Triangle Congruency Theorems: Edge High School Geometry

Answer is below:

I don't know what you mean by g. and h., so I'll just skip that part.

I'm assuming you're asking about some arbitrary finite set [tex]A[/tex].

a. If [tex]A[/tex] has 64 subsets, then [tex]A[/tex] has [tex]\log_2(64) = \boxed{6}[/tex] elements. This is because a set of [tex]n[/tex] elements has [tex]2^n[/tex] subsets/elements in its power set.

b. A proper subset is a subset that doesn't contain all the elements of the parent set. This means we exclude the set [tex]A[/tex] from its power set. The power set itself would have 32 elements, so [tex]A[/tex] would have [tex]\log_2(32) = \boxed{5}[/tex] elements.

c. The empty set is a proper subset of any non-empty set. However, if [tex]A=\emptyset[/tex], then it has no proper subsets. So [tex]A[/tex] must be the empty set and have [tex]\boxed{0}[/tex] elements.

d. By the same reasoning as in part (b), if [tex]A[/tex] has 255 proper subsets, then it has a total of 256 subsets, and [tex]\log_2(256) = \boxed{8}[/tex].

The value of x when the richter scale rating scale is 8.4 is 251188643.151

A richter scale is a numerical scale that is used for expressing the magnitude of an earthquake in a geographical area

The richter scale takes the amplitude of the earthquake's largest seismic as an input and calculate (and display) the magnitude of an earthquake in the geographical area using a logarithmic function

The formula of a richter scale is expressed as:

log(x) = n

Where n represents the scale rating of the scale

In this case, n = 8.4.

So, we have:

log(x) = 8.4

Express as an exponent

x = 10^8.4

Evaluate the exponent

x = 251188643.151

Hence, the value of x when the richter scale rating scale is 8.4 is 251188643.151

Read more about richter scale rating at

https://brainly.com/question/19799610

#SPJ1

Answer:

25, 26, and 27 are the three consecutive integers.

Step-by-step explanation:

Let the numbers be represented as x, x + 1 and x + 2.

We can write the equation:

[tex]x+(x+1)+ (x+2)=78[/tex]

Opening the brackets and simplifying:

[tex]x+x+1+x+2=78[/tex]

[tex]3x+3=78[/tex]

Subtract 3 from both sides.

[tex]3x=75[/tex]

Divide both sides by 3.

[tex]x=25[/tex]

Since the three consecutive integers are x, x + 1 and x + 2, replace x with 25.

∴ 25, 26 and 27 are the three consecutive integers.

Answer:

25 , 26 and 27

Step-by-step explanation:

\cos (\tan \left( -1\right) (\frac{x}{2}))

c

o

s

(

t

a

n

(

−

1

)

(

2

)

)

Simplify

1

Combine multiplied terms into a single fraction

\cos (\tan \left( -1\right) \cdot \frac{x}{2})

c

o

s

(

t

a

n

(

−

1

)

⋅

2

)

\cos (\frac{\tan \left( -1\right) x}{2})

c

o

s

(

t

a

n

(

−

1

)

2

)

Solution

\cos \left( \frac{\tan \left( -1\right) x}{2}\right)

c

o

s

(

t

a

n

(

−

1

)

2

)

Answer:

Step-by-step explanation:

[tex]cos(tan^{-1}(\frac{x}{2} ))\\put~tan^{-1}(\frac{x}{2} )=t\\\frac{x}{2} =tan~t\\sec^2t-tan^2t=1\\sec^2t=1+tan^2t=1+(\frac{x}{2} )^2=\frac{x^2+4}{4} \\sec~t=\pm\frac{\sqrt{x^2+4}}{2} \\cos ~t=\pm\frac{2}{\sqrt{x^2+4}} \\hence~cos(tan^{-1}(\frac{x}{2} ))=cos~t=\pm\frac{2}{\sqrt{x^2+4}}[/tex]

Answer: 70 and 60 degrees

Step-by-step explanation:

Angle AOB = 180 - 50 - 60 = 70 degrees so x is 70 degrees

Angle OCD = 180 - 130 = 50 so y = 180 - 70 - 50 = 60 degrees

Answer: 470.4 N

Step-by-step explanation:

Concept:

1 kg on Earth = 9.8 N

Given information:

Mass = 48 kg

Find the weight on Earth

1 kg = 9.8 N

48 kg = 48 * 9.8 = [tex]\Large\boxed{470.4N\\}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Solving for y:

6y - 2x = 20

6y = 2x + 20

y = [tex]\frac{2x + 20}{6}[/tex]

y = [tex]\frac{2x}{6} + \frac{20}{6}[/tex]

y = [tex]\frac{1x}{3} + \frac{10}{3}[/tex]

Hope it helps!

