The table shows the linear relationship between x, the altitude in feet, and y, the boiling point of water in degrees Fahrenheit.


What are the slope and y-intercept of the line that models this situation? I

Answer:

[tex]t=75[/tex]

Step-by-step explanation:

Given

[tex]\frac{1}{5} t+2-2=17-2[/tex]

Lets solve for [tex]t[/tex].

Subtract 2 from 2.

[tex]\frac{1}{5} t=17-2[/tex]

Subtract 2 from 17.

[tex]\frac{1}{5} t=15[/tex]

Combine [tex]\frac{1}{5}[/tex] and [tex]t[/tex].

[tex]\frac{t}{5} =15[/tex]

Multiply both sides of the equation by 5.

[tex]\frac{t}{5}*5 =15*5[/tex]

[tex]t=75[/tex]

Answer: x= -2, -3

Step-by-step explanation: Move all terms to the left side and set equal to zero. Then set each factor equal to zero.

In most cases, the inverse of a linear function is also a linear function.

The term "linear function" in mathematics applies to two different but related ideas: A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.

A function with the formula f(x) = ax + b, where a and b are real values, is referred to as a linear function.

Here, stands for the line's gradient and b for the y-axis intercept (which is sometimes called the vertical intercept).

These functions' graphs are mirror images of one another when viewed along the line y=x.

As a result, the points on the graph of f(x) are the points on the graph of f(x) that have been turned around.

A linear function's inverse is typically also a linear function.

Therefore, in most cases, the inverse of a linear function is also a linear function.

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Answer:

Slope: -1; y-intercept: -5

Step-by-step explanation:

Given:

2x + 2y = -10

Question:

What is the slope and y intercept?​

Work:

The "template" for the slope of a line is: y = mx + b. "m" is the slope, "x" is a variable, and "y" is the y-intercept.

Hope this helped! :D

When f(x) = x - 5 and g(x) = 2x + 3, the value of f(g(1)) is 0 and the value of g(f (2)) is -2.

Mathematics encompasses the study of numbers, formulas and related structures, shapes and the spaces in which they exist, quantities and their variations, and spaces in which they exist. A function is an association between a set of inputs, each of which has an output. Simply described, a function is a relationship between inputs and outputs, where each input results in a single, distinct output. Each function has a domain and a codomain, often known as a scope. Typically, the letter f is used to denote functions (x). is the input. There are four different categories of functions. one-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions

given

a) f(g(1)  

g(1) = 5  and f(g(1)) = 0

b) g(f (2))

f(2) = -3

g(f (2)) = -2

so When f(x) = x - 5 and g(x) = 2x + 3, the value of f(g(1)) is 0 and the value of g(f (2)) is -2.

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A unit for each quantity in the worksheet for the mat width are 5.357 inches.

The size of a rectangle. A = l × b. Once the length and width are known for any rectangle, the area may be determined. The area of the rectangle is calculated as a square-unit dimension by multiplying length and width.

Add the height and the width together to get the area of a rectangle. Given that each side of a square is the same length, all you need to do to determine its area is multiply the length of one of its sides by itself.

Length = 7 inches  

Width = 6 inches

Area of photograph = length  width = 7  6 = 42

Total area of photograph and frame = 84

frame length ( 7 + 2x)

frame width ( 6 + 2x)

Total area = Total area of photograph and frame

( 7 + 2x)  ( 6 + 2x) = 84

2 + 13x - 21 = 0

x = 5. 357

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Answer:

30

Step-by-step explanation:

perimeter is the outside of a shape so just add them all together honestly

The sample space between A to C is A,B,C

The likelihood that a sample point will occur is quantified by its probability.

The likelihood of a sample point

According to tradition, statisticians have adopted the following guidelines.

Any sample point's probability can be between 0 and 1.

The probability of every sample point in a sample space added together is 1.

Let's say we run a straightforward statistical experiment. One coin is flipped. Heads or tails are the possible results of the coin flip. These results taken as a whole serve as our experiment's sample space. Each result stands in for a single sample point in the sample space. What is each sample point's probability?

Solution: the total of all sample points' probability

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The Rs. 10,000 Regan lent to Sandip and Saline and the Rs.2160 more interest Saline paid than Sandip after 3 years at an 18% simple interest rate, indicates by expressing the amounts using equations, that the amount Regan gives to Sandip and Saline is Rs. 3,000 and Rs. 7,000 respectively.

An equation is the presentation of a statement of the equivalence between quantities, or expressions, by joining the expressions with a '=' sign.

The amount Regan has = Rs. 10,000

Let x represent the amount Regan lent to Sandip, we get;

The amount Regan lent to Saline = 10,000 - x

The interest rate of the loan Regan lent to Sandip and Saline = 18% simple interest

The interest Saline paid to Regan after 3 years, using simple interest = Rs. 2160 + The interest Saline paid to Regan

The simple interest formula is; I = P·R·T/100

Where;

P = The principal amount loaned

R = The interest rate = 18%

T = The time or duration of the loan = 3 years

Therefore;

(10000- x) × 18/100 × 3 = 2160 + x × 18/100 × 3

5400 - 0.54·x = 2160 + 0.54·x

5400 - 2160 = 0.54·x + 0.54·x = 1.08·x

3240 = 1.08·x

x = 3240 ÷ 1.08 = 3000

The amount Regan lent to Sandip, x = Rs. 3000

The amount Regan lent to Saline = 10,000 - x

x = 3000

10,000 - x = 10,000 - 3000 = 7,000 (substitution property)

The amount Regan lent to Saline = Rs. 7,000

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Let's say we have an expression P^A then the negation of  P^A  will be not(  P^A  ). This is an example of negation.

As the name suggests negation means the negative of a term or expression and it comes under the branch of mathematical logical reasoning.

When not word is added in front of an expression it becomes the opposite , this is how we negate something. A statement is only admissible if it is always true or always false.

It is sometimes required in mathematics to find the inverse of a particular mathematical statement, this is when negation is used. Negation thus, refers to the process of determining the inverse of a given assertion.

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Answer: 32x

Step-by-step explanation:

4x (3 + 5)

add 3 and

⇒ 4x (8)

⇒ 32x answer .

hope that helps...

The time taken for 21,000 spectators to vacate the stadium, if only 15 exits are functional is 28 minutes

A variation is a relation between a set of values of one variable and a set of values of other variables

Let E, N and T represent the number of exits, the number of spectators and the time taken to exit the stadium respectively

We can write the variation as:

T α N/E

T = kN/E  (where k is constant of proportionality)

when N = 25,000, E = 25, T = 20:

T = kN/E

k = TE/N

k = (20×25)/25000 = 0.02

when N = 21,000 and E = 15:

T = kN/E

T = (0.02×21,000)/15 = 28 minutes

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Angles are classified into three. They are acute angles, obtuse angle and right angle.

Therefore the three names of angles are - acute angles, obtuse angle and right angle.

Acute angles are angles that measure less than 90 degrees. They are smaller than a right angle and are often described as "sharp."

Right angles are angles that measure exactly 90 degrees. They are often represented by a square corner or the letter "L" shape.

Obtuse angles are angles that measure greater than 90 degrees but less than 180 degrees. They are larger than a right angle and are often described as "blunt."

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The whole section is 9/4 unit.

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:

Mr.Parrillo’s class has adopted a section of a highway to keep clean.

1/3 of the section is 3/4.

To find the length of the whole section:

Multiply by 3.

So,

The length of the whole section = 3 (3/4)

The length of the whole section = 9/4

Therefore, 9/4 unit is the length.

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Answer:

17.85

Step-by-step explanation:

175% * 10.20 = 17.85

On solving the provided question, we can say that since it it is right angled triangle so the relation that be formed is  [tex]m^2 = p^2 + z^2[/tex]

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

since it it is right angled triangle

so the relation that be formed is

[tex]m^2 = p^2 + z^2[/tex]

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Answer:

Yes, the zeros can be used as place holders. When using place holders, the value does not change.

When two inner angles are stated as 61° and 52° in the sixth figure, x and y are both set to 67°.

A circle is created in the plane by each point that is a specific distance from another point (center). Thus, it is a curve made up of points that are separated from one another by a defined distance in the plane. Additionally, it is rotationally symmetric about the center at every angle. Every pair of points in a circle's closed, two-dimensional plane are evenly spaced apart from the "center." A circular symmetry line is made by drawing a line through the circle. Additionally, it is rotationally symmetric about the center at every angle.

given

in 6th figure

61° + 52° + x = 180° ( sum of exterior angle )

113° + x = 180°

x = 67°

y = 67°

When two inner angles are stated as 61° and 52° in the sixth figure, x and y are both set to 67°.

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The value of volume of pyramids is 448 cubic meter.

A triangular pyramid's volume can be calculated using the formula Volume= 1/3 Base area Height. The side, height, and slant height of a triangular pyramid are the three parameters needed to calculate its surface area.

The basic formula for volume is length, breadth, and height, as opposed to length, width, and height for the area of a rectangular shape. The calculation is unaffected by how you refer to the various dimensions; for instance, you can use "depth" instead of "height."

Given,

Length=12m

Width=7m

height=16m

volume =l * w * h / 3

= 12*7*16/3

= 448 cubic meter

Therefore volume of pyramid is 448 cubic meter .

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The length of the sides of ΔABC are; AB = 2√5, BC = √13, and AC = √17

The length of the sides of ΔDEF are; DE = 2√5, EF = √13, and DF = √17

By the SSS Congruence Theorem, ΔABC ≅ ΔDEF

We are given the coordinates of Triangles ABC and DEF as;

A(5, 3), B(7, 7), C(9, 4)

D(-8, 6), E(-12, 8), F(-9, 10)

The formula for distance between two coordinates is;

Distance = √[(y₂ - y₁)² + (x₂ - x₁)²]

Thus;

AB = √[(7 - 3)² + (7 - 5)²]

AB = √20

AB = 2√5

Similarly;

BC = √[(4 - 7)² + (9 - 7)²]

BC = √13

AC = √[(4 - 3)² + (9 - 5)²]

AC = √17

Likewise;

DE = √[(8 - 6)² + (-12 + 8)²]

DE = √20

DE = 2√5

Similarly;

EF = √[(10 - 8)² + (-9 + 12)²]

EF = √13

DF = √[(10 - 6)² + (-9 + 8)²]

DF = √17

Since the corresponding sides of the two triangles are equal and as such they can be said to congruent by SSS Congruency.

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Answer: Triangle ABC is a right triangle, because it satisfies the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

c^2 = a^2 + b^2

25^2 = 17^2 + 21^2

625 = 289 + 441

625 = 730

Since it is a right triangle, angle A is the angle opposite side a, which is the side that is the length of 17.

A right triangle also has one angle which is always 90 degree, that is the angle opposite the hypotenuse, so the remaining angle is A, which is 90- angle C, which is

90 - 42.3 = 47.7 degree.

Therefore the measure of angle A is 47.7°

So the correct answer is C. 42.3°

Step-by-step explanation:

To find the difference between (-7*-7) + -(7*7), we first need to calculate the values of each expression.

(-7*-7) = 77 = 49

-(77) = -49

The difference between these two values is 49 - (-49) = 49 + 49 = 98.

Therefore, the answer is A) 98.

The Correct answer is Option (A) = 98.

We need to determine the value of each part and calculate their difference. after that.

Here,    (-7*-7)= 49

and,     -(7*7) = -49

Now, their difference is to be calculated as follows:

          =49 - (-49)

          = 49+ 49

          = 98.

So, the answer is 98.

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Answer:

7/2

Step-by-step explanation:

7x – 2y = 10

using ( y = mx + b) as our guideline

where m is the slope

7x – 2y = 10

subtract 7x from both sides

7x – 7x – 2y = 10 – 7x

–2y = 10x – 7x

when arranged in slope form

–2y = –7x + 10

divide both sides by (–2) to get y

[tex] \frac{ \\ - 2y}{ - 2} = \frac{ - 7x}{ - 2} + \frac{10}{ - 2} [/tex]

[tex]y = \frac{ \\ 7y}{2} - 5[/tex]

[tex]the \: slope \: will \: be \: \frac{ \\ 7}{2} [/tex]

This is our answer.

i hope i

x = 6 does not satisfy the given equation.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that an equation, 5(x – 3) = x + 13

Checking if x = 6 satisfy the equation or not,

5(x – 3) ? x + 13

5(6-3) ? 6+13

5×3 ? 19

15 ≠ 19

Hence, x = 6 does not satisfy the equation.

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Step-by-step explanation:

.....................

Answer:

Game 1

Equal chance

Game 2

Step-by-step explanation:

A BETTER CHANCE OF WINNING

Each of the problems below describes two different games you can play with a random number generator. In each case, you will win if the random number generator gives you the indicated kind of number. Find the theoretical probability that you win each game below. Decide and justify whether Game I or Game II in each part, (a) through (c), gives you a better chance of winning.

Game I

a.Picking a prime number from the integers between 1 and  20

b.Picking a multiple of 5 from the integers between 1 and  20

c.Picking a multiple of 7 from the integers between 1 and 40  

Hint:

Find the percent chance that each event will occur and compare the results.

a.Picking a prime number from the integers between 21 and  40

b.Picking a multiple of 5 from the integers between 1 and  40

c.Picking a multiple of 6 from the integers between 1 and  25

Answer:

Game 1

Equal chance

game 2