What is the equation of the line that goes through (2, 2) and isperpendicular to y = 5x + 3?A. y-2=-1/5(x-2)B. y=-1/5(x+2)C. y-2 =5(x - 2)D. y-2=1/5(x-2)

Answer:

B ... An isosceles triangle has an order 1 rotational symmetry because it does not have all congruent angles.

Step-by-step explanation:

Got it correct on Edge2020

The statement B is correct which states that the An isosceles triangle has an order 1 rotational symmetry because it does not have all congruent angles.

Rotational symmetry, also known as radial symmetry in geometry, is the property a shape has when it looks the same after some rotation by a partial turn.

According to the statement

We have to find that the correct statement about the rotational symmetry for an isosceles triangle.

So, For this purpose, we know that the

From the given information:

Then from isosceles triangle,

An isosceles is a triangle that has two sides of equal length.

The isosceles theorem says that the angles opposite to the equal sides of a triangle are equal.

Thus, it also has two equal angles and one non equal angle. Thus,  it does not have all congruent angles.

The order of rotational symmetry of a  figure is the number of times we rotate up to 360° the figure such that it looks exactly the same as the original figure.

When we rotate the isosceles triangle up to 360° , only 1 time it looks exactly same as in the beginning because at each rotation the order of angles changes.

Therefore, The statement B is correct which states that the An isosceles triangle has an order 1 rotational symmetry because it does not have all congruent angles.

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The data that is considered univariate is, Shoe size, salary, height, sports played in high school, years of experience, favorite color.

Data that just has one variable is said to be univariate data. Since there is only one variable that varies, univariate data analysis is the most straightforward type of analysis. The analysis's primary goal is to explain the data and identify any patterns in it; it does not deal with causes or correlations. Height is an example of a univariate data.

We know that univariate data only has one variable thus the data that can be represented with a single variable is:

Shoe size, salary, height, sports played in high school, years of experience, favorite color.

Hence, the data that is considered univariate is, Shoe size, salary, height, sports played in high school, years of experience, favorite color.

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Answer:

49.5 meters of linen were left after the sale.

Step-by-step explanation:

Given that there are 100 meters of linen

And 15.75, 22.50 and 12.25 meters are sold.

This means that the sold linen has to be added  to find the total linen sold.

And then the quantity of sold linen will be subtracted from 100 to find the meters of linen left.

\(Total\ linen\ sold = 15.75+22.50+12.25 = 50.5\ meters\)

Left linen will be:

\(=100-50.5 = 49.5\)

Hence,

49.5 meters of linen were left after the sale.

Answer:

Step-by-step explanation:

So negitive have the - besides it and + mean its negative .

Answer:

-29

-6

.5

105

Step-by-step explanation:

Answer:

0.324m^2 ; 18 ft

Step-by-step explanation:

Given the triangle :

Base (b) of triangle = 54cm

Height (h) of triangle = 1.2m

Area(A) of a triangle is given by:

0.5 * base * height

Base = 54cm = 54/100 = 0.54 m

Therefore,

A = 0.5 * 0.54m * 1.2m

A = 0.324m^2

2.) Average of the two bases in the trapezoid :

From the trapezium Given :

Base 1 = 15 feets

Base 2 = 7 yards

1 yard = 3 Feets

Therefore, base 2 in Feets = 7 * 3 = 21 Feets

Average of the two bases :

(21 Feets + 15 Feets) / 2

= 36 Feets / 2

= 18 Feets

Answer:

136+56 ig

Step-by-step explanation:

Answer:

f(g(x))=9-x-\(x^{2}\)

Step-by-step explanation:

Given ,

f(x)=9-x

g(x)=\(x^{2}\) +x

here,.

fog

=f(g(x))

=f(\(x^{2}\) +x)

=9-(\(x^{2}\) +x)

=9-\(x^{2}\) -x

=9-x-\(x^{2}\)

The solution for the given functions are

f(6) = -28

g(-3) = 79

To find f(6), we substitute x = 6 into the function f(x) = -5x + 2:

f(6) = -5(6) + 2

     = -30 + 2

     = -28

Therefore, f(6) = -28.

