The gas mileage for Peter's car is 21 miles per gallon when the car travels at an average speed of 50 miles per hour. The car's gas tank has 17 gallons of gas at the beginning of a trip. If. Peter's car travels at an average speed of 50 miles per hour, which of the following functions fmodels the number of gallons of gas remaining in the tank thours after the trip begins? 21 A. f(t) = 17 - 50T B. f(t) = 17 - 500 21 17-500 C. f(t) 17-210 50 D. f(t) = 21​

Yes, this equation is a quadratic equation.

What is a quadratic equation?

Quadratic equation are the polynomial equations of degree 2 in one variable of type f(x) = ax² + bx  + c = 0 where a, b, c ∈ R and a ≠ 0.

The given equation 3x² + 5x + 9x² + 7x + 3 = 0 can be written as 12x² + 12x +3 = 0, which is a general form of quadratic equation where a = 12, b = 12 and c =3.

Hence, the equation is a quadratic equation.

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Answer:

y = -3x + 6

Step-by-step explanation:

According to the information given, your two points are (2, 0) and (4, -6).

First you want to find the slope of the line that passes through these points. To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)

Plug in these values:

(-6 - 0) / (4 - 2)

Simplify the parentheses.

= (-6) / (2)

Simplify the fraction.

-6/2

= -3

This is your slope. Plug this value into the standard slope-intercept equation of y = mx + b.

y = -3x + b

To find b, we want to plug in a value that we know is on this line: in this case, I will use the second point (4, -6). Plug in the x and y values into the x and y of the standard equation.

-6 = -3(4) + b

To find b, multiply the slope and the input of x(4)

-6 = -12 + b

Now, add 12 to both sides to isolate b.

6 = b

Plug this into your standard equation.

y = -3x + 6

This is your equation.

Check this by plugging in the other point you have not checked yet (2, 0).

y = -3x + 6

0 = -3(2) + 6

0 = -6 + 6

0 = 0

Your equation is correct.

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Answer:

Step-by-step explanation:

you will need a 10ft tall ladder

i hope that helped

A checking account is used for daily basis transaction and a debt and is usually associated with it.Saving accounts is just used for saving money.It has a time limit then you can withdraw your money.It is not on daily basis.

A bank account that allow the user to withdraw the money ,pay bill,transfer money to other person or make a purchase anything by writing checks.Check accounts typically don't earn interest.By checking accounts we can easily deposit and withdraw money for daily transaction.

Saving accounts are intended for storing your money which you don't plan to use daily.saving accounts earns interest at your money.saving account is designed for the accumulation of money in a safe place for future use.saving accounts offer easy access to your money in any emergency.so keeping your money in a saving account means that your money is safe for your future use.

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this was an accident how do I delete?

To manufacture a panels that are u = 48 in. wide and 2 in. thick with the profile of the roofing takes the shape of a sine wave with equation y = sin(pi x/12) from flat sheet, the width of the flat sheet would be 49.59in.

Therefore the answer is 49.59

To find the arc length of a continuous function, you need to first define the function and the interval over which you want to find the arc length. Then you can use the following formula:

Arc Length = ∫√(1+(f'(x))^2) dx

Here, f(x) is the function and the interval is [a, b].

The width, w of the flat metal sheet needed to make the panel is the arc length of the sine curve from x = 0 to x = 48in

In this case, f(x) = sin(pi x/12), so the derivative of f(x) is

f'(x) = (pi/12)cos(pi x/12)

Arc Length = ∫√(1+((pi/12)cos(pi x/12))^2) dx from x=0 to x=48

Arc Length ≈ 49.59 in

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a sampling plan in which an initial sample is selected and the audit team either draws a final conclusion or selects additional items before drawing a final conclusion is known as Sequential sampling

Sequential sampling is a non-probability sampling strategy where the researcher selects one or more populations within a time frame, conducts his research, evaluates the findings, and then selects further populations as necessary. This sampling strategy offers the researcher limitless opportunities to adjust his research procedures and obtain a keen understanding of the study he is currently conducting.

Sequential sampling has a number of benefits, including limitless options for sample size selection and sampling schedule, little cost and labor requirements, and the ability to make minor alterations and modifications to the primary research even during the early stages of the project.

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The fractions equivalent to 2/5 are 4/10, 6/15, 8/20, etc.

Now, According to the question:-

Equivalent fractions can be written by multiplying or dividing both the numerator and the denominator by the same number. This is the reason why these fractions get reduced to the same number when they are simplified.