Answer:

Step-by-step explanation:

6y - 2x = 20

     -6      -6

-2x = 20 - 6y

divide both sides by -2

[tex]\frac{-2x}{-2}[/tex] = [tex]\frac{20 - 6y}{-2}[/tex]

Dividing by -2 undoes the multiplication by -2.

[tex]x = \frac{20 - 6y}{ -2}[/tex]

Divide 20 -6 by -2

x = 3y - 10

Or

y = [tex]\frac{10}{3}[/tex]x +[tex]\frac{x}{3}[/tex]

Answer:

205

Step-by-step explanation:

We start with 235, this will be our y-intercept.

6 Is deducted from our value every visit, making our slope -6.

Put the two into slope intercept form:

[tex]y=235-6x[/tex]

To find the value after 5 visits substitute x for 5:

[tex]y=235-6(5)[/tex]

Solve

[tex]y=235-6(5)\\y=235-30\\y=205[/tex]

Therefore you have 205 left in your account after 5 visits.

The algebraic expression that represents the number of hours Anna and Tamara traveled the first two days is (2x - 1) hours.

We are told that;

On the first day, Anna and Tamara stop for sightseeing and lost 2 hours of travel time.

On the second day, they did not stop for lunch and gained 1 hour.

Now, we are told that x is the number of hours driven per day. Thus, for two days, number of hours driven is expressed as 2x.

Now, since they lost 2 hours on the first day, then total hours travelled is;

2x - 2 hours

On the second day, they gained 1 hour. Thus;

Final total number of hours traveled = 2x - 2 + 1

Final total number of hours traveled = (2x - 1) hours

Thus, we can conclude that the algebraic expression that represents how many hours Anna and Tamara traveled the first two days is (2x - 1) hours.

Read more about Algebraic Word Problems at; https://brainly.com/question/13818690

#SPJ1

a.

Solution Given:

Slope of the line passing through the point is

m= [tex] \frac{y_2-y_1}{x_2-x_1}=\frac{3-(-5)}{-2-2}=\frac{8}{-4}=-2[/tex]

slope=-2

b.

Solution given:

equation is

2x-5y=-10

2x+10=5y

y=2x/5 +10/5

y=2/5 x +3

comparing above equation with y=mx+c

we get

m=2/5

slope=2/5

c.

Slope of the line passing through the point is

m=[tex] \frac{y_2-y_1}{x_2-x_1}[/tex]

-4=[tex] \frac{1-(-9)}{0-x}[/tex]

-4=10/-x

doing criss cross multiplication

-4*-x=10

4x=10

x=10/4

x=5/2

slope=5/2

d.

we have

equation of line passing through the one point is

[tex] y-y_1=m(x-x_1)[/tex]

y-5=-7(x-(-1))

y=-7(x+1)+5

y=-7x-7+5

y=-7x-2 is a required equation:

Given the measure of angle B, side b and side, the measure of angle C to the nearest whole number is 43 degrees.

From the Rule of Sine;

sinA/a = sinB/b = sinC/c

Where A,B and C are the angles of the triangle and a, b and c are the corresponding opposing sides.

Given that;

Using the rule of sine.

sinB/b = sinC/c

We substitute the given values into the equation

sin( 18° )/9 = sinC/20

We solve for C.

sin( 18° ) × 20 = sinC × 9

0.309016994 × 20 = sinC × 9

6.18033988 = sinC × 9

Divide both sides by 9

6.18033988/9 = (sinC × 9)/9

sinC = 0.686704431

C = sin⁻¹( 0.686704431 )

C = 43.3697°

C = 43°

Given the measure of angle B, side b and side, the measure of angle C to the nearest whole number is 43 degrees.

