the hypotenuse of a right triangle has a length of 14 units and side that is 9 units long. which equation can be used to find the length of the reaming side?

Answer:

907

Step-by-step explanation:

Circumference = 34pi

radius, r = 34pi/2pi = 17

Area, A = pi r^2 = pi (17^2) = 289pi=907 approximately

Step-by-step explanation:

you can just put in some values to check.

I actually used p =2 and q=3

the It will be

2^3-1 + 3^2-1 = 1 (mod 2×3)

2^2 +3^1 = 1 (mod 6)

4+3= 1 (mod6)

7= 1 (mod6)

which is true.

therefore p^(q-1) + q^( p-1) = 1 ( mod pq) is true

To show that p^(q-1) + q^(p-1) = 1 (mod pq), we can use Fermat's Little Theorem, which states that if p is a prime number and a is an integer not divisible by p, then a^(p-1) = 1 (mod p). Using this theorem, we can first show that p^(q-1) = 1 (mod q), since q is a prime number and p is not divisible by q. Similarly, we can show that q^(p-1) = 1 (mod p), since p is a prime number and q is not divisible by p.

Therefore, we can write:

p^(q-1) + q^(p-1) = 1 (mod q)
p^(q-1) + q^(p-1) = 1 (mod p)

By the Chinese Remainder Theorem, we can combine these two equations to obtain:

p^(q-1) + q^(p-1) = 1 (mod pq)

Thus, we have shown that p^(q-1) + q^(p-1) = 1 (mod pq).
We'll use Fermat's Little Theorem to show that p^(q-1) + q^(p-1) = 1 (mod pq).

Fermat's Little Theorem states that if p is a prime number and a is an integer not divisible by p, then:
a^(p-1) ≡ 1 (mod p)

Step 1: Apply Fermat's Little Theorem for p and q:
Since p and q are prime numbers, we have:
p^(q-1) ≡ 1 (mod q) and q^(p-1) ≡ 1 (mod p)

Step 2: Add the two congruences:
p^(q-1) + q^(p-1) ≡ 1 + 1 (mod lcm(p, q))

Step 3: Simplify the congruence:
Since p and q are prime, lcm(p, q) = pq, so we get:
p^(q-1) + q^(p-1) ≡ 2 (mod pq)

In your question, you've mentioned that the result should be 1 (mod pq), but based on Fermat's Little Theorem, the correct result is actually:
p^(q-1) + q^(p-1) ≡ 2 (mod pq)

To learn more about integer : brainly.com/question/15276410

#SPJ11

Jimmy ate 8 , 16 , 24 sandwiches in 1 , 2 and 3 hours respectively .

To find : the no . of sandwiches Jimmy eat in 1 hour , 2 hour and 3 hours .

Given : y = the no . of sandwiches Jimmy can eat

      x = no . of hours he take in eating

Relation : y = 8 x

( i ) No . of sandwiches eaten  by Jimmy in 1 hour

x = 1

y = ( 8 * 1 )

y = 8

( ii )   No . of sandwiches eaten  by Jimmy in 2 hours

x = 2

y = ( 8 * 2 )

y = 16

( iii ) No . of sandwiches eaten  by Jimmy in 3 hours

x = 3

y = ( 8 * 3 )

y = 24

Hence , Jimmy ate 8 , 16 , 24 sandwiches in 1 , 2 and 3 hours respectively .

To learn more on functions follow link :

https://brainly.com/question/21145944?referrer=searchResults

#SPJ4

Answer:

35 degrees

Step-by-step explanation:

for all positive angles less than 360°, if csc (2x+30°)= cos (3y-15°), the sum of x and y is?​

Let the given expression be equal to 1, hence;

csc (2x+30°)= cos (3y-15°) = 1

csc (2x+30°) = 1

1/sin(2x+30) = 1

1 = sin(2x+30)

sin(2x+30) = 1

2x+30 = arcsin(1)

2x+30 = 90

2x = 90-30

2x = 60

x = 60/2

x = 30 degrees

Get the value of y;

cos (3y-15°) = 1

3y - 15 = arccos (1)

3y - 15= 0

3y = 0+15

3y = 15

y = 15/3

y = 5

Sum of x and y;

x+y = 30 + 5

x+y = 35degrees

Hence the sum of x and y is 35 degrees

Answer:

Plan B

Step-by-step explanation:

Answer:

add all the sides up

Step-by-step explanation:

yw

The value of m and n from the obtained probability is equal to 3 and 14 respectively.

