What is the length of the hypotenuse of the triangle?

Answer:

x=4

Step-by-step explanation:

To solve the equation (sin x)(cos x) = 0, we find that sin x equals zero when x is an integral multiple of π , while cos x equals zero at odd multiples of π/2 . Therefore, our solutions are x = nπ and x = (2n + 1)π/2 for any integer n.

To find all solutions to the equation (sin x)(cos x) = 0, we need to identify the values of x at which either sin x = 0 or cos x = 0, because if either factor on the left-hand side is zero, the product will be zero.

For sin x = 0, the solutions are where x is an integral multiple of π . This can be written as x = nπ, where n is any integer (..., -3, -2, -1, 0, 1, 2, 3, ...).

For cos x = 0, the solutions occur at odd multiples of π/2. Therefore, the solutions can be represented as x = (2n + 1)π/2, where n is any integer.

Combining both sets of solutions, we have x = nπ and x = (2n + 1)π/2, for n being any integer.

The value of a larger number is 39 and the smaller number is 25.

Given that,

The sum of the two numbers is 64.

And, the smaller number is 14 less than the larger number.

Let us assume that,

The larger number is = x

Then, the value of smaller numbers = x - 14

Since the sum of the two numbers is 64.

Hence we get;

x + (x - 14) = 64

2x - 14 = 64

2x = 64 + 14

2x = 78

x = 78/2

x = 39

Thus, The larger number is = 39

Then, the smaller number = 39 - 14

                                            = 25

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Let us say that the intersection point of lines AB and CD is called point E. The lines AB and CD are perpendicular to each other which also means that the triangle CEB is a right triangle.

Where the line CB is the radius of the circle while the side lengths are half of the whole line segment:

EB = 0.5 AB = 0.5 (8 ft) = 4 ft

CE = 0.5 CD = 0.5 (6 ft) = 3 ft

Now using the hypotenuse formula since the triangle is right triangle, we can find for the radius or line CB:

CB^2 = EB^2 + CE^2

CB^2 = (4 ft)^2 + (3 ft)^2

CB^2 = 16 ft^2 + 9 ft^2

CB^2 = 25 ft^2

CB = 5 ft = radius

Answer:

5ft

Step-by-step explanation:

Answer:

.C

Step-by-step explanation:

After 5 year term, the distance covered is 140000 km, the charge paid is, $1200

The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the components that are multiplied are referred to as the factors.

Given that,

In lease agreement, the distance allowed 25000 km per year for free

After that the charge will be $0.08 per km

After 5 year term, you drove a total of 140000 km

The owed amount  = ?

So, in 5 year term the distance which is free according to agreement,

⇒   5 × 25000

⇒    125000

Now, the distance for which charge has given

⇒   140000 - 125000

⇒   15000

Charged amount = $0.08 per km

The owed amount  =  0.08 × 15000

                                =   $1200

Hence, the amount owed is $1200

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There are total 56 ways to fill the open spot .

A combination is a way for determining the number of possible arrangements in a collection of items where the order of selection does not matter.

[tex]C(n, r) =\frac{n!}{(n - r)!r!}[/tex]

where,

n is the number of items in set.

r is the number of items selected from the set.

According to the question we have,

Number of altos, n = 8

Number of  open spots, r = 3

Therefore, the number of ways to fill open spots = C(8, r)

Number of ways = [tex]\frac{8!}{3!(8-3)!}[/tex]

Number of ways = [tex]\frac{8!}{5!3!}[/tex][tex]= \frac{(8)(7)(6)(5!)}{5!3!}[/tex] = [tex]\frac{(8)(7)(6)}{(3)(2)} =8(7) = 56[/tex]

Hence, there are total 56 ways to fill the open spot .