Let us understand the two ways in which we can make equivalent fractions:

Hence, the equivalent fractions for 2/5 are:

(2/5) × (2/2) = (2 × 2) / (5 × 2) = 4/10

(2/5) × (3/3) = (2 × 3) / (5× 3) = 6/15

(2/5) × (4/4) = (2 × 4) / (5 × 4) = 8/20

Thus, 4/10, 6/15, 8/20 are equal to 2/5,

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The reasons and statements that completes the two-column table method used to prove that triangle ΔRVX is congruent to ΔTWU (ΔRVX ≅ ΔTWU) are as follows;

Statement                                   [tex]{}[/tex]         Reason

12. UW = VX                   [tex]{}[/tex]                   Transitive Property of Equality

13. ΔRVX ≅ ΔTWU [tex]{}[/tex]                           SSS

Two triangles are congruent if the lengths of the three sides of one triangle are the same as the lengths of the three sides of the other triangle.

The details and reasons for the statements used to prove the congruency of the ΔRVX and ΔTWU are as follows;

RV = RS + SV; Additive property of length

The additive property of length states that a point B can be located on a segment AC only if, we get; AC = AB + BC

RV = ST + SW Substitution

The substitution property states that if a = b then a can substitute b in equations and expressions, such that the values of the expressions and equations remain the same.

RV = TW Transitive Property of Equality

The transitive property of equality states that if a = b and b = c, then a = c

ΔRVX ≅ ΔTWU SSS

The SSS (Side-Side-Side) congruency postulate states that two triangles are congruent if the lengths of all three sides of one triangle are congruent to the lengths of the sides of the other triangle.

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The figure of Pumpkin according to the transformation is shown below.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

Given:

The Transformation rule are as follow:

1. T(-4 , -18) reflect across x = -4.

2. T(-3, 4) (R0, 180)

3. [tex]R_0[/tex] , 180 ( [tex]r_y[/tex] = x+ 11)

4. [tex]r_y[/tex] = 11 ( [tex]R_0[/tex] , 90)  T(6, -10)

5. T(-12, 0),  [tex]r_y[/tex] = -10, ( [tex]R_0[/tex] , 270)

6. T(0, -3),  [tex]r_y[/tex] = x

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Answer:

They are both irrational

Step-by-step explanation:

so the square root of 8 is 2.82842712475 which is irrational because it is not a perfect square or repeated decimal pattern.

the square root of 98 is also irrational for the same reason but the square root is 9.89949493661.

The product of two √8 and √98 irrational number is irrational.

A rational number is any number that can be expressed as a ratio (or fraction) of two integers.

Any real number that cannot be represented as the quotient of two integers is irrational.

Given:

The rational number are : √8 and √78

As, the √8=  2.82842712475 which is irrational because it is not a perfect square or repeated decimal pattern.

and, √98 = 9.89949493661 is also irrational.

Hence, the product of two irrational number is irrational.

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The inverse calculator is a function calculator which finds the inverse of the given function.

Any function can have its inverse value computed using an inverse function calculator. Recall that an inverse function is one that can make another function do the opposite. Another name for it is an anti-function.

It is denoted as:

f(x) = y ⇔ f⁻¹(y) = x

Any function's inverse can be found by first substituting the other variable for the function and then solving for the other variable by substituting each other.

This online calculator for finding the inverse function is very simple to use. To find the inverse of any function, follow the directions below.

Step 1: Type any function into the input field, which is located across the sentence "The inverse function of."

Step 2: Press the "Submit" button located at the calculator's base.

Step 3: A different window will open in which the supplied function's inverse will be calculated.

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The mean of the given observation is 9.

What are the mean, median, and example?

The ratio between the total number of observations in a data set and the sum of all observations is known as the mean in statistics. The most frequent number, or the one that happens the most frequently, is known as the mode.

                   Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.

Mean = Sum of all the observations/Number of observations

Mean = 4+6+8+10+12+14/6

Mean = 54/6

Mean = 9

Hence, the mean of the given observation is 9.

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As opposed to last year when 113 pies were prepared for the bake sale, 219+ d  expression pies have been prepared throughout the past two years.

A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.

Since we have given that

Number of pies baked for bake sale last year = 219

Number of pies baked for bake sale this year = d

So, total number of pies baked in two years is given by

219 +d

Hence, there are 219+d pies baked in two years.

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Criteria for congruence of triangles are SSS, SAS, ASA, AAS, RHS.

As per the given data we have to determine the criteria for the congruence of triangles.

The criteria is SSS, SAS, ASA, AAS, RHS.

SSS- Two triangles are congruent if all the 3 corresponding sides of the given triangles are equal.

SAS- Two triangles are congruent if 2 corresponding sides of the given triangles and the angle included between those sides are equal to each other.

ASA- Two triangles are congruent if two angles and the included side of one triangle are equal to the corresponding angles and sides of another triangle.

AAS- if two angles and the non-included side one triangle are congruent to two angles and the non-included side of another triangle, then two triangles are congruent with each other.

RHS- If the hypotenuse and a side of a right angled triangle are congruent with the hypotenuse and the corresponding side of another right angled triangle, then the two triangles are congruent with each other.