As given in the question,

Nine tiles numbered 1, 2, .....9

Number of odd numbered tiles are 1,3,5,7,9 = 5

Number of even numbered tiles are 2,4,6,8 = 4

Number of players =3

Possibility to choose 3 tiles by first player out of 9 tiles = ⁹C₃

                                                                                            = 84 ways

Possibility to choose 3 tiles by second player out of 6 tiles = ⁶C₃

                                                                                                 =20 ways

Possibility to choose 3 tiles by third player out of 3 tiles = ³C₃

                                                                                             = 1 way

Total number of ways = 84× 20 ×1

                                     = 1680

To have a sum of 3 tiles is odd number at least one tile should be odd.

Chances of first player all the 3 tiles are 0dd out of 5 = ⁵C₃

Next two players must 2 even tiles and 1 odd tile.= ²C₁

One player can be selected in ³C₁ way

Remaining 4 even tiles distributed equally = (4!)(2!)/ (2!)² ( 2!)

Number of favourable outcomes =  ⁵C₃ × ²C₁ ׳C₁  × (4!)(2!)/ (2!)² ( 2!)

                                                       = 10 × 2 × 3 × 6

                                                       = 360

Probability (m/n) =  360 /1680

                            = 3/14

m = 3 and n = 14.

Therefore, from the probability that all three players obtain an odd sum is m/n , the value m = 3 and n = 14.

Learn more about probability here

brainly.com/question/11234923

#SPJ4

Based on the formula of the quadratic function y=-x^2+6x-5, we know that its graph is a downward-facing parabola that opens wide, with a vertex at (3,-14), and an axis of symmetry at x=3.

Based on the formula of the quadratic function y=-x^2+6x-5, we can determine several properties of its graph, including its shape, vertex, and axis of symmetry.

First, the negative coefficient of the x-squared term (-1) tells us that the graph will be a downward-facing parabola. The leading coefficient also tells us whether the parabola is narrow or wide. Since the coefficient is -1, the parabola will be wide.

Next, we can find the vertex using the formula:

Vertex = (-b/2a, f(-b/2a))

where a is the coefficient of the x-squared term, b is the coefficient of the x term, and f(x) is the quadratic function. Plugging in the values for our function, we get:

Vertex = (-b/2a, f(-b/2a))

= (-6/(2*-1), f(6/(2*-1)))

= (3, -14)

So the vertex of the parabola is at the point (3,-14).

Finally, we know that the axis of symmetry is a vertical line passing through the vertex. In this case, it is the line x=3.

Know more about quadratic function here;

https://brainly.com/question/18958913

#SPJ11

The total of the areas under the standard normal curve to the left of z₁=−2.575 and to the right of z₂=2.575 is 0.0100 square units.

What is standard normal curve?

The horizontal axis is approached but never touched by the typical normal curve as it stretches infinitely in both directions. The centre of the bell-shaped standard normal curve, which has z=0 as its centre, is. Between z=3 and z=3, almost all of the area under the standard normal curve is located.

As given,

z₁=−2.575 and z₂=2.575

Then, required area,

= P (Z < -2.575) + P (Z > 2.575)

= P (Z < -2.575) + {1 - P (Z < 2.575)}

Using z table substituting values,

= 0.0050 + {1 - 0.9950}

= 0.0050 + 0.0050

= 0.0100

Hence, the total of the areas under the standard normal curve to the left of z₁=−2.575 and to the right of z₂=2.575 is 0.0100 square units.

To learn more about standard normal curves from the given link.

https://brainly.com/question/13781953

#SPJ4

This pyramid has the same base as the prism and its height is three times the height of the prism. What is the ratio of the volume of the

pyramid to the volume of the prism?

1

A} volume of Pyramid

volume of priam

B} volume of pyramid

volume of priuam

C} volume of pyramid

volume of priim

D} Volume of pyramid

volume of

prime

____________________________________________

volume of the prism

If n is a positive integer, then the expression is equivalent to option A) \(\sqrt[3]{n^2}\).

Rational exponents are numbers which are written in the form of \(x^\frac{p}{q}\), where x is the base with positive integer and p/q is the rational exponent and q ≠ 0.

The given expression is (\(\frac{1}{n}\))^\(^\frac{-2}{3}\).

A number in the form, 1/a can be written as a⁻¹.

So 1/n can be written as n⁻¹.

So,

(\(\frac{1}{n}\))^\(^\frac{-2}{3}\) = (n⁻¹)^\(^\frac{-2}{3}\)

We have a rule for exponent that (xᵃ)ᵇ = xᵃᵇ

Using the rule,

(\(\frac{1}{n}\))^\(^\frac{-2}{3}\) = (n⁻¹)^\(^\frac{-2}{3}\)

         = \(n^{-1*\frac{-2}{3}\)

         = \(n^\frac{2}{3}\)

         = \(n^{2*\frac{1}{3}\)

         = \((n^{2})^\frac{1}{3}\)

By the definition of radicals, \(\sqrt[n]{x}\) = \((x)^\frac{1}{n}\), where x is positive integer.

