What two theorems are being used ?

The sin ratio will be helpful in finding the missing side length and the missing side length is 29.50 units.

The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.

We have a right-angle triangle in the figure in which:

Length of the hypotenuse = x unit

Length of the side opposite to the angle = 12

And the angle is given between sides adjacent to the angle to the hypotenuse = 24°

We know the:

\(\rm sin\theta = \frac{Side \ opposite \ to \ the \ angle}{hypotenuse }\)

\(\rm sin24 = \frac{12}{x}\)

\(\rm x = \frac{12}{sin24}\)

x = 29.50 units

Thus, the sin ratio will be helpful in finding the missing side length and the missing side length is 29.50 units.

Know more about trigonometry here:

brainly.com/question/26719838

A quadratic equation that is given in the form:

can be solved using the quadratic formula:

Answer:22.5

Step-by-step explanation:think of 500.000 as an 500 then multiply 0.045 so I got 22.5

Answer:

22.5

Step-by-step explanation:

 500.000

x 0.045

22.5

You just have to use long multiplication

The correct option is A, equilibrium price increases from $6 to $8.

In economics, equilibrium is a state in which the supply and demand for a product or service are balanced, resulting in a stable price. This can occur in a free market, where the price of a good or service is determined by the interaction of buyers and sellers.

Overall, equilibrium is a fundamental concept in many different fields, representing a state of balance or stability in a system or situation.

If the demand schedule changes from D2 to D1, then the demand curve shifts to the left. As a result, the new equilibrium point will be where the new demand curve (D1) intersects with the supply curve (S1).

From the table, we can see that the new equilibrium point is at a price of $8 and a quantity of 15. Therefore, the equilibrium price increases from $6 to $8, but the equilibrium quantity decreases from 15 to 13.

So the correct answer is: equilibrium price increases from $6 to $8.

To know more about equilibrium price visit:

https://brainly.com/question/28527601

#SPJ1

Answer:

2 1/4kms = how many meters?

Step-by-step explanation:

You're welcome.

Answer:

M = 2250

Step-by-step explanation:

First of all solve the mixed number which is 9/4 and as a decimal it is 2.25

Now as the meters it is....

2250!!!!

Hope this helps, have a great day!!!!!!

(Multiply 2.25 times 1000 and that gives you 2250)

Answer:

P(p∩Q) = 0.

Step-by-step explanation:

Given the Addition Rule:

P(p∪Q) = P(p) + P(Q) - P(p∩Q)

P(p or Q) = P(p) + P(Q) - P(p and Q)

Events p and Q are disjoint (or mutually exclusive) if they cannot occur at the same time. (That is, disjoint events do not overlap.)

Hence, whenever p and Q are disjoint, P(p and Q) becomes zero in the formal addition rule, so for disjoint events p and Q we have:

P(p or Q) = P(p) + P(Q).

Therefore, the cardinal number of P(p∩Q) = 0.

Answer:

___________________________________________________________

By finding the product of a point's x coordinate times the next point's y coordinate, then subtracting the y coordinate of the first point times the x coordinate of the second coordinate and dividing by two, you will find the area of the polygon.

___________________________________________________________

Answer:

1. y = 3x - 2

2. \(y = \frac{1}{2} \)

3. \(y = \frac{3}{2} x + 4\)

4. y = -3x + 5

5. y = x - 6

▪Happy To Help <3

Our assumption that two consecutive elements of the Fibonacci sequence can be divisible by 13 is false, and the proposition is proved.

We begin with the fact that the Fibonacci sequence is an increasing sequence; that is, each element is greater than the one before it.

The sequence is defined as follows:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, 1346269, 2178309, 3524578, 5702887, 9227465, 14930352, 24157817, 39088169, 63245986, 102334155, 165580141, 267914296, 433494437, 701408733, 1134903170, 1836311903, and so on.

Now, let us prove the proposition by contradiction. Assume that there are two consecutive elements of the Fibonacci sequence that are divisible by 13. Then there must be some integer n such that:

F(n) = 13m, andF(n + 1) = 13p,

where m and p are integers.

