Finding unknown measures in similar triangles
- how do i do the problem?

Answer and Step-by-step explanation:

To solve this equation, we will assume the given that is x will be assumed equal to twelve.

We will replace the place value of x with 12 everywhere in the given equation.

3(x - 2) =30+x-2-x+2

3 (12 - 2) = 30 + 12 - 2 - 12 + 2

3 (10) = 44 - 14

30 = 30

We can see that the left-hand side is the same as the right-hand side i.e. LHS = RHS.

This means that the value of the equation is stable after we put (x=12) in the above-given equation.

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Answer:

-3

Step-by-step explanation:

Write the equation in slope -intercept form: y = mx + b

where m is the slope.

       y - 5 = -3x

            y = -3x + 5

Slope = -3

[tex]y-5 =-3x[/tex]

[tex]y-5+5 =-3x+5\\ \\y=-3x+5[/tex]

The slope of a linear equation will always be the coefficient of the "x" variable when the equation is equalled to "y". The coefficient is just the number that multiplies the variable. Hence, the coefficient of this line is "-3". Check the attached image.

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Altogether 50 adult tickets were sold and 175 student tickets were sold.

An equation of degree one is known as a linear equation.

A linear equation of two variables can be represented by ax + by = c.

Let, The number of adult tickets be 'x' and the number of students

ticket be  'y'.

Therefore, From the given information x + y = 225...(i) and 4x + 2y = 650...(ii)

Multiplying equation (i) by 2, we have 2z = 2y = 550 and subtracting it from

equation (ii) we have,

2x = 100.

x = 50 and y = 175.

So, 50 adult tickets were sold and 175 student tickets were sold.

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Step-by-step explanation:

the area of a triangle is

baseline × height / 2

so, we only have to sum all 6 triangles and the base area :

6 × 6×8/2 + 93.5 = 36×4 + 93.5 = 144 + 93.5 =

= 237.5 in²

The the length of each side of the triangle are: 5 units, 8.7 units and 10 units respective

A triangle is a polygon with three sides, three angles, three vertices and sum of angles equal to 180 degrees

From the triangle, Using the trigonometric ratio of sine

Sin C = opposite/Hypothenuse

Sin30 = 5/H

Making h the subject of the relation we have

h= 5/sin30

h=5/0.5

Therefore the value of h=10 units

To find the third side use Pythagoras theorem

10² = 5²+p²

100-25 = p²

75 = p²

Taking the square of both sides

p=√75

p=8.7 units

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A sample space the set of all the possible outcomes in a probability experiment.

The sample space in probability theory is the set of all possible outcomes of a random experiment.

It is the set of all possible results of an action, experiment, or random process. In other words, it is the set of all possible values that a random variable can take.

For example, in a coin flip experiment, the sample space could be defined as the set {heads, tails}.

In a dice roll experiment, the sample space could be defined as the set {1, 2, 3, 4, 5, 6}.

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The grouping of all numbers with the formula a+bi is referred to as the complex number set. If b0, the number is also referred to as an imaginary number. The quantity is referred to be a real number if b=0.

A real number and an imaginary number added together is referred to by this phrase. It is symbolized by the letter z and has the formula a + bi.

Any number that is composed of both rational and irrational numbers is considered to be real. R is used to write these numbers, which may be native or positive.

Complex numbers are those that are expressed as a+ib, where a, b are actual numbers, and I is a fictitious number termed a "iota." I = (-1) is the value. A complex number, such as 2+3i, is one where the real number 2 (Re) and the imaginary number 3 I are both present (Im).

The number that is represented by the square root of a particular negative number is referred to by this phrase.

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The number of terms in the nth row is n + 1. The sum of the terms in the first n rows is equal to the sum of the first n + 1 triangular numbers, which is given by the formula n(n + 1)(n + 2)/6.

So to find m and n, we need to solve the following two equations simultaneously:

n(n + 1)(n + 2)/6 + m = 123000

n + 1 = 2m

Substituting the second equation into the first equation, we get:

m(2m + 1)(2m + 2)/6 = 123000

We can then solve for m using a numerical method, such as the bisection method or Newton-Raphson method. The solution is approximately m = 142.

So the values of m and n are 142 and 284, respectively.