To find g(-3), we substitute x = -3 into the function g(x) = -3x^3 - 2:

g(-3) = -3(-3)^3 - 2

     = -3(-27) - 2

     = 81 - 2

     = 79

Therefore, g(-3) = 79.

Here, the given problem produces the following results, f(6) = -28, g(-3) = 79.

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Using the given natural abundances of titanium-46, titanium-47, and titanium-48, we find that the average atomic mass of titanium on this planet is approximately 46.4 amu.

To calculate the average atomic mass of titanium on another planet, we need to consider the natural abundances of its isotopes. The average atomic mass is calculated by multiplying the mass of each isotope by its relative abundance and summing up these values.

Let's assume that the three isotopes of titanium on this planet are denoted as titanium-46, titanium-47, and titanium-48. The natural abundances of these isotopes are given as follows:

Isotope Natural Abundance

Titanium-46 70%

Titanium-47 20%

Titanium-48 10%

To calculate the average atomic mass, we multiply the mass of each isotope by its relative abundance and sum up these values. The atomic masses of titanium-46, titanium-47, and titanium-48 are approximately 46.0 amu, 47.0 amu, and 48.0 amu, respectively.

Average Atomic Mass of Titanium:

(46.0amu×70%)+(47.0amu×20%)+(48.0amu×10%)

=(32.2amu)+(9.4amu)+(4.8amu)

=46.4amu

Therefore, the average atomic mass of titanium on this planet is approximately 46.4 atomic mass units (amu).

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Answer:

5th - 13

6th - 20

7th - 27

8th - 34

Step-by-step explanation:

You add seven

Answer:

The slope is negative

Step-by-step explanation:

The equation is y+2x=24

We need to put this in slope intercept form to find the slope:

Subtract 2x on both sides:

y=-2x+24

(y=mx+b)

(m is slope) (b is y-intercept)

Thus the slope is negative

Since it is -2x

Hope this helps!

As per the linear regression analysis, the predicated depression score if the MHPG level was 1100 is 20.41

Linear regression analysis:

In math , linear regression analysis means a regression model that estimates the relationship between one independent variable and one dependent variable using a straight line.

Given,

linear regression analysis calculated a slope of -0.017 and a y intercept of 39.11.

Here we need to predict the depression score if the mhpg level was 1100.

We know the that standard form of the line of equation for straight line is written as,

y = mx + c

where m refers the slope and c refer the y intercept.

Then the line of the equation of this linear regression analysis is written as,

=> y = -0.017x + 39.11

In this equation x refers the MHPG level.

So, the value of x is 1100, then the predicated depression score is calculated as,

=>  y = -0.017(1100) + 39.11

=> y = -18.7 + 39.11

=> y = 20.41

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The frequency of the data sets is defined as the number of times the data is repeated in the given dataset. The frequency of the given data is calculated in the table below.

The frequency of the data sets is defined as the number of times the data is repeated in the given dataset.

Height (cm)              Frequency

146           --             2

147           --              1  

148           --              1                

149           --              1                  

150           --             2                  

151            --              1                      

152           --             6                                  

153           --             2                                      

154          --              3                                                  

155          --              1          

As we can see that the height of 146 cm is repeated two times so its frequency is 2. From this concept, all the frequencies are calculated above.

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A)The probability of exactly four buses arriving in the next 2 hours is\($P(X=4)=e^{\wedge}(-2)\left(2^{\wedge} 4 / 4 !\right)=0.090$\) ≈ 0.090.

B) The probability of at least two buses arriving in the next 2 hours is =0.865

C)  The probability of no buses arriving in the next 2 hours is =0.135

d) The probability that it will be between 30 and 90 minutes before the next bus arrives is ,0.185

a) Let \($X$\) be the number of buses that arrive in a 2-hour period. Since the time between arrivals of buses follows an exponential distribution with a mean of 60 minutes, the arrival rate λ is given by\($\lambda=1 / 60$\) 0 buses per minute.

Therefore, the number of buses that arrive in a 2-hour period is a Poisson distribution with parameter \(\mu=\lambda t=(1 / 60) \times 120=2$.\). Thus, X has a Poisson distribution with parameter μ = 2.

