solve for r: 12 = r + 6 - 2r​ please answer I don't need work shown tho

Answer:

refer to the pic attached

The prove of ∠1 equal to ∠2 is shown below.

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

⇒ AB = AC, AD = AE and DC = EB

Now,

In ΔDBC and ΔEBC;

⇒ DC = EB   (Given)   ..(i)

Since,  AB = AC

So, the ΔABC is a isosceles triangle.

Hence, ∠DBC = ∠ ECB   ..(ii)

Here,  AB = AC and AD = AE

So, BD = EC   ..(iii)

Hence, By the condition (i), (ii) and (iii);

By SAS condition,

⇒ ΔDBC ≅ ΔEBC

Hence, We get;

⇒ ∠1 = ∠2

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Answer:

The car's rate is 50 miles per hour, and it will travel 150 miles in 3 hours

Step-by-step explanation:

There are about 1.6 kilometres in a mile, meaning that in 80 miles there are about 50 miles. This means that the car's rate in miles per hour is about 50. This means that in 3 hours, it will travel about 50*3=150 miles. Hope this helps!

Answer:

30 degrees

Step-by-step explanation:

A full turn is 360 degrees. The question asks for a twelfth of a turn, so all you need to do is divide 360 by 12! 360/12=30...30 is your answer!

Hope this helps you out...have an amazing day c:

The equation of the tangent line to the curve `y = 2ex cos(x)` at the point (0,2) is given by `y = 2ex + 2`.

To find an equation of the tangent line to the curve at the given point (0,2) whose equation is given by `y = 2ex cos(x)`, we need to determine the derivative `y'` of `y = 2ex cos(x)` first. Using the product rule, we have;

`y = 2ex cos(x)`...let `u = 2ex` and `v = cos(x)`, then `u' = 2ex` and `v' = -sin(x)`.`y' = u'v + uv'` `= 2ex cos(x) - 2ex sin(x)` `= 2ex(cos(x) - sin(x))`

Therefore, the derivative of `y = 2ex cos(x)` is `y' = 2ex(cos(x) - sin(x))`.

The equation of the tangent line to the curve at the point (0,2) is obtained by using the point-slope formula, which is given by: `y - y1 = m(x - x1)`where `(x1,y1)` is the point of tangency, `m` is the slope of the tangent line.

Substituting the values of `m`, `x1` and `y1`, we obtain: `m = y' |(0,2)` `= 2e(1 - 0)` `= 2e`Using the point-slope formula with `(x1,y1) = (0,2)` and `m = 2e`, we have: `y - 2 = 2e(x - 0)` `y - 2 = 2ex` `y = 2ex + 2`

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For solving the inequalities, there are more than four steps.

The step to solve given inequalities, the first step is to add the same number to both sides, the second step is to  Subtract the same number from both sides and the third step is to  Multiply both sides by the same positive number, and the fourth step is to  Divide both sides by the same positive number, and the fifth step is to Multiply both sides by the same negative number and reverse the sign and the last step is to Divide both sides by the same negative number and reverse the sign. Out of which steps 2,3,4 and 5 are the most important steps.

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The area of the kite is 40 square meters, calculated by using the area of a kite formula.

To calculate the area of a kite, you need to know the lengths of both the diagonals. Once you have those values, you can use the following formula to find the area:

Area = (d1 x d2) / 2

where d1 and d2 are the lengths of the diagonals.

Here is an example of how to use this formula:

Let's say you have a kite with diagonals of 8 meters and 10 meters. To find the area, you would use the formula:

Area = (8 x 10) / 2

Area = 40 square meters

So the area of the kite is 40 square meters.

There are also many online calculators available that can help you find the area of a kite if you enter the values of the diagonals.