Learn about cosine rule here: https://brainly.com/question/20839703

#SPJ1

Answer:W ^10

Step-by-step explanation:

The solution is in the

Answer:

4days atlases in the week

Quantity             day

  25------------------1

 1000---------------x

We solve

                  [tex]\boldsymbol{\sf{x=\dfrac{1000\times1}{25}=\dfrac{1000}{25}=40 }}[/tex]

Answer: To spend $1,000 it will take 40 days.

ヘ( ^o^)ノ＼(^_^ )If you want to learn more about mathematics, I share this link to complement your learning:

https://brainly.com/question/28182944

The statements which are correct about the equation of circle [tex]x^{2} +y^{2}-2x-8=0[/tex] are 1) The radius of the circle is 3 units,2) The center of the circle lies on the x axis,5) The radius of this circle is the same the radius of the circle whose equation is [tex]x^{2} +y^{2} =9[/tex].

Given the equation of circle be [tex]x^{2} +y^{2}-2x-8=0[/tex].

We are required to find the appropriate statements related to the equation [tex]x^{2} +y^{2}-2x-8=0[/tex].

[tex]x^{2} +y^{2}-2x-8=0[/tex] can be written as under:

[tex]x^{2} +y^{2} -2x+1-9=0[/tex]

[tex]x^{2} +1^{2}-2x+y^{2} -9=0[/tex]

[tex](x-1)^{2}+y^{2}[/tex]-9=0

[tex](x-1)^{2} +y^{2} =9[/tex]

[tex](x-1)^{2}+y^{2} =3^{2}[/tex]

Equation of a circle usually in the form [tex]x^{2} +y^{2} =a^{2}[/tex] in which a is radius.

From the comparison of both the equations we get that radius is 3 units.

From the equation point will be (1,0). It is on the x axis.

Hence the statements which are correct about the equation of circle [tex]x^{2} +y^{2}-2x-8=0[/tex] are 1) The radius of the circle is 3 units,2) The center of the circle lies on the x axis,5) The radius of this circle is the same the radius of the circle whose equation is [tex]x^{2} +y^{2} =9[/tex].

Learn more about radius at https://brainly.com/question/24375372

#SPJ1

Answer: 1,2,5 on edge

Step-by-step explanation:
see above ans for work

The inference is that the author suggest that looking at birds is silly A. to create a sense of doubt in the reader.

It should be noted that that an inference simply means the conclusion that can be deduced based on the information given in a story.

In this case, A Big Year" is a year in which a person attempts to see as many different species of birds as possible within a particular region. For most in North America who participate in a "Big Year," this region is the lower 48 American states, plus Alaska, Canada, and a couple of French islands off the Canadian coast.

The inference is that the author suggest that looking at birds is silly is to create a sense of doubt in the reader. Therefore, the correct option is A.

Learn more about inference on:

brainly.com/question/25280941

#SPJ1

The number with the given properties is 17

Let the tens be x and the units be y.

So, the number is 10x + y

The relationship between the digits is

[tex]y = x + 6[/tex]

The relationship between the number and the reverse is

[tex]2(10x + y + 10y + x) = 6 + 10 * (10x + y)[/tex]

Simplify the second equation

[tex]2(11x + 11y) = 6 + 100x + 10y[/tex]

Open the brackets

[tex]22x + 22y = 6 + 100x + 10y[/tex]

Substitute y = x + 6

[tex]22x + 22(x + 6) = 6 + 100x + 10(x + 6)[/tex]

Expand

[tex]22x + 22x + 132 = 6 + 100x + 10x + 60[/tex]

Collect like terms

[tex]22x + 22x - 100x - 10x = 6 + 60 - 132[/tex]

Evaluate the like terms

[tex]-66x = -66[/tex]

Divide by -66

x = 1

Substitute x = 1 in y = x + 6

[tex]y = 1 + 6[/tex]

y = 7

Recall that the number is 10x + y

So, we have

Number = 10 * 1 + 7

Evaluate

Number = 17

Hence, the number is 17

Read more about numbers and digits at:

https://brainly.com/question/12992284

#SPJ1

Answer:

The original price was $30

Step-by-step explanation:

40% = 40/100 = 0.4

[tex]\frac{12}{0.4} =30[/tex]

Hope this helps

Answer:

  understand the meaning of m > 0 and c > 0.

