The monthly cot of driving a car depend on the number of mile driven. Lynn found that in May it cot her $428 to drive 460 mi and in June it cot her $494 to drive 680 mi. (a) Expre the monthly cot C a a function of the ditance driven, d, auming that a linear relationhip give a uitable model

According to Maths, in order to solve a system of linear equations by graphing, we must first graph both equations in the same coordinate plane and then locate the intersection of the two lines.

A system of equations in algebra consists of two or more equations and looks for common answers to the equations. "A set of equations satisfied by the same set of variables is called a system of linear equations."

According to the discussion above, a system of equations is a collection of equations that aim to find a common solution for all of the variables. An illustration of a system of equations is the set of equations below.

2x - y = 12

x - 2y = 48

Finding the values of the variables employed in a system of equations entails solving the set of equations. While keeping the equations balanced on both sides, we compute the values of the unknown variables. Finding the value of the variable that makes the condition of all the given equations true is the primary goal when solving an equation system. A given system of equations may have a variety of solutions,

There are numerous ways to solve any set of equations. We require at least two equations in order to solve a system of two-variable equations. Similar to this, we will need at least 3 equations to solve a system of 3 equations. Let's examine three approaches to solving a set of equations, presuming that they are linear equations in two variables.

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To write 300000000 in standard form, we need to move the decimal point to the left or right so that there is only one non-zero digit to the left of the decimal point.

300000000 in standard form would be written as 3 x 10^8.

To arrive at this form, we move the decimal point 8 places to the left (since there are 8 zeros in 300000000) and add the power of 10 notation, indicating that we moved the decimal point 8 places to the left. The number 3 is the coefficient and 8 is the exponent. This way, we get 3 x 10^8 which is the standard form of 300000000.

Standard form, also known as scientific notation, is a way of expressing a number in a compact and efficient manner. It is typically used for very large or very small numbers.

When a number is written in standard form, the decimal point is moved so that there is only one non-zero digit to the left of the decimal point. The number of places the decimal point is moved is indicated by a power of 10.

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The wrapping paper Marcus have left is 5 5 / 12 feet.

Marcus buys 7 3/4 feet of wrapping paper. He lets his sister use 2 1/3 feet of the wrapping paper to wrap a gift.

The amount of wrapping paper Marcus have left can be calculated as follows:

The amount of wrapping paper Marcus have left is the subtraction of the paper used by the sister by the wrapping paper he had initially.

Hence,

wrapping paper Marcus have left = 7 3 / 4 - 2 1 / 3

wrapping paper Marcus have left = 31 / 4 - 7 / 3

wrapping paper Marcus have left = 93 - 28 / 12

wrapping paper Marcus have left = 65 / 12

Therefore,

wrapping paper Marcus have left = 5 5 / 12 feet

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Answer:

218 with a remainder of 2

Step-by-step explanation:

656 divided by 3 = 218.6666667

218 times 3 = 654

656 - 654 = 2

When 656 is divided by 3 is 218 with a remainder of 2.

In mathematics, divides left-hand operands into right-hand operands in the division operation.

To divide 656 by 3, we can perform long division as follows:

 3 ) 656 (218

     -6

     ____

     15

    -12

   _____

      35

    - 33

    _____

       2

We first divide the first digit of 656 (which is 6) by the divisor 3, which gives us 6 with a remainder of 15.

We then bring down the next digit (which is 56) to form the dividend 18, and we perform the division again.

This gives us 218 with a remainder of 2.

Therefore, 656 divided by 3 is 218 with a remainder of 2.

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Answer:40+4x

Step-by-step explanation:

1) distribute the 4 to each term

4(10+x)

40+4x

Answer:  y=17.3

refer to the image for the steps

Part A:

The graph of the function g(x) = |x - 7| is a V-shaped graph that opens upwards and has a vertex at x = 7. The vertex is the midpoint of the graph and occurs at the value of x where the absolute value changes from positive to negative. The domain of the function is all real numbers and the range is all non-negative numbers.

Part B:

The transformation from f(x) to h(x) occurs by shifting the graph of the parent function up by 2 units along the y-axis. In other words, every y-coordinate in the graph of f(x) is increased by 2 in the graph of h(x). The vertex of the parent function is (0,0) and is shifted to (0,2) in the transformed function. The range of h(x) is all non-negative numbers greater than or equal to 2.