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Answer:yea its 3

Step-by-step explanation:

20 shares purchased at $30, means that the initial inversion is 20 times 30 = $600

they are sold for $710, so the difference is 710 - 600 = 110

the commision is 6, so the final gain is 110 -6 =104

profit divided by the inversion:

104/600 = 0.1733

the answer is 17.33 %

Answer:

x-3+2x+3+2x = 5x

x+8+4x-3x-4 = 2x+4

4x+x-11-5X+25+4x = 4x+14

3x+5-2x-5x+9+8x = 4x+14

5+9x-7-4X-3x+6 = 2x+4

6x-9-5x+4-x+5x+5 = 5x

Step-by-step explanation:

Simplified by adding like terms

The 49th term of the given arithmetic sequence with the first term of 3550 and the common difference of -17 is equal to 2734.

Given the first term, a1 = 3550

The common difference, d = -17

The formula to find the nth term of an arithmetic sequence is given by,

an = a1 + (n - 1)d

Where, n - the required nth term

an - nth term of the sequence

a1 - first term of the sequence

d - common difference of the sequence

To find the nth term of the sequence that is equal to 2734, we have to plug in the given values in the above formula as follows;

2734 = 3550 + (n - 1) (-17)

2734 - 3550 = -17(n - 1)

-816 = -17(n - 1)

⇒ -816 / (-17) = n - 1

⇒ 48 = n - 1

⇒ n = 49

Therefore, the 49th term of the arithmetic sequence is equal to 2734.

The 49th term is 2734.

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Answer:

Area of the composite figure = 42 in²

Step-by-step explanation:

Composite area of the given figure = Area of the rectangle + Area of the right triangle

Area of the rectangle = Length × Width

                                    = 6 × 5

                                    = 30 in²

Area of the right triangle = \(\frac{1}{2}(\text{Base})(\text{Height})\)

                                         = \(\frac{1}{2}(4)(6)\)

                                         = 12 in²

Area of the composite figure = 30 + 12

                                                  = 42 in²

Answer: A

Step-by-step explanation:

In the diagram, we see that we have two pairs of congruent angles, so it is going to be either ASA or AAS congruence.

To determine if it is ASA or AAS congruence, we can use the fact that for ASA, the side is included between the congruent angles, whereas in AAS, the side isn't.

Since the congruent side is included between the two angles, there is ASA congruence.

Answer:

3 is first

4 is second

1 is third

2 is fourth

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

it helps keep the insulation in so their feet get cold

Answer:

ALTERNATE EXTERIOR ANGLES

Step-by-step explanation:

If the two angles that lie on two different lines cut by a transversal and are placed on the opposite sides of the transversal are equal, it means they are ALTERNATE EXTERIOR ANGLES. Then, j is parallel to k.

The required, expression -7 + 24i with the form a + bi, we can see that the value of b is 24.

To find the value of b in the expression (3 + 4i)^2, we can simply expand the expression and identify the coefficient of the imaginary part.

(3 + 4i)² = (3 + 4i)(3 + 4i)

Using the FOIL method, we can multiply the terms:

= 3 * 3 + 3 * 4i + 4i * 3 + 4i * 4i

= 9 + 12i + 12i + 16i²

Since i² is defined as -1, we can substitute it:

= 9 + 12i + 12i - 16

= -7 + 24i

Comparing the expression -7 + 24i with the form a + bi, we can see that the value of b is 24.

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Complete question:

(3+4i)²

if the expression above is written in the form a+ bi, where a and b are real numbers, what is the value of b?

Answer:

2.5002 × 10^3 i think, dont quote me on that

Step-by-step explanation:

Recall that the opposite of 2 is

Therefore, the opposite of the opposite of 2 is

Now, recall that a horizontal number line is of the form:

Therefore, 2 is to the right of zero.

Answer:

On a horizontal number line, the opposite of the opposite of 2 is to the right of zero and is written as 2.

the probability that the computer contains a virus but not a worm is 0.10.

To find the probability that a computer contains a virus but not a worm, we can use the formula:

P(V and not W) = P(V) - P(V and W)

Given that P(V) = 0.13, P(W) = 0.04, and P(V∪W) = 0.14, we need to find P(V and W).

Using the formula for the probability of the union of two events:

P(V∪W) = P(V) + P(W) - P(V and W)

We can rearrange the formula to find P(V and W):

P(V and W) = P(V) + P(W) - P(V∪W)

Substituting the given values:

P(V and W) = 0.13 + 0.04 - 0.14

P(V and W) = 0.03

Now, we can calculate P(V and not W):

P(V and not W) = P(V) - P(V and W)

P(V and not W) = 0.13 - 0.03

P(V and not W) = 0.10

Therefore, the probability that the computer contains a virus but not a worm is 0.10.