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T = total cost

X= number of rides

T=4.00x+9.00

Answer: D. 1816214400

Step-by-step explanation:

When we select r things from n things in order we apply permutations and the number of ways to select r things = [tex]^nP_r=\dfrac{n!}{(n-r)!}[/tex]

Given : Total player = 15

Required number of players for Batting order = 9

Then the number of different ways to select 9 person batting order so that he arrange the players in the lineup would be [tex]^{15}P_9=\dfrac{15!}{(15-9)!}[/tex]

[tex]=\dfrac{15\times14\times13\times12\times11\times10\times9\times8\times7\times6!}{6!}[/tex]

[tex]=1816214400[/tex]

∴ The number of different ways can he arrange the players in the lineup = 1816214400

Hence, the correct answer is D. 1816214400

To find out when the car and truck will pass each other, set up an equation where the sum of the distances covered by each at their respective speeds equals 305 miles. After solving, it's determined they will pass each other at 4:00 p.m.

To determine at what time the car and truck will pass each other, we need to calculate how far each vehicle will have traveled before they meet. The car leaves St. Louis at 1:00 p.m., while the truck leaves Chicago at 2:00 p.m., one hour later. We assume they meet after the car has been traveling for t hours and the truck for t - 1 hours.

The distance the car travels is the product of its speed and time, which can be calculated as 65 miles per hour times t hours. The truck's distance is 55 miles per hour times (t - 1) hours. Since the total distance between St. Louis and Chicago is 305 miles, we combine these distances to form the equation:

65t + 55(t - 1) = 305

Solving this equation:

Since the car has been traveling for 3 hours after 1:00 p.m., the two vehicles will pass each other at 4:00 p.m.

The quantity equal to sin ∠DPB is sin(x/2), corresponding to option B.

In the given diagram, overline PN serves as the perpendicular bisector of overline AB, implying that point N lies on the midpoint of segment AB.

Additionally, overline PN functions as the angle bisector of ∠CPD. Since ∠CPD measures x degrees, by the angle bisector theorem, ∠DPN and ∠DPB each measure x/2 degrees.

Now, to determine sin ∠DPB, we consider the right triangle DPN. By definition, sin θ = opposite/hypotenuse.

In this triangle, the opposite side to ∠DPB is overline DN, and the hypotenuse is overline DP.

Therefore, sin ∠DPB = DN/DP.

Since ∠DPN = x/2, applying trigonometric ratios in right triangle DPN, sin(x/2) = DN/DP.

Hence, the quantity equal to sin ∠DPB is sin(x/2), corresponding to option B.

The probable question may be:

In the diagram, overline PN is the perpendicular bisector of overline AB and is also the angle bisector of ∠ CPD If m∠ CPD=x , which quantity is equal to sin ∠ DPB ?

A. sin π /2

B. sin x/2

C. cos x/2

D. cos π /3

To solve this problem, we use the combination equation to find for the possible groups of answer to the questions. Since we are looking for at least 5 correct answers out of 10 questions, therefore we find for 10 ≥ r ≥ 5. We use the formula for combination:

nCr = n! / r! (n – r)!

Where,

n = total number of questions = 10

r = questions with correct answers

For 10 ≥ r ≥ 5:

10C5 = 10! / 5! (10 – 5)! = 252

10C6 = 10! / 6! (10 – 6)! = 210

10C7 = 10! / 7! (10 – 7)! = 120

10C8 = 10! / 8! (10 – 8)! = 45

10C9 = 10! / 9! (10 – 9)! = 10

10C10 = 10! / 10! (10 – 10)! = 1

Summing up all combinations will give the total possibilities:

Total possibilities = 252 + 210 + 120 + 45 + 10 + 1 = 638

Answer: 638

Doing this, we get that 32 feet are needed.

Square:

The area of a square of side s is:

[tex]A = s^2[/tex]

And the perimeter is:

[tex]P = 4s[/tex]

Area of 64 square feet

This means that:

[tex]s^2 = 64[/tex]

[tex]s = \sqrt{64}[/tex]

[tex]s = 8[/tex]

The side of the square is of 8 feet.

Perimeter:

Side of 8 feet, so:

[tex]P = 4s = 4(8) = 32[/tex]

32 feet of chain fence are needed.

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