Evaluate each expression

Here we have a dilation of scale factor 2.

We can see that bot figures we have the same slope, so we just have a dilation of scale factor K to go from figure A to figure B.

To find the value of K, notice that for some side length L in figure A, the correspondent length L' in figure B must be:

L' = K*L

Here if we use the left sides, we will get:

for figure A; L= 2

for figure B: L = 4

4 = K*2

4/2 = K

2 = K

So this is a dilation of scale factor k = 2.

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Answer:

the y is -2 and there's is no slope i think

Step-by-step explanation:

Triangle ABC and ADE are similar triangles

Similar triangles have the same corresponding angle measures and proportional side lengths.

This means that for two triangles to be similar, the corresponding angles must be equal and the ratio of corresponding sides of similar triangles are equal.

It has been shown that angles in ABC and ADE are equal.

To show that the ratio of corresponding sides are equal

6/12 = 8/16 = 10/20

The ratios all give a value of 1/2

Therefore we can say that the triangles ABC and ADE are similar.

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Answer:

Below

Step-by-step explanation:

Earnings, e, will be divided by 4  friends to equal 12

e/4 = 12      multiply both sides of the equation by 4

4 * e/4 = 12 * 4

    e = 48

1 cm = 10 mm. Length of book : 28 cm. Length of book = 280 mm. This shows that measurements in mm are the same but look to have a higher number .

The conversion factor provided states that 1 cm is equal to 10 mm, which means that 1 cm is made up of 10 individual millimeters.

The length of my book in when measured in millimeters is 280 mm.

In centimeters, this is therefore:

= 280 mm / 10 cm /mm

= 28 cm

Although the numerical value appears higher when expressed in millimeters, it is important to note that the actual length of the book remains the same.

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Smaller t = 2

Larger t = 5

Step-by-step explanation:

Given:

The given function is.

Find the zeros of the function.

Solution:

Simplify the equation above equation.

Now, we first find the root of the above equation.

Use quadratic formula with .

Put a, b and c value in above equation.

For positive sign

t = 2

For negative sign

t = 5

Put t = 2 in given function.

Put t = 5 in given function.

So, the zeros of the function is t = 2 or 5

Therefore, the smaller value of t = 2 and larger value of t = 5.

Answer: Permutation Problem

There are 5040 permutations possible

==================================================

Explanation:

Order matters because the positions are different.

(A,B,C,D) is different from (B,A,C,D) because the first means person A is the assistant while the second means person B is the assistant.

We have 10 choices for the first slot, 9 for the second, 8 for the third, and 7 for the fourth. We count down the values because a person cannot be reselected to serve multiple positions simultaneously.

Multiply out those values to get 10*9*8*7 = 5040

There are 5040 permutations possible.

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

As an alternative, you can use the nPr permutation formula with n = 10 and r = 4 like so

\(_n P_r = \frac{n!}{(n-r)!}\\\\_{10} P_{4} = \frac{10!}{(10-4)!}\\\\_{10} P_{4} = \frac{10!}{6!}\\\\_{10} P_{4} = \frac{10*9*8*7*6!}{6!}\\\\_{10} P_{4} = 10*9*8*7 \ \ \text{ ... note how this shows up again}\\\\_{10} P_{4} = 5040\\\\\)

We get the same answer as before.

Answer:

Combination

Step-by-step explanation:

This is the answer because:

1) The difference between combinations and permutations is the ordering of each term.

Combinations - the order doesn't matter

Permutations - the order matters.

An example of this is, if you enter the number combination 5324 into your locker/cabinet, it won't open up because it is a different ordering and needs a specific combination which means it's permutation.  

2) In this situation, the order doesn't not matter since they just want different ways to select an assistant, a representative, a treasurer, and a recorder.

Hope this helps! :D

By applying the concept of corresponding angles in similar triangles, we were able to establish the value of x as 25 in the given scenario.

