Solve for x please help show proofs

The quadrilateral with diagonals that are always perpendicular bisectors of each other is a square. Correct option is 1.

In a square, the diagonals bisect each other at right angles, which means they intersect at a 90-degree angle. Moreover, since a square has four congruent sides and four right angles, the diagonals are also congruent. Thus, each diagonal is a perpendicular bisector of the other diagonal, splitting it into two equal segments.

In contrast, a rectangle has diagonals that bisect each other, but they are not always perpendicular. A trapezoid has only one pair of opposite sides that are parallel, and its diagonals do not bisect each other.

A parallelogram has opposite sides that are parallel, but its diagonals do not necessarily bisect each other or intersect at a right angle.

Therefore, the correct answer is a 1 (square).

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Hence, combine all the solutions we get,

[tex]x=\frac{\pi}{2} +2n\pi,x=\frac{3\pi}{2} +2\pi n ,[/tex][tex]x= sin^{-1} (\frac{1}{3} )+ 2\pi n ,x= sin^{-1 }(\frac{1}{3})+2\pi n[/tex].

Trigonometric identities are equalities which involves trigonometric functions which are true for every value of variables that occur on both sides of the identities.

Given,[tex]3\sin \left(2x\right) = 2\cos \left(x\right)[/tex]

[tex]3\sin \left(2x\right)-2\cos \left(x\right)=0[/tex]

Using trigonometric identities, [tex]sin2x= 2sinx cosx[/tex]

we get,[tex]-2\cos \left(x\right)+6\cos \left(x\right)\sin \left(x\right)=0[/tex]

Taking [tex]2cos(x)[/tex] as factor, we get,

⇒[tex]2cos(x)(3sin(x) -1)[/tex]

⇒[tex]2cos(x) = 0 , (3sin(x) -1)=0[/tex]

⇒[tex]cos (x)= 0[/tex] for x= [tex]x=\frac{\pi}{2} +2n\pi,\frac{3\pi}{2} +2\pi n[/tex] and

[tex](3sin(x) -1)=0 for x= sin^{-1} (\frac{1}{3} )+ 2\pi n , sin^{-1 }(\frac{1}{3})+2\pi n[/tex]

Hence, combine all the solutions we get,

[tex]x=\frac{\pi}{2} +2n\pi,x=\frac{3\pi}{2} +2\pi n ,[/tex][tex]x= sin^{-1} (\frac{1}{3} )+ 2\pi n ,x= sin^{-1 }(\frac{1}{3})+2\pi n[/tex].

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Yes, the table represents the proportional relationship.

The proportional relationship between the variables {x} and {y} is such that -

y/x = K {constant}

y = Kx

y₁/x₁ = y₂/x₂ = k  

A proportional relationship is represented by a straight line {where K is the slope}. It is concluded from the fact that the equation of the straight line passing through origin is of the form y = mx.

Given is a table as shown in the image.

For a direct or proportional  variation -

y₁/x₁ = y₂/x₂ = k                                                {k is constant parameter}

1/2 = 2/4 = k {constant}

1/2 = 1/2 = k {constant}

Therefore, yes, the table represents the proportional relationship.

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The boys will have same the height after 48 months.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, two boys are increasing with the rate of 1/4 and 1/2 of an inch every month, they have height 60 in and 48 in, will need to find that when will they have equal height,

The height increased in x month of them is given by,

x/4 + 60 or x/2 + 48

Let they have equal height after y months,

y/4 + 60 = y/2 + 48

y/4 = 12

y = 48

Hence, the boys will have same the height after 48 months.

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The graph of a piecewise-defined function y=c is a horizontal line reaching height c from the x-axis.

A piecewise function is arithmetic that is constructed from bits of various functions across various time intervals.

To determine which of the above intervals (as well as inequalities) -

Keep in mind that the function is represented by the line y=1 and is from -∞ to 0, or the left side.

Similar to that, the function is y=-1 from 0 to ∞ (doesn't include) .

Hence, the rule provides the function:

y=1, for x≤0,

y=-1, for x>0.

Thus, the graph of a function y=c is a horizontal line reaching height c from the x-axis.

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The complete question is-

The graph of a piecewise-defined function is shown below.

Check the correct option-

On the interval (x≤0, x≤1, x<1, x<0) the function is given by the rule (x= - 1, y= - 1, y=1, x=1), and on the interval (x≥0, x>1, x≥1, x>0) the function is given by the rule (y= - 1, x= - 1, y= 1, x= 1).

