Round 6.027 to the nearest hundredth

16.  Valid

Reason: congruency can be represented by the symbol ≅ hence  the statement still reads <1 and <2 are congruent.

17. Invalid

Reason: A rectangle also has four right angles, It is only a square when all the sides are equal.

18. Valid

Reason: congruency can be represented by the symbol ≅ hence the statement still reads <JKM and <MKL are congruent.

19. Valid

Reason: The conclusion of the battery dying is in support of the premise giving which is leaving the light on when the car is off.

20.Valid

Reason: The conclusion, Dante obtained a part time job is in line with the premise that obtaining a pert time job, is a way to afford a car payment

21. Valid

Reason: The premise which has that selling 75% of the prom tickets will make the prom hold at country club is fulfilled, hence the prom will be held at the country club

An argument is vailed when the premises or conditions of the argument are all true. when some part of the argument is not true then it will lead to invalid conclusion.

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The simplified value of y in the equation is x = 38 + -3.5y

Simplifying

[tex](14y + -4) + (3x + 11) + (x + 21) = 180[/tex]

Reorder the terms:

[tex](-4 + 14y) + (3x + 11) + (x + 21) = 180[/tex]

Remove parenthesis around (-4 + 14y)

[tex]-4 + 14y + (3x + 11) + (x + 21) = 180[/tex]

Reorder the terms:

[tex]-4 + 14y + (11 + 3x) + (x + 21) = 180[/tex]

Remove parenthesis around (11 + 3x)

[tex]-4 + 14y + 11 + 3x + (x + 21) = 180[/tex]

Reorder the terms:

[tex]-4 + 14y + 11 + 3x + (21 + x) = 180[/tex]

Remove parenthesis around (21 + x)

[tex]-4 + 14y + 11 + 3x + 21 + x = 180[/tex]

Reorder the terms:

[tex]-4 + 11 + 21 + 3x + x + 14y = 180[/tex]

Combine like terms: -4 + 11 = 7

[tex]7 + 21 + 3x + x + 14y = 180[/tex]

Combine like terms: 7 + 21 = 28

[tex]28 + 3x + x + 14y = 180[/tex]

Combine like terms: 3x + x = 4x

[tex]28 + 4x + 14y = 180[/tex]

Solving

[tex]28 + 4x + 14y = 180[/tex]

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-28' to each side of the equation.

[tex]28 + 4x + -28 + 14y = 180 + -28[/tex]

Reorder the terms:

[tex]28 + -28 + 4x + 14y = 180 + -28[/tex]

Combine like terms: 28 + -28 = 0

[tex]0 + 4x + 14y = 180 + -28\\4x + 14y = 180 + -28[/tex]

Combine like terms: 180 + -28 = 152

[tex]4x + 14y = 152[/tex]

Add '-14y' to each side of the equation.

[tex]4x + 14y + -14y = 152 + -14y[/tex]

Combine like terms: 14y + -14y = 0

[tex]4x + 0 = 152 + -14y\\4x = 152 + -14y[/tex]

Divide each side by '4'.

[tex]x = 38 + -3.5y[/tex]

Simplifying

[tex]x = 38 + -3.5y[/tex]

Therefore, we can simplify that the value of y can be expressed as   x = 38 + -3.5y

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Solving the question with the help of geometrical progression, we get that the value of this finite series is 31.

A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.

As we know the formula for geometric progression is:

aₙ = a₁ r ⁿ⁻¹

Where , a₁ is the first term and r is the ratio , and n is the number of terms.

Here, the ratio is 4/2 = 2

Here, a₅ = 1 . 2⁵ ⁻ ¹ = 2⁴ = 16

a₄ = 1 . 2⁴ ⁻ ¹ = 2³ = 8

Now, We should calculate the value 1 + 2 + 4 + 8 + 16 = 31.

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The coordinates of the centroid of the triangle with the given vertices X (5, 7), Y (9, -3), Z (13, 2) is (13 - 4,2) or (9, 2).

The centroid is the object's center point. The centroid of a triangle is the point where the three medians of the triangle intersect. It is also defined as the point at which all three medians intersect. A median line connects the midpoint of a side and the opposite vertex of a triangle.

The midpoint D of XY is [tex]$\left(\frac{5+9}{2}, \frac{7-3}{2}\right)$[/tex] or (7, 2).

Note that DZ is a line that connects the vertex Z and D, the midpoint of XY. The distance from D(7, 2) to Z(13, 2) is 13 - 7 or 6 units.

If P is the centroid of the triangle XYZ, then [tex]$P Z=\frac{2}{3} D Z$[/tex].

So, the centroid is [tex]$\frac{2}{3}(6)$[/tex] or 4 units to the left of Z. The coordinates of the centroid (P) are (13 - 4, 2) or (9, 2).