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The decomposed relations are R2 (ABCEI), R3 (CDI), and R4 (CD).

a. To calculate the candidate key for the relation R1, we will calculate the closure of all the attributes using the functional dependencies given in F1. We can start by calculating the closure of attribute A, which is A+ = A, C, and D.

However, A does not form a candidate key since it does not contain all the attributes of R1. We can move on to calculating the closure of attribute AB.

A+ = AB, C, D, and I.

Since A and B together can generate all attributes of R1, AB is a candidate key. We can verify this by checking if the closure of AB+ generates all attributes of R1, and indeed it does.

Similarly, we can calculate the closure of attributes CD, EC, and EI to see if they can form candidate keys.

CD+ = C, D, and I, EC+ = A, B, C, and E, and EI+ = C and D. Therefore, the candidate keys for R1 are AB, CD, EC, and EI.

b. Attribute closure for (ACD) and (BCI):

ACD+ = A, C, D, IBCI+ = B, C, D, E, I

c. To find the minimal cover (Fc) of the relation R1, we can start by eliminating the redundant functional dependencies in F1 using the following steps:

Eliminate redundant dependencies: We can eliminate the dependency CD → I since it is covered by the dependency C → DI

Obtain only irreducible dependencies: We can simplify the dependency EC → AB to E → AB since C can be eliminated since it is a non-prime attribute.

Remove extraneous attributes: We can remove the attribute C from A → C since A is a superkey for R1. Therefore, the minimal cover (Fc) of the relation R1 is:

A → CC → DDI → CE → ABE → C

d. To decompose the relation R1 into BCNF form, we can use the following steps:

Identify dependencies violating BCNF:

The dependencies AB → C and EC → AB are violating BCNF since the determinants are not superkeys for R1.

Decompose the relation: We can create two new relations R2 and R3 as follows:

R2 (ABCEI) with dependencies AB → C and E → ABR3 (CDI) with dependencies C → DI and CD → I

Both R2 and R3 are in BCNF since all the determinants are superkeys for the respective relations.

However, they are not a lossless join decomposition since there is no common attribute between R2 and R3.

Therefore, we need to add a new relation R4 (CD) with the primary key CD, which has a foreign key in R3.

This ensures that the join of R2, R3, and R4 is lossless. Therefore, the decomposed relations are R2 (ABCEI), R3 (CDI), and R4 (CD).

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The domain that best describes the function f(x)= (x > 0, x € R) (x < 0, x = R) (x=0, x= R) U (XER) is xER.

A domain is the set of all possible values that an independent variable can take. When discussing the domain of a function, we must first consider the set of all values that the input variable can assume. In interval notation, the domain of a function f(x) is written as [a, b], where a and b are the endpoints of the interval. Along these lines, let us look at the given function,

f(x)= (x > 0, x € R) (x < 0, x = R) (x=0, x= R) U (XER)

For any real number x, the function is defined as follows: if x is greater than zero, f(x) equals R; if x is less than zero, f(x) equals R; if x is zero, f(x) equals R. It's important to remember that R represents the set of all real numbers, which includes both negative and positive numbers.

Therefore, the domain of the function f(x) is all real numbers. Domain of f(x) is xER.The range that best describes the function is y>0, y € R, meaning that the function f(x) has only positive values. Therefore, the range of f(x) is greater than zero and belongs to the set of all real numbers. Domain of f(x) is all real numbers, represented as xER. The range of f(x) is greater than zero and belongs to the set of all real numbers, represented as y>0, y € R.

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The probability that the average amount of paid time lost during a three-month period for the 100 blue-collar workers will exceed 1.5 days is null or 0.

We need to use the central limit theorem and assume that the distribution of the average amount of paid time lost during a three-month period for the 100 blue-collar workers is approximately normal with a mean of 1.8 days and a standard error of 0.2 days.