This is not a random sample of the restaurant's customers.

The offer of a coupon in exchange for completing a brief survey about favorite desserts may bias the sample and result in a non-random sample of the restaurant's customers.

Only those customers who were interested in the coupon may have participated in the survey, which may not be representative of the overall customer population. Additionally, those who chose to participate may have different tastes and preferences compared to those who did not participate.

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Andrea has 6 hours to spend training for an upcoming race. She completes her training by running full speed the distance of the race and walking back the same distance to cool down. If she runs at a speed of 8 mph and walks back at a speed of 2 mph, she will spend 72 minutes walking back.

This is referred to as the measured period during which an action, process, or condition exists or continues .

'x' rill represent the amount of time spent running in hours, then 3-x represents the time spent walking in hours.

Distance = Speed × time

Distance = 8x

Speed = 2mph

Time = (6-x)hours

Substitute the values

8x = 2 (6-x)

8x = 12 - 2x

10x = 12

x = 12/10 = 6/5

6/5 × 60 = 72minutes.

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The length of MK is given as follows:

MK = 36.

Similar triangles are triangles that share these two features presented as follows:

The similar triangles for this problem are given as follows:

MNO and MKL.

Hence the proportional relationship for the side lengths is given as follows:

15/MK = 20/48

Applying cross multiplication, the length MK is given as follows:

20MK = 15 x 48

MK = 15 x 48/20

MK = 36.

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The percentage of data between 20 and 50 is 25%

The boxplot in the complete question is added as an attachment

From the attached box plot, we have

From the given box plot it is clear that 20 is the median and 50 is the third quartile.

As a general rule:

There are 25% of data values between the median and the third quartile.

Hence, 25% of the data values are between 20 and 50.

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The wavelength will be "0.125 m".

The wavelength, as well as frequency, have an inverse relationship. It shows  that whenever a short wavelength exists, a high frequency exists, and when a big wavelength exists, a lower frequency exists.

The distance of a single wave-particle travels after completing one oscillation would be its wavelength.

According to the given information,

Speed of transverse, s = 25 m/s

Frequency, f = 200 Hz

We know the formula,

→ Wavelength, λ = velocity/ frequency

By substituting the values, we ger

λ = 25/200

 λ = 0.125

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The number of yes votes would be 4,836.

Solution:

Given,

The ratio of yes votes to no votes is 5:6. So, assuming the actual values of yes votes and no votes be 5x and 6x respectively. We can frame an equation as follows,

5x + 6x = 10,640

=> 11x = 10,640

=> x = 967.27272727

So, the number of yes votes would come out to be,

5*967.272727 = 4836.3636

Since the answer can not be a fractional integer,

therefore, we will round it up to 4,836.

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Answer:

Axis of Symmetry is 3 or x=5

vertex is (3,5)

Step-by-step explanation:

the vertex is either the highest or the lowest point on a quadratic function's graph, here (3,5) is the highest point, therefore it is the vertex.

Axis of symmetry is usually always the x value of the vertex, that is that in (3,5). 3 is the axis of symmetry. This is because along the line x=5 the graph shows perfect symmetry

please do say thanks.

The required values are;

(2). x = 88°

(3). x = 5.

Angles inside a polygon are referred to as interior angles. A triangle, for instance, has three internal angles. Interior angles are sometimes defined as "angles confined in the interior area of two parallel lines when they are crossed by a transversal."

Given:

(2). The exterior angle is 52°.

So, the sum of all the interior angles in the polygon = (5 - 2)180

x + (180 - 52) + 2x + x + 2 + 90 = 560

4x + 208 = 560

4x = 352

x = 88

(3). From the diagram of the triangle,

12x - 20 = 2 (3x + 5)

12 x - 6x = 10 + 20

6x = 30

x = 5

Therefore, the values are x = 88 and x = 5.

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Answer:

Step-by-step explanation:

The area of a round pizza with a 17 inch diameter is:

A = πr^2 = π(8.5)^2 ≈ 226.98 square inches

To find the length of the sides of a triangle with the same area, we can use the formula for the area of a triangle:

A = (1/2)bh

where b is the base of the triangle and h is the height.

