6. (4 points) prove by contraposition for arbitrary x 6= 0: if x is irrational, then so is 1/x.

In the given Geometric shape/figure ∠1=∠4 i.e. C.

What are geometric shapes?

In Mathematics, Geometric shapes are the figures which demonstrate the shape of the objects we see in our everyday life. In geometry, shapes are the forms of objects which have boundary lines, angles and surfaces. There are different types of 2d shapes and 3d shapes.

Shapes are also classified with respect to their regularity or uniformity. A regular shape is usually symmetrical such as a square, circle, etc. Irregular shapes are asymmetrical. They are also called freeform shapes or organic shapes. For example, the shape of a tree is irregular or organic.

In plane geometry, the two-dimensional shapes are flat shapes and closed figures such as circles, squares, rectangles, rhombus, etc.  In solid geometry, the three-dimensional shapes are cube, cuboid, cone, sphere and cylinder. We can observe all these shapes in our daily existence also. For example books (cuboid shape), glasses (cylindrical shape), traffic cones (conical shape) and so on.

Now,

    As we know, If two lines intersect and make an angle, say X=45°, then its opposite angle is also equal to 45°.

The same theorem is applied here

hence

          The opposite angles ∠1 and ∠4 equal.

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The angle opposite to the smallest angle is the smallest side. Thus,

TS < US < TU.

If you have the perimeter P and width w , its length can be found with h = P/2−w . If you have the diagonal d and width w , it's length is h = √(d²−w²). When we're trying to find the hypotenuse we substitute our two known sides for a and b. It doesn't matter which leg is a and which is b. Then we solve for c by adding the squared values of a and b and taking the square root of both sides.

The sides of a triangle rule asserts that the sum of the lengths of any two sides of a triangle has to be greater than the length of the third side.

Every triangle has three sides and three angles, some of which may be the same. The sides of a triangle are given special names in the case of a right triangle, with the side opposite the right angle being termed the hypotenuse and the other two sides being known as the legs.

In the given triangle the angle of interior angle is 180:

43z + z + 66 + z + 69 = 180

45z + 135 = 180

45z = 180 - 135

45z = 45

z = 1

The three angles are:

U = 43(1) = 43

T = 1 + 66 = 67

S = 1 + 69 = 70

The angle opposite to the smallest angle is the smallest side. Thus,

TS < US < TU

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Answer:

he will need 360g of margarine

Step-by-step explanation:

u need 180g to make 12 cakes...so all u need to do is double it

The measures of those two angles are 105° and 135°

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

We have to given that;

Two angles of a quadrilateral measure 110° and 10°.

And, The other two angles are in a ratio of 7 : 9.

Now, We know that;

The sum of all four interior angles of a quadrilateral are 360°.

Here, The other two angles are in a ratio of 7 : 9.

Hence, Measure of both angles are 7x and 9x.

So, We get;

⇒ 110° + 10° + 7x + 9x = 360°

⇒ 120 + 16x = 360

⇒ 16x = 360 - 120

⇒ 16x = 240

⇒ x = 15

Thus, Measure of both angles are;

⇒ 7x = 7 × 15 = 105°

⇒ 9x = 9 × 15 = 135°

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The equation of the line that passes through the point (2, -3) and is parallel to the line y = 8 is y = -3.

What is the equation ?

The equation is a mathematical statement that shows the relationship between different values. It can be written using symbols, numbers and operations to describe the relationship between one or more variables. An equation usually consists of an equal sign (=) that separates two expressions which have the same value. For example, the equation 2+2=4 states that two plus two is equal to four.

The equation of a line is given by y = mx + b, where m is the slope and b is the y-intercept. Since the line is parallel to the line y = 8, they have the same slope, which is 0. Thus, the equation of the line that passes through the point (2, -3) is y = 0x + (-3). Simplifying this equation, we get y = -3.