Step-by-step explanation:

The slope-intercept form of the equation of a line tells you its slope and its y-intercept.

  y = mx +c . . . . line with slope m and y-intercept c

The slope is the rate of increase moving from left to right. It is positive (m>0) when the line slants upward to the right. It is negative (m<0) when the line slants down to the right.

The y-intercept is where the line crosses the (vertical) y-axis. It is positive (c>0) when the line crosses above the x-axis, where y-values are positive. It is negative (c<0) when the line crosses below the x-axis. If the line passes through the origin, then c=0.

The amount of the mortgage on this house is given as $300000, while the 1.5 points on the house is given as 3000 dollars

The data from the questions says that the cost of the house = $245000

The down payment amount amount is 45000

Given that they already paid 45000 from the cost of the house, the mortgage would be 245000 - 45000

= $200000

The cost of 1.5 points is the same as the cost of 1.5% of the mortgage of this house.

This is calculated as 0.015 x 200000

= $3000

The conclusion is that the amount of the mortgage on this house is given as $300000, while the 1.5 points on the house is given as 3000 dollars

Read more on mortgage here: https://brainly.com/question/1318711

#SPJ1

Trabajando con porcentajes, concluimos que la pérdida es de $4800.

Sabemos que la inversión inicial es de $60000, y de esta cantidad, se pierde un 8%.

Entonces la pérdida va a ser el 8% de $60000.

Podemos escribir las relaciones:

$60000 = 100%

x = 8%

Queremos resolver esto para x, tomando el cociente entre esas relaciones y resolviendo para x obtenemos:

x = $60000*(8%/100%) = $60000*0.08 = $4800

Así, concluimos que la pérdida es de $4800.

Sí quieres aprender más sobre porcentages:

https://brainly.com/question/843074

#SPJ1

Using the sample space and probability concepts, we have that:

A) All the possibilities for the sample space are: {{G,G,G}, {G,G,B}, {G,B,G}, {G,B,B}, {B,G,G}, {B,G,B}, {B,B,G}, {B,B,B}}.

B) The probability is: 7/8.

C) The probability is: 1/2.

D) The probability is: 1/4.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

The sample space is the set that contains all possible outcomes, hence in this problem, considering G for girl and B for boy, it is given by:

{{G,G,G}, {G,G,B}, {G,B,G}, {G,B,B}, {B,G,G}, {B,G,B}, {B,B,G}, {B,B,B}}.

For item B, 7 outcomes have at most two boys, hence the probability is 7/8.

For item C, 4 outcomes have at least two girls, hence the probability is 4/8 = 1/2.

For item D, 2 outcomes have all the babies with the same sex, hence the probability is 2/8 = 1/4.

More can be learned about probabilities at https://brainly.com/question/14398287

#SPJ1

Answer:

(a - b)(a + b)(a² + b²)([tex]a^{4}[/tex] + [tex]b^{4}[/tex] )

Step-by-step explanation:

by repeated use of the difference of squares factorising method, that is

a² - b² = (a - b)(a + b)

given

[tex]a^{8}[/tex] - [tex]b^{8}[/tex]

= ([tex]a^{4}[/tex] )² - ([tex]b^{4}[/tex] )²

= ([tex]a^{4}[/tex] - [tex]b^{4}[/tex] )([tex]a^{4}[/tex] + [tex]b^{4}[/tex] ) ← factor left parenthesis using difference of squares

= ( a² - b²)(a² + b²)([tex]a^{4}[/tex] + [tex]b^{4}[/tex] ) ← factor left parenthesis by difference of squares

= (a - b)(a + b)(a² + b² )([tex]a^{4}[/tex] + [tex]b^{4}[/tex] )

Answer:

A = $11; C = $7 tickets

Step-by-step explanation:

Using the given info, we can create a system of equations to find the price of adult and children tickets.

Thus, we have 5A + 7C = 104 and 7A + 3C = 98

The easiest method to solve would be elimination:

Answer:

Step-by-step explanation:

The sales on the two days can be expressed using equations that can be solved for ticket prices.

Let x and y represent the prices of adult and children's tickets, respectively. Then the sales revenue for the two days can be expressed in the equations ...

One of the easiest solution methods is to use a graphing calculator. The first attachment shows the prices are $11 for an adult ticket; $7 for children tickets.