The probability of exactly four buses arriving in the next 2 hours is\($P(X=4)=e^{\wedge}(-2)\left(2^{\wedge} 4 / 4 !\right)=0.090$\) ≈ 0.090.

b) The probability of at least two buses arriving in the next 2 hours is

\($P(X \geq 2)=1-P(X=0)-P(X=1)=1-e^{\wedge}(-2)\left(2^{\wedge} 0 / 0 !\right)-e^{\wedge}(-2)\left(2^{\wedge} 1 / 1 !\right)=0.865$.\)

c) The probability of no buses arriving in the next 2 hours is

\(P(X=0)=$ $e^{\wedge}(-2)\left(2^{\wedge} 0 / 0 !\right)=0.135$\)

d) Let Y be the time between the first and second bus arrivals. Then Y follows an exponential distribution with a mean of 60 minutes. We want to find the probability that \($30 \leq Y \leq 90$\).

This is equivalent to finding \(P(Y \leq$ $90)-P(Y \leq 30)$,\), which is equal to F(90) - F(30), where F is the cumulative distribution function of the exponential distribution with \($\lambda=1 / 60$\)

Therefore, the probability that it will be between 30 and 90 minutes before the next bus arrives is\(F(90)-F(30)=\left(1-e^{\wedge}(-90 / 60)\right)-(1$ $\left.e^{\wedge}(-30 / 60)\right)=e^{\wedge}(-1.5)-e^{\wedge}(-0.5)=0.185$\)

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The statement, When two events are disjoint, they are also independent is false.

In a sample space, we can use probability laws to determine the probabilities of these events and how they relate to each other. Disjoint Events: Two events are non-overlapping or mutually exclusive if they have no common outcome. Mathematically, this can be written as, P(B ∩ A) = 0 --(1)

Independent Events: Events are independent when they do not "affect" the probability of another event occurring. Mathematically written as:

P(B/A) = P(B) P(A and B)

=> P(B ∩ A) = P(B) × P(A) --(2)

(1) ) and (2) events cannot be independent unless they overlap. That is, if events do not overlap, they are also dependent. Hence, disjoint events are not independent that means the above statement is false.

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The expression to evaluate is sin(θ − φ), where θ is in Quadrant III and tan θ = 12/5, and φ is in Quadrant IV with sin φ = −3√10/10. The evaluation of sin(θ − φ) involves finding the values of sin θ and sin φ and then using the trigonometric identity for the sine of the difference of two angles.

In the given conditions, tan θ = 12/5 means that the ratio of the opposite side to the adjacent side in the triangle with angle θ is 12/5. Since θ is in Quadrant III, both the opposite side and the adjacent side are negative. Using the Pythagorean theorem, we can find the hypotenuse of the triangle as √(12^2 + 5^2) = 13.

Using the information of sin φ = −3√10/10 and φ in Quadrant IV, we can construct a triangle in Quadrant IV where the opposite side is −3√10 and the hypotenuse is 10. By applying the Pythagorean theorem, we find the adjacent side as √(10^2 - (−3√10)^2) = 7√10.

Now, we can apply the trigonometric identity sin(θ − φ) = sin θ cos φ − cos θ sin φ. Since we know the values of sin θ, cos φ, and sin φ, we can substitute them into the identity. The resulting expression will give us the evaluation of sin(θ − φ).

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The Relationship between the points D(6, 9) and A(8, 12) can be described as a dilation with a factor of 1.5. Point A is located 1.5 times farther from the origin compared to point D, in both the horizontal and vertical directions. Additionally, A is an enlargement of D.

The relationship between the points D(6, 9) and A(8, 12) can be described in terms of dilations. In mathematics, a dilation is a transformation that changes the size of an object while keeping its shape intact. It involves scaling the object by a certain factor, either enlarging or reducing it.

To understand the relationship between D and A, we can calculate the dilation factor. The dilation factor, denoted by 'k', is the ratio of the corresponding side lengths or distances between the pre-image (original object) and the image (transformed object).

The dilation factor between D(6, 9) and A(8, 12):

First, we need to find the change in x-coordinates and y-coordinates:

Δx = 8 - 6 = 2

Δy = 12 - 9 = 3

Next, we calculate the dilation factor:

k = Δy / Δx = 3 / 2 = 1.5

The dilation factor of 1.5 indicates that the image point A is 1.5 times as far from the origin (point D) compared to the pre-image. This means that A is located at a greater distance from the origin than D, both horizontally and vertically.