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Answer:

LMK and QPM

Step-by-step explanation:

When two lines are crossed by another line (called the transversal), the angles in matching corners are called corresponding angles.

The factors of x²+19x-42 are (H) (x-2).

To find the factors:

Factors are: (x-2) and (x+21)

Therefore, factors of x²+19x-42 are (H) (x-2).

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Answer:

jimmy

Step-by-step explanation:

The population of Smalltown in 2018, using the mathematical operation of addition, was 3,554.

An addition is one of the basic mathematical operations involving combining two or more numbers or values to form a single value.

Additions are used to find the sum or total of a group of numbers.

2016 population of Smalltown = 3,187

2017 addition to the population of Smalltown = 148

The total population of Smalltown in 2017 = 3,335 (3,187 + 148)

2018 addition to the population of Smalltown = 219

The total population of Smalltown in 2018 = 3,554 (3,335 + 219)

Thus, in 2018, the total population of Smalltown was 3,554, 219 more than the population in 2017.

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Answer:

20

Step-by-step explanation:

2+2x45\5

=2+90/5

=2+18

=20

If a school has a total of 900 pupils and 400 pupils are boys and the rest are girls, then the ratio of the boys to the girls in the simplest form is 4:5.

A ratio in mathematics can be defined as the number of times a number contains another number or is contained in another number to express the connection between two or more things in quantity or size.

To find the ratio of boys to girls, first, we calculate the number of girls in the school. The number of girls can be found by subtracting the total number of pupils which is 900 from the number of boys which is 400.

Hence,

number of pupils that are girls = total number of pupils - number of boys

number of pupils that are girls = 900 - 400

number of pupils that are girls = 500

Hence the ratio of boys to girls can be given as,

400 : 500

Simplifying,

400/100 : 500/100

4:5

Hence, the simplest ratio of boys to girls is 4:5.

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By elimination, the system of equations, 3x + 2y = 10 , 6x + 4y = 15, has no solutions.

A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.

There are three methods that can be used to solve system of equations.

1. Elimination

2. Substitution

3. Graphing

Using the elimination method, given two equations in x and y, a variable should be eliminated by adding/subtracting the two equations.

First, multiply the first equation by 2.

3x + 2y = 10 ⇒ 6x + 4y = 20     (equation 1)

6x + 4y = 15     (equation 2)

Since the new equation of equation 1 has the same coefficients with those in equation 2, but different constants, then the two lines are in parallel.

Hence, the system of equations has no solutions.

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The sum of two given expressions will be -

h(x) = [tex]-3x^{-3} -8x^{2} -17x[/tex].

We have two expressions.

We have to add them.

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation in it.

According to the question -

f(x) = [tex]-4x^{2} -3x^{-3} -4x[/tex]

g(x) = [tex]-4x^{2} -9x -4x[/tex]

Now -

h(x) = f(x) + g(x) =  [tex]-4x^{2} -3x^{-3} -4x[/tex] + ( [tex]-4x^{2} -9x -4x[/tex])

h(x) = [tex]-3x^{-3} -8x^{2} -17x[/tex]

Hence, the sum of two given expressions will be -

h(x) = [tex]-3x^{-3} -8x^{2} -17x[/tex]

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The linear equation which has no solution is  5x+12=5x-7

Given set of linear equations are:

23(9x+6)=6x+4, 5x+12=5x-7, 4x+7=3x+7, -3(2x-5)=15-6x.

We try to solve each equations one-by-one.

Consider the first equation:

23(9x+6)=6x+4

⇒207x+138 = 6x+4

⇒201x = -134

⇒ x =-134/201.

So this linear equation has a solution.

Now consider the second linear equation:

5x+12=5x-7

⇒12 = -7, which has no meaning.

Therefore, this linear equation has no solution.

Now consider 3rd linear equation:

4x+7=3x+7

⇒x = 0

It has a solution.

Consider the 4th linear equation:

-3(2x-5)=15-6x.

⇒ -6x+15=15-6x

⇒ 0=0

In this case, any value for x is a solution. So there are infinitely many solutions.

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Answer: 5=10.25, 13=26.65, 19=38.95

Based on the information, it can be inferred that the number that is the change in height of the elevator is 12 feet.

To complete the table we must take into account the height of the elevator at a given time of seconds. Additionally, we must take into account that the elevator goes down 12 ft every second. So the table would look like this:

To calculate the height of the basement with respect to the first floor, we must take into account the following information:

To calculate this height we must multiply the time it takes for the elevator to go down to the basement by the distance it travels each second.