When the diagonal of a rectangle splits the rectangle into two producing angles 30 - 60 - 90 the sides of the rectangle is

Area of a rectangle is solved to get 191 square in

The problem is solved using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

The shape describes a right triangle of

opposite = width

adjacent = length

hypotenuse = diagonal

The dimensions are calculated using SOH and CAH

sin 30 = opposite / hypotenuse

sin 30 = width / 21

width = 21 * sin 30

width = 10.5

For the length

cos 30 = adjacent / hypotenuse

cos 30 = length / 21

length = 21 * sin 30

length = 18.19

Area of a rectangle = length * width

Area of a rectangle = 18.19 * 10.5

Area of a rectangle = 190. 995

Area of a rectangle = 191 square in

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The lengths of all three sides of the triangle are;

43.6 inches

52.3 inches

61.1 inches

The arcs are seen to be two times the angles and as such, the arc made by the 50° angle is 100° and then we see that the one made by the 60 degree angle given as 120°.

Formula for the circumference of a circle is;

C = 2πr

C = 50π inches

C = 157 inches

The arc made by the 50° angle is;

Arc length = 157*100/360

=  43.6 inches

The arc length made by the 60° angle = 157(120/360)

=  52.3 inches

The arc length made by the remaining 70° angle is;

Arc length = 157(140/360)

Arc length = 61.1 inches

Total arc length = 43.6 + 52.3 + 61.1

= 157 inches.

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A square's side to perimeter ratio is one to four.

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Step-by-step explanation:

the perimeter of a rectangle is

2×length + 2×width

in our case we have

268 = 2×86 + 2x = 172 + 2x

96 = 2x

x = 96/2 = 48 m

The characteristics of parallel lines:

1) Parallel lines lie in the same plane

2) The parallel lines  never intersect each other.

3) The slopes of parallel lines are equal.

We know that two lines are parallel to each other if they lie in the same plane and never intersect each other.

Parallel lines are always equidistant from each other.

Also, the parallel lines are coplanar.

Mathematically, the parallel lines are represented by the symbol, ‘||‘.

If two lines l₁ and l₂ are parallel to each other then they are represented as l₁ || l₂.

Also, the slopes of parallel lines are equal.

Let m₁ be the slope of line l₁ and m₂ be the slope of line l₂.

If line l₁ and l₂ are parallel to each other then m₁ = m₂

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The process of find the x and y coordinates of the vertex of a parabola is y = -b/2a

Coordinates in math is known as  a number on the x-axis called an x-coordinate and a number on the y-axis called a y-coordinate.

Here we need to write down the process of finding the x and y coordinates of the vertex of a parabola.

The first step is to Get the equation in the form y = ax² + bx + c.

And then we have to calculate -b / 2a ad this is the x-coordinate of the vertex.

In order to find the y-coordinate of the vertex, then we have to simply plug the value of -b / 2a into the equation for x and solve for y.

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The equivalent expression is -4m -2

An algebraic expression can be defined as an expression that is composed of terms, variables, coefficients, factors and constants.

These algebraic expressions are also known to consist of some arithmetic operations, such as;

From the information given, we have that;

4m−2+(−8m)

Now, expand the bracket

4m - 2 - 8m

Collect like terms, we get;

4m - 8m - 2

Subtract the like terms

-4m - 2

Hence, the expression is -4m - 2

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If the two lines crossed are parallel, the alternate angles are equal. It is proven that the sum of the three angles of a triangle is equal to 180 degrees.

We have to prove that ∠A + ∠B + ∠C is equal to 180 degrees.

The measure of A = ∠1

B = ∠2

C = ∠3

Given, l || BC

We know that the alternate angles are equal in parallel lines.

∠2 = ∠4 -------------- (1)

∠3 = ∠5 -------------- (2)

Adding (1) and (2),

∠2 + ∠3 = ∠4 + ∠5

By adding ∠1 on both sides,

∠1 + ∠2 + ∠3 = ∠4 + ∠5 + ∠1

From the figure,

The sum of the angles at a point on a line is equal to 180 degrees.

∠4 + ∠1 + ∠5 = 180°

So, ∠1 + ∠2 + ∠3 = 180°

Therefore, ∠A + ∠B + ∠C = 180°

Thus, If the two lines crossed are parallel, the alternate angles are equal. It is proven that the sum of the three angles of a triangle is equal to 180 degrees.

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The value of x for the given angles is 23

A transversal is a line that, at two different locations in the geometry, cuts through two lines in the same plane. The angles that result from a transversal crossing of two lines in pairs can be successive internal angles, matching angles, or alternate angles.

Given lines m and n, where m ║ n

and t intersect at both the lines as shown in the figure,

so line t works s transversal,

and angles,

(8x - 27)° and (7x - 4)°

both the angles are at the bottom of the line and same side so they are corresponding angles,

and corresponding angles for any transversal are equal,

(8x - 27)° = (7x - 4)°

8x - 27 = 7x - 4

8x - 7x = -4 + 27

x = 23

Hence the value of x is 23.

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The midpoint of the line segments with

1) (-4,-2), (3, 3) is ( -1/2 , 1/2).

2) (−1, −6), (−6, 5) is ( -7/2 , -1/2 ).

3) (2, 4), (1, −3) is ( 3/2 , -1/2).

In geometry, the midpoint is defined as the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment. To determine the midpoint, just add the two X-values, then divide by 2 and add the two Y-values, then divide by 2. Mathematically, let (xm , ym) be coordinates of mid point of line segment ents with end points ( x₁, y₁) , (x₂, y₂). Then, xₘ =( x₁ + x₂)/2 and yₘ = ( y₁ + y₂)/2

We have , the line segments with coordinates

1) (-4,-2), (3, 3)

Midpoint = ( (-4 + 3)/2 , (-2 + 3/2) )

= ( -1/2 , 1/2)

2) (−1, −6), (−6, 5)

Midpoint = ( ( -6 +(-1))/2 , ( -6 + 5)/2)

= ( -7/2 , -1/2 )

3) (2, 4), (1, −3)

Midpoint = ((2 + 1)/2 , (4+(-3))/2)

= ( 3/2 , -1/2)

Hence, we got all midpoints for line segments.

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Complete question:

Geometry - Clark Midpoint and Distance Formulas

© 2011 Kuta Software LLC. All rights reserved.

Find the midpoint of the line segment with the given endpoints.

1) (-4,-2), (3, 3)

2) (−1, −6), (−6, 5)

3(2, 4), (1, −3)

Isosceles Triangle Theorem: If two triangle sides are similar, then their corresponding angles must also be similar. The sides of a triangle that correspond to two angles that are congruent are also congruent.

According to the isosceles Angle Theorem, the angles in an isosceles triangle that face congruent sides are also congruent.

A triangle with two equal sides is said to be isosceles. Isosceles triangle is basically such triangle which have two sides equal in magnitude. It is to be noted that because two angles should also be equal because of the two equal sides.

Angles opposing two triangle sides are congruent if their two sides are as well.

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Answer:

50%

Step-b50%y-step explanation:

Joint relative frequency

The key is to check whether the given side measures satisfy the triangle inequality theorem or not, if yes then we can create a unique triangle, if no then no triangle can be created, and if the given measures are the perimeter of a triangle, we can create many triangles.

When given three side measures of a triangle, the following scenarios can occur:

Unique triangle: If the three side measures given are the lengths of the three sides of a triangle and they satisfy the triangle inequality theorem, then we can create a unique triangle. The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

No triangle: If the three side measures given do not satisfy the triangle inequality theorem, then it is not possible to create a triangle with those side lengths.

Many triangles: If the three side measures given are the perimeter of a triangle, and we are allowed to vary the lengths of the three sides of the triangle within a certain range, then we can create infinitely many triangles.

Example: A triangle with perimeter 12cm, we can create a unique triangle with sides 3,4,5, or we can create many triangle with sides (2,5,5), (4,4,4),(3,4,5) and so on.

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The revised form of the sentence would be as follows: Mark Twain, who was born in Florida, is one of America's most famous authors.

Nonrestrictive elements are sets of words that can be deleted from a statement without affecting its meaning.

A nonrestrictive element is nonessential because we don't need the information it provides. These elements are always separated with commas from the rest of the sentence to specify that they are not essential. If they were dropped, the meaning of the sentence would be left unchanged.

Mark Twain, is one of America's most famous authors. - In the above sentence the nonrestrictive element is a nonessential relative clause.

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Answer:8534.46

Step-by-step explanation:

The depreciated value of the bike after 12 years is $8534.46

Depreciated value is the minimum amount that an asset is worth after depreciation.

Given that, the value of a motorcycle is depreciating by 2.8% each year, the bike was purchased for $12,000,

We know that, the depreciation value is given by,

A = P(1-r)ⁿ

A = final amount

P = initial amount

r = rate

n = years or time

Therefore,

A = 12000(1-0.028)¹²

A = 12000(0.972)¹²

A = 8534.46

Hence, the depreciated value of the bike after 12 years is $8534.46

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Answer:

$389.5

Step-by-step explanation:

621/2 = 310.5 assuming they're equal therefore, it is stated that the table cost cost 79 less than the bench so we substract.

310.5 - 79 = 231.5

This is the cost of garden table, lets find the bench now.

621(both table and bench)-231.5(garden table)= 389.5 is the cost of the bench.

Answer:

5x + 7y + 4

Step-by-step explanation:

5x + (6y+y) ( 3+1)

5x + 7y + 4

Answer:

327 miles

Step-by-step explanation:

Answer:

327.5 miles

Step-by-step explanation:

45 times 4.5 + 50 times 2.5 = 327.5

The angle that are equal to m∠5 are ∠9 and ∠12, therefore, C and D.

When two straight lines or rays intersect at a shared endpoint, an angle is generated. An angle's vertex is the common point of contact. Angle is derived from the Latin word angulus, which means "corner."

As per the given image, the two streets 1st ave and 2nd ave are parallel to each other while D street acts as a transverse and intersects both 1st ave and 2nd ave. Therefore, the angle that will be equal to m∠5 are:

m∠5 = m∠9, Becuase the two angles are the corresponding angles

m∠5 = m∠9m = m∠12, Becuase ∠9 and ∠12 are vertically opposite angles.

Hence, the correct options are C and D.

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The graph of the function f(x) = −15|x−40|+8 will be a piecewise linear function.

Graph explain: What is it?

A graph is defined as a mathematical structure that connects a collection of points to express a specific function. A pairwise relationship between the objects is established using it. The edges that connect the graph's vertices (also known as nodes) are its vertices (lines).

It will be a V-shape, with the vertex at x = 40 and y = 8.

On the left side of the vertex, the function will be decreasing, representing Tyra moving away from home.

On the right side of the vertex, the function will be increasing, representing Tyra moving towards home.

The vertex at x = 40 and y = 8 represents the point in time where Tyra reaches her furthest distance from home (8 miles) and then begins to head back towards home.

Key features of the graph in the context of the situation:

The vertex at x = 40 and y = 8 represents the point in time where Tyra reaches her furthest distance from home (8 miles) and then begins to head back towards home.

The left side of the vertex represents the time period when Tyra is moving away from home, and the right side represents the time period when Tyra is moving towards home.

The slope of the graph on the left side of the vertex is negative, indicating that Tyra is moving away from home at a decreasing rate, while the slope of the graph on the right side of the vertex is positive, indicating that Tyra is moving towards home at an increasing rate.

The y-intercept is at 8, which means Tyra starts 8 miles away from home.

The graph is symmetric about the y-axis because for every time x on the left side of the vertex, there is a corresponding time on the right side of the vertex.

The graph is not a function because for every x value, there are two y values, one for when Tyra is moving away from home and one for when Tyra is moving towards home.

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I would be paid $310.4 for 32 hour of work at the same rate

They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

To solve this problem we must perform the following algebraic operations with the given information

Information about the problem:

We transform the mixed fraction into improper fraction and we have:

24 1/2 =

[(24*2) + 1)] /2=

[48+1] /2=

49/2

Calculating the amount of dollars paid for 1 hour worked:

Dollar per hour = Paid  / Hours worked

Dollar per hour = $236.64 / (49/2)

Dollar per hour = $236.64 * 2 / 49

Dollar per hour = $473.28/49

Dollar per hour = $9.70

Calculating the amount of dollars paid for 32 hours worked:

Paid (32h) = Dollar per hour * Hours

Paid (32h) = $9.70/h * 32 h

Paid (32h) = $310.4

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