In the given problem, we are provided with information about the angles in two similar triangles: triangle ABC and triangle STU. It is stated that angle UTS in triangle STU is 100 degrees, and since corresponding angles of similar triangles are congruent, we can conclude that angle STU is also 100 degrees.

Next, we examine angle BAC in triangle ABC, which is given as 4x. Using the same logic, we know that angle BAC is also congruent to angle STU. Therefore, we can equate the two angles:

angle BAC = angle STU

4x = 100

To find the value of x, we divide both sides of the equation by 4:

x = 100/4

x = 25

Hence, we determine that x is equal to 25. This method allows us to leverage the known information about one triangle to infer the measurements of corresponding angles in the other similar triangle.

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The percent error of the estimate is -2.14%

In this question, the figures are given as

Estimate = 5.5 cm

Actual = 5.62 cm

The percentage of the error is then calculated using the following equation

Error percentage = (Estimate - Actual)/Actual * 100%

Substitute the known values in the above equation, so, we have the following representation

Error percentage = (5.5 - 5.62)/5.62 * 100%

Evaluate

Error percentage = -2.14%

Hence, the error percentage is -2.14%

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Answer:

1. 54 = 0.6x

2. 90 dollars (see below)

Step-by-step explanation:

54 = 0.6x

0.6 is the decimal equivalent of 60%

Divide both sides by 0.6:

54/0.6 = 0.6x/0.6

90 = x

Answer:

x=15

Step-by-step explanation:

3*5=15

15/5=3

Answer:

x = 15

Step-by-step explanation:

x/3 = 5

3* x/3 = 3*5

x=15

Answer:3

Step-by-step explanation GCF of 6 and 9 is 3.

Answer:

y=3x+6

Step-by-step explanation:

the equation of a line in

slope-intercept form

is.

xy=mx+b

The largest total number of people who attended 3 matches on the day was 17, 000 people.

The largest total number of people who attended 3 matches on the day would be the sum of the largest rounded attendance numbers for each match:

Match 1: 5,000

Match 2: 8,000

Match 3: 4,000

Rounding each attendance number to the nearest 1,000 gives us:

Match 1: 5,000

Match 2: 8,000

Match 3: 4,000

Adding these rounded numbers together gives us:

5,000 + 8,000 + 4,000 = 17,000

Therefore, the largest total number of people who attended the three matches on the day was 17,000.

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The full question is:

Match 1 - 5, 000 people

Match 2 - 8, 000 people

Match 3 - 4, 000 people

This was the attendance at 3 football matches one day, each round to the three nearest 1,000. what's the largest total number of people who attended 3 matches on the day

The drop down menu is used to match each situation as below.

1. The rocket reached its maximum  the x-value of the vertex

height in 5 s.

2. ground level                                    the y-intercept

3. The rocket launcher was                the y-value of the point containing

on the ground.                                     the x-intercept on the right

4. The rocket was in the air 10           the x-intercept on the right                                                                                    

5. The maximum height of the           the y-value of the vertex

rocket is 50 ft.

6. the time the rocket was                the x-value of the point containing the

launched                                          y-intercept

The key features of the curve such as the x intercept is the point the launcher and the rocket were on ground.

The vertex is the point the rocket had the maximum and height.

Generally, the curve traces a parabolic path

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Answer:

A)      \(y_g = e^-^2^t*\frac{15}{37}cos(6t) + e^-^2^t*\frac{5}{74}sin(6t) + \frac{5}{74}sin(6t) - \frac{15}{37}cos(6t) \\\\y_g =\frac{15}{37}cos(6t)* [ e^-^2^t - 1 ] + \frac{5}{74}sin(6t)* [ e^-^2^t + 1 ]\)

B)       \(\frac{5}{74}sin(6t) - \frac{15}{37}cos(6t) = y_p\)

Step-by-step explanation:

- The following initial value problem is given as follows:

                      \(my'' + cy' + ky = F(t) \\\\y(0) = 0\\y'(0) = 0\)

- The above equation is the Newtonian mathematical model of a spring-mass-dashpot system. The displacement ( y ) and velocity ( y' ) are zeroed at the initial value t = 0.