Moreover, since the dilation factor is positive, the dilation is an enlargement. This means that A is enlarged with respect to D. The ratio of the corresponding side lengths will also be 1.5.

the relationship between the points D(6, 9) and A(8, 12) can be described as a dilation with a factor of 1.5. Point A is located 1.5 times farther from the origin compared to point D, in both the horizontal and vertical directions. Additionally, A is an enlargement of D.

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The general solution of the system x'(t) = Ax(t), where A is the given matrix, can be found by solving the system of linear differential equations associated with it.

To find the general solution, we need to solve the system of linear differential equations x'(t) = Ax(t), where x(t) is a vector-valued function and A is the given matrix.

The solution involves finding the eigenvalues and eigenvectors of the matrix A. The general solution will have the form x(t) = c₁v₁e^(λ₁t) + c₂v₂e^(λ₂t) + ... + cₙvₙe^(λₙt), where c₁, c₂, ..., cₙ are constants, v₁, v₂, ..., vₙ are eigenvectors, and λ₁, λ₂, ..., λₙ are eigenvalues of A.

This general solution represents a linear combination of exponential functions, where each term corresponds to an eigenvalue-eigenvector pair. The specific values of the constants are determined by initial conditions or boundary conditions provided in the problem.

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Answer:

"Incorrect values of the variable, such as those that are introduced as a result of the squaring process are called extraneous solutions. Extraneous solutions may look like the real solution, but you can identify them because they will not create a true statement when substituted back into the original equation."

Step-by-step explanation:

Amy is correct, -7.1 is between -7 and -8.  

A number pattern is a pattern in a series of numbers that represents the common relationship between the numbers.

Two students were asked to graph a rational number -7.1.

Amy states that The number is between -8 and -7, but Laura states that the point is between -7 and -6.

In order to be in between -6 and -7, the number would have to be a decimal with a whole number of 6.

But -7.1 has a whole number of 7 then it is in between -7 and -8.

Thus, Amy is correct, -7.1 is between -7 and -8.  

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Answer:

\(\frac{27y^6}{8x^{12}}\)

Step-by-step explanation:

1) Use Product Rule: \(x^ax^b=x^{a+b}\).

\((\frac{3x^{-5+2}{y^3}}{2z^0yx}) ^3\)

2) Use Negative Power Rule: \(x^{-a}=\frac{1}{x^a}\).

\((\frac{3\times\frac{1}{x^3} y^3}{2x^0yx} )^3\)

3) Use Rule of Zero: \(x^0=1\).

\((\frac{\frac{3y^3}{x^3} }{2\times1\times yx} )^3\)

4) use Product Rule: \(x^ax^b=x^{a+b}\).

\((\frac{3y^3}{2x^{3+1}y} )^3\)

5) Use Quotient Rule: \(\frac{x^a}{x^b} =x^{a-b}\).

\((\frac{3y^{3-1}x^{-4}}{2} )^3\)

6) Use Negative Power Rule: \(x^{-a}=\frac{1}{x^a}\).

\((\frac{3y^2\times\frac{1}{x^4} }{2} )^3\)

7) Use Division Distributive Property: \((\frac{x}{y} )^a=\frac{x^a}{y^a}\).

\(\frac{(3y^2)^3}{2x^4}\)

8) Use Multiplication Distributive Property:  \((xy)^a=x^ay^a\).

\(\frac{(3^3(y^2)^3}{(2x^4)^3}\)

9) Use Power Rule: \((x^a)^b=x^{ab}\).

\(\frac{27y^6}{(2x^4)^3}\)

10)  Use Multiplication Distributive Property:  \((xy)^a=x^ay^a\).

\(\frac{26y^6}{(2^3)(x^4)^3}\)

11) Use Power Rule: \((x^a)^b=x^{ab}\).