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Slope intercept form is written as follows:

[tex]y=mx+b[/tex]

With this information, isolate y on the left side of the provided equation:

[tex]4y=10x-14[/tex]

Now, divide both sides of the equation by 4:

[tex]y=\frac{10}{4} x-\frac{7}{2}[/tex]

This equation cannot be simplified anymore, and is therefore the answer!

[tex]y=\frac{10}{4} x-\frac{7}{2}[/tex]

Answer:

y = (5/2)x - (7/2)

Step-by-step explanation:

–10x + 4y + 14 = 0

                 -14     -14

-----------------------------

-10x + 4y = -14

+10x                 + 10x

--------------------------------

4y = 10x - 14

÷4    ÷4     ÷4

----------------------

y = (10/4)x - (14/4)

simplified

y = (5/2)x - (7/2)

I hope this helps!

Note that where in the picture above PA = PD and AB = CD.

Since AB = CD

∠APB = ∠CPD  - open mouth theorem

Based on the above,

∠BPC = ∠APD - (∠APB +∠CPD)

Since points A, B, C and D are all on a straight line, thus, it is proven that

PB = PC - open mouth theorem.

The Hi. nge theorem (also known as the open mouth theorem) states in geometry that if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is greater than the included angle of the second, the third side of the first triangle is longer than the third side of the second triangle.

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The Gini coefficient for this nation cannot be calculated from the given information

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

f(x) = 0.3x^4 +0.3x³ +0.4x²

The Gini coefficient for this nation cannot be calculated from the given information.

This is so because the Lorenz curve which is a graphical representation of the income distribution of a population is required

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Answer: The probability that vowels occupy even places in the word "jvuyojzrxccome" is 3/7.

Step-by-step explanation:

1) To find the probability that vowels occupy even places in the word "jvuyojzrxccome", we can use the following steps:

2) Break down the word into individual characters: "jvuyojzrxccome"

3) Identify the vowels in the word: "u, o, o, e"

4) Count the number of vowels in the word: 4

5) Count the number of even-positioned characters in the word: (1st, 3rd, 5th, 7th, 9th, 11th, 13th) 7

6) Identify the vowels in the even positions: "u, o, e"

7) Count the number of vowels in the even positions: 3

Use the formula for probability: P(vowels in even positions) = (number of favorable outcomes) / (number of total outcomes)

8) P(vowels in even positions) = 3/7

Therefore, the probability that vowels occupy even places in the word "jvuyojzrxccome" is 3/7.

Answer:

x >5 and x <-2

Step-by-step explanation:

x >5 and x <-2

Therefore , the solution of the given problem of compound sentence's comes out to be { x|–2< x < 5}

Indicated by the conjunction "or," the compound sentence is true as long as either of the two statements is true. In other words, it is the union or combination of the solution sets for each unique assertion. The term "conjunction" refers to a compound inequality that contains the word "and". The words "and" and "or," which are considered to be variables of speech, have a different meaning in mathematics than they do in grammar.

Here,

Given :

=> On the number line

=> -5 to -2

and 5 to infinity .

So,

Both x| x > -2 and x < 5

The following is another method to state this solution set:

{ x|–2< x < 5}

It is assumed that the word "and" will always be used in compound inequality expressions when neither "and" nor "or" is explicitly used. You say, "x is more than  -2 and (reading to the right) x is less than 4," reading from the "x" position as "x|-2" "x," "x," and "x," respectively. This is the solution set's graph.

The Complete Question.

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The z-score for the male is more than the z-score for the female.

The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.

The z-score is given as

z = (x - μ) / σ

Where μ is the mean, σ is the standard deviation, and x is the sample.

The z-score for males is given as,

z = (1600 - 3260.1) / 761.9

z = - 1660.1 / 761.9

z = - 2.179

The z-score for females is given as,

z = (1600 - 3080.7) / 523.1

z = - 1480.7 / 523.1

z = - 2.830

The z-score for the male is more than the z-score for the female.

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The right side of the equation 9 - 3x +6+8 + 3x+7 can be simplified by combining like terms as: 30.

2(x - 5) can be simplified using the Distributive Property as: 2x - 10.

In Mathematics, the distributive property of multiplication states that when the sum of two or more addends are multiplied by a particular numerical value, the same result and output would be obtained as when each addend is multiplied respectively by the same numerical value, and the products are added together.

Next, we would combining like terms in the right side of the equation as follows;

9 - 3x +6+8 + 3x+7 = (9 + 8 + 6 + 7) + (3x - 3x)

9 - 3x +6+8 + 3x+7 = 30.