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The value of y obtained after solving the given equation will be equal to 11/3 or 3 2/3.

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given equation in the question,

3/4y + 1/2 = 3 1/4

Firstly, write the equation in a simplified way,

3/4y + 1/2 = 13/4

3/4y = 13/4 - 1/2

3/4y = (13 - 2)/4

3/4y = 11/4

Now, solve the equation for y,

y = (11 × 4)/(4 × 3)

y = 11/3

In mixed fraction form, it can be written as 3 2/3.

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The correct answer to the expression is 10.

By using BODMAS rule,

BODMAS stands for Brackets, Orders, Division, Multiplication, Addition, and Subtraction in its entire form. Therefore, in BODMAS, the orders or exponents are given the second choice here (x n ) A method or sequence called the BODMAS rule is used in mathematics to simplify arithmetic expressions with many operators. When there are several operators in an equation, we must first determine the correct sequence in which to solve the equation. The BODMAS rule assists in the solution of this issue.

Given expression,

2+5*4-8/⅘

=2+20- 40/4    

= 22-10

= 10

Hence, the correct answer to the expression is 10.

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Answer:

y = - 5/4x -12

Step-by-step explanation:

Original slope= (0- -4)/(5-0)=4/5

slope of perpendicular line of original = -5/4

so the line passes through the point (-8,-2)

(y - -2) = -5/4 (x - -8)

y + 2 = -5/4x - 10

y = - 5/4x -12

The equation of line u passing through the point (-8, -2) and which is perpendicular to the line y that cut the x-axis at x = 5 and y-axis at y = -4 is 5x + 4y + 18 = 0

Given that line, u passes through (-8,-2) and is perpendicular to line y

line y cut x-axis at x=5 and y-axis at y=-4

that is the point of intercept are : (x1, y1) = (5,0) and (x2, y2) = (0, -4)

Now, the equation of line = (y - y1) = m1*(x - x1)

Here m is the slope of line y

m1 = (y1 - y2)/(x1 - x2)

On solving,

m1 = (0 - (-4))/(5 - 0) = 4/5

We know that when two equations are perpendicular then the multiplication of their slopes = -1

m1 * m2 = -1

Now, m2 = -1/m1 = -5/4

Equation of line u passing through the point (-8, -2) and perpendicular to the line = (y - y1) = m2*(x - x1) =>  (y - (-2)) = -5/4*(x - (-8)

5x + 4y + 18 = 0

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The expression for area of a rectangle is A = 12x² + 55x + 50, the equation is second degree and the expression for perimeter is P = 14x + 30.

If a mathematical operation includes at least two words that are connected by an operator and either comprise numbers, variables, or both, it is referred to as an expression.

The operations with reflection coefficients include adding, subtracting, multiplying, and dividing. In order to include terms into an expression, a mathematical operation like reduction, addition, multiplication, or division is used.

As per the given information in the question,

Let the length of rectangle, l = (4x + 5) and,

The width of rectangle, w = (3x + 10)

a.

Use the formula of area of rectangle,

A = wl

A = (3x + 10)(4x +5)

So, the expression will be,

A = 12x² + 55x + 50

b.

The degree of the equation for area is second degree.

c.

Use the formula of perimeter of rectangle,

P = 2(l + w)

P = 2(4x +5 + 3x + 10)

P = 2(7x + 15)

Then, the expression of perimeter will be,

P = 14x + 30

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The measures of the angles are 72°, and 108°.

What is Angle Sum Property?

The sum of all angles of a triangle is equal to the angle of a straight line i.e. 180°. If we have a triangle ABC, then the Sum of angles A , B, and angle C will be 180 ° and the value of the exterior angle is equal to the sum of two interior opposite angles.

We have,

two angles form a linear pair. one angle measure is 36° more than the other.

If two angles form a linear pair, then the sum of the degree measure of the angles is 180°.

Let x be the measure of the smaller angle.

Then,

36° + x is the measure of the other angle.

So,

36° + x  + x = 180°

2x = 180° - 36°

2x = 144°

x = 144°/2

x = 72°

the measure of the smaller angle is  x = 72°,

the measure of the other angle is

36° +  72° = 108°

Hence, the measures of the angles are 72°, and 108°.

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Answer:

Step-by-step explanation:

hfhgfvbbkgb 56789+7567t+2345

y-mx+b

y=-3/2x+4

m- -3/2

b-4

y=-3/2x+4

Answer:

Step-by-step explanation:

D?

The rule of reflection for the points (x, y) for the graph is (y, - x).

Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

Dilation: The preimage is scaled up or down to create the image.

Reflection: The picture is a preimage that has been reversed.

Rotation: Around a given point, the preimage is rotated to create the final image.

Translation: The image is translated and moved a fixed amount from the preimage.

The preimage of the given line has points(x, y), B(2, 3) and C(1, 6).

Now, The graph has been translated down 2 units and reflected 180° along the x-axis so the image of the graph has points(y, - x) B'(3, - 2) and C'(6, - 1).

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The four fundamental translations or transformations in geometry are translation, reflection, rotation, dilation, and resizing.

For a function graph, four different transformations are feasible (and translation in math is one of them). When we translate, we move a figure in any direction. When we reflect, we turn a figure or a line over. The act of rotating a figure around a point is known as rotation.

In mathematics, a translation merely moves a shape up, down, left, or right without turning it. The image or the translated shapes seem to be the same size as the original shape, proving that they are congruent. Simply said, they have changed their path or directions.

Three types of translation are described in Jakobson's On Linguistic Aspects of Translation (1959, 2000): intralingual (inside one language, such as rewording or paraphrasing), interlingual (between two languages), and intersemiotic (between sign systems).

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The vector A is (49.9m) x and vector B is (1.5m) x.

In the given question, A − B = (−51.4m)x, C =(62.2m)x, and A +B +C =(13.8m)x.

Find the vector A. Find the vector B.

We may disregard the vector x and treat the issue as an arithmetic one since all of the measurements are in the same direction (simultaneous equations).

A − B = −51.4.............................(1)

C = 62.2.............................(2)

A + B + C = 13.8.............................(3)

Now putting the value of C from Equation (2) in Equation (3)

A + B + C = 13.8

A + B + 62.2 = 13.8

Subtract 62.2 on both side, we get

A + B = 13.8 - 62.2

A + B = - 48.4.....................(4)

Adding the equation (1) and (4), we get

2A = - 99.8

Divide by 2 on both side, we get

A = - 49.9

Now subtracting the equation (1) and (4), we get

2B = -48.4 - ( -51.4)

2B = 3

Divide by 2 on both side, we get

B = 1.5

Since all of the calculations are done in terms of the unit vector x.

So the answer is vector B = (1.5m) x and vector A = (49.9m) x.

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Square root of 1, √1 is a real number as it is a rational number.

√  is a symbol that means square root in mathematics.

Real number is a set of all rational and irrational numbers. It can be plotted on a number line.

A rational number is a number that can be expressed in the form of p/q, where p and q are integers and denominator, q not equal to 0.

Numbers that cannot be plotted on number line, numbers that are not real number are called imaginary numbers.

√1 = 1

1 is a rational number as it can be written as 1/1. All integers are rational numbers in the similar way.

Therefore square root of 1 is a rational number and hence it is a real number.

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We can find the domain and range of the function without the help of graphing calculator by the following steps mentioned below.

The domain of a function is the set of values that we are allowed to enter into our function.

This set consists of the x values for a function like f. (x).

The set of values that a function can accept as input is known as its range.

The function outputs this list of values once we enter an x value.

The domain of a function refers to the set of input values.

These numbers, which stand in for the independent variable, are corresponding to the x-axis value.

The range of a function refers to the set of output values.

These values, which indicate the dependent variable, are corresponding to the y-axis value.

Find a function's domain and range without graphing as follows:

(A) Place y = f(x)

(B) In terms of y, solve the equation y = f(x) for x. Let x = g (y)

(C) Discover the values of y and its domain of f for which the values of x, as determined by x = g(y), are real.

(D) The range of the supplied function is the collection of y values produced in step 3.

Therefore, we can find the domain and range of the function without the help of graphing calculator by the following steps mentioned above.

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10 more than 37 will be Addition of 10 and 37 which is supposed to be 10 plus 37 = 47.

Addition is the process of combining items and counting them as a single large group. The process of adding two or more numbers together is known as addition in mathematics. The terms addends and total both refer to the numbers that are added and the result of the operation.

The SUM is the result or conclusion that results from adding two or more integers. Addends are the numbers that are added.

We simply changed "more than" to "plus" and found the answer to the straightforward math issue. It is equivalent to 10 + 37 to add 10 to 37. Therefore, the answer is 47 once more.

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Yes , SAS (Side-Angle-Side) is a second Congruence postulate to prove triangle congruence by showing that two sides and their included angles are congruent.

Side-Angle-Side is the rule used to prove whether a given set of triangles are congruent. The SAS rule states: Triangles are congruent if two sides and an included angle of a triangle are equal to two sides and an included angle of another triangle. An included angle is the angle formed by two given sides.. For example : let's us consider two triangles ∆SQR and ∆TSR ,

In above given figure, sides

RS = RS ( common side)

QS = ST ( S divides QT in two equal parts) and angle between QS and SR equal to angle between SR and ST i.e. ∠QSR = ∠RST = 90° (right angle ) and it is included angle . So, by SAS Congruence rule, both of triangles are congruent. Hence, Δ ABC ≅ Δ PQR.

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