So, \((n^{2})^\frac{1}{3}\) = \(\sqrt[3]{n^2}\)

Hence the equivalent expression is \(\sqrt[3]{n^2}\).

Learn more about Rational Exponents here :

https://brainly.com/question/29128230

#SPJ1

Answer:

Step-by-step explanation:

8 faces and 12 vertices means hexagon as its base

That means 6+6 edges of its bases and 6 side edges.

6+6+6=18  

Given:

Christms bonus = 7800

total earn in year =89100

So only salary is:

In a year ( 12 months) salary is 81300 so per month salary is:

So monthly salary is 6775.

Answer:

- 2, 7 , - 8

Step-by-step explanation:

substitute the given values of x into the expression

(a)

x = 0 : 3(0) - 2 = 0 - 2 = - 2

(b)

x = 3 : 3(3) - 2 = 9 - 2 = 7

(c)

x = - 2 : 3(- 2) - 2 = - 6 - 2 = - 8

To find out how much each ticket costs, we can use this equation:

Total cost ÷ Number of tickets = Price of each ticket

Inserting the numbers into the equation would look like this:

To check our work, we can multiply the number of tickets by the price of each ticket to see if it matches up to the correct total price.

Therefore, each ticket costs $8.

Answer:

that is no answer you don't need to type stuff if it is not for work/school

Answer:

14

Step-by-step explanation:

bako has spoken

The crossover point for options A and B is at 0 units sold, where the total costs and revenues for both options are equal to zero.

The crossover point is the point at which two options have equal costs or revenues. In this case, we need to determine the number of units sold for options A and B that result in the same total cost.

Let's denote the number of units sold as 'x'. The cost for option A is given as $10 per unit, so the total cost for option A is 10x. Similarly, the cost for option B is $14 per unit, so the total cost for option B is 14x.

To find the crossover point, we need to set the total costs for both options equal to each other and solve for 'x':

10x = 14x

Now, we can solve this equation:

10x - 14x = 0

-4x = 0

Dividing both sides by -4:

x = 0

The crossover point occurs at 0 units sold. This means that at this point, both options have zero cost. However, since selling zero units does not generate any revenue, we need to consider the revenue generated as well.

The revenue generated by each unit is given as $18. To find the revenue generated by each option, we multiply the number of units sold ('x') by the revenue per unit.

For option A, the revenue generated is 18x. For option B, the revenue generated is also 18x.

Since the crossover point occurs at 0 units sold, both options have zero revenue at this point.

In summary, the crossover point for options A and B is at 0 units sold, where the total costs and revenues for both options are equal to zero.

To know more about the crossover point, refer here:

https://brainly.com/question/32414177#

#SPJ11

If a random sample of 40 UCF students has a mean electricity bill of $110, the 90% confidence interval for the mean electricity bill of all UCF students is $105.34 to $114.66.

To construct a 90% confidence interval for the mean electricity bill of all UCF students, we can use the following formula:

Confidence interval = sample mean ± (z-score)(standard error)

where the z-score for a 90% confidence level is 1.645 and the standard error is the population standard deviation divided by the square root of the sample size, or:

standard error = 17.90 / √40 = 2.83

Substituting the given values, we get:

Confidence interval = 110 ± (1.645)(2.83)

Confidence interval = 110 ± 4.66

Therefore, the 90% confidence interval for the mean electricity bill of all UCF students is $105.34 to $114.66.

More on mean: https://brainly.com/question/16108617

#SPJ11

Statement 1: Some cats like turkey, the form is I, the subject class is Cats, and the predicate class is Turkey, statement 2: There are burglars coming in the window, the form is E, the subject class is Burglars, and the predicate class is Not coming in the window and statement 3: Everyone will be robbed, the form is A, the subject class is Everyone, and the predicate class is Being robbed.

The given categorical propositions and their forms are as follows:

(1) Some cats like turkey - Form: I:

Subject class: Cats,

Predicate class: Turkey

(2) There are burglars coming in the window - Form: E:

Subject class: Burglars,

Predicate class: Not coming in the window

(3) Everyone will be robbed - Form: A:

Subject class: Everyone,

Predicate class: Being robbed

In the first statement:

Some cats like turkey, the form is I, the subject class is Cats, and the predicate class is Turkey.

In the second statement:

There are burglars coming in the window, the form is E, the subject class is Burglars, and the predicate class is Not coming in the window.