By applying the distributive property of multiplication to left side of the equation, we have:

2(x - 5) = 2x - 10.

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twelve is two percent of six hundred

The triangles' corresponding angles are identical.The pre-image was reduced to create the picture.The triangle's form is unaffected by either dilation or rotation.

Reason: For forms to resemble one another:

1. The sides should be proportionate to one another.

Angles in the first and second shapes should be same.

With a scale factor of 0.2, the sides of the picture are now 0.2 of the original shape's length. Angles, however, are not modifications.

Let's examine the options:

1. The triangles' corresponding sides are congruent:

Due to the fact that dilation alters the side lengths, this choice is wrong.

2- The triangles' corresponding angles are identical:

This is the best choice because neither rotation nor dilation change the angles' measurements.

3. The image's matching sides are five times longer than the pre- image's:

The sides of the picture are only 0.2 times as long as those of the pre-image, therefore this choice is erroneous.

4. The picture is a condensed version of the original:

This choice is appropriate since the sides of the picture are 0.2 times those of the pre-image, reducing the form.

5- The triangle's shape is unaffected by either dilation or rotation: This choice is valid because dilation and rotation are rigid transformations that do not modify the triangle's shape (a triangle stays a triangle).

The complete question is

A triangle is dilated by a scale factor of 1/5 and then rotated 90 degree clockwise about the origin. Why is the image similar to the pre-image? Check all that apply.

A) The corresponding sides of the triangles are congruent.

B) The corresponding angles of the triangles are congruent.

C) The corresponding sides of the image are 5 times as long as those of the pre-image.

D) The image is a reduction of the pre-image.

E) Neither the dilation nor the rotation change the shape of the triangle.

F) The rotation reduces the size of the triangle.

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In the weights of seven people, the 36th percentile is 135.

The following are the weights (in pounds) of seven people:

100, 115, 135, 140, 180, 197, 230

We have to determine the 36th percentile.

The term "percentile" describes how a score contrasts with other scores from the same collection. The percentage of values in a set of data scores that fall below a specific value is a typical way to represent percentile, despite the fact that there is no single meaning for this term.

The formula is:

= Percentile/100 × Total number of weights

There have total weights of 7 people and percentile is 36.

Now putting the value

= 36/100 × 7

= 2.52

= 3(approx)

To find the percentile value we count from left to right.

The 3rd number from left to right is 135.

So the 36th percentile is 135.

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For the given frequency distribution table the answer of the following questions are:

a. sample size is equal to n = 20.

b. Proportion , relative frequency , and the percentage are :

 f           Proportion                Relative frequency              Percentages

1                 0.05                        0.05                                     5

2               0.1                            0.1                                        10

3                0.15                           0.15                                    15

4                 0.2                            0.2                                    20

5                 0.25                         0.25                                   25

a. Sample size of the number of hours students slept before exam is :

n = 2+ 2 + 3+ 4+ 5 + 2+ 1+ 1

   = 20

b. Organization of the data in the form of frequency distribution table form is:

X       f           Proportion                Relative frequency              Percentages

8        2           2/20 = 0.1                   2/ 20 = 0.1                      0.1 × 100 = 10

7        2            2/20 = 0.1                   2/ 20 = 0.1                     0.1 × 100 = 10

6        3           3/20 = 0.15                   3/ 20 = 0.15                 0.15 × 100 =15

5        4           4/20 = 0.2                  4/ 20 = 0.2                     0.2 × 100 = 20

4        5          5/20 = 0.25                  5/ 20 = 0.25               0.25 × 100 = 25

3        2         2/20 = 0.1                   2/ 20 = 0.1                      0.1 × 100 = 10

2        1          1/20 = 0.05                   1/ 20 = 0.05                0.05 × 100 =5

1        1         1/20 = 0.05                   1/ 20 = 0.05                0.05 × 100 =5        

         20

Therefore, the sample size of the frequency distribution is 20 and the proportion , relative frequency ,and percentage are shown in the above table.

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Answer:

yes because see below

Step-by-step explanation:

300²+400²=500²

so it has to be right angle

Answer:

Step-by-step explanation:

yes, the parcel of land will have a right angle.

