5x-1=3x+5 an equation

Answer:3; the ride costs $3 per mile

Step-by-step explanation:

Rate of Change of the function is 3. then the ride costs $3 per mile.

The average Rate of Change of the function f(x) can be calculated as;

[tex]f(x) = \dfrac{f(b) - f(a)}{b-a}[/tex]

We are given  the total cost of a ride-sharing trip, y, is a function of the distance traveled,

Distance (mi), Total Cost ($). y

2                       0

5                       1  

8                        2

11                       3

14                       4

Therefore,

Rate of Change of the function

(5 - 2) / (1- 0)

= 3 / 1

Hence, we can conclude that the ride costs $3 per mile.

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The relation:

(9, -1) (4,2) (5,3) (8, -1) (3, 0)

Is a function, because each element of the domain appears only once.

A relation maps elements from a set, called the domain, into elements from another set, called the range.

Such that the element x being mapped into the element y is written as:

(x, y).

A relation is a function only if each element in the domain is mapped into only one element of the range.

Here we have the relation:

{  (9, -1) (4,2) (5,3) (8, -1) (3, 0)}

We can see that no element of the domain appears twice, so yes, this is a function.

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The correct answer is the 5 ways to find if two triangles are congruent are SSS, SAS, ASA, AAS and HL.

Two triangles are congruent if and only if they have the same three sides and angles.

SSS (side, side, side): SSS, which stands for "side, side, side," denotes that there are two triangles with identical angles on all three sides. The triangles are congruent if their third sides are the same as those of another triangle.

SAS (side, angle, side): "Side, Angle, Side" stands for two triangles whose two sides and one included angle are known to be equal. The triangles are congruent if two sides and the included angle of one triangle equals the corresponding sides and angle of another triangle.

ASA (angle, side, angle): ASA, which stands for "angle, side, angle," denotes the existence of two triangles whose included side and two known angles are equal. The triangles are congruent if two angles and the included side of one triangle match the corresponding angles and side of another triangle.

AAS (angle, angle, side): AAS, which stands for "angle, angle, side," denotes the equality of the non-included side and two angles in two triangles. The triangles are congruent if two of one triangle's angles and its excluded side are equal to the corresponding angles and sides of another triangle.

HL (hypotenuse, leg): The two triangles are congruent if one right-angled triangle's hypotenuse and one of its legs are equal to its corresponding hypotenuse and leg in another right-angled triangle.

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Isosceles triangle problem can be solved by given steps

what is isosceles triangle ?

An isosceles triangle in geometry is a triangle with two sides that are the same length. Sometimes it is stated as having exactly two sides that are the same length, and other times it is specified as having at least two sides that are the same length, the latter form containing the equilateral triangle as a particular case.

explanation:

In isosceles triangle

1. Two sides of the triangle are congruent

2. The angle opposite those sides are congruent

x + 72 +72 = 180

             x  = 180 -144

             x = 36

Hence the isosceles triangle problem can be solved by above steps and explanation

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The value of the variables x and y are,

11) x = 13,  y = 18.4

12) x = 6.9,  y = 8.

What is right angle triangle?

A right triangle is a triangle with one angle at a right angle, meaning that two of its sides are perpendicular. It is also known as a right-angled triangle, an orthogonal triangle, or more commonly as a rectangled triangle. Trigonometry's foundation is the right triangle's relationship between its sides and other angles.

11)Let the given triangle is a right angle triangle.

So we can use trigonometric ratio,

[tex]tan(45) = \frac{x}{13} \\x = 13(tan(45))\\x = 13[/tex]

Using this to find the value of y.

[tex]sin(45) = \frac{x}{y} \\sin(45) = \frac{13}{y} \\y = \frac{13}{sin(45)} \\y = 18.4[/tex]

So, the values of x and y are x = 13 and y = 18.4.

12) The given triangle is a right angle triangle.

So we can use trigonometric ratio,

[tex]tan(30) = \frac{4}{y}\\ y = \frac{4}{tan(30)} \\y = 6.9[/tex]

Now to find the value of x.

[tex]sin(30) = \frac{4}{x} \\x = \frac{4}{sin(30)} \\x = 8[/tex]

Hence, the values of x and y are, x = 6.9 and y = 8.

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The various types of inverse function are the inverse of trigonometric functions, rational functions, hyperbolic functions and log functions

If the function is denoted by ‘f’ or ‘F’, then the inverse function is denoted by f⁻¹or F⁻¹.

A function accepts values, performs particular operations on these values and generates an output. The inverse function agrees with the resultant, operates and reaches back to the original function.

The various types of inverse function are:

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Total 56 pencils are needed for the exam.

Multiplication is one of the arithmetic operation used to find total numbers of items or things.

Given,

Total students in the classroom = 28

Total number of pencils needed by each student for the exam=2 pencils

Total number of pencils needed for the exam are,

= Total student ×  Number of pencils needed by each student

= 28 × 2

= 56 pencils

Hence , The total number of pencils needed by the students for the exam would be 56 .

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The area of the rectangular paper left after two semi circles are cut out of it is 186.96 cm².

A rectangle is a closed 2-D shape, having 4 sides, 4 corners, and 4 right angles (90°).The opposite sides of a rectangle are equal and parallel.

To caluculate the area of the paper that remains, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the area of the paper left is 186.96 cm².

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There are four basic properties of numbers: commutative, associative, distributive, and identity.

1.Commutative Property

a. Addition

. When two numbers are added, the sum is the same regardless of the order in which the numbers are added.

3 + 5 = 8       or       5 + 3 = 8

b. Multiplication. When two numbers are multiplied together, the product is the same regardless of the order in which the numbers are multiplied.

3 x 5 = 15       or       5 x 3 = 15

2.Associative Property

a. Addition. When three or more numbers are added, the sum is the same regardless of the way in which the numbers are grouped.

6 + (4 + 3) = 13   or   (6 + 4) + 3 = 13

b. Multiplication. When three or more numbers are multiplied, the product is the same regardless of the way in which the numbers are grouped.

6 x (4 x 3) = 72   or   (6 x 4) x 3 = 72

3.Distributive Property

The sum of two numbers times a third number is equal to the sum of each addend times the third number.

5 x (7 + 2) = 45   or   5 x 7 + 5 x 2 = 45

4.Identity Property

a. Addition. The sum of any number and zero is that number.

12 + 0 = 12

b. Multiplication, The product of any number and one is that number.

18 x 1 = 18

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The slope of the perpendicular line to the equation 5x - 4y = -24, is: 4/5.

The slope values of two lines which lie perpendicular to each other on a coordinate plane are always negative reciprocals to each other.

Rewrite the equation, 5x - 4y = -24 in slope-intercept form:

5x - 4y = -24

-4y = 5x - 24

Divide both sides by -4

-4y/-4 = 5x/-4 - 24/-4

y = -5/4x + 6

The slope of y = -5/4x + 6 is -5/4. The negative reciprocal of -5/4 is 4/5. Thus, the slope of the line that is perpendicular to the equation of the given line is: 4/5.

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The perimeter of triangle CED is 58 in

What is a Parallelogram ?

A unique variety of quadrilateral called a parallelogram has both pairs of its opposite sides parallel and equal.

Parallelograms' characteristics

(1) The opposing sides of a parallelogram are parallel to one another. In this case, AB || CD and AC || BD

(2) A parallelogram has equal-length opposing sides. In this case, AB = CD and AC = BD

(3) In a parallelogram, the measurements of the opposing angles are equal. In this case, A Equals C and B = D.

(4) The total of all the angles of a parallelogram, like all other quadrilaterals, is 360°.

(5) A parallelogram has neighboring or contiguous angles that sum to 180 degrees. As a result, A + B, B + C, C + D, and D + A all equal 180 degrees.

(6) A parallelogram's diagonals cut each other in half. In this case, OA = OC and OB = OD

(7) The parallelogram in the figure is split into two congruent triangles by the diagonals AC and BD.

The diagonals of a parallelogram bisect each other AC = 2 CE

Substitute AC= 50 into AC = 2CE = 50 = 2CE

Calculate 50 = 2 CE=>  CE = 25

The diagonals of a parallelogram bisect each other BD = 2DE

Substitute BD= 30 into BD = 2DE =>  30 = 2DE

Calculate 30 = 2DE  => DE = 15

Opposite sides of parallelogram are congruent AB = CD

Substitute AB = 18 into AB = CD =>  CD = 18

Perimeter of a triangle PΔCDE = CE + CD + DE

Substitute  CE = 25, DE = 15, CD = 18.

PΔCDE = CE + CD + DE

PΔCDE = 25+ 18 + 15

PΔCDE = 58 in

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In order to show that △ ABC ≅ △ DEF by SAS congruence, we need the sides of triangles ABC and DEF with the angle between the respective sides.

Triangle congruence: Two triangles are said to be congruent if all three of their corresponding sides and all three of their corresponding angles have the same measurements. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved. "" is the congruence symbol. When two figures are comparable to one another in terms of their size and shape, this is what mathematicians mean by congruence. In essence, there are four congruence principles that demonstrate if two triangles are congruent. However, locating all six dimensions is essential. As a result, the congruence of triangles can be assessed using just three of the six variables.

Congruency Requirements:

SSS (Side-Side-Side)

SAS (Side-Angle-Side)

ASA (Angle-Side-Angle)

AAS (Angle-Angle-Side)

RHS (Right angle-Hypotenuse-Side) 

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The range of a graph can be found using the values depicted on the y-axis.

According to the question,

We have the following information:

We have a graph and we need to know how do we find the range of that graph.

We know that the domain of a graph is the collection or in other words set of input values depicted on x -axis and the range of a graph is the set of possible output values portrayed on y-axis of the graph.

In noting down the range of a graph, we first list down the down value and then the up value or in other words we move from down to up in order to find the range of a graph.

Hence, the range of a graph can be found using the values depicted on the y-axis.

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The equation that best represents the area of the forest each year is A. y = 2,000(0.94)^x.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Since the certain forest covers an area of 2,000 square kilometers and each year, this area decreases by 6%.

The equation will be:

= 2000(1 - 6%)^x

= 2000(0.94)^x

In conclusion, the correct option is A.

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Answer:

To find a polynomial, you must identify the terms, coefficients, and degrees. The degree of a polynomial is the highest exponent of the variable in the equation. The coefficients of a polynomial are the values that are multiplied by the variables. The terms of a polynomial are the pieces of the equation, including the coefficients and the variables. After identifying the terms, coefficients, and degree of the polynomial, you can write it in standard form.

Step-by-step explanation:

The area of the polygon EFG with given vertices is, 7.5 units.

What is area of triangle?

The area of a triangle is the area that it completely encloses in a two-dimensional plane. A triangle is a closed shape that, as we all know, has three sides and three vertices. As a result, the total area occupied by a triangle's three sides is known as its area. The general formula for calculating a triangle's area is the product of the triangle's base and height divided by half.

Let the given vertices are,

E(3, 1), F(3, -2), G(-2, -2)

There are three vertices, so the polygon is a triangles.

Since,

Area of triangle = 1/2 x base x height.

If we draw the given vertices on the coordinate plane then the base is FG and the height of the triangle is EF.

Now to find the lengths of side FG and EF.

By using the distance formula,

[tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\EF =\sqrt{(3-3)^2+(-2-1)^2} = \sqrt{9} = 3\\ FG = \sqrt{(-2-3)^2 + (-2-(-2))^2} = \sqrt{25+0} = 5[/tex]

⇒ Area = 1/2 x 5 x 3

             = 1/2 x 15

    Area = 7.5

Hence, the area of the polygon EFG is 7.5 units.

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Answer: If two parallel lines are cut by a transversal, then corresponding angles are congruent.

Step-by-step explanation:

If triangle has 2 congruent sides and 2 congruent angles ,such a triangle is known as Isosceles triangle.

What is congruent triangle?

Congruence of triangles: 2 triangles square {measure} aforesaid to be congruent if all 3 corresponding sides square measure equal and every one the 3 corresponding angles square measure equal in measure. These triangles may be slides, rotated, flipped and turned to be looked identical. If repositioned, they coincide with one another. The image of congruity is’ ≅’.

Main Body:

A triangle with two congruent sides and congruent base angles is termed as an isosceles triangle.

If two sides of a triangle are congruent, then by isosceles triangle property, the angles opposite to these sides are congruent.

That is, base angles of the triangle are congruent.

Then, such a triangle is known as Isosceles triangle.

Therefore, option B is correct.

The actual question with option is in figure.

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Answer:

At least 8 rows

Step-by-step explanation:

45 divided by 9 is 5. That is 5 rows

9x3= 27 and there are 23 adults. So that is 3 rows

5+3=8

8 rows in total.

Answer:

A)  61.93 minutes

B)  40.93 minutes

Step-by-step explanation:

Newton's law of cooling

[tex]T(t)=T_S+(T_0-T_S)e^{-kt}[/tex]

where:

Given values:

Substitute the given values into the formula and solve for k:

[tex]\implies 60=20+(90-20)e^{-25k}[/tex]

[tex]\implies 40=70e^{-25k}[/tex]

[tex]\implies e^{-25k}=\dfrac{4}{7}[/tex]

[tex]\implies \ln e^{-25k}=\ln \dfrac{4}{7}[/tex]

[tex]\implies -25k \ln e=\ln \dfrac{4}{7}[/tex]

[tex]\implies -25k=\ln \dfrac{4}{7}[/tex]

[tex]\implies k=-\dfrac{1}{25}\ln \dfrac{4}{7}[/tex]

Given values:

Substitute the given values into the formula and solve for t:

[tex]\implies 30=20+(60-20)e^{\frac{1}{25}t\ln \frac{4}{7}}[/tex]

[tex]\implies 10=40e^{\frac{1}{25}t\ln \frac{4}{7}}[/tex]

[tex]\implies e^{\frac{1}{25}t\ln \frac{4}{7}}=\dfrac{1}{4}[/tex]

[tex]\implies \ln e^{{\frac{1}{25}t\ln \frac{4}{7}}}=\ln \dfrac{1}{4}[/tex]

[tex]\implies {\dfrac{1}{25}t\ln \dfrac{4}{7}}\ln e=\ln \dfrac{1}{4}[/tex]

[tex]\implies {\dfrac{1}{25}t\ln \dfrac{4}{7}}=\ln \dfrac{1}{4}[/tex]

[tex]\implies t=\dfrac{\ln \dfrac{1}{4}}{{\frac{1}{25}\ln \frac{4}{7}}}[/tex]

[tex]\implies t=61.93063129...[/tex]

[tex]\implies t=61.93\;\; \sf minutes[/tex]

Given values:

Substitute the given values into the formula and solve for t:

[tex]\implies 30=-10+(90-(-10))e^{\frac{1}{25}t\ln \frac{4}{7}}[/tex]

[tex]\implies 40=100e^{\frac{1}{25}t\ln \frac{4}{7}}[/tex]

[tex]\implies e^{\frac{1}{25}t\ln \frac{4}{7}}=0.4[/tex]

[tex]\implies \ln e^{\frac{1}{25}t\ln \frac{4}{7}}=\ln 0.4[/tex]

[tex]\implies{\dfrac{1}{25}t\ln \dfrac{4}{7}}\ln e=\ln 0.4[/tex]

[tex]\implies {\dfrac{1}{25}t\ln \dfrac{4}{7}}=\ln 0.4[/tex]

[tex]\implies t=\dfrac{\ln 0.4}{{\frac{1}{25}\ln \frac{4}{7}}}[/tex]

[tex]\implies t=40.93392072...[/tex]

[tex]\implies t=40.93\;\; \sf minutes[/tex]

There are 125 of the smallest cubes that will fill the largest cube using the size of their respective volume

The volume of cube is calculated by using a × a × a = a³ where "a" is the edge.

The volume of the smallest cube = 1.5inches × 1.5inches × 1.5inches

The volume of the smallest cube = 3.375inches³

The volume of the largest cube = 7.5inches × 7.5inches × 7.5inches

The volume of the largest cube = 421.875inches³

Thus, the number of the smallest cubes it would take to fill the largest cube is derived by

421.875inches³/3.375inches³ = 125.

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Answer: [tex](-\infty, \infty)[/tex]

Step-by-step explanation:

Absolute value is always non-negative.

Answer: -23

Step-by-step explanation:

[tex]jk^2 -m=(-5)(2^2)-3=-5(4)-3=-20-3=-23[/tex]

Answer:

The height of the 4th bounce would be 4.7458321; rounded would be 4.8.

Step-by-step explanation:

We can figure this question out by first converting the 83% into a decimal, by bringing back 2 decimal places:

0.83.

And then setting up this equation:

0.83 x 10 = 8.3

Now, this is for 1 bounce. We have to do this 4 more times:

0.83 x 8.3 = 6.889

3rd time:

0.83 x 6.889 = 5.71787

4th time:

0.83 x 5.71787 = 4.7458321.

Now, we can round this answer to:

4.8

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The used postulate is explained below.

What is congruent triangles?

Two triangles are stated to be congruent if the 3 facets and the 3 angles of each the angles are same in any orientation.

When angles and facet blanketed in among those angles of 1 triangle are identical as any other one, each those triangle are Congruent.

This standards of congruency is is aware of as ASA criterion as a facet blanketed among angles are all identical.

Two triangles are congruent, if angles and the facet blanketed among them in a single triangle is same to the 2 angles and the facet blanketed among them of the alternative triangle.

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The area of triangle ABC is 18cm².

A triangle is a three-sided polygon that consists of three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees.

This property is called angle sum property of a triangle. A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry.

= 72*sin(75)*cos(75)

= 36*(2sin(75)cos(75))

= 36*sin(150)

=  18

In conclusion, the area of the triangle is 18cm².

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What is division?

Division is the process by which value of single unit can be calculated from the value of multiple unit.

The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.

There is a well known formula for division

Divisor x Quotient + Remainder = Dividend.

This is a problem sum of division

Cost of 15 flowers = $200

Cost of 1 flower = $200 [tex]\div[/tex] 15 = $13.33

Cost of 5 flowers = $70

Cost of 1 flower = $70 [tex]\div[/tex] 5 = $14

So unit price of 15 flower arrangement of $200 is lower than unit price of 5 flower arrangement of $70

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The multiples of a number are numbers found by multiplying the original number by any whole number. Prime multiples are number which multiply each other and form a prime

What are Prime Numbers ?

A prime number is a number that is only divisible by 1 and itself. So, prime numbers have only two factors, 1 and the number itself.

This means these numbers cannot be divided by any number other than 1 and the number itself without leaving a remainder.

Numbers that have more than 2 factors are known as composite numbers.

For example :

The factors of 3 are 1 and 3.

Therefore, the prime multiples of 3 are 1 and  3.

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Using trigonometric ratio the distance to the control tower is 750.7ft

In trigonometry, there are six trigonometric ratios, namely, sine, cosine, tangent, secant, cosecant, and cotangent. These ratios are written as sin, cos, tan, sec, cosec(or csc), and cot in short.

The values of these trigonometric ratios can be calculated using the measure of an acute angle, θ in the right-angled triangle given below. This implies that the value of the ratio of any two sides of the triangle here depends on angle C.

Using trigonometric ratio, the distance is

tan θ = opposite / adjacent

tan 47 = x / 700

x = 700 tan 47

x = 750.7 ft

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Answer:

-2

Step-by-step explanation:

a is -3

d is -1

you subtract the two

-3 - (-1)

when you have two negatives they cancel each other out and become positive

-3 + 1

-3 + 1 = -2

that is your answer