Use a proof by contraposition to prove that if m and n are integers and mn is even, then m is even or n is even.

The solution of the system of equations by the graphical methods yields  x equals 9 and y is 6 i.e, 9 hours of landscaping and 6 hours of waiting tables.

Bella worked x hours working landscaping at $10 per hour.

Total amount earned = 10x

Bella worked y hours working on clearing tables at $ 15 per hour

Amount earned = 15 y

x and y are variables as given

She worked a total of 15 hours and she gets $180 for the combined efforts.

The system of equation can be represented as:

x + y = 15

10x + 15y = 180

Now we will solve the two equations graphically:

So from the attached graph we can see that the point (9,6) is the required solution.

Hence she worked landscaping for 9 hours and clearing tables for 6 hours.

Let us solve by substitution to verify the results:

x + y = 15

or, x = 15 - y

Now 10x + 15y = 180

or, 10 (15-y) + 15y = 180

or, 150 - 10y +15y = 180

or, 5y = 180 - 150

or, y = 6

At y = 6 , x = 15 - 6 = 9

Hence (9,6) is the solution.

System of equations also known as simultaneous equations can also be solved by the elimination method.

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A set-to-set function f is a relation that assigns one element of the set A to each element of the other set B. The set A is the domain of the function (also called the set of inputs) and the set B contains the range (also called the set of outputs).

Let's denote f as exponential function with the base 'a':

                                  f(x) = a ˣ

where, a > 0 and a ≠ 1 and x is any real number.

1. Not an exponential function:

We have the following equation:

[tex]y = 100 (1 - 12)^{t}[/tex]

We can write the equation as:

[tex]y = 100 (-11)^{t}[/tex]

Let's denote f as exponential function with the base 'a':

                                  f(x) = a ˣ

where, a > 0 and a ≠ 1 and x is any real number.

Therefore: a must be more than 01.

In this problem, a = -11, therefore this is not an exponential function.

2. Growth.:

The function:

[tex]y= 0.1(1.25)^{t}[/tex]

The above equation is an exponential function because is a function of the form

[tex]f(t) = ka^t[/tex]

where, a > 0 and k is constant

Therefore, k = 0.1 and  a = 1.25 . So, a is greater than 1.

3. Growth:

The function:

[tex]y = {(1 - 0.03)12}^2t[/tex]

The above equation can be written as:

[tex]y = 11.64^{2t}[/tex]

which  is an exponential function because is a function of the form

[tex]f(t) = a^{bt}[/tex]

where, a > 0 and b is constant.

So, a = 11.64 and b = 4 . Since a is greater than 1.

4. Decay:

The function:

[tex]y = 426(0.98)^t[/tex]

This is an exponential function because is a function of the form

[tex]f(t) = ka^t[/tex]

where, a > 0 and k is constant

So, k = 426 and a = 0.98. Since, a is less than 1.  

5. Growth:

The function:

[tex]y = 2050(12)^t[/tex]

This is an exponential function because is a function of the form

[tex]f(t) = ka^t[/tex]

where, a > 0 and k is constant.

So, k = 2050 and a = 12  . Since, a is greater than 01.  

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We had written an algorithm, using pseudo code.

//Define the required variables.

total_number_of_steps = 0

number_of_steps = 0

//robot stands up to walk.

stand

//the robot moves forward till the wall is not reached.

while (wall is not reached)

//the robot senses the wall with the help of arms.

raise arms

sense_the_wall

if (wall is not there)

//if the wall is not found, the robot lowers the arms

lower arms

//if wall is not detected, the robot moves forward.

step_forward

//increment the number of steps forward.

number_of_steps=number_of_steps+1

//increment the total number of steps.

total_number_of_steps=total_number_of_steps+1

else

exit

end if

end while

//else if the wall is found, lower the arms

lower arms

//the robot turns 90 degrees right once.

turn_right_90

//the robot turns 90 degrees right again.

turn_right_90

//till the number of steps does not reach 0, move

for (number_of_steps! = 0)

step

//increment the total number of steps.

total_number_of_steps=total_number_of_steps+1

//the robot moves backwards on detecting the wall, so

//decrement the number of steps.

number_of_steps = number_of_steps-1

//end the for loop.

end for

//the robot turns 90 degrees left once.