- The equivalent mass ( m ) , damping constant ( c ) and the equivalent spring stiffness ( k ) are given as follows:

                      \(m = 2 kg\\\\c = 8 \frac{kg}{s} \\\\k = 80 \frac{N}{m} \\\\\)

- The system is subjected to a sinusoidal force F ( t ) given. We will plug in the constants ( m , c, and k ) and applied force F ( t ) into the given second order ODE.

                      \(2y'' + 8y' + 80y = 20sin(6t)\)

- The solution to a second order ODE is comprised of a complementary function ( yc ) and particular function ( yp ).

- To determine the complementary function ( yc ) we will solve the homogeneous part of the given second order ODE. We will assume the independent solution to the homogeneous ODE takes the form:

                           \(y = e^-^a^t\)

Where,

                          a: The root of the following characteristic equation

- Substitute ( y ) into the given ODE as follows:

                          \(( 2a^2 + 8a + 80 )*e^-^a^t = 0\\\\2a^2 + 8a + 80 = 0\)

- Solve the above characteristic quadratic equation:

                           \(a = 2 +/- 6i\)

- The complementary solution for the complex solution to the characteristic equation is of the form:

                           \(y_c = e^-^\alpha^t * [ Acos (\beta*t) + Bcos (\beta*t) ]\)

Where,

                          a = α ± β

Therefore,

                           \(y_c = e^-^2^t * [ Acos (6t) + Bcos (6t) ]\)

- To determine the particular solution we will scrutinized on the non-homogeneous part of the given ODE. The forcing function F ( t ) the applied force governs the form of the particular solution. For sinusoidal wave-form the particular solution takes form as following:

                           \(y_p = Csin (6t ) + Dcos(6t )\)

Where,

                           C & D are constants to be evaluated.

- Determine the first and second derivatives of the particular solution (yp) as follows:

                            \(y'_p = 6Ccos(6t) - 6Dsin(6t)\\\\y''_p = -36Ccos(6t) - 36Dcos(6t)\\\)

- Plug in the particular solution ( yp ) and its derivatives ( first and second ) into the given ODE.

        \(-72Csin(6t) - 72Dcos(6t) + 48Ccos(6t) - 48Dsin(6t) + 80Csin(6t) + 80Dcos(6t) = 20sin(6t) \\\\sin(6t)* ( 8C -48D ) + cos(6t)*(8D + 48C ) = 20sin(6t)\\\\D + 6C = 0\\\\C - 6D = 2.5\\\\C = \frac{5}{74} , D = -\frac{15}{37}\)

- The particular solution can be written as follows:

                        \(y_p = \frac{5}{74}sin(6t) - \frac{15}{37}cos(6t)\)

- Now we use the principle of super-position and combine the complementary and particular solution and form a function of general solution as follows:

                        \(y_g = y_c + y_p \\\\y_g = e^-^2^t* [ Acos(6t) + Bsin (6t) ] + \frac{5}{74}sin(6t) - \frac{15}{37}cos(6t)\)

- To determine the complete solution of the given ODE we have to calculate the constants ( A and B ) using the given initial conditions as follows:

                        \(y_g ( 0 ) = 1*[A(1) + 0 ] + 0 - \frac{15}{37}(1) = 0\\\\A = \frac{15}{37}\\\\y'_g = -2e^-^2^t*[Acos(6t) + Bsin(6t) ] +e^-^2^t*[-6Asin(6t) + 6Bcos(6t) ] + \\\\\frac{15}{37}cos(6t) +\frac{90}{37}sin(6t) \\\\y'_g(0) = -2*[A(1) + 0] + 1*[0 + 6B] + \frac{15}{37}(1) +0 = 0\\\\B = \frac{15}{6*37} = \frac{5}{74}\)

- The complete solution to the initial value problem is:

           \(y_g = e^-^2^t*\frac{15}{37}cos(6t) + e^-^2^t*\frac{5}{74}sin(6t) + \frac{5}{74}sin(6t) - \frac{15}{37}cos(6t) \\\\y_g =\frac{15}{37}cos(6t)* [ e^-^2^t - 1 ] + \frac{5}{74}sin(6t)* [ e^-^2^t + 1 ]\)          

- To determine the long term behavior of the system we will apply the following limit on our complete solution derived above:

                 \(Lim (t->inf ) [ y_g ] = \frac{15}{37}cos(6t)* [ 0 - 1 ] + \frac{5}{74}sin(6t)* [ 0 + 1 ]\\\\Lim (t->inf ) [ y_g ] = \frac{5}{74}sin(6t) - \frac{15}{37}cos(6t) = y_p\)

- We see that the complementary part of the solution decays as t gets large and the particular solution that models the applied force F ( t ) is still present in the system response when t gets large.

The triangle similarity can be proven by three methods, and the AA similarity postulate states that two triangles are similar if and only if their corresponding angles are congruent.

If they have the same shape but different sizes. This is what is known as similarity. In mathematics, there are three ways to prove that two triangles are similar: AA, SAS, and SSS.

In the case of AA similarity postulate, two triangles are similar if and only if two corresponding angles are congruent, meaning they have the same degree measure.

Similarly, if triangle ABC is similar to triangle JKL by AA similarity postulate, it means that the corresponding angles of both triangles are congruent.

Therefore, it is possible that triangle ABC is similar to one or more of the triangles given, but it is not possible to say without further information such as the angles and lengths of the sides.

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Complete Question:

Define triangle is ​△ABC​ similar to Similarity property and why?

Which triangle is ​△abc​ similar to and why? responses △abc is similar to △ghi by ​aa similarity postulate. triangle a b c, is similar to , triangle g h i, by , ​, a a similarity postulate, ., △abc is similar to △jkl by ​aa similarity postulate​. triangle a b c, is similar to , triangle j k l, by , ​, a a similarity postulate, ​, . △abc is similar to △def by ​aa similarity postulate​. triangle a b c, is similar to , triangle d e f, by , ​, a a similarity postulate, ​, . ​△abc​ is not similar to any of the triangles given.

Answer:

$600

Step-by-step explanation:

Let x = og price

x - 0.29x = 426

0.71x=426

÷0.71 ÷0.71

x = 600

The only set of side lengths that can form a triangle is 9, 4, 8.

Option A is the correct answer.

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Let's check if each of the given sets of side lengths satisfies this condition:

A.

9, 4, 8

9 + 4 > 8 ✓

9 + 8 > 4 ✓

4 + 8 > 9 ✓

All three inequalities are true, so these side lengths can form a triangle.

B.

14, 7, 6

14 + 7 > 6 ✓

14 + 6 > 7 ✓

7 + 6 > 14 ✗

The last inequality is false, so these side lengths cannot form a triangle.

C.

3, 8, 1

3 + 8 > 1 ✓

3 + 1 > 8 ✗

8 + 1 > 3 ✓

The second inequality is false, so these side lengths cannot form a triangle.

Therefore,

The only set of side lengths that can form a triangle is A. 9, 4, 8.

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The mean of a population set can be calculated through the formula:

in which, n is the total number of data points that are in the set

then, with the sample given the mean can be found as,

Answer:

The sample mean is 13.

The graph of the linear inequality y ≥ 2x - 5 is attached below with it's shaded part included.

The graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality.

In the given problem, the inequality presented is;

y ≥ 2x - 5

To graph this, we would use a graphing calculator to find the boundary lines and plane.

In the graph below, the x and y intercept is at (2.5, -5) and the shaded part is on the left side of the graph.

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Answer: 2.5 quarts

Step-by-step explanation: I looked it up

Answer:

40 cups in 10 quarts

Step-by-step explanation:

1 quart = 4 cups

So...

4*10=40

Answer: 18 inches.