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Answer:

y = -1/4x + 5

Step-by-step explanation:

(y - y1) = m(x - x1)      Point - slope form

y - 3 = -1/4(x - 8)

y - 3 = -1/4x + 2

y = -1/4x + 2 + 3

y = -1/4x + 5

Answer:

8.1

Step-by-step explanation:

12/x = tan56

12/x =1.48

so x = 12/1.48 =8.1

Answer:

$54.3

Step-by-step explanation:

17% of 319.41

so u need only to multiply them

Advantages of using a permutation as in problem 1 include increased efficiency and simplicity, while disadvantages include reduced flexibility and a potential loss of information.

Permutations are mathematical operations that rearrange elements in a list or sequence, and there are different ways to define and generate permutations. A permutation specified in problem 1 may have certain desirable properties, such as being easy to compute, having low computational complexity, or having a simple mathematical form.

These advantages, however, can also be disadvantages if they limit the ability to capture more complex or subtle relationships between elements, or if they prevent the use of other methods that may be more appropriate for a particular application. Therefore, the choice of a specific permutation method depends on the requirements of the problem and the available computational resources.

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Answer:

Account A:

$1,149.15

Account B

$1,906.80

The statement ∀x∃y∃z(y 6= z → p(x, y) ∧ p(x, z)) is false.

Let's start by understanding what "p" is. "p" is a function that takes in two arguments, x and y. It tells us whether the relationship between x and y is true or false.

Now, let's look at the statement

=>∀x∃y∃z(y 6= z → p(x, y) ∧ p(x, z)).

This statement says that for every x, there exists a y and a z such that y is not equal to z and both p(x, y) and p(x, z) are true.

This statement is actually false.

Why? Imagine if p(x, y) only returned true when y was equal to x. Then, there would be no y and z such that y is not equal to z and both p(x, y) and p(x, z) are true.

Therefore, it is possible for the function "p" to return false for the statement

=> ∀x∃y∃z(y 6= z → p(x, y) ∧ p(x, z)).

It depends on the definition of the function. To determine if the statement is true or false, we need to know what the function "p" is.

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Answer: 484 in^3

Step-by-step explanation:

The volume equation of a rectangular prism is length x width x height. You will plug in the 4, 11, and 11 inches into your calculator, multiplying all the values to end up with the answer. For the units, it will be in^3, as that is cubic inches.

The compound inequality that is graphed on the number line is:

x ≤ -6 or x > 2.

Here we have a number line that represents a compound inequality.

First, let's look at the left side, we can see a closed circe at x = 6, and then a line that extends to the left. The closed circle means that the value is a solution.

Then that inequality is:

x ≤ -6

Then we have an open dot at x = 2, and a line that goes to the right, that one will be written as:

x > 2.

Then the compound inequality is:

x ≤ -6 or x > 2.

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Danika walks 50 blocks in one week.

Multiplication is a mathematical operation that embodies the fundamental concept of repeated addition of the same integer. The multiplied numbers are known as the factors, and the outcome of the multiplication of two or more numbers is known as the product of those numbers. Multiplication is used to make repetitive adding of the same number easier. It is used for combining groups of identical size.

As per the data given,

We have,

Danika lives at 5 blocks from her school.

As Danika walks 5 blocks to and from school, making her round trip

So, total distance covered by Danika will be: 5 blocks + 5 blocks = 10 blocks.

As Danika walks to and from school 5 days a week,

Hence, she walks 10 blocks * 5 days = 50 blocks in one week.

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The next string produced by the next subset algorithm will be 111101. This is achieved by adding one to the rightmost bit of the given string, which in this case is the last digit of 110101. This causes the last digit to change from a 0 to a 1, resulting in the new string 111101.

The next subset algorithm works by taking the given string, in this case 110101, and adding one to the rightmost bit of the string. This causes the rightmost bit to change from a 0 to a 1, and all of the digits to the left of this bit will remain unchanged. In the case of 110101, the rightmost bit is the last digit, so it will change from a 0 to a 1, resulting in the new string 111101. This process can be repeated for any given string, and the result will always be the string with one more 1 than the given string. For example, if the given string was 111000, the result would be 111001, and if the given string was 111111, the result would be 1000000.

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The formula for the slope a of the regression line is:

a = r(sy/sx)

The reason for the connection between the value of r and the slope of the least squares line has to do with the formula that gives us the slope of this line. For paired data (x,y) we denote the standard deviation of the x data by sx and the standard deviation of the y data by sy.