Since the Fibonacci sequence is defined recursively by F(n) = F(n-1) + F(n-2), we can obtain an expression for F(n-2) in terms of F(n) and F(n-1):

F(n-2) = F(n) - F(n-1)Since F(n) and F(n-1) are both divisible by 13, their difference must also be divisible by 13.

Therefore, F(n-2) is divisible by 13 as well. However, this contradicts the well-ordering principle, which states that every non-empty set of positive integers has a least element.

Since the Fibonacci sequence is an increasing sequence, there must be some least element k such that F(k) is divisible by 13 but F(k-1) is not. But this means that F(k-2) cannot be divisible by 13, which contradicts our assumption that both F(n) and F(n-1) are divisible by 13.

for such more question on Fibonacci sequence

https://brainly.com/question/29764204

#SPJ11

If we let Z = 3 - X, then Z is another exponential random variable with mean 1 that is negatively correlated with X.

Let Y = 2 - X, where X is an exponential random variable with mean 1.

To show that Y is negatively correlated with X, we need to show that Cov(X,Y) < 0.

Cov(X,Y) = E[XY] - E[X]E[Y]

Since X and Y are both exponentially distributed with mean 1, we have:

E[X] = 1, E[Y] = 2 - E[X] = 1

E[XY] = E[X(2-X)] = 2E[X] - E[X^2] = 2 - Var(X)

Var(X) = E[X^2] - (E[X])^2 = 1 - 1^2 = 0

Therefore, Var(X) = 0, which means that E[XY] = 2, and Cov(X,Y) = E[XY] - E[X]E[Y] = 2 - 1*1 = 1 > 0.

Since Cov(X,Y) > 0, we know that Y is positively correlated with X. To find a random variable that is negatively correlated with X, we can use Y = 3 - X instead.

Therefore, if we let Z = 3 - X, then Z is another exponential random variable with mean 1 that is negatively correlated with X.

Learn more about variable here:

https://brainly.com/question/29696241

#SPJ11

The value of the missing length LN of the similar triangles is; LN = 18

Similar triangles are defined as triangles that have the same shape, but their sizes may vary. This means therefore that, if two triangles are similar, then we can say that their corresponding angles are congruent and also their corresponding sides are in equal proportion.

In the given triangle attached, we can say that if we apply the concept of similar triangles, we will get;

LN/LK = MN/JK

We are told that;

MN is 12 more than LN. Thus; MN = 12 + LN

LK = 33

JK = 55

Thus;

LN/33 = (12 + LN)/55

55LN = 33(12 + LN)

55LN = 396 + 33LN

22LN = 396

LN = 396/22

LN = 18

Read more about Similar Triangles at; https://brainly.com/question/14285697

#SPJ1

Based on the recorded results, purple appeared 12 times out of a total of 55 spins. If the spinner is spun 1000 more times, we can estimate that purple would appear approximately 218 times.

In the recorded results, the spinner was spun a total of 55 times, with purple appearing 12 times. To estimate the expected frequency of purple in 1000 additional spins, we can calculate the probability of landing on purple based on the recorded frequencies. The probability of landing on purple can be calculated by dividing the frequency of purple (12) by the total number of spins (55):

Probability of landing on purple = Frequency of purple / Total number of spins = 12 / 55

We can use this probability to estimate the expected frequency of purple in the additional 1000 spins:

Expected frequency of purple = Probability of landing on purple * Total number of additional spins

≈ (12 / 55) * 1000

≈ 218

Therefore, based on this estimation, we would expect purple to appear approximately 218 times if the spinner is spun 1000 more times.

Learn more about Probability here:

https://brainly.com/question/32560116

#SPJ11

Answer:

Answer:

a. 9

b. The slope represents the cost for every new DVD

c. 6

d. The song represents the base price, or the price that it would cost for 0 DVDs

e. y = 9x + 6

Explanation:

I made a graph on a piece of graph paper and these were the answer I got.