turn

//the robot turns 90 degrees left again.

turn

//the robot sits down.

sit

//display the total number of steps taken by robot

display total_number_of_steps

The last line ends the pseudocode

Stop

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Answer:

9

Step-by-step explanation:

3.4^0 = 1

9^1 = 9

1 * 9 = 9

The correct matching regarding the linear functions are given as follows:

i. A set of points where the coordinates of each point has a sum of 2: Line n.

ii. A set of points where the y-coordinate of each point is 10 less than the x-coordinate: Line m.

b - i) Two numbers with a sum of 2: A and C.

b - ii) Two numbers where the y-coordinate is 10 less than the x-coordinate: D and E.

b - iii) Two numbers with a sum of 2 and where the y-coordinate is 10 less than the x-coordinate: B.

The set of points where the coordinates of each point has a sum of 2 is defined by the following linear function

x + y = 2.

In slope-intercept form, it is of:

y = 2 - x.

Which is the decreasing line n, with an intercept of 2.

A set of points where the y-coordinate of each point is 10 less than the x-coordinate is defined by the following linear function

y = x - 10.

Which is the increasing line m, which an intercept of m.

The coordinates of each point are given as follows:

These points are then used to match the sentences in item b.

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Answer:0.1875

Step-by-step explanation: you would take the miles and divide it my the minutes which would be 3 divided by 16 which equals 0.1875

The best estimate of the solution to the system of linear equations is the point are (x,y) will be (0.76, 4.30).

A linear equation in two variables is one that is written in the form axe + by + c=0, where a, b, and c are real numbers and the coefficients of x and y, i.e. a and b, are not equal to zero.

Given:

as x,y are variables,

-3x + y = 2 ..............(1)

- 4x + 7y = 1 ...........(2)

We know that,

The solution of the system of linear equations is the intersection point of both graphs

Multiply equation (1) by 7 on both sides and then subtract it from eq (2)

- 4x + 7y = 1 ...........(2)

-21x + 7y = 14 ..............(1)

⇒- 17 x = -13

⇒ 17 x = 13

⇒ x =[tex]\frac{13}{17}[/tex]

⇒ x = 0.76

Now on putting value of x  = 0.76 in eq (1) we get

- 3x + y = 2 ............ (1)

⇒- 3(0.76) + y = 2

⇒y = 4.30

The best estimate of the solution to the system of linear equations is the point (x,y) will be (0.76, 4.30).

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The solution in inequality notation and in interval notation is (-∞ . -√5]∪[√5,36)

The term inequality refers the a relationship between two expressions or values that are not equal to each other is called 'inequality.

Here we have given the inequality (x² - 5)/ (x - 36) < 0

And we need to find the solution in inequality notation and in interval notation.

In order to find the inequality notation, we have to solve the given inequality, then we get.

(x² - 5)/ (x - 36) < 0

(x² - 5) < 0

x² < 5

x < √5

While we looking into the inequality we must know that the denominator must not be 0.

So, the interval notation can be written as,

=>  (-∞ . -√5]∪[√5,36)

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The graph that shows the linear relationship of the table is attached below.

To determine the graph of a linear relationship, do the following:

Given the table which represents a linear relationship above, use two pairs of values, (0, 0) and (2, 1) to find the slope:

Slope = change in y / change in x = (1 - 0) / (2 - 0)

Slope = 1/2.

The y-intercept (b) = 0.

Thus, this means that the graph of the linear relationship will have a slope of 1/2 and crosses the y-axis at 0.

Thus, the graph is shown below.

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It has been (mathematically) proven that there is no polynomial time algorithm for any np-complete problem. the given statement is false.

In order to solve previously unsolvable issues, Leonid Khachiyan developed a polynomial-time method, in which the number of processing steps increases as a power of the number of variables rather than exponentially.

Determining whether NP-complete problems are tractable or intractable remains one of the most crucial concerns in theoretical computer science since it is unknown if any polynomial-time algorithms will ever be developed for them.

So, it is unknown if any polynomial-time algorithms will ever be developed for them.

By applying different constraints, a linear function is maximized or reduced in linear programming, a mathematical modelling approach. In commercial planning, industrial engineering, and—to a lesser extent—the social and physical sciences, this method has proven helpful for directing quantitative decisions.

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The answer: A

35.8 inches

the measure of ∠LPM is 90°

the measure of ∠PMN is 102°

the length of LN is 10 units.

Define Rhombus.

A rhombus is a special case of a parallelogram, and it is a four-sided quadrilateral. In a rhombus, opposite sides are parallel and the opposite angles are equal.

For a Rhombus, LMNO

∠LON = 102°

NP = 5 units

By the properties of Rhombus, we know that

All sides of a rhombus are congruent (equal)

So, LM = MN = NO = OL

and

Opposite angles are equal and the opposite sides are parallel.

So, ∠LON = 102° = ∠LMN

Since Adjacent angles add up to 180°.

Therefore ∠L + ∠M = 180°

                 ∠M + ∠N = 180°

                 ∠N + ∠O = 180°

                 ∠O + ∠L = 180°

So, ∠N = 180° - ∠O = 180° - 102° =78°

      ∠L = 180° - ∠O = 180° - 102° =78°

      ∠M = 180° - ∠L = 180° - 78° =102°

Diagonals bisect each other at 90° or we can also say that each of the two diagonals in a rhombus is the perpendicular bisector of the other.

So, ∠LPM = ∠NP0 = ∠MPN = ∠LPO =90°

Thus, the measure of ∠LPM is 90°

         the measure of ∠PMN is 102°

         the length of LN is 10 units.

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Answer:

Lpm= 90

PMN=51

LN= 10

Step-by-step explanation:

How many hours per pound does it take to thaw a turkey?

Allow 30 minutes of thawing time for each pound of turkey, which translates to two to six hours for a 4- to 12-pound turkey. A 12- to 15-pound bird will thaw in six to eight hours. Still having trouble determining the thaw time of the turkey?

Hope this helps :D

A solid figure is a three-dimensional object. That is, it has length, width, and height. Because they are three-dimensional, they have depth and occupy space in our universe. Body types are identified according to characteristics specific to each body type. In particular, we can observe the number of faces, edges, vertices, and the shape of the base.

A flat face of a solid is its face or side, as it is commonly called. The base is the surface on which the figure rests. A solid edge is a line segment where two faces meet. A vertex  is an angle formed where the endpoints of two or more face segments meet.

A sphere is a solid figure that has no faces, edges, or vertices. This is because it is perfectly round. No flat sides or corners.

A cone has faces but no edges or vertices. His face is circular. A circle is a plane because it is a flat planar shape. However, since it is rounded on the outside, it does not form edges or corners.

Cylinder that has two circular faces but no edges or corners:

A pyramid has a base and at least three triangular faces. There are edges where faces meet each other or meet the bottom, vertices where two faces meet the bottom, and top vertices where all the triangle faces meet. Pyramids are named for the shape of their base.

A triangular pyramid has a triangular base and his other three triangular faces, or four triangles in total.

A pyramid has a rectangular base and a pyramid has a square base. Both have four triangular faces, for a total of five faces.

Prism:

A prism is a solid with two congruent parallel faces and any number of sides. That is, it can have any number of faces, but at least two faces must be parallel. The shape of the two parallel faces can be triangles, squares, rectangles, pentagons, hexagons, or other types of polygons. Prisms are named after the shape of the base.

Sphere:

A sphere is a geometric object that is the three-dimensional analogue of the two-dimensional circle. A sphere is a set of points that are all the same distance r from a given point in 3D space. This given point is the center of the sphere and r is the radius of the sphere. Spheres are fundamental objects in many areas of mathematics. Spherical and near-spherical shapes also occur in nature and industry. Bubbles, like soap bubbles, are spherical in equilibrium. The Earth is often approximated as a sphere in geography, and the celestial sphere is an important concept in astronomy.

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The total income from the machines over the first 5 years is $185.89

From the question, we have the following parameters that can be used in our computation:

f(t) = 160e0.03t

Where

Rewrite the function properly

so, we have the following representation

f(t) = 160e⁰.⁰³ⁿ

The above function is an exponential function

So: In the first 5 years, we have the value of t to be 5

This is represented as follows

t = 5

Substitute the known values in the above equation, so, we have the following representation

f(5) = 160e⁰.⁰³ ˣ ⁵

Evaluate the product of the exponents

f(5) = 160e⁰.¹⁵

The products above give

f(5) = 185.89

Hence, the total income is $185.89

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Answer:

0.65 pens

2.25 rubber

Step-by-step explanation

You can make two equations with the information given and solve them simultaneously to find x and y. Assume x is pens and y is rubber.

Answer:

Answer is y = 11

Step-by-step explanation:

8 = y - 3

or, 8 + 3 = y - 3 + 3

or, 11 = y

or, y = 11

Answer:

The sequence is not arithmetic. In an arithmetic sequence, the difference between consecutive terms is constant. However, in this sequence, the difference between the terms is not constant. For example, the difference between the first and second terms is 1^5 - 2^5 = -3, while the difference between the second and third terms is 2^5 - 3^5 = -6. Since the difference between consecutive terms is not constant, this sequence is not arithmetic. Therefore, the common difference is NONE.

Answer:

No, the sequence is not arithmetic.

d = NONE

Step-by-step explanation:

An Arithmetic Sequence has a common difference between each term (the difference between each term is the same).

Given sequence:

[tex]1^5, 2^5, 3^5, 4^5, 5^5, ... = 1, 32, 243, 1024, 3125, ...[/tex]

Calculate the difference between each term:

[tex]1 \underset{+31}{\longrightarrow} 32 \underset{+211}{\longrightarrow} 243 \underset{+781}{\longrightarrow} 1024 \underset{+2101}{\longrightarrow} 3125[/tex]

As the difference between each term is not constant, the sequence is not an arithmetic sequence.

Therefore, the common difference, d = NONE.

Sister's age will be equal to 12 and Kim's age is 24.

An equation is an expression that shows the relationship between two or more numbers and variables. Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Consider that x is sister's age, Kim's age is twice that of her sister

Thus Kim's age = 2x

Kim’s age + Sister’s age = 36

The equation:

x + 2x = 36

Now solve the equation;

x + 2x = 36

3x = 36

 x = 36 / 3

 x = 12

Therefore, Kim's age = 2x = 2(12) = 24

Hence, Sister's age is 12 and Kim's age is 24.

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The equation of a hyperbola can be written in the form:

(x-h)^2/a^2 - (y-k)^2/b^2 = 1

where (h, k) is the center of the hyperbola, a is the distance from the center to the vertices on the x-axis, and b is the distance from the center to the vertices on the y- axis.

In this case, the vertices of the hyperbola are (6,4) and (0,4), and the center of the hyperbola is at (3,4). The distance from the center to the vertices on the x- axis is 3, and the distance from the center to the vertices on the y- axis is 0.

Plugging these values into the equation for a hyperbola, we get:

(x-3)^2/3^2 - (y-4)^2/0^2 = 1

This equation is not defined, because the value of b is 0. This means that the hyperbola has a horizontal orientation, and its vertices are on the y-axis.

To find the equation of the hyperbola, we need to rewrite the equation in a different form. We can do this by using the fact that the distance between the center of the hyperbola and a point on the hyperbola is given by:

√ ((x-h)^2 + (y-k)^2) = a*√ (1 + (y-k)^2/b^2)

Substituting in the values for h, k, and a, we get:

√ ((x-3)^2 + (y-4)^2) = 3*√ (1 + (y-4)^2/0^2)

This equation can be simplified to:

√ ((x-3)^2 + (y-4)^2) = 3*√((y-4)^2/0^2)

The value of b is still 0, so the equation for the hyperbola is:

(x-3)^2 = 9*(y-4)^2

This is the equation for a horizontal hyperbola with vertices (3,4) and (9,4) and asymptotes y = 1/3x + 3 and y = -1/3x + 5.

A hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces which is known as connected components, that are mirror images of each other and resemble two infinite bows.

Therefore, the correct answer is as given above

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Answer:

0.1904

Step-by-step explanation:

4/7 ÷ 3 is = 0.1904

Answer: I hope this helps

Step-by-step explanation:

4/7 divided by 3

Dividing is equivalent to multiplying by the reciprocal
4/7 times 1/3 or 4/7•1/3

Multiply the fractions

And you get

4/21 or 0.190476

As per the linear equation, the x-intercept of the graph of the equation will be (-8, 0).

It is possible to determine a line's direction and steepness by looking at its slope. Finding the slope between lines inside a coordinate plane can aid in anticipating if the lines are perpendicular, parallel, or none at all without physically using a compass.

As per the information given in the question,

The given equation is,

y= -1/4 x + 2

Now, let's take y = 0 for x- intercept,

So, the equation will be,

0 = 1/4x + 2

1/4x = -2

x= -8

The x-intercept is (-8, 0).

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The question sees incomplete, your question may be:

Here is a linear equation: y = 1/4x + 2 What is the x-intercept of the graph of the equation?

The value of down payment will be;

⇒ $705

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

Monique buys a $4700 air conditioning system using an installment plan that requires 15% down.

Now,

Since, Monique buys a $4700 air conditioning system using an installment plan that requires 15% down.

Hence, The value of down payment = 15% of $4700

                                                        = 15/100 × 4700

                                                        = 15 × 47

                                                        = 705

Thus, The value of down payment = $705

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The population standard deviation [tex]\sigma[/tex] is 6.697.

The average distance between each data item and the mean is known as the mean absolute deviation.

The gap between each data value and the mean in absolute terms is represented by this average.

The given data set can be arranged as 4, 7, 8, 10, 12, 12, 15, 18, 23, 26.

Mean[tex](\overline{x})[/tex] = (4 + 7 + 8 + 10 + 12 + 12 + 15 + 18 + 23 + 26)/10.

Mean[tex](\overline{x})[/tex] = 135/10 = 13.5.

We know variance[tex](\sigma)[/tex] = [tex](\[ \sum_{i=1}^{n}x_i^2 \]/n) - \overline{x}^2[/tex].

= (4² + 7² + 8² + 10² + 12² + 12² + 15² + 18² + 23² + 26²)/10 - (13.5)².

= (16 + 49 + 64 + 100 + 144 + 144 + 225 + 324 + 529 + 676)/10 - 182.25.

= 44.85

And we also know the standard deviation is [tex]\sqrt{\sigma}[/tex] = [tex]\sqrt{44.85}[/tex] = 6.697

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The expression (4c − 3d)(3c + d) is equivalent to 12c² - 5cd - 3d²

An expression is combination of variables, numbers and operators.

(4c − 3d)(3c + d) is the given expression.

Four times c minus three times d into three times f c plus d.

In the given expression c and d are variables.

Plus and minus are operators.

We need to find the equivalent expression of (4c − 3d)(3c + d).

(4c − 3d)(3c + d)

4c(3c+d)-3d(3c + d)

Apply the distributive property.

12c² + 4cd - 9cd - 3d²

Add the like terms

12c² - 5cd - 3d²

Hence, 12c² - 5cd - 3d² is the equivalent expression of (4c-3d)(3c+d).

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Answer:

-41.328

Step-by-step explanation:

Answer:

-41.328

Step-by-step explanation:

Addition multiplied by subtraction gets you subtraction. +-=-

so now, ()= multiplication

so now all you have to do is 17.22 times 2.4 which gets us 41.328

then, add the negative sign which gives you -41.328

yw :)

Answer:

B, F

Step-by-step explanation:

[tex]2x^2(x-4)^2=0 \\ \\ \implies x^2=0, (x-4)^2=0 \\ \\ \implies x=0,4[/tex]

When tiles are drawn, with replacement, from a bag of lettered tiles, X is the number of vowels in 5 draws variable has binomial distribution

The possibility that a value would take one of two independent values given a particular combination of factors or assumptions is summarised by the statistical distribution known as the binomial distribution.

The basic presumptions of the binomial distribution are:

As opposed to a continuous distribution, like the normal distribution, the binomial distribution is a frequent discrete distribution used in statistics.

The probability of success raised to the power of the number of successes and the probability of failure raised to the power of the difference between the number of successes and the number of trials are multiplied to create the binomial distribution.

The result is then multiplied by the sum of the number of attempts and the number of successes.

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Answer:

  7.2 cm

Step-by-step explanation:

You want the value of C to the nearest tenth centimeter, given that 4^2 + 6^2 = C^2.

Simplifying gives ...

  4^2 + 6^2 = C^2

  16 +36 = C^2 = 52

  C = √52 ≈ 7.2

The length of the missing side is about 7.2 cm.