The formula for the slope a of the regression line is:

a = r(sy/sx)

The calculation of a standard deviation involves taking the positive square root of a non-negative number. As a result, both standard deviations in the formula for the slope must be nonnegative. If we assume that there is some variation in our data, we will be able to disregard the possibility that either of these standard deviations is zero. Therefore the sign of the correlation coefficient will be the same as the sign of the slope of the regression line.

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Answer: Richard is 36 and Teo is 12

Step-by-step explanation:

Let Richard be "R" and Teo be "T",

R + T = 48 (1)

R = 2T + 12 (2)

2T + 12 + T = 48 <-- Plug (2) into (1)

3T = 36

T = 12

R + 12 = 48 <-- Plug T=12 into (1)

R = 36

Therefore Richard is 36 and Teo is 12

Answer: 12 and 36

Step-by-step explanation:

(12x2)+12=36

12=36=48

12 and 36

Answer:

Below

Step-by-step explanation:

Use triangle side length rule : any two sides must sum to greater than the remaining side

A  nope....   4 + 14 is not GREATER than 18

B  nope  27 + 39  in not greater than 39

C  nope   8 + 8 is not greater than 20

D Yes   13 + 32 > 44     and  13+44>32    and 44+ 32 > 13

The speed of the scooter is 1/2 miles per minute.

The time traveled by an object or person in any direction in a particular period of time is called speed. Speed is a scalar quantity that has no direction, it has only magnitude.

Uniform speed, variable speed, average speed, and instantaneous speed are the four kinds of speed.

To find the required speed of a scooter, you can use the following formula:

Speed= Distance/Time

Here given that, the scooter traveled 1/4 miles in 1/2 minute.

By applying the formula,

speed=(1/4)miles/(1/2)minutes

=1/2 miles/minute

Therefore, the speed of the scooter is 1/2 mile/minute.

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Half a mile per minute is the speed at which the scooter moves.

Speed is the amount of time it takes for a person or object to move in any direction over a predetermined amount of time. Speed is a scalar quantity with only magnitude and no direction.

Uniform, variable, average, and instantaneous speeds are the four different types of speed.

Apply the following formula to determine the required speed for a scooter:

Time/Distance = Speed

As a result, the scooter traveled a quarter mile in just over a minute.

Using the equation,

speed=(1/4)miles/(1/2)minutes

50/60 miles per hour

The scooter moves at a speed of half a mile per minute as a result.

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Answer:

they both last 1,25 hours

Step-by-step explanation:

Friday: 5*A + 3*B =10 hours

Saturday: 2*A + 6*B = 10 hours  --> A = (10-(6*B)) / 2

                                                          A = 5-(3B)

5*(5-3B) + 3B = 10

25 - 15B + 3B = 10

15= 12B

B=1,25 hours

A=5-3*1,25

A= 1,25 hours

Answer:

the answer is B: 218.14 miles

By using the quadratic formula, the solution to this quadratic equation is equal to -0.5251 or -3.8081.

In Mathematics, a quadratic equation can be defined as a mathematical expression that can be used to define and represent the relationship that exists between two or more variable on a graph. In Mathematics, the standard form of a quadratic equation is given by;

ax² + bx + c = 0

Mathematically, the quadratic formula is modeled or represented by this mathematical expression:

[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}[/tex]

From the information provided, we have the following values;

3x² + 13x + 4 = 0

Where:

a = 3

b = 13

c = 4

Substituting the values into the quadratic formula, we have the following;

[tex]x = \frac{-(13)\; \pm \;\sqrt{(13)^2 - 4(3)(13)}}{2(3)}\\\\x = \frac{-13\; \pm \;\sqrt{169 - 72}}{6}[/tex]

x = (-13 + √97)/6

x = -0.5251 or -3.8081.

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Therefore , the solution of the given problem of polynomial comes out to be (x-4)²(x-1)(x+2) is a four degree polynomial.