Explanation: A simple way to see this problem is to convert the width and length of the photo into a ratio. Width to Length. Now that ratio would be 4:6

or in other words 4 to 6. Ratios can be written as fractions. In this case 4:6 can be written as 4/6. Now all that is left to do is find the missing number of the next ratio since we know that the next ratio is 12 to unknown number.

Step 1.) Once you convert the ratio into a fraction find your variables.

4/6 = 12/?

Step 2.) Let's change the unknown number to x in value according to algebra.

4/6 = 12/x

Step 3.) Solve using cross multiplication.

4/6 = 12/x

4(x) = 6(12)

4x = 72

4x/4 = 72/4

x=18

Hope this helps.  Let me know if you have any questions.

Your Welcome, :-)

Answer:

The answer is D. Hope this helps

The component form of the following vectors is Option A. V = (38.3, 32.1).

To find the component form of a vector given its magnitude and direction angle, we can use trigonometry.

The component form of a vector in two dimensions is represented as (x, y), where x is the horizontal component and y is the vertical component.

In this case, the magnitude of the vector is given as 50, and the direction angle θ is 50°. We can use this information to calculate the horizontal and vertical components.

The horizontal component (x) can be found using the formula x = magnitude * cos(θ), and the vertical component (y) can be found using y = magnitude * sin(θ).

Let's calculate the components:

x = 50 * cos(50°) ≈ 38.3

y = 50 * sin(50°) ≈ 32.1

Rounding the answers to the nearest tenth, we get the component form of the vector V as (38.3, 32.1).

Therefore, the correct answer is A. V = (38.3, 32.1).

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The question is incomplete. Find the full content below:

Find the component form of the following vectors. Round your answers to the tenth.

Magnitude of v = 50, direction angle θ = 50°

A. V = (38.3, 32.1)

B. V = (33.8, 31.2)

C. V = (32.1, 38.3)

D. V = (31.2, 33.8)

Answer:

There are many sources of student credit cards. One can obtain a student credit card through companies such as Capital One, Discover, Visa, or Mastercard.

Step-by-step explanation:

The probability that a student has either a Visa card or a Mastercard is 0.98 or 98%.

To find the probability that a student has either a Visa card or a Mastercard, we can use the principle of probability for the union of two events.

Let V be the event of having a Visa card, and M be the event of having a Mastercard.

The probability of having either a Visa card or a Mastercard (V or M) is given by:

P(V or M) = P(V) + P(M) - P(V and M)

Where:

P(V) = Probability of having a Visa card = 0.81

P(M) = Probability of having a Mastercard = 0.17

P(V and M) = Probability of having both a Visa card and a Mastercard = 0.06

Now, plug in the given values:

P(V or M) = 0.81 + 0.17 - 0.06

P(V or M) = 0.98

So, To find the probability that a student has either a Visa card or a Mastercard, we can use the principle of probability for the union of two events.

Let V be the event of having a Visa card, and M be the event of having a Mastercard.

The probability of having either a Visa card or a Mastercard (V or M) is given by:

P(V or M) = P(V) + P(M) - P(V and M)

Where:

P(V) = Probability of having a Visa card = 0.81

P(M) = Probability of having a Mastercard = 0.17

P(V and M) = Probability of having both a Visa card and a Mastercard = 0.06

Now, plug in the given values:

P(V or M) = 0.81 + 0.17 - 0.06

P(V or M) = 0.98

So, the probability that a student has either a Visa card or a Mastercard is 0.98 or 98%.

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Answer: 1/5

Step-by-step explanation:

Answer:

The answer to your problem is, D. The range is the best measure of variability, and it equals 32.

Step-by-step explanation:

We know the scores earned in a flower-growing competition are represented in the stem-and-leaf plot.

The key will equal 2|1 means 21

Which we conclude to 17, 19, 21, 25, 29, 30, 31, 32, 46, 49.

Quartile:

Median, Minimum, Maximum, & Range:

Thus the answer to your problem is, D. The range is the best measure of variability, and it equals 32.

Answer:

B

Step-by-step explanation: