The hypotenuse of a right triangle measures 17 cm. One leg of the triangle measures 15 cm. Find the length of the other leg of the triangle.

Answer:

x=25.

Step-by-step explanation:

We know because of corresponding angles, the sum of the angle adjacent to (2x-5) and (2x-5) is 180 degrees

2x-5+5x+10=180

7x+5=180

7x=175

x=25

Answer:

Can you add a picture if there are any?

Step-by-step explanation:

2x2 + 7x + 3 -answer

(2x + 1) (x + 3)

(2x * x) + (2x * 3) + (1 * x) + (1 * 3)

2x2 + 6x + x+3

2x2 + 7x + 3

Answer:2730

Step-by-step explanation:

The number of ways we can choose three different numbers in order for a unique code for this case is 2730

We can use combinations for this case,

Total number of distinguishable things is m.

Out of those m things, k things are to be chosen such that their order doesn't matter.

This can be done in total of [tex]^mC_k = \dfrac{m!}{k! \times (m-k)!}[/tex] ways.

If the order matters, then each of those choice of k distinct items would be permuted k! times.

So, total number of choices in that case would be:

[tex]^mP_k = k! \times ^mC_k = k! \times \dfrac{m!}{k! \times (m-k)!} = \dfrac{m!}{ (m-k)!}\\\\^mP_k = \dfrac{m!}{ (m-k)!}[/tex]

This is called permutation of k items chosen out of m items (all distinct).

Given that:

In a lock, the order of the way numbers are arranged matters.

Because of no repetition allowed, we can simulate this situation as:

The number of ways we can choose 3 numbers out of 15 numbers with order = The number of different ways we can choose three different numbers in order for a unique code.

And we have:

The number of ways we can choose 3 numbers out of 15 numbers with order = [tex]^{15}P_3 = \dfrac{15!}{(15-3)!} = \dfrac{15 \times 14 \times 13 \times 12!}{12!} = 2730[/tex]

Thus, the number of ways we can choose three different numbers in order for a unique code for this case is 2730

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Answer: there are 3150 boys and 3850 girl

Step-by-step explanation:

45÷100×7000= 3150 and 7000- 3150 = 3850

Hope this helps!!

Answer:

759

Step-by-step explanation:

Answer:

16.2

Step-by-step explanation:

a²+b²=c²

a=10, b=y, c=19

100+y²=361

y²=361-100

y²=261

√y²=√261

y=√261

y=16.2

Answer:

Option 2: 1 + 1/2 + 1/4 + 1/8+...

Step-by-step explanation:

When a geometric series converges, it has a common ratio that is in between -1 and 1. We can start by finding the common ratios of all the options and then see which one converges.

In the first option, each term is 3 times the term before it, meaning it has a ratio of 3. 3 does not fit in the range we defined, so this series does not converge.

In the second option, each term is half the term before it. This means the common ratio is 1/2. 1/2 is in the range, so this series converges.

In the third option, we can see that the common ratio is -4 since it is the number being brought to a power. -4 does not fit in the range we defined, so this series does not converge.

In the fourth option, we can see the common ratio is 2 since it is the number you multiply by tone more time to get the next term. 2 does not fit in the range we defined, so this series does not converge.

From this, we can see the second option(1 + 1/2 + 1/4 + 1/8+...) is the solution.

The geometric series [tex]1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}[/tex] converges by the rule of convergence. Thus, the option [tex]2[/tex]  from the given options is correct.

     When a geometric series converges, it has a common ratio that is in between [tex]-1[/tex] and [tex]1[/tex].

The convergence of the geometric series depends on the common ratio [tex]r[/tex]. When [tex]r[/tex]>1, then the series diverges.When [tex]r[/tex]<1, then the series converges, and when [tex]r[/tex] = 1, then the series oscillates.

The common ratio [tex]r[/tex] of the series  [tex]\dfrac{1}{81} +\dfrac{1}{27} +\dfrac{1}{9} +\dfrac{1}{3}[/tex]  is greater than [tex]1.[/tex] So, the series diverges.

For the series, [tex]1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}[/tex] , the common ratio  [tex]r[/tex] is  [tex]\dfrac{1}{2}[/tex], which is less than [tex]1[/tex] . So, the series converges.

For the series, [tex]\sum 7(-4)^n[/tex] , here the common ratio is [tex]-4[/tex]  which does not lie in the range of convergence. Thus the given series is not convergent.

For the series,[tex]\sum \dfrac{1}{5}(2)^{n-1}[/tex] the common ratio is 2.  So, the series is not convergent.

The geometric series is [tex]1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}[/tex].

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Answer:

area = 42.8 in²

Step-by-step explanation:

Height = 7 1/8 in

area = 7 1/8 x 12 x 1/2 = 42.8 in²

Answer:

Commutative Property of Addition

Answer:

Commutative property

Step-by-step explanation:

The commutative property is when the order of the addends is changed, the sum stays the same.