A polynomial is a mathematical statement with coefficients or uncertainty that uses only additions, erasures, multiplications, and powers of positive integer variables. There is just one indeterminate x polynomial identified by the formula x2 4x + 7. The term "polynomial" refers to a phrase in mathematics that consists of variables (sometimes referred to as "indeterminates") and coefficients that can be added, deducted, multiplied, then raised to negative number powers of non-variables.

Here,

Given :

=> (x-4)(x-1)(x+2)

=>(x-4)²(x-1)(x+2)

So,

=> (x-4)²(x-1)(x+2) is a four degree polynomial.

The two zeros of the degree four polynomial presented are x = 2 and x = 4. The two components of the above polynomial are (x - 2) and since x = 2 and x = 4 are its two zeros (x - 4).

The quadratic expression with the coefficients 1, 8, and 15 can be factored to find additional components. This equals x2 + 8x + 15.

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The value of k is 1/5.

A relation is a function if it has only One y-value for each x-value.

The given function is  f(x) and

g(x) = f(k⋅x)

We have to find the value of f(x) and g(x)

For f(x), we have:

(x, y)={(-10, -6)(-5, -1)}

Slope=-1+6/-5+10

=5/5=1

For g(x), we have:

(x, y)={(-2, -6)(-1, -1)}

Slope=-1+6/-1+2=5

g(x)=kf(x)

5=k(1)

k=1/5

Hence, the value of k is 1/5.

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The flow duration is regarded the independent variable in the proposed research design.The independent variable is the element that the researcher manipulates or changes in order to observe its influence on another component, known as the dependent variable. .

It is controlled or quantified to explore its influence on the porosity of the sample material chosen as the possible container. The flow time is the variable in the experiment that is being manipulated, and its influence on porosity is being observed, making it the independent variable.

The idea of independent and dependent variables is critical in experimental design because it allows researchers to investigate causality and anticipate how changes in one component will impact another.

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Answer:

24:1 or 24/1

Step-by-step explanation:

288/12 = 24

This is the unit rate.  There are 24 tennis balls for each racket.

Answer: 24

Step-by-step explanation:

288/12=24

THERE ARE 24 BALLS PER TENNIS RACKET.

Answer:

8000 pounds

Step-by-step explanation:

1 ton is 2000 pounds

Therefore we can use the equation: 4x2000 which is:

8000 pounds

Answer:

4 tonnes =

8818.49 pounds

[tex]4 \: tones \: = \: 8818.49 \: pounds \\ \: is \: the \: answer \: of \: ur \: question[/tex]

Answer:

[tex]\boxed{y = \dfrac{2}{5}x - 4}[/tex]

Step-by-step explanation:

Let's find the equation for the line

Take two distinguishable points on the graph.

(0, 4) and (2, -1) are two points with integer values for coordinates through which the line passes

The equation of a line in slope-intercept form is
y = mx + b

where
m = slope
b = y-intercept

Slope m = rise/run

rise = difference in y values of any two chosen points

run = difference in corresponding x values for the same chosen points

Taking the two points (0, 4) and (2, -1)

rise = -1 - 4 = -5

run = 2 - 0 =2

So slope = - 5/2

The y-intercept of this line is 4, - this is the y-value where the line crosses the y-axis and corresponds to the value of y when x = 0

The equation of the line is
y = mx + b
[tex]\rightarrow y = -\dfrac{5}{2}x + 4 \;\;\cdots \cdots (1)\\\\[/tex]

A line perpendicular to this line will have a slope that is the negative of the reciprocal of the slope.

The product of the two slopes will be -1

Reciprocal of -5/2 = -2/5
Negative of this is -(-2/5) = 2/5

So slope of perpendicular line = 2/5

Equation of line is
[tex]y = \dfrac{2}{5}x + b[/tex]

To find b plug in x, y values for (5, -2) and solve for b

[tex]-2 = \dfrac{2}{5}\cdot 5 + b\\\\[/tex]

[tex]-2 = 2 + b\\\\-4 = b\\\\b = -4\\[/tex]

[tex]\textrm{Equation of the line is}\\\\\boxed{y = \dfrac{2}{5}x - 4}[/tex]