300x300=90,000

400x400=160,000

500x500=250,000

90,000+160,000 = 250,000

The intersection is - 7< <x<  4 after resolving the compound inequalities -20<  2x - 6 <2.

A relation between two terms or concepts that is equal in mathematics is referred to by the term inequality. Thus, disparity originates from imbalance. In economics, an inequality explains the connection between two non-equal numbers. Egality and equality are not the same. Use the same equal symbol most frequently when two results are not equal (). Values of any size can be contrasted using a variety of inequalities. By changing the two aspects until only the variables are left, many straightforward inequalities can be solved. However, a range of variables support inequality: Both sides' negative values are split or added. Exchange the left and the right.

given

-20 < 2x - 6 < 2

Divide a system of inequalities into compound inequalities:

1) 2x - 6 > -20

2) 2x - 6 > 2

x> 7 and x < -4

the intersection, then: - 7 < x < 4

The intersection is - 7< x<  4 after resolving the compound inequalities -20<  2x - 6 <2.

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The complete question is :-

Solve the following compound inequality:

-20<  2x - 6 <2.

To find the area of the regular 12-gon inscribed in a unit circle, first calculate the area of a regular octagon. The area of a regular octagon is equal to two times the length of one side squared, multiplied by the constant π/2. Since all the sides of a regular octagon inscribed in a unit circle have length 1, we can calculate the area of the octagon as 21^2(π/2) = π.

Next, divide the octagon into four red regions, each with an area of 12. To calculate the area of the blue region, subtract the total area of the four red regions (12*4 = 48) from the area of the octagon (π). This gives us an area of π - 48 = 8 for the blue region.

To find the distance from O to PQ in the isosceles triangle OPQ, use the Pythagorean theorem. Since the base of the triangle has length 2, and the legs of the triangle have length OP=OQ, we can calculate the distance from O to PQ as the square root of 2^2 - (OP)^2, which is equal to √2.

To find the area of the smaller hexagon, subtract the area of triangle ACE from the area of triangle BDF. The area of an equilateral triangle with side length 2 is √3/4, so the area of triangle ACE is (√3/4)2 = √3/2. Similarly, the area of triangle BDF is (√3/4)2 = √3/2. Subtracting these two values gives us an area of 0.5 for the smaller hexagon.

Lastly, to find the measure of [ABCDE], use the fact that the sum of the interior angles of a regular polygon is equal to (n-2)180°, where n is the number of sides of the polygon. In this case, n = 5, so the measure of [ABCDE] is (5-2)180° = 120°.

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The required interest rate would be approximately 6%.

The Compound Annual Growth Rate (CAGR) is a measure of the average rate of return of an investment over a specified time period, assuming the investment is compounded at regular intervals. It gives the average growth rate that would have transformed the initial investment value into the final investment value over the specified time period.

To calculate the required interest rate, we need to find the CAGR using the following formula:

[tex]\text{CAGR} = (\frac{V_\text{final}}{V_\text{begin}} )^{(1/n) }- 1[/tex] where,

Substituting the given values, we get:

CAGR = ($20,886.24 / $5,000)^(1/15) - 1

= (4.17248)^(1/15) - 1

= 1.06 - 1

= 0.06 or 6%

So, the required interest rate to have $20,886.24 at the end of 15 years, assuming compounded interest, would be 6%.

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Answer:

  y = 4

Step-by-step explanation:

You want the equation of the horizontal line containing the point (-1, 4).

On a horizontal line, the y-coordinates of every point are the same. The equation can be written ...

  y = constant

In order for the horizontal line to go through a point with y-coordinate 4, the constant must be 4. The equation is ...

  y = 4

<95141404393>

The  average rate of change between the intervals x = -2 and x = 4 of the function f(x) = 4x³ - 15x + 3 is; 33

The average rate of change is defined as a measure of how much the function changed per unit, on average, over a given interval.

We are given the function;

f(x) = 4x³ - 15x + 3

Between the intervals x = -2 and x =4, the average rate of change can be gotten from;

[f(4) - f(-2)]/(4 - (-2)

f(4) = 4(4)³ - 15(4) + 3

f(4) = 199

f(-2) = 4(-2)³ - 15(-2) + 3

f(-2) = -32 + 30 + 3

f(-2) = 1

Thus;

Average rate of change = (199 - 1)/(4 - (-2)

= 198/6

= 33

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Answer:

Step-by-step explanation:

i don't know convert