Applying notable products, the expanded expressions are given by:

a) (x + 1)² = x² + 2x + 1.

b) (x - 2)² = x² - 4x + 4.

c) (x + 3)² = x² + 6x + 9.

The notable product for the square of the sum is given by:

(a + b)² = a² + 2ab + b².

Hence:

a) (x + 1)² = x² + 2x + 1.

c) (x + 3)² = x² + 6x + 9.

The notable product for the square of the subtraction is given by:

(a - b)² = a² - 2ab + b².

That is, just the middle term changes compared to the square of the sum.

Hence:

b) (x - 2)² = x² - 4x + 4.

More can be learned about notable products at https://brainly.com/question/14577819

#SPJ1

The convergence set of the power series ∑n=1∞ \((x-2)^n/n^2\) is [1, 3). The series converges for x values in the interval [1, 3), and diverges for x values outside of this interval.

At the endpoints x = 1 and x = 3, the series converges for x = 1 and diverges for x = 3.

To find the convergence set of a power series, we can use the ratio test:

lim[n→∞] |\((x - 2)(n+1)^2 / n^2\)| = lim[n→∞] |\((x - 2)(1 + 2/n)^2\)| = |x - 2| lim[n→∞] \((1 + 2/n)^2\)

Since lim[n→∞] \((1 + 2/n)^2 = 1\), the series converges if |x - 2| < 1, and diverges if |x - 2| > 1.

If |x - 2| = 1, then the ratio test is inconclusive, so we need to check the endpoints x = 1 and x = 3 separately.

For x = 1, the series becomes:

∑n=1infinitynn2 = ∑n=1infinitynn2

which is the alternating harmonic series, which converges by the alternating series test.

For x = 3, the series becomes:

∑n=1infinitynn2 = ∑n=1[infinity]nn2

which diverges by the p-series test with p = 2.

Therefore, the convergence set of the series is:

1 ≤ x < 3

In interval notation, this can be written as:

[1, 3)

Learn more about convergence set of a power series

brainly.com/question/31440916

#SPJ11

Answer:

y-1=2/3(x+4)

Step-by-step explanation:

YOUR WELCOME SJJDJDJ

The statement illustrates the transitive property of congruence, which is a fundamental concept in geometry.

This property states that if two geometric figures are congruent to a third figure, then they are congruent to each other.

In the given statement, ΔABC is congruent to ΔDEF, and ΔDEF is congruent to ΔXYZ. By the transitive property, we can conclude that ΔABC is also congruent to ΔXYZ.

This property is important because it allows us to establish relationships between geometric figures based on their congruence. It is used in many geometric proofs and applications, such as proving theorems, solving problems involving similar triangles, and determining the congruence of geometric shapes.

To know more about geometric figures visit:

https://brainly.com/question/5026441

#SPJ1

Answer:

3

Step-by-step explanation:

11g - 9k + 3

Let g = 9 and k =11

11 * 9 - 9*11 +3

Multiply

99 - 99 +3

Add

3

Answer:

3

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

Identify

11g - 9k + 3

g = 9

k = 11

Step 2: Evaluate

(A - B) u (A n B) = A is proved using several properties from Theorem 6.2.2. of Set Identities.

To prove (A - B) u (A n B) = A algebraically, we can use the following steps:

(A - B) u (A n B) // Given

[(A n B) U (A - B)] // Definition of union

[(B n A) U (A - B)] // Commutative law of intersection

[(B U (A - B)) n (A U (A n B))] // Distributive law of union over intersection

[(B U (A n B)') n (A U B)] // Complement law of intersection and De Morgan's law

[(B U (A - B)) n (A U B)] // Complement law of A n B

[(B U (A n B)') n (A U B)] // Definition of A - B

[(B U (A n B)') n (B U A')] // De Morgan's law

[(B n (B U A')) U ((A n B)'' n (B U A'))] // Distributive law of intersection over union

[(B n U) U (Ø n (B U A'))] // Complement law of B U A' and B n (B U A')

B U Ø // Identity law of intersection and complement law of B U A'

B // Identity law of union

Therefore, (A - B) u (A n B) = A is proved. We used several properties from Theorem 6.2.2, including the commutative law of intersection, distributive law of union over intersection, complement law of intersection, De Morgan's law, complement law of A n B, definition of A - B, distributive law of intersection over union, complement law of B U A', and identity law of intersection and union.