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Based on the graph (see attachment), John's speed on each section of the walk are as follows:

Speed can be defined as the distance covered by a physical object per unit of time. This ultimately implies that, speed can be measured as meter per seconds.

Distance can be defined as the amount of ground covered (travelled) by a physical object over a specific period of time and speed, regardless of its direction, starting point or ending point.

Mathematically, speed can be calculated by using this formula;

Speed = distance/time

Based on the graph (see attachment), John's speed on each section of the walk can be calculated as follows.

For the first interval, we have:

Speed = 6/1.5

Speed = 4 km/h.

For the first interval, we have:

Speed = 6/1.5

Speed = 4 km/h.

For the second interval, we have:

Speed = 6/0

Speed = 0 km/h.

For the third interval, we have:

Speed = 6/4

Speed = 1.5 km/h.

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The area of the circle with center located at Point B (3, 1) and tangent to the y-axis is 9π units^2. The answer is E.

The area of a circle is the area enclosed by the circle. It is the product of the square of the radius and the constant π. The Greek letter π represents the constant ratio of the circumference of any circle to its diameter, approximately equal to 3.14159.

Area of circle = πr^2

To know the radius of a circle given its center and tangent line to it, find the distance between the the center and the point of tangency. As the radius is the distance from the center of the circle to any point in the circumference of the circle

If the circle is tangent to y-axis, then the radius is the absolute value of the x-coordinate.

r = 3 units

Using the formula for the area of a circle:

Area of circle = πr^2

Area of circle = π(3 units)^2

Area of circle = 9π units^2

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The amount of money available after x number of years is given by y = 1000(1.05)ˣ

An equation is an expression that shows the relationship between two or more numbers and variables.

Let y represent the amount of money after x years. Assume our initial amount is $1000, the rate is 5% (0.05) and it will only compound once per year. The equation is given by:

y = 1000(1 + 0.05)ˣ

y = 1000(1.05)ˣ

The amount of money available after x number of years is given by y = 1000(1.05)ˣ

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1 = -4(2) + 9 is an equation in slope-intercept form for the line passing through points (-2,17) and (2,1)

A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane allows one to anticipate whether a line is parallel, perpendicular, or not.

The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. Δy is the net change in the y coordinate, while Δx is the net change in the x coordinate.  

Therefore,

m =  y₂-y₁/x₂-x₁ (where m denotes the slope) can be used to express how the y coordinate changes in relation to the x coordinate.

Be aware that tan ∅ = y/x

We also refer to this tan as the line's slope

We have been asked to write an equation in slope-intercept form for the line passing through (-2,17) and (2,1)

First we will find the slope(m)

We know that slope = m = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

For the pairs of points (-2,17) and (2,1)

⇒ m = [tex]\frac{1- 17}{2 - (-2)}[/tex]

⇒ m = [tex]\frac{-16}{4}[/tex]

⇒ m = -4

We know that the equation for slope(m) and y - intercept(b) of a line is given by :

y = mx + b

Here lets take equation 1 = -4(2) + b .Here x and y is substituted with the second two points.

⇒  1 = -4(2) + b

⇒  1 = -8 + b

⇒  b = 1 +8

⇒  b = 9

The equation in the slope intercept is as follows:-

1 = -4(2) + 9

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The dimensions given the maximum volume will be 9 cm by 9 cm by 4 cm. The volume of the box with a quadratic function will be V = 72L - 4L².

Let the prism with a length of L, a width of W, and a height of H. Then the volume of the prism is given as

V = L x W x H

Imagine you work for a packaging firm and are building a box with a 36 cm-long rectangular bottom. The box has to be 4 cm tall.

The perimeter is given as,

36 = 2 (L + W)

W = 18 - L

Then the volume is given as,

V = L x W x H

V = L x (18 - L) x 4

V = 72L - 4L²

For the maximum volume, V' = 0

V' = 0

72 - 8L = 0

8L = 72

L = 9

Then the width will be

W = 18 - 9

W = 9

The dimensions given the maximum volume will be 9 cm by 9 cm by 4 cm. The volume of the box with a quadratic function will be V = 72L - 4L².

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The value of a cannot be determined because the expression is not an equation

The expression is given as:

a/2 - 3/2 + 22

The above is an expression, and not an equation

For the value of the variable a to be solved, the expression must be an equation

Equations are mathematical expressions that are represented by the equal to or equality sign i.e =

Examples of equations are:

a + b = c

y = mx + c

Ax + By = C

y = ax^2 + bx + c

y =  x

Hence, the value of a cannot be determined because the expression is not an equation

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Answer:

The answer is $86.80. The lunch service gains $86.80 in 3 1/2 hours if they get $24.80 per hour.

Step-by-step explanation:

You have to multiply how much they earn per hour, $24.80, by the number of hours they work, 3 1/2. $24.80 times 3 1/2 equals 86.80 so the lunch service earns $86.80 in 3 1/2 hours.

Hope this helps!

Answer:

10 times 3.50 + 10x= f(x)

Step-by-step explanation:

35+28

f(x)= 63

The function f(x) that presents the total cost of the candy will be f(x) = 35 - 0.70x.

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

Mark decided to make Christmas presents for his classmates. he bought 10lb of two types of candies: caramel candies for $2.80 per pound and chocolate candies for $3.50 a pound.

Let x be the number of pounds of caramel candies and (10 - x) be the number of pounds of chocolate candies. Then the equation is given as,

f(x) = 2.80x + 3.50(10 - x)

f(x) = 2.80x + 35 - 3.50x

f(x) = 35 - 0.70x

The function f(x) that presents the total cost of the candy will be f(x) = 35 - 0.70x.

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The simplification form of the given complex fraction [tex]\frac{1}{1+\frac{x}{y} }[/tex]  is equal to

(y)/ (y +x).

As given in the question,

Given complex fraction is equal to  [tex]\frac{1}{1+\frac{x}{y} }[/tex]

Simplify the given complex fraction by taking the least common multiple of the denominator,

[tex]\frac{1}{1+\frac{x}{y} }\\\\\\= \frac{1}{\frac{y+x}{y} } \\\\\\=\frac{ (1)(y)}{y+ x} \\\\= \frac{y}{y+x}[/tex]

Therefore, the simplification form of the given complex fraction [tex]\frac{1}{1+\frac{x}{y} }[/tex]  is equal to (y)/ (y +x).

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Money received in tenth month: $104

Difference between explicit formula and a recursive formula is: the use of (n-1)th term, nth term and the common difference (d) brings a great difference between the two formulae of an arithmetic progression.

A series of numbers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.

Given:

To find: Money received in tenth month.

Finding:

As we can see, the pattern followed here is: increment in each amount received each month by $1. Thus it is an arithmetic progression.

That is: 50, 52 (0+2), 55 (2+3), 59 (2 + 3 + 4) and so on.

Thus, for the tenth month, we can use the formula of recursion, given by: [tex]a_n=a_{n-1}+n[/tex], n ≥ 1.

For a₁ = 50, a₂ = a₁ + 2

=> a₂ = 50 + 2

This way, a₅ = a₄ + 5

=> a₅ = 59 + 5 = 64

a₆ = a₅ + 6

=> a₆ = 64 + 6 = 70

a₇ = a₆ + 7

=> a₇ = 70 + 7 = 77

a₈ = a₇ + 8

=> a₈ = 77 + 8 = 85

a₉ = a₈ + 9

=> a₉ = 85 + 9 = 94

a₁₀ = a₉ + 10

=> a₁₀ = 94 + 10 = 104

Thus, the payment received in tenth month will be $104.

(b) Difference between explicit formula and recursive formula of an arithmetic progression:

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The area of the enlarged photograph will be 16 times the area of original photograph.

For the given scale in the question;

Noah enlarges a photograph using the scale 1 inch : 4 inches.

Let the original length of photograph is 'L'.

Let the original width of photograph is 'B'

Old Area  = LB

Thus, the length and width of the scale will get increased by 4 times.

The new length and width will be 4L and 4B.

Thus, the new area will be;

New Area = (4L)(4B)

New Area = 16 LB

New Area = 16 × (old area)

Thus, the new area of the photograph is increased by 16 times.

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The values of x associated with each case are listed below:

Herein we find two cases of geometric systems generated by two parallel lines and auxiliary line segments, wherein we must use the concept of supplementary angles and triangle properties to determine the value behind angles. Now we proceed to determine the value of the variable x for each case:

Case 1

Case 2

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Sarah's charges per hour for working during the week will be $9.5.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

Sarah is a nanny who bills clients at various prices depending on whether she is working during the week or on the weekend. She worked 45 hours in a single week for a salary of $902.50, of which 5 hours were on the weekend. She worked 50 hours the next week, 10 of which were on the weekend, and made 1045 dollars.

Let x be the charge per working hour and y be the number of charges per hour during the weekend. Then the equation will be

45x + 5y = 902.5           ...1

50x + 10y = 1045

25x + 5y = 522.5          ...2

Subtract equation 2 from equation 1, then we have

45x - 25x = 902.5 - 522.5

20x = 380

x = 19

And the value of y will be

25 (19) + 5y = 522.5

475 + 5y = 522.5

5y = 47.5

y = 9.5

Sarah's charges per hour for working during the week will be $9.5.

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Answer:

16

Step-by-step explanation:

the first thing is to rearrange terms