In the third statement:

Everyone will be robbed, the form is A, the subject class is Everyone, and the predicate class is Being robbed.

To know more about categorical propositions visit:

https://brainly.com/question/29856832

#SPJ11

Answer:

25.5

Step-by-step explanation:

Using SOH CAH TOA, you can see that x is the hypotenuse, and 24 is adjacent to the angle 20, so you will need to use CAH.

CAH is cos=adjacent/hypotenuse. Substituting our values in means cos(20) will be equal to 24/x. By cross multiplying, you receive cos(20) x =24. To find x, divide 24 by cos(20) to get 25.5 to the nearest tenth.

Answer:

This is true.

Step-by-step explanation:

I hope this helped you! :)

Answer:

Step-by-step explanation:

To make 'x' as the subject isolate 'x'.

To isolate 'x',

Step 1: Multiply the entire equation by q

Step 2: Then Divide by T

\(q*\dfrac{Tx}{q}=q*y\\\\\\Tx=qy\\\\\dfrac{Tx}{T}=\dfrac{qy}{T}\\\\\\x=\dfrac{qy}{T}\)

Answer:

x = qy/T

Step-by-step explanation:

We want to isolate the x term. To do that, first multiply by q to end up with Tx = qy.

Then divide by T to get x = qy/T.

x is by itself, and we have our answer.

The approximate solutions are: x = 1.505 and x = 2.688

The solutions to an equation can be solved by graphing calculators and by solving them explicitly.

The equation is given as:

\(|2x-3|=\log(2x-3)+2\)

Start by splitting the given equation, as follows:

Rewrite the above equations as follows:

Plot the graphs of the above equations (see attachment).

From the graph, the equations intersect at the following points

Hence, the approximate solutions are: x = 1.505 and x = 2.688

Read more about approximate solutions at:

https://brainly.com/question/13729904

Answer: 1/2 it cant be an integer bc the graph is positive it can't be 2 bc 2/1 wouldn't match the line.

The required answer is 1/2

Step-by-step explanation:

Answer:

\(\frac{1}{2}\)

Step-by-step explanation:

\(\frac{rise}{run}\) = slope

Pick point on the line where it crosses the y axis.

Notice it crosses at a corner of a square on the grid.

Find how many squares you must rise, and must run until it crosses another corner of a square on the grid.

You rise up 1 square, and run 2 squares to the right.

Step 1: Multiply a and c

a = 1

c = 20

a * c = 20

Step 2: Find factors of +20 that add up to +9

Factors of 20 = 1, 2, 4, 5, 10, 20

The two factors that add up to 9 are 4 and 5.

Step 3: Factor

(x + 4)(x + 5) = 0

Answer: (x + 4)(x + 5) = 0

Hope this helps!

Answer:

  (x+3)(x+3)(x-4)

Step-by-step explanation:

I find a graphing calculator immensely helpful for factoring problems. Of course the constant in the binomial factor is the opposite of the x-intercept value. The x-intercept at -3 just touches the axis, so has even multiplicity. It will give rise to a repeated factor.

The x-intercepts of -3, -3 and +4 mean the factorization is ...

  f(x) = (x +3)(x +3)(x -4)

Answer: 11 and 9 1/2!

Step-by-step explanation:

Because look at the chart the most are? You guessed it! 11 and 9 1/2 hope it helps!

We can conclude that ΔMSP ≅ ΔRQP under SAS conditions.

So,

Given: MS ≅ RQ, MS || RQ

To Prove: ΔMSP ≅ ΔRQP

ΔMSP ≅ ΔRQP is proved.

Therefore, ΔMSP ≅ ΔRQP under SAS condition.

Know more about the congruency of a triangle here:

brainly.com/question/2938476

#SPJ4

The cost of the shirt, in dollars, after the 30% discount is $17.50.

What is discount?

A discount is a reduction in the price of a product or service that is offered by a seller to a buyer. Discounts can be offered for a variety of reasons, such as to attract customers, increase sales, or clear out inventory. Discounts can be expressed as a percentage or a fixed amount, and they can be applied at the time of purchase or deducted from an invoice or bill. Discounts are often used in sales promotions, marketing campaigns, and loyalty programs to incentivize customers to buy or use a product or service.

If a store is offering a 30% discount on shirts that cost $25 originally, then the discount amount is:

30% of $25 = 0.30 x $25 = $7.50

The discount amount is $7.50, so the new price of the shirt after the discount is:

$25 - $7.50 = $17.50

Therefore, the cost of the shirt, in dollars, after the 30% discount is $17.50.

To know more about discount visit:

https://brainly.com/question/1548141

#SPJ1