\(\frac{27y^6}{8x^12}\)

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Answer:

\(\displaystyle \frac{27y^{6}}{8x^{12}}\)

Step-by-step explanation:

\(\displaystyle \biggr(\frac{3x^{-5}y^3x^2}{2z^0yx}\biggr)^3\\\\=\biggr(\frac{3x^{-5}y^2x}{2}\biggr)^3\\\\=\frac{(3x^{-5}y^2x)^3}{2^3}\\\\=\frac{3^3x^{-5*3}y^{2*3}x^3}{8}\\\\=\frac{27x^{-15}y^{6}x^3}{8}\\\\=\frac{27y^{6}x^3}{8x^{15}}\\\\=\frac{27y^{6}}{8x^{12}}\)

Notes:

1) Make sure when raising a variable with an exponent to an exponent that the exponents get multiplied

2) Variables with negative exponents in the numerator become positive and go in the denominator (like with \(x^{-15}\))

3) When raising a fraction to an exponent, it applies to BOTH the numerator and denominator

Hope this helped!

Answer:

20

Step-by-step explanation:

19/0.95=20

Range is about subtracting the lowest number from the highest number!

The lowest number is 54.

The highest number is 65.

65 - 54 = 11

Answer:

11

Step-by-step explanation:

Subtract the highest and lowest values 65-54, and you get 11

The missing sides of the special right triangles are listed below:

Case 1: y = √2 · 13, x = 13

Case 2: x = y = 15√2

Case 3: x = 6, y = 3√3

Case 4: x = 17√3, y = 17

Case 5: x = y = 10

Case 6: x = 50, y = 25

Case 7: x = y = 4√7

Case 8: x = 16√3, y = 8√3

Case 9: x = 11√3, y = 33

Case 10: x = 3√2, y = 2√6

Case 11: x = √10, y = 2√5

Case 12: x = 4√7, y = 8√21

Herein we find twelve cases of special right triangles whose missing sides must be determined by using the following rules:

45 - 90 - 45 Right triangle

r = √2 · x = √2 · y

30 - 60 - 90 Right triangle

x = (1 / 2) · r

y = (√3 / 2) · r = √3 · x

Where:

Case 1

y = √2 · 13

x = 13

Case 2

x = y = 15√2

Case 3

x = 3 / (1 / 2)

x = 6

y = 3√3

Case 4

x = 34 · (√3 / 2)

x = 17√3

y = 34 · (1 / 2)

y = 17

Case 5

x = y = 10

Case 6

x = 25√3 / (√3 / 2)

x = 50

y = 25√3 / √3

y = 25

Case 7

x = y = 2√14 · √2 = 2√28 = 4√7

Case 8

x = 24 / (√3 / 2)

x = 48 / √3

x = 16√3

y = 24 / √3

y = 8√3

Case 9

x = 22√3 · (1 / 2)

x = 11√3

y = 22√3 · (√3 / 2)

y = 33

Case 10

x = √18

x = 3√2

y = √6 / (1 / 2)

y = 2√6

Case 11

x = √10

y = √20

y = 2√5

Case 12

x = 4√21 / √3

x = 4√7

y = 4√21 / (1 / 2)

y = 8√21

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(d.) Each run of the simulation only provides a sample of the actual system's operation.

This assertion is right, not mistaken. Indeed, each simulation run is a sample of the actual system's operation. A single simulation run cannot account for all possible outcomes and variations in the real system because simulations are based on mathematical models and involve random variations.

In order to take into consideration various scenarios and variations, multiple simulation runs are typically carried out. By running numerous reenactments, specialists can assemble a scope of results and measurable data to acquire a superior comprehension of the framework's way of behaving and go with informed choices.

The analysis and confidence in the simulation study's conclusions increase with the number of simulation runs performed.

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Answer:

B. The deposit increases by 3% of its current value, compounded monthly.

Step-by-step explanation:

When compounded monthly that means the account is getting more money monthly rather than annually, or each year, so this answer choice would give the best benefit to the account holder. I did this problem on Khan Academy myself and this was the correct answer.

Answer:

Answer: B. The deposit increases by 3% of its current value, compounded monthly.

Step-by-step explanation: When compounded monthly that means the account is getting more money monthly rather than annually, or each year, so this answer choice would give the best benefit to the account holder. I did this problem on Khan Academy myself and this was the correct answer.

Compare the quantity in Column A with the quantity in Column B.

Column A Column B, The two quantities are equal.

Generally, the surface that has one end or side that is higher than the other (or vice versa); is a surface that slopes up or down.

In conclusion, Compare the number in Column A with the number in Column B.

The two amounts are identical in Columns A and B.

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