Since the triangle is equilateral (i.e., all sides are equal), the base and height are the same. Let's call this length x. Then:

A = (1/2)bh = (1/2)x(x/2) = x^2/4

Setting this equal to the area of the round pizza, we get:

x^2/4 = 226.98

Multiplying both sides by 4, we get:

x^2 = 907.92

Taking the square root of both sides, we get:

x ≈ 30.13

So the sides of the equilateral triangle should be about 30.13 inches long to have the same area as a round pizza with a 17 inch diameter. Rounded to the nearest inch, the sides of the triangle should be 30 inches long.

An exponential function of the form y = 20aˣ can be 20 at the y-intercept

when a = 1.

An exponential function in which the independent variable is the exponent.

An exponential function can be written in the form as, y = aˣ, where a is a constant and 'x' is the variable.

We know, the y-intercept is when the value of x = 0.

Therefore, An exponential function of the form y = 20aˣ can be 20 at y-intercept when a = 1.

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The linear equation is f(x) = 2^2 + x, while the other two functions are nonlinear functions

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

The three equations

A linear equation is any equation that has a degree of 1

From the three equations, we can see that

Degree = 1

Degree = 2

Degree = 3

Hence, the linear function is f(x) = 2^2 + x

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The lateral area of the cone with a radius of 7ft and a slant height of 13ft is 285.7 ft².

A cone is simply a 3-dimensional geometric shape with a flat base and a curved surface pointed towards the top.

The lateral area of a cone is expressed as;

A = π × r × l

Where r is radius and l is slant height.

Given the data in the question;

Plug the given values into the above formula and solve for the lateral area of the cone.

A = π × r × l

A = 3.14 × 7ft × 13ft

A = 285.7 ft²

Therefore, the lateral area is 285.7 square feet.

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The speed of the river is given as follows:

4 kilometers per hour.

The lowest speed that can be assumed by the boat is given as follows:

8 - r.

In which r is the speed of the river.

The lowest velocity is of 4 kilometers per hour, hence the speed of the river is obtained as follows:

8 - r = 4

r = 8 - 4

r = 4 kilometers per hour.

Then the maximum velocity is of:

8 + 4 = 12 kilometers per hour.

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The point (- 1, 2) lies on the new graph.

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

Given that;

The graph of f(x) = |x| has been translated left 2 units and up 1 unit.

Now, The function is,

⇒ f (x) = |x|

After translated 2 unit left we get;

⇒ f (x) = |x + 2|

And, After translated 1 unit down we get;

⇒ f (x) = |x + 2| + 1

Now, We can check all the given points as;

For point (- 1, 2);

Put x = -1 , f (x) = 2;

⇒ f (x) = |x + 2| + 1

⇒ 2 = |- 1 + 2| + 1

⇒ 2 = 1 + 1

⇒ 2 = 2

Thus, The point (- 1, 2) lies on the new graph.

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The value of x  for The quadrilateral which is a trapezoid is if the top is 21 and the bottom is 27 is option 2 that is 5.

Quadrilaterals called trapezoids have two parallel and two non-parallel sides. It also goes by the name Trapezium. A trapezoid is a closed, four-sided form or figure that has a perimeter and covers a specific area. It is a 2D figure rather than a 3D one. The bases of the trapezoid are the sides that are parallel to one another. Legs or lateral sides refer to the non-parallel sides. The height is the separation between the parallel sides.

From the given diagram, the expression below is true:

2(5x - 1) = 21 + 27

Expand

10x - 2 = 48

10x = 48 + 2

10x = 50

Divide both sides by 10

10x.10 = 50/10

x = 5

Hence the value of x is 5

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The value of x in the triangle is 10 units

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

The triangle

On the triangle, we have the following equivalent ratio

x : 15 = 4 : 6

Express as fraction

So, we have

x/15 = 4/6

This gives

x = 15 * 4/6

Evaluate

x = 10

Hence, the value of x is 10

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A linear function is demonstrated by the line a.

Line a has a slope of one.

Y = x + 2 is the equation for the line a.

How do you calculate a line's slope?

Following points on line a (x,y) = (0,2) and are available in the figure (2,4)

Calculating the slope (m) involves using:

m= y^2-y^1/x^2-x^1

This results

m= 4-2/2-0

Analyze m = 1

Consequently, the line's slope is 1.

The formula for this is y = m(x - x1) + y1.

We thus have:

y = (x - 0) + 2

y = x + 2: Compare the difference and the result.

Consequently, y = x + 2 is the equation for the line a.

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The number of unit cubes whose dimensions are 3/5 inch fill up the rectangular prism is (125/27)abc.

The total volume, in cubic inches, is represented in the diagram n cubic inches.

A cube is a three-dimensional object who has six faces.

