division, is subtraction.

Removal of items from a collection is represented by the operation of subtraction.

For instance, in the following image, there are 5 2 peaches, which means that 5 peaches have had 2 removed, leaving a total of 3 peaches.

Subtraction in mathematics is the process of subtracting one integer from another. In other words, the result of subtracting two from five is three. After addition, subtraction is usually the second operation you learn in math class.

So, to find the weight of apples, perform subtraction as follows:

= 6.7 - 2.5

= 4.2 kilograms

Therefore, by performing subtraction we know that the farmer sold 4.2 kilograms of apples in the market.

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The standard form of the equation of the parabola is  \(y=-(\frac{x^2-12x+36}{24})\)

The general form of a parabola is  (x-h)=4p(y-k)

Where, (h,k) is vertex, (h,k+p) is the focus, and y=k-p is directrix.

The focus of the parabola is (6,6).

comparing the values with (h,k+p)=(6,6)

h=6

k+p=-6.... (1)

Directrix of the parabola is

k-p=-6.... (2)

On adding (1) and (2) we get

2k=0

k=0

Put this value in equation (1).

0+p=-6

The value of p= -6.

Substituent h=6,k=0, and p=-6 in the general form of a parabola, we get

(x-h)^2=4p(y-k)

(x-6)^2=4(-6)(y-0)

x^2-12x+36=-24y

Divide both sides by 24.

y=(x^2-12x+36/24)

Therefore the standard form of the equation of the parabola is

y=-(x^2-12x+36/24)

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Answer:

x = 31.3

Step-by-step explanation:

100° and (3x + 6)° are vertical angles. Vertical angles are congruent.

To find the value of x, set both equal to each other.

3x + 6 = 100

3x = 100 - 6 (subtraction property of equality)

3x = 94

x = 94/3 (division property of equality)

x = 31.3 (nearest tenth)

Answer:

Whats the question

Step-by-step explanation:

From the information given, we have that:

1. The null hypothesis is: \(H_0: \mu = 85\)

2. The t-statistic is t = 3.78.

Item 1:

We want to test if there is a significant difference from the population mean of 85, thus, at the null hypothesis, it is tested if the population mean is of 85, that is:

\(H_0: \mu = 85\)

Item 2:

The t-statistic is given by:

\(t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}\)

In which:

For this problem, we have that: \(X = 90, \mu = 85, s = 7, n = 28\). Then:

\(t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}\)

\(t = \frac{90 - 85}{\frac{7}{\sqrt{28}}}\)

\(t = 3.78\)

The t-statistic is t = 3.78.

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If we restrict the domain of the function to the portion of the graph with a positive slope, the domain of the inverse function will be the range of the original function for values of x greater than 4, and its range will be all real numbers greater than or equal to 4.

The given function f(x) = |x – 4| + 6 is a piecewise function that contains an absolute value. The absolute value function has a V-shaped graph, and the slope of the graph changes at the point where the absolute value function changes sign. In this case, that point is x=4.

If we restrict the domain of f(x) to the portion of the graph with a positive slope, we are essentially considering the piece of the graph to the right of x=4. This means that x is greater than 4, or x>4.

The domain of the inverse function, f⁻¹(x), will be the range of the original function f(x) for values of x greater than 4. This is because the inverse function reflects the original function over the line y=x. So, if we restrict the domain of f(x) to values greater than 4, the reflected section of the graph will be the range of f⁻¹(x).

The range of f(x) is all real numbers greater than or equal to 6 because the absolute value function always produces a positive or zero value and when x is greater than or equal to 4, we add 6 to that value. The range of f⁻¹(x) will be all real numbers greater than or equal to 4, as this is the domain of the reflected section of the graph.

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Answer:

they are really different

Answer:

y = 2x-3

Step-by-step explanation:

y – 1 = 2(x – 2)

Distribute

y-1 =2x-4

Add 1 to each side

y-1+1 = 2x-4+1

y = 2x-3

Answer:

25/4 quarts of cranberry juice

40/3 quarts of apple juice

25/8 quarts of lemonade

Step-by-step explanation:

just multiply everything by 5

:)

The formula for calculating the volume of a cone is expressed as

Volume = 1/3πr^h

where

r is the radius of the cone

h is the height of the cone

From the information given,

diameter = 6

r = diameter/2 = 6/2 = 3

h = 8

π = 3.14

Thus,

Volume = 1/3 x 3.14 x 3^2 x 8

Volume = 75.36 ft^3

The value of given expressions is -4\(x^{-2}\) + 3\(y^{0}\) = 19 and 2\(x^{0}\)\(y^{-2}\) = 0.08

Simplifying an equation is simply another way of saying solving a math problem. When you simplify a phrase, you are attempting to write it in the simplest way feasible. In conclusion, there should be no more adding, subtracting, multiplying, or dividing to do.

Given expression 1. -4\(x^{-2}\) + 3\(y^{0}\)  2. 2\(x^{0}\)\(y^{-2}\)

Expression for x =2 and y=5

-4x-2 + 3y0

= -4(2)-2 + 3(5)0

= 16+3

=19

Now

2x0y-2

= 2(2)0x(5)-2

= 2 x (1/25)

= 2 x 0.04

= 0.08

Therefore the value of given expressions is -4\(x^{-2}\) + 3\(y^{0}\) = 19 and 2\(x^{0}\)\(y^{-2}\) = 0.08

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If wheel on a scooter completes 124 revolutions and travels 22.4 meters then  diameter of the wheel is 57 mm

Each revolution of the wheel covers a distance equal to the circumference of the wheel.