Ex. 3+7 = 7+3

Both 3+7 and 7+3 = 10

Answer:

115°

Step-by-step explanation:

65 +65 = 130

360-130= 230

230÷2= 115

Answer:

it's

-21

or 12

which one you mean

Answer:

1.23 x 10^8

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

2 out of 5 play so if there is 10 students 10*2/5 = 4 students

Answer:

4 students would play soccer

Step-by-step explanation:

To make the total students 10 instead of 5 we multiply the information by 2. 2/5 times 2 equals 4/10. So 4 out of 10 studento play soccer

Answer:

It is better to have a variety of plants because if the species of plants die out, the whole ecosystem becomes extinct.

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

12/13=0.923 , and also sinb is ac/ab

Answer:

C. 0.923

Step-by-step explanation:

I calculated it logically

Answer:

(1 , –1)

Step-by-step explanation:

bro, you can see it if you draw on graph paper, or you just need to use your imagination more

Answer:

1,-1

Step-by-step explanation:

Answer:

first blank is 3

second blank is 126

Step-by-step explanation:

the ratio is 2:3 so you must keep that the same in the table

The one for chocolates is 3 and the one for peppermints is 126

In geometry, a hypotenuse is the longest side of a right-angled triangle, the side opposite the right angle. The length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides.

It is useful in different situations involving the need to find distance or the measure of an angle.

Use the Pythagorean theorem to calculate the hypotenuse from right triangle sides. Take a square root of sum of squares: c = √(a² + b²)

Answer:

-\left(x-1\right)\left(x+6\right)

Step-by-step explanation:

-\left(x^2+5x-6\right)

Answer:

cos theta=4/5

b/h=4/5

b=4 and h=5

p=?

H^2=P^2+B^2

5^2=P^2+4^2

25-16=P^2

9=P^2

[tex]\sqrt{9}[/tex]=P

3=P

Now,

sin2theta

=p/h2

=3/5*2

=9/5

Step-by-step explanation:

Answer:

About 36.87 degrees; sinθ=3/5

Step-by-step explanation:

Note: I made an assumption with the Find: sin2θ part of your question, as it turned up as invalid when working on it on my end. Therefore, I assumed that it was sinθ. If it was something else, tell me and I can correct the answer/content.

Since within a triangle there are three sides when solving an angle, being opposite, adjacent and hypotenuse.

By already having cosθ=4/5. the rest of the problem can be solved. Since cosine is adjacent over hypotenuse, we can use the Pythagorean Theorem, solving for one of the legs of the triangle with:

c^2-b^2=a^2

Now, just plug in c as the 5 (the hypotenuse) and b as 4 (one of the legs).

5^2-4^2=a^2

25-16=a^2

9=a^2

a=3

The other leg is 3. With this, 3 would be the opposite angle from sin 20. Therefore, it can be plugged in the sine equation to get the answer. Remember, sine is Opposite/Hypotenuse.

sinθ=3/5

Move over the sine to then opposite side, inverse it:

θ=sin-1 3/5

Use a calculator.

θ = about 36.87 degrees.

There could only be one aolition

Answer:

(-4,-2)

Step-by-step explanation:

B(3,4)

x=3 , y=4

(3-7,4-6)

(-4,-2)

Transformation involves changing the position of a shape.

The coordinates of B after the translation is (-4,-2)

The vertices are given as:

[tex]\mathbf{A =(1,1)}[/tex]

[tex]\mathbf{B =(3,4)}[/tex]

[tex]\mathbf{C =(-1,8)}[/tex]

The translation rule is given as:

[tex]\mathbf{(x-7,y-6)}[/tex]

So, the coordinates of B' is calculated using:

[tex]\mathbf{(x,y) \to (x-7,y-6)}[/tex]

This gives

[tex]\mathbf{(3,4) \to (3-7,4-6)}[/tex]

[tex]\mathbf{(3,4) \to (-4,-2)}[/tex]

Rewrite as:

[tex]\mathbf{B' = (-4,-2)}[/tex]

Hence, the coordinates of B after the translation is (-4,-2)

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Answer:

O.75

Step-by-step explanation:

The value of x in the equation 1.5(4)^2x is equal to 12 is 3/4 after equation the power of same base.

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

We have an equation:

[tex]\rm 1.5(4)^2^x=12[/tex]

[tex]\rm (4)^2^x=8[/tex]

[tex]\rm (2^2)^{2x}= 2^3[/tex]

[tex]\rm 2^{4x}=2^3[/tex]

4x = 3  (equating powers of same base)

x = 3/4

Thus, the value of x in the equation 1.5(4)^2x is equal to 12 is 3/4 after equation the power of same base.

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Answer:

C. x = 6

Step-by-step explanation:

2*6 + 4 = 16