Since each side of the unit cube has a length of 1 inch, the number of unit cubes that fill up the rectangular prism is equal to its volume in cubic inches. If the rectangular prism has dimensions a x b x c inches, then its volume is V = abc cubic inches.

Now, we need to find how many unit cubes whose dimensions are 3/5 inch fill up the rectangular prism. First convert the dimensions of the unit cube and the rectangular prism to a common unit, such as inches. Since 1 inch = 5/3 unit cubes, each side of the unit cube has a length (3/5) inch. Therefore, each side of the rectangular prism has dimensions (5a/3) x (5b/3) x (5c/3) unit cubes.

To find the number of unit cubes that fill up the rectangular prism, we can divide its volume (abc cubic inches) by the volume of each unit cube, which is (3/5)³ cubic inches. Thus, the number of unit cubes whose dimensions are 3/5 inch that fills up the rectangular prism is:

(abc) / [(3/5)³] = (125/27)abc

To find the total volume represented in the diagram, we need to add up the volumes of all the unit cubes shown in the diagram. Since we don't know the dimensions of the rectangular prism, we can't calculate its volume directly.

Therefore, the total volume represented in the diagram is n cubic inches.

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The money borrowed by Alonzo at a simple interest rate of 8% for a time period of 2 years is $7000.

What is simple interest?

In the fields of finance and economics, interest is the payment made at a set rate by a borrower or deposit-taking financial institution to a lender or depositor in excess of the principal amount (the amount borrowed). It is not the same as a fee that the borrower might pay to the lender or another entity.

Borrowers must pay lenders simple interest as a fee in exchange for a loan. For simple interest calculation, compounding interest is excluded from the calculation and just the original principal is used. Simple interest applies to all loans, not just specific ones. Additionally, it refers to the kind of interest that banks give their customers on their savings accounts.

Given,

 Time period = 2 years

Rate of interest = 8%

The simple interest paid at the end of 2 years = $ 1120

The money borrowed or the principal amount is

Simple interest = (Principal amount *  rate * time)

1120                  = P * 0.08 * 2

P = 1120/0.16 = $7000

Therefore the money borrowed by Alonzo at a simple interest rate of 8% for a time period of 2 years is $7000.

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Answer: 9/56

Step-by-step explanation:

Answer: 38

Step-by-step explanation:

Subtract 1/8 from 1/2

12 - 18 is 38.

Steps for subtracting fractions

Find the least common denominator or LCM of the two denominators:

LCM of 2 and 8 is 8

Next, find the equivalent fraction of both fractional numbers with denominator 8

For the 1st fraction, since 2 × 4 = 8,

12 = 1 × 42 × 4 = 48

Likewise, for the 2nd fraction, since 8 × 1 = 8,

18 = 1 × 18 × 1 = 18

Subtract the two like fractions:

48 - 18 = 4 - 18 = 38

The inequality that  this situation, where s is the number of shirts she can buy is S>81.5.

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.

We are given that;

Budget of lelah for clothes= $135

For shoes= $35.25

For shirts= $18.25

Now,

S+$18.25+35.25>135

S>135-18.25-35.25

S>135-53.5

S>81.5

Therefore, the inequality will be S>81.5.

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a) This situation represents exponential growth, as the number of bacterial cells is doubling every hour.

b) Let N be the number of bacterial cells on the petri dish at time t in hours. The equation to model the situation is:

N = 30 x 2^t

This equation represents exponential growth, as the number of bacterial cells is doubling every hour. The initial number of bacterial cells is 30 (when t = 0), and the number of bacterial cells at any time t is given by multiplying the initial number by 2 raised to the power of t.

c) After 5 hours, the number of bacterial cells on the petri dish is:

N = 30 x 2⁵ = 30 x 32 = 960

So there are 960 bacterial cells on the petri dish after 5 hours.

The math subject that is relevant to the case above is exponential growth and exponential decay. These are mathematical concepts that describe the behavior of quantities that increase or decrease at a constant percentage rate over time.

Exponential growth refers to a situation where a quantity grows at a constant percentage rate over time. In the case above, the number of bacterial cells doubles every hour, which is an example of exponential growth.

Exponential decay, on the other hand, refers to a situation where a quantity decreases at a constant percentage rate over time. An example of exponential decay could be the decay of a radioactive substance.

In summary, the case above involves the mathematical concept of exponential growth, which is a key concept in the field of mathematics and has important applications in fields such as biology, economics, and finance.

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