The diameter of the wheel "d".

The distance covered in 124 revolutions is:

distance = 124 x circumference

= 124 x pi x d

= 124 x 3.14 x d

We know that this distance is equal to 22.4 meters, so we can set up an equation:

124 x 3.14 x d = 22.4

Simplifying and solving for d:

d = 22.4 / (124 x 3.14)

d = 0.057 meters

As we know that 1 meter is equal to thousand millimeters so multiply by 1000 to get in millimeters

d = 57 millimeters

Therefore, the diameter of the wheel is approximately 57 mm.

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Given the following expression shown in the exercise:

You can identify that it has four terms.

In order to simplify it you need to remember the definition of "Like terms". By definition, Like terms are those terms that have the same veriables and the same exponents.

Therefore, you can simplify the expression given in the exercise by adding the like terms. Then, you get:

The answer is:

Answer:

1000 tiles

Step-by-step explanation:

Determine total floor space
800 x 10 = 8000 squared cm total floor space.
Divide floor space by size of tile
8000 / 8 = 1000 tiles now required to cover the floor.

The statement of the theorem can be written in if-then form. The correct option is D.

A two-column geometric proof is made up of a list of statements and the reasons why we know they are true. The statements are listed in the left column, and the reasons for making them are listed in the right column.

In a two-column proof, the theorem is written as an "if-then" statement, where the "if" part is the given information or hypothesis, and the "then" part is the conclusion or the statement to be proven.

The theorem serves as the ultimate goal of the proof and guides the logical sequence of statements and reasons in the two-column format.

The correct option is D. That is written in if-then form.

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Answer:

-4m+10

Step-by-step explanation:

Answer:

-4m+10

explanation:

6m-10=-4m

+10

-4m+10

Step-by-step explanation:

Number one, 743

× 63

2229

Number four is 2.5/3 (don't trust me too much with this one)

number five, multiply 8.5 by 3 and you'll get 25.5

Answer:

28,125

Step-by-step explanation:

There are 10 digits between 0 and 9.  5 of them are odd, and 5 of them are even.

If a six-digit number has all odd digits, then there are 5 numbers that can be the first digit, 5 numbers that can be the second digit, 5 numbers that can be the third digit, and so on.

The number of permutations is 5×5×5×5×5×5 = 5⁶ = 15,625.

For all even digit numbers, the first digit can't be 0, so the number of permutations is 4×5×5×5×5×5 = 4×5⁵ = 12,500.

So the total permutations of six-digit numbers of equal parity is 15,625 + 12,500 = 28,125.

Answer:

The expense of the visit to dental specialist is equivalent to (50+100n)

Step-by-step explanation:

Answer:

(50+100n)

Step-by-step explanation:

khan

Step-by-step explanation:

sin Φ  = 5/6 = .8333

Arcsin ( sin Φ) =  arcsin (.8333)

Φ = 56.4 degrees

Domain - the set of possible x-coordinates of a function.

Range - the set of possible y-coordinates of a function.

Domain is:

Range is:

This is not a function as it fails the vertical line test.

Domain is:

Range is:

This is not a function as it fails the vertical line test.

Answer:

30.a)  Domain:  [-6, 6]

30.b)  Range:  [-3, 7]

30.c)  Function:  No

31.a)  Domain:  [-2, 2]

31.b)  Range:  [-6, 6]

31.c)  Function:  No

Step-by-step explanation:

Definitions

Interval notation

The domain is the set of all possible input values (x-values).

The range is the set of all possible output values (y-values).

The graph is a conic section (ellipse) and therefore it is not a function.

The smallest x-value is x = -6 and the greatest x-value is x = 6.

The smallest y-value is y = -3 and the greatest y-value is y = 7.

Therefore, the domain and range in interval notation are:

The graph is a not a function as almost all the inputs (x-values) are related to more than one output (y-value).

From inspection of the graph, the endpoints of the continuous line are:

Both endpoints are closed circles, so the values are included in the domain and range.

The smallest x-value is x = -2 and the greatest x-value is x = 2.  

Therefore, the domain in interval notation is:

The smallest y-value is y = -6 and the greatest y-value is y = 6.  

Therefore, the range in interval notation is:

The graph is a not a function as not all inputs (x-values) are related to one output (y-value).

Answer:

Distance between points = 8.6

Step-by-step explanation:

Formula :

Distance between two points = √(xB−xA)2+(yB−yA)2(xB-xA)2+(yB-yA)2

Solution :

Distance between two points = √(−2−−9)2+(−6−−1)2(-2--9)2+(-6--1)2

= √72+(−5)272+(-5)2

= √49+2549+25

= √7474 = 8.6023

Distance between points (-9, -1) and (-2, -6) is 8.6023

We know that:

h(x) = 2x - 1

g(x) = 3x + 1

We are trying to find h(x) / g(x)

(h/g) (x) = (2x - 1) / (3x + 1)

This is simplest form.