Using the matrix functions of a calculator, the augmented matrix of the equation coefficients can be reduced to row-echelon form. This, too, shows the solution to be (adult price, children price) = ($11, $7). See the second attachment. (The solution is the right-most column of the reduced matrix.)

Yet another solution method can use the coefficients from the equations written in general form:

In this form, we define three products of "cross multiplication":

  Δ1 = (5)(3) -(7)(7) = -34

  Δ2 = (7)(-98) -(3)(-104) = -374

  Δ3 = (-104)(7) -(-98)(5) = -238

Using those, we find the variable values to be ...

  x = Δ2/Δ1 = -374/-34 = 11

  y = Δ3/Δ1 = -238/-34 = 7

(adult price, children price) = ($11, $7)

__

You can read more about the cross-multiplication method here:

https://brainly.com/question/26397343

Answer:

The answer is B if the octagon has side lengths of 8

Since we know the sequence is quadratic, we expect the [tex]n[/tex]-th term to have the general form

[tex]x_n = an^2 + bn + c[/tex]

Plug in the first 3 known values of the sequence to form a system of equations.

[tex]x_1 = 3 = a + b + c[/tex]

[tex]x_2 = 12 = 4a + 2b + c[/tex]

[tex]x_3 = 25 = 9a + 3b + c[/tex]

Eliminating [tex]c[/tex] gives

[tex](4a + 2b + c) - (a + b + c) = 12 - 3 \implies 3a + b = 9[/tex]

[tex](9a + 3b + c) - (a + b + c) = 25 - 3 \implies 8a + 2b = 22 \implies 4a + b = 11[/tex]

Eliminating [tex]b[/tex] gives

[tex](4a + b) - (3a + b) = 11 - 9 \implies a = 2[/tex]

Solving for [tex]b,c[/tex], we get

[tex]4a + b = 11 \implies b = 11-4\cdot2 = 3[/tex]

[tex]a+b+c=3 \implies c=3-2-3 = -2[/tex]

So, the [tex]n[/tex]-th term of the sequence is

[tex]x_n = \boxed{2n^2 + 3n - 2}[/tex]

Samuel is incorrect because he didn't subtract the power of the numbers.

The number of rod and cone cells in the human eye is written in scientific notation. Scientific notation is used in expressing large numbers in smaller numbers. To write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10. For example, 1 x 10² is equivalent to 100

(9.1 x 10^7) - (4.5 x 10^6)

= (9.1 - 4.5) x 10^(7 - 6)

4.6 x 10 = 46

To learn more about scientific notation, please check: https://brainly.com/question/25334755

#SPJ1

Hello and Good Morning/Afternoon:

Let's take this problem step-by-step:

When we expand a function, everything must be multiplied out evenly.

      [tex](x+6)*(x+6)\\=x*x +x*6+6*x+6*6\\=x^2 + 6x + 6x+36\\x^2 +12x+36[/tex]

Answer: x² + 12x + 36

Hope that helps!

#LearnwithBrainly

Polynomials are mathematical expressions made up of many terms.

To simplify the polynomial to the maximum, all like terms must be grouped together and rearranged from highest to lowest power.

Distribute

Combining like terms.

The sum of the two rational equations is equal to (3 · n² + 5 · n - 10) / (3 · n³ - 6 · n²).

In this question we must use algebra definitions and theorems to simplify the addition of two rational equations into a single rational equation. Now we proceed to show the procedure of solution in detail:

To learn more on rational equations: https://brainly.com/question/20850120

#SPJ1

We conclude that the starting average grade is 79.17%

There are 50 students, let's say that the grades are measured between 1% and 100%.

And the average grade of the 50 students is A.

We know that after it increased by 20%, the average of the grades is 95.

Then we just need to solve the percentage equation:

95 = A*(1 + 20%/100%) = A*(1.2)

95/1.2 = A = 79.17

We conclude that the starting average grade is 79.17%

If you want to learn more about percentages:

https://brainly.com/question/843074

#SPJ1

Answer:

75%

Step-by-step explanation:

You need to do the following equation: x+20≤95 and you will have the answer. (I am sorry if it is wrong but this is what my teacher told the answer was. I put this answer and got it correct.) Hope it helped. Have a nice day.