Learn more about set identities

brainly.com/question/14974663

#SPJ11

Answer:

16,500

Step-by-step explanation:

thats it

Answer:

e) none of these​

Explanation:

Answer:

e) None of these.

Step-by-step explanation:

Let the unknown number be x, then:

0.65*320 + x = 686

208 + x = 686

x = 686 - 208

= 478

Answer:

I got −7.53112887414 and 0.531128874149

Step-by-step explanation:

plugged in

Answer:

whats the question..........

Step-by-step explanation:

The equation 2x+1=2(x+1) can be simplified to 2x+1=2x+2 since the right-hand side of the equation can be expanded to 2x+2. By subtracting 2x from both sides of the equation, we get 1=2, which is not true for any value of x. Therefore, the equation 2x+1=2(x+1) has no solution.

On the other hand, the equation 2x+2=2(x+1) can be simplified to 2x+2=2x+2 by expanding the right-hand side of the equation to 2x+2. We can see that both sides of the equation are equal, so the equation is true for any value of x. Therefore, the equation 2x+2=2(x+1) has infinitely many solutions, meaning that any value of x will satisfy the equation.

In summary, the equation 2x+1=2(x+1) has no solution, while the equation 2x+2=2(x+1) has infinitely many solutions. The term "solution" refers to the value of x that makes the equation true, while "infinitely many solutions" means that there are an infinite number of values of x that satisfy the equation.

Answer:

x = 135°

Step-by-step explanation:

x and y are supplementary angles, that is they sum to 180° , then

x + y = 180 ← substitute x = 3y into the equation

3y + y = 180

4y = 180 ( divide both sides by 4 )

y = 45

then

x = 3y = 3 × 45° = 135°

The required measure of the angle ∠spq of a rhombus is 110°.

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

Here,
For rhombus,
m∠spr=(2x + 15)°
m∠qpr=(3x−5)°

And,
m∠spr = m∠qpr
2x + 15 = 3x - 5
x = 20

Now,
∠spq = m∠spr + m∠qpr
        = 2x + 15 + 3x - 5

        = 5x + 10
        = 5(20) + 10
        = 110°

Thus, the required measure of the angle ∠spq of a rhombus is 110°.

Learn more about Angles here:

https://brainly.com/question/13954458

#SPJ1

Answer:

j=|x|

Step-by-step explanation:

Answer:

The sum of the squares of the two sides equals the square of the hypotenuse (a² + b² = c²).

Let's say you have a triangle with a 90º angle (also known as a right angle). The two equal legs are a and b while the hypotenuse is the longer side. Hypotenuse is and always will be c.

Here's a problem:

c ⊿ a (12)

  b (6)

C is missing, we have to find C, so here's what we do:

Step 1: You square all the numbers in the equation

12² + 6² = c²

↓

144 + 36 = c

Step 2: You add 144 + 36 and you get 180

Step 3: Then you find the square root >>  \(\sqrt{180\\\) and you get ≈13.4

Now sometimes, the a or b would be missing, for example:

c (13)⊿ a

     b (5)

A is missing (when a or b is missing, use the following formula, do not use the same formula when c is missing)

Step 1: You square all the numbers in the equation

a² + 5² = 13²

a + 25 = 169

For this next part, you must subtract a or b (in this case, b) on both sides, for example:

25 – 25 = 169 - 25

25 – 25 cancels itself out so now we subtract 169 by 25 and we get 144.

Then we find the square root of 144 and we get 12

I hope this helps :)