To find the probability that the average amount of paid time lost during a three-month period for the 100 blue-collar workers will exceed 1.5 days, we need to find the corresponding z-score and look up the probability in a standard normal distribution table or use a calculator.

The z-score can be calculated using the z score formula,

Putting the values in the calculator given in the problem, we get:

z = (1.5 - 1.8) / (0.2 / √(100)) = -7.5

Looking up the probability corresponding to a z-score of -7.5 in a standard normal distribution table or using a calculator, we get a probability of approximately 0.

Therefore, the probability that the average amount of paid time lost during a three-month period for the 100 blue-collar workers will exceed 1.5 days is approximately 0.

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Answer:

\(a_{n}\) = 3n + 32

Step-by-step explanation:

There is a common difference d between consecutive terms, that is

d = 38 - 35 = 41 - 38 = 3

This indicates the sequence is arithmetic with n th term ( explicit formula )

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 35 and d = 3 , then

\(a_{n}\) = 35 + 3(n - 1) = 35 + 3n - 3 = 3n + 32

The slope of the line above include the following: 1/5.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the formula for the slope of a line, we have the following;

Slope (m) = (3 - 0)/(7 + 8)

Slope (m) = (3)/(15)

Slope (m) = 1/5.

Based on the graph, the slope is the change in y-axis with respect to the x-axis and it is equal to 1/5.

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Answer:

Step-by-step explanation:

Use Pythagorean to find the missing side x of the triangle.

It is a hypotenuse with other sides 18 in and half of 15 in:

The perimeter is:

The average yearly salaries for women with each level of education are as follows: associate's degree: $33,000, bachelor's degree: $47,000, and master's degree: $59,000.

In this problem, we are given information about the average yearly salaries of women with three different levels of education: associate's degree, bachelor's degree, and master's degree. We are asked to find the average yearly salary for each level of education.

Let A represent the average yearly salary of a woman with an associate's degree, B for a bachelor's degree, and M for a master's degree.

From the problem, we have the following relationships:

1. B = A + $14,000
2. M = A + $26,000
3. A + B + M = $139,000

Now, we can substitute the relationships (1) and (2) into equation (3):

A + (A + $14,000) + (A + $26,000) = $139,000

Combine the terms:

3A + $40,000 = $139,000

Subtract $40,000 from both sides:

3A = $99,000

Now, divide by 3:

A = $33,000

Using the relationships from the problem, we can now find the salaries for the other two levels of education:

B = A + $14,000 = $33,000 + $14,000 = $47,000
M = A + $26,000 = $33,000 + $26,000 = $59,000

So, the average yearly salaries for women with each level of education are as follows: associate's degree: $33,000, bachelor's degree: $47,000, and master's degree: $59,000.

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Before and After pictures of a 50 kg arc would look something like this: Before picture (50 kg arc is at rest) and After picture (50 kg arc is moving) - the picture has been attached below:

To define the symbols relevant to the problem: - Arc - it's an object that rotates around a fixed point or axis. - \(m\) - mass - \(r\) - radius - \(v\) - velocity - \(\theta\) - angular displacement, and - \(I\) - moment of inertia

To include the knowns and unknowns in your diagrams:- Knowns: Mass of the arc = 50 kg- Unknowns: velocity of the arc after it has movedThus, in this case, the unknown is the velocity of the arc after it has moved, which can be solved by using the formula \(v=\sqrt{2*g*h}\), where \(g\) is the acceleration due to gravity and \(h\) is the height from which the arc has been dropped.

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Answer:

Step-by-step explanation:

Use the equation x = -b/2a => x = -12/6 = -2.

Answer:

3/8

Step-by-step explanation:

Let us represent the total fabric as an integer = 1

Ellen divides a piece of fabric into 8 equal sections by drawing chalk lines.

= 1/8, hence each section = 1/8

Then she cuts off 5 of the sections to make into placemats.

This is written as: 5 sections × 1/8 = 5/8

The fraction of the fabric that is left is calculated as:

1 - 5/8

Lowest Common Denominator = 8

Hence: 8 - 5/8 = 3/8

The fraction of the fabric that is left is 3/8