Data on the fuel consumption y of a car at various speeds x is given. Fuel consumption is measured in mpg, and speed is measured in miles per hour. Software tells us that the equation of the least‑squares regression line is ^ y = 55. 3286 − 0. 02286 x

Elimination is a method of solving a system of equations using addition or subtraction to eliminate one of the variables.

Here we will use the elimination method to solve a system of three equations with three variables.

Let's say we have three equations with three variables x, y and z.

Equation 1:  ax + by + cz = d

Equation 2:  ex + fy + gz = h

Equation 3:  ix + jy + kz = l

We will start by multiplying the first equation by a number that will make the coefficients of y in the two equations the same.

Let's say we choose to multiply the first equation by -f, so that we get:

-fax -fby -fcz = -fd

Now we add the two equations to eliminate y:

ax + by + cz + (-fax -fby -fcz) = d -fd

ax -fax + by -fby + cz -fcz = d -fd

(a -f)x + (b -f)y + (c -f)z = d -fd

Now we can multiply the second equation by a number that will make the coefficients of z in the two equations the same. Let's say we choose to multiply the second equation by -k, so that we get:

-kex -kfy -kgz = -kh

Now we add the two equations to eliminate z:

(a -f)x + (b -f)y + (c -f)z + (-kex -kfy -kgz) = d -fd -kh

(a -f)x + (b -f)y + (c -f)z -kex -kfy -kgz = d -fd -kh

(a -f -k)x + (b -f -k)y = d -fd -kh

We can now solve this equation for x:

x = (d -fd -kh - (b -f -k)y) / (a -f -k)

Now we can substitute this expression for x in any of the original equations and solve for y:

Let's choose to substitute in the first equation:

ax + by + cz = d

(d -fd -kh - (b -f -k)y) / (a -f -k) + by + cz = d

y = (d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k) -cz) / (b -f -k)

Now we can substitute this expression for y in any of the original equations and solve for z:

Let's choose to substitute in the second equation:

ex + fy + gz = h

e(d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k)) + f(d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k)) + gz = h

gz = h -e(d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k)) -f(d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k))

z = (h -e(d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k)) -f(d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k))) / g

Now we have

x = (d -fd -kh - (b -f -k)y) / (a -f -k)

y = (d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k) -cz) / (b -f -k)

z = (h -e(d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k)) -f(d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k))) / g

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Answer:

180-25-60=95

Step-by-step explanation:

To solve 3 composite functions, you would need to break each function down into its individual components. Then, you would need to combine each component one at a time, starting with the outermost function and working your way inwards.

1. Break each function down into its individual components. This may involve splitting them into simpler functions such as polynomials, exponentials, trigonometric functions, and so on.

2. Start with the outermost function and combine each component one at a time. Make sure to apply the order of operations to each step in order to get the correct result.

3. Evaluate the combined function. This means solving for the output of the function, which may involve plugging in values for certain variables.

4. Repeat the same process for the other two functions.

5. When you have evaluated all three functions, you can combine the results of each to get the answer to the composite functions.

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Equivalence Relation is a type of Relation that satisfies the property of Reflexive , Symmetric and Transitive , and an example of such relation is [tex][(1, 1), (1, 3), (2, 2), (2, 4), (3, 1), (3, 3), (4, 2), (4, 4)][/tex] .

What is an Equivalence Relation ?

A relation R on a set A is can be called as an equivalence relation if and only if the relation is reflexive, symmetric and transitive.

It is a relationship on the set which is represented by symbol “∼”.

(i) Reflexive: A relation is termed as reflexive, if [tex](a, a) \in R[/tex], for every [tex]a \in A[/tex].

(ii) Symmetric: A relation is termed as symmetric, if [tex](a, b) \in R[/tex] , then [tex](b, a) \in R[/tex] .

(iii) Transitive: A relation is termed as transitive if [tex](a, b) \in R[/tex] and [tex](b, c) \in R[/tex], then [tex](a, c) \in R[/tex] .

An Example of Equivalence Relation is [tex][(1, 1), (1, 3), (2, 2), (2, 4), (3, 1), (3, 3), (4, 2), (4, 4)][/tex] because ;

(i) [tex][ (1, 1),(2, 2), (3, 3), (4, 4) ] \in R[/tex] , So , R is Reflexive .

(ii) [tex](2,4) \in R[/tex] and [tex](4,2)\in R[/tex] , Thus ,  relation given by R is Symmetric .

(iii) [tex](3,1) \in R[/tex] and [tex](1,3) \in R[/tex] ⇒ [tex](3,3) \in R[/tex] , So R is Transitive .

Therefore , the Relation given by R is Equivalence Relation .

The given question is incomplete , the complete question is

What is Equivalence Relation and its Example ?

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Answer:

4x-24

Step-by-step explanation:

assume x=Length

perimeter

= x+(x-12)+x+(x-12)

= x+x -12+x+x-12

=4x-24

It’s angle 1 and angle 8

The pair of angles that are formed on the other side of the pearl lines, but on the opposite side of the transversal

goodluck

Answer:

the answer is (a) x² - 2hx + h²

Step-by-step explanation:

(x-h)² = (x-h)(x-h) = x(x-h)-h(x-h)

x² - hx -hx + h²

= x² - 2hx + h²

Answer:

-----------------------------

Use the identity:

Substitute a = x, b = h to get:

This is the option A.

Answer:

x = 2 and x = 5

Step-by-step explanation:

assuming you require to solve for x

the sum of the 3 angles in a triangle is 180°

the third angle in both diagrams is right , that is 90° as they are the angle in a semicircle.

sum the 3 angles and equate to 180

6

90 + 16x + 40 + 11x - 4 = 180

27x + 126 = 180 ( subtract 126 from both sides )

27x = 54 ( divide both sides by 27 )

x = 2

10

90 + 6x + 18 + 3x + 27 = 180

9x + 135 = 180 ( subtract 135 from both sides )

9x = 45 ( divide both sides by 9 )

x = 5

Therefore ,In other words  the solution of the given problem of fraction is even though 21 can be divided by 3, it cannot be divided by 6. (for an integer anyway)

A fractional or ratio element is a portion of the whole. The numerator a denotes the number of parts that are included, and the denominator b denotes the number of pieces of equal size into which the whole has been divided. The least common multiple (LCD) of two fraction denominators is called the LCM of those denominators.

Here,

21/3 = 7    21/6 = 3.5

18/3 = 6   18/6 = 3

24/3 = 8   24/6 = 4

12/3 = 4     12/6 = 2

Each can be split to get an integer, with the exception of:

21/6 = 3.5

Therefore ,In other words, even though 21 can be divided by 3, it cannot be divided by 6. (for an integer anyway).

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Answer: (4+2)•(3^2?

Step-by-step explanation: I hope that helps I don't know how to explain but ya. But that's where u put the parentheses.

Answer:

(4+2×3)^(2)

Step-by-step explanation:

First, because parenthesis are being used, we will start by multiplying 2 by 3, giving us 6

(4+6)^(2)

Then, we add 6 to 4

(10)^2

and we then raise 10 to the 2nd power

100

Let x equal the x³-1 coefficient. Thus, x=1 is the coefficient of the given function.

Coefficient definition.

A number or symbol that multiplies another number or symbol is referred to as a "coefficient" (used as a mathematical variable).

Give a co-efficient example in writing.

A coefficient is a result of multiplying an amount by a variable. 6z, for instance, is short for six times z. 6 is a coefficient since z is a variable. The coefficient is one for variables that don't have a value.

Let x equal the x³-1 coefficient. Thus, x=1 is the coefficient of the given function.

The expression's coefficient is the term multiplied by x³. Since x³ is not a word, the answer is 1.

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The full question should be:

What is the coefficient form of X³ 2 *?

Answer:

50+100x=300x+75x

Step 1: Simplify both sides of the equation.

50+100x=300x+75x

100x+50=(300x+75x)(Combine Like Terms)

100x+50=375x

100x+50=375x

Step 2: Subtract 375x from both sides.

100x+50−375x=375x−375x

−275x+50=0

Step 3: Subtract 50 from both sides.

−275x+50−50=0−50

−275x=−50

Step 4: Divide both sides by -275.

[tex]\frac{-275x}{-275}[/tex] =  [tex]\frac{-50}{-275}[/tex]

x= [tex]\frac{2}{11}[/tex]

Answer:

5

Step-by-step explanation:

4x-3=17

+3 on both sides = 4x=20

divide 20 by 4 and your answer is 5

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{4x - 3 = 17}[/tex]

[tex]\text{ADD 3 to BOTH SIDES}[/tex]

[tex]\mathsf{4x - 3 + 3 = 17 + 3}[/tex]

[tex]\text{SIMPLIFY IT}[/tex]

[tex]\mathsf{4x = 17 + 3}[/tex]

[tex]\mathsf{4x = 20}[/tex]

[tex]\text{DIVIDE 4 to BOTH SIDES}[/tex]

[tex]\mathsf{\dfrac{4x}{4} = \dfrac{20}{4}}[/tex]

[tex]\text{SIMPLIFY IT}[/tex]

[tex]\mathsf{x = \dfrac{20}{4}}[/tex]

[tex]\mathsf{x = 5}[/tex]

[tex]{\huge\text{Therefore, your answer should be:}[/tex][tex]\huge\boxed{\mathsf{x = 5}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

N > -2/21

Step-by-step explanation:

Move -4/7 to the other side

n - 4/7 > - 2/3

n > - 2/3 + 4/7

Find a common denominator

n > - 14/21 + 12/21

Add

n > - 2/21

The missing part is 1/5. The complete expression is 1/7 of 1/5 is 1/35.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

We have the expression:

1/7 of (...) = 1/35

To find the missing fraction:

Let n be the number.

So,

1/7(n) = 1/35

n = 7/35

n = 1/5

Therefore, 1/5 is the missing part.

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The car's speed in kilometers per minute is 1.01667. And the number of kilometers will the car travel in 20 minutes will be 20.33 kilometers.

Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.

We know that the speed formula

Speed = Distance/Time

A car is traveling at a speed of 61 kilometers per hour.

Convert the speed into a kilometer per minute. Then we have

Speed = 61 / 60

Speed = 1.01667 kilometers per minute

Then the number of kilometers will the car travel in 20 minutes will be given as,

1.01667 = d / 20

d = 1.01667 x 20

d = 20.33 kilometers

The car's speed in kilometers per minute is 1.01667. And the number of kilometers will the car travel in 20 minutes will be 20.33 kilometers.

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The solution for 3x 2y 5 is x = 0 and y = -2.5

The solution for 3x 2y 5 can be found by first rewriting the equation in standard form, which is ax + by = c. In this case, the standard form would be 3x + 2y = -5.

Next, we can calculate the value of y in terms of x by using the following formula:

y = (c - ax) / b

Substituting in the values, we get:

y = (-5 - 3x) / 2

Now, we can substitute this expression for y into the original equation to solve for x:

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

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

6x + -5 = -5

6x = 0

x = 0

Finally, substituting x = 0 into the expression for y, we get:

y = (-5 - 3(0)) / 2

y = (-5 - 0) / 2

y = -5 / 2

y = -2.5

The solution for 3x 2y 5 is x = 0 and y = -2.5

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Answer:

supplementary angles

Step-by-step explanation:

140 + 40 = 180.

After evaluating the value of 8 + w/4 = 12.

In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.When performing calculations but unsure of the precise amount, algebra is used.

Equations come in two varieties which are  identities and conditional equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true.

as the details given,

the equation given is 8 + w/4

the value of w is 16

by placing the value of w in the given equation we get

=> 8 + 16/4

=> 8 + 4

=> 12

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Answer: 40

Step-by-step explanation:

   We will substitute x = 8 and simplify the given expression.

 Given:

6x-x

 Substitute:

6(8) - 8

 Multiply:

48 - 8

 Subtract:

40

The equation of the line that passes through the points (-4, -6) and (9, 2) is

y = (8/13)x - 46/13.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The line passes through points (-4, -6) and (9, 2).

Let the equation of the line y = mx + c.

Now,

m = (2 + 6) / (9 + 4) = 8/13

(-4, -6) = (x, y)

-6 = (8/13) x -4 + c
-6 = -32/13 + c

c = -6 + 32/13

c = (-78 + 32)/13

c = -46/13

Thus,

The equation of the line is y = (8/13)x - 46/13.

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Answer: Lyda wants to score 80% on a test that is worth 50 points. To figure out how many points she needs to accomplish her goal, we can set up a proportion using her desired percentage as the proportion of points she wants to score over the total number of points on the test.

score / total points = percentage / 100

To figure out the number of points Lyda needs to score, we can use the proportion above and cross-multiply:

score * 100 = percentage * total points

We know that percentage=80 and total points =50, so we can substitute these values:

score * 100 = 80 * 50

score = (80*50) / 100 = 40

So Lyda needs to score 40 points to accomplish her goal of 80%.

The proportion would be score / total points = x/100 = percentage/100 = 40/50 = 8/10

It's worth to mention that scoring 80% on a test means she scored 40 points on a test worth 50, the minimum score to pass is 30 so she got a good grade already.

Step-by-step explanation:

No matter how far it is moved away, the midline of a function stays the same. because a sinusoidal function is involved.

A function's amplitude is the distance that the graph of the function moves above and below its midline. The value of the amplitude when graphing a sine function is comparable to the value of the sine coefficient. the greatest displacement or distance that a point on a wave or vibrating body can travel in relation to its equilibrium position A wave or vibration's amplitude or peak amplitude is a gauge of how far from the central value it deviates. All amplitudes are positive numbers.

given

( A)if pendulum were pulled away from its resting position, then Amplitude is the distance from its resting position to the end where it was released.

Amplitude is the same distance it was pulled away if more distance was pulled away then Amplitude is more.

(B). The midline of function s will not change, it will same irrespective of the distance pulled away. Because it's a sinusoidal function.

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To begin, our game organizer will introduce participants to the escape game instructions and backstory. Teams will have 60 minutes to complete their chosen quest

An escape room, also known as an escape game, puzzle room, exit game, or riddle room is a game in which a team of players discover clues, solve puzzles, and accomplish tasks in one or more rooms in order to accomplish a specific goal in a limited amount of time. The goal is often to escape from the site of the game.

Once you’re ready to start the game, your team will watch a mission video. This video explains the world your team is now a part of, what you’re trying to accomplish, and why you only have 60 minutes to do so!Some missions are about escaping the room, like in a prison break room. Other missions might not be centered around escaping, but instead, you might be completing a heist or launching a martian spaceship.Here’s an example of the type of mission video that plays at the beginning of a game. This one is from The Escape Game’s The Heist!

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Answer:21 teams

Step-by-step explanation:because if you cont the black dots and read the question that would be the answer

The Additive inverse of 3/2 is -2/3.

Additive Reciprocal

An additive reciprocal is a number that is added to a given number to bring the sum to zero. For example, adding -3 to the number 3 will result in zero. So the additive reciprocal of 3 is -3. In our daily life, we come across situations where we cancel the value of a quantity by forming its additive reciprocal.

Additive Reciprocal in Fraction:

The additive reciprocal of the fraction a/b is -a/b and vice versa. This is because a/b + (-a/b) = 0. The additive reciprocal of a positive fraction is the same fraction with a negative sign, but for negative fractions the additive reciprocal is the same fraction without a negative sign.

Given, the number is 2/3

We have to find the additive inverse of the given number.

In mathematics, the additive inverse of a number ‘a’ is the number that, when added to ‘a’, yields zero.

So, 2/3 + (-2/3)= 0

Therefore, the additive inverse of 2/3 is -2/3.

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F ∘ G is a mathematical operation that is used to find the composite of two functions, f and G. This operation is also known as function composition or composition of functions.

Function composition (also known as function composition of functions) is a mathematical operation that allows one to combine two or more functions into a single, larger function. This operation is symbolized by F ∘ G. The composite of two functions, f and G, is defined as the composite of two functions f and G, which is a new function h, such that h(x) = f(G(x)) for all x in the domain of the function. This means that the output of G is the input of f and the output of f is the output of h. Function composition is a useful tool for combining functions in order to create more complex functions. It can also be used to simplify and shorten existing functions, as well as to simplify an equation by reducing the number of operations that need to be performed.

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Therefore, amu (atomic mass unit) and Avogadro's number are not the same things.

A unit of measurement for atomic and molecular weight is the atomic mass unit (amu).

Molecular weight, commonly known as molecular mass, is the mass of a substance's molecules, calculated using the atomic weight of carbon-12, which is 12.

No, amu and Avogadro's numbers are not the same things because An atomic mass unit (amu) is a unit of measurement for atomic and molecular weight. It is defined as one twelfth of the mass of a neutral atom of carbon-12. It is commonly used in chemistry to express the masses of atoms and molecules While Avogadro's number (N) is a fundamental constant of nature that relates the number of atoms or molecules in a sample to the mass of that sample. It is defined as the number of atoms or molecules in one mole of a substance. It is approximately 6.022 x 10^23 atoms or molecules per mole.

So, amu is a unit of measurement for atomic and molecular weight, while Avogadro's number is a constant that relates the number of atoms or molecules in a sample to the mass of that sample.

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The sum of two functions, f and g: (f + g)(x) = f (x) + g(x) and The difference of two functions f and g: (f - g)(x) = f (x) - g(x).

What is operation function ?

The operations function refers to all the activities that focus on producing goods and services for the customers. It includes the production process of converting raw material into final products. It helps to reduce costs and make process improvements.

Have given ,

Two function f and g then ,

There is one more way that functions can be combined. The fifth operation is called the composition of two functions. The composition of the functions f (x) and g(x) is symbolized this way: (fog)(x). It is equivalent to f (g(x)). It is read "f of g of x." The concept is simple. First, the value of g at x is taken, and then the value of f at that value is taken. Let's try an example to clear things up.

So , The sum of two functions, f and g: (f + g)(x) = f (x) + g(x) and The difference of two functions f and g: (f - g)(x) = f (x) - g(x).

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Answer:

Step-by-step explanation:

analyze the graph, we found ∠1=∠5,∠2=∠6,

one.because ∠5+∠6=180, so ∠2=∠6=180-∠5=180-55=125

two.∠3=∠2=125

three.∠8=∠5=55

four.∠12=∠9=80

five.∠14=∠10=180-∠9=100

so, the three options are ∠2,∠8,∠14