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valentinak56 [21]
3 years ago
5

A right triangle is shown below. Which measurement is the closest to the value of x?

Mathematics
1 answer:
REY [17]3 years ago
6 0

Answer:

35°

Step-by-step explanation:

First you find the sine of x. That would be

sinx = opposite/hypotenuse

sinx = 57/100

sinx = 0.57

You can look it up if you want, but sin35 = 0.574

so the answer is 35°

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Use mathematical induction to show that 4^n ≡ 3n+1 (mod 9) for all n equal to or greater than 0
cestrela7 [59]
When n=0, you have

4^0=1\equiv3(0)+1=1\mod9

Now assume this is true for n=k, i.e.

4^k\equiv3k+1\mod9

and under this hypothesis show that it's also true for n=k+1. You have

4^k\equiv3k+1\mod9
4\equiv4\mod9
\implies 4\times4^k\equiv4(3k+1)\mod9
\implies 4^{k+1}\equiv12k+4\mod9

In other words, there exists M such that

4^{k+1}=9M+12k+4

Rewriting, you have

4^{k+1}=9M+9k+3k+4
4^{k+1}=9(M+k)+3k+3+1
4^{k+1}=9(M+k)+3(k+1)+1

and this is equivalent to 3(k+1)+1 modulo 9, as desired.

3 0
3 years ago
Write an expression that can be used in over a temperature from degrees Celsius see to degrees Fahrenheit and then use the expre
densk [106]

Answer:

25°C = 77 degree Fahrenheit.

Step-by-step explanation:

In this question we have to write the expression showing the relation between degree Celsius and degree Fahrenheit first.

C=\frac{5}{9}(F-32)  where C = degree centigrade and F = degree Fahrenheit

Although the question is not clear in the next part but assuming that we have to use this expression to convert 25°C to degree Fahrenheit,

We will plug in the value of C in the expression,

25=\frac{5}{9}(F-32)

F=(\frac{9}{5}\times 25)+32

F = 45 + 32

F = 77

Therefore, 25°C = 77 degree Fahrenheit will be the answer.

4 0
3 years ago
When you have 25 numbers, and Jake picks 3 random numbers and puts them back, what is the chance Bob has of picking those 3 numb
tensa zangetsu [6.8K]

Answer:

4 out of 25 percent chance

Step-by-step explanation:

if you divide the number and range them out. That's all i can tell you for now. Kinda busy. sorry

7 0
3 years ago
Can someone please help me with this
Sholpan [36]

Answer:

39 sq inches

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
What is the nth term rule of the quadratic sequence below? 4,15,30,49,72,99,130,...
navik [9.2K]

Answer:

The nth term rule of the quadratic sequence is 2n^{2} +5n-3.

Step-by-step explanation:

We are given the following quadratic sequence below;

4, 15, 30, 49, 72, 99, 130,...

As we know that the formula for the nth term of the quadratic sequence is given by =  an^{2}+bn+c

Firstly, we will find the difference between the term of the given sequence;

1st difference of the given sequence;

(2nd term - 1st term), (3rd term - 2nd term), (4th term - 3rd term), (5th term - 4th term), (6th term - 5th term), (7th term - 6th term)

= (15 - 4), (30 - 15), (49 - 30), (72 - 49), (99 - 72), (130 - 99),....

= (11, 15, 19, 23, 27, 31,.....)

Now, we will find the second difference of the given sequence, i.e;

= (15 - 11), (19 - 15), (23 - 19), (27 - 23), (31 - 27),....

= (4, 4, 4, 4, 4)

Since the differences are same now, so to find the value of a we have to divide the value of second difference by 2, i.e;

The value of a  =  \dfrac{4}{2} = 2

SO, the first term of the nth term rule equation is an^{2} = 2n^{2}.

Now, in the term 2n^{2}, put the value of n = 1, 2, 3, 4 and 5 and then form the sequence, i.e;

If n = 1, then 2n^{2} = 2 \times (1)^{2} = 2

If n = 2, then 2n^{2} = 2 \times (2)^{2} = 8

If n = 3, then 2n^{2} = 2 \times (3)^{2} = 18

If n = 4, then 2n^{2} = 2 \times (4)^{2} = 32

If n = 5, then 2n^{2} = 2 \times (5)^{2} = 50

SO, the sequence formed is (2, 8, 18, 32, 50).

Now, find the difference of this sequence and the original quadratic sequence, i.e;

= (4 - 2), (15 - 8), (30 - 18), (49 - 32), (72 - 50)

= (2, 7, 12, 17, 22)

Now, as we can see that the above sequence resembles the general form of (5n - 3) because:

If we put n = 1, then (5n - 3) = 5 - 3 = 2

If we put n = 2, then (5n - 3) = 10 - 3 = 7 and so on....

From this, we concluded that the value of b and c are 5 and (-3) respectively.

Hence, the nth term rule for the given quadratic sequence is 2n^{2} +5n-3.

7 0
3 years ago
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