In ΔNOP, the measure of ∠P=90°, NP = 35, ON = 37, and PO = 12. What ratio represents the sine of ∠N?

Answer:

Step-by-step explanation:

We could use the Law of Sines if we only knew what angle A was. It just so happens that by the Triangle Angle-Sum Theorem, angle A is equal to

180 - B - C. Therefore,

angle A = 180 - 11 - 75 so

angle A = 94. And the Law of Sines is

[tex]\frac{sin94}{a}=\frac{sin11}{600}[/tex] and cross multiply to get

600sin94 = asin11 and solve for a:

[tex]a=\frac{600sin94}{sin11}[/tex] gives you that

a = 3136.85

Answer with Step-by -step explanation:

Sequence A;4,7,10,13,16

[tex]a_2-a_1=7-4=3[/tex]

[tex]a_3-a_2=10-7=3[/tex]

The difference between two consecutive terms is equal. Therefore, it forms arithmetic sequence.

Common difference, d=3

a=4

[tex]a_n=a+(n-1)d[/tex]

[tex]a_6=a+5d=4+5\times 3=19[/tex]

[tex]a_7=a+6d=4+6(3)=22[/tex]

[tex]a_8=a+7d=4+7(3)=25[/tex]

Sequence B: 5,10,20,40,80,...

[tex]a_1=5,a_2=10,a_3=20[/tex]

[tex]\frac{a_2}{a_1}=\frac{10}{2}=2[/tex]

[tex]\frac{a_3}{a_2}=\frac{20}{10}=2[/tex]

The ratio  of two consecutive terms is equal. Therefore, it forms geometric sequence.

Common ratio, r=2

a=5

[tex]a_n=a r^{n-1}[/tex]

[tex]a_6=ar^5=5(2)^5=160[/tex]

[tex]a_7=ar^6=5(2^6)=320[/tex]

[tex]a_8=ar^7=5(2^7)=640[/tex]

Sequence C:2,5,10,17,26,..

a1=2

[tex]a_2=5=2+3=a_1+3[/tex]

[tex]a_3=10=5+5=a_2+5[/tex]

[tex]a_4=17=10+7=a_3+7[/tex]

[tex]a_5=26=17+9=a_4+9[/tex]

From the following pattern

We can get

[tex]a_6=a_5+11=26+11=37[/tex]

[tex]a_7=a_6+13=37+13=50[/tex]

[tex]a_8=a_7+15=50+15=65[/tex]

Answer:

1. = x^2 -5x+6

Step-by-step explanation:

2. = 2x^2 +5x+3

3. =2x^2 +(x-1) +((x)/x^2 -x+6)

Answer:

140 degrees

Step-by-step explanation:

Answer:

47.01 ft

Step-by-step explanation:

answer in photo above

Answer:

15 is larger than -4

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

15 ÷ (-4) = -3.75

Answer:

First Term = 6

Common Ratio = 3

Step-by-step explanation:

According to the Question,

Thus, [tex]S_{8} = 19680[/tex] & [tex]S_{4} = 240[/tex] .

Now, on solving  [tex]\frac{S_{8} }{S_{4} }[/tex]  we get,

[tex]\frac{19680}{240} = \frac{\frac{a(r^{8-1)} }{r-1}}{\frac{a(r^{4-1)} }{r-1}}[/tex]  

[tex]82 = \frac{r^{8}-1 }{r^{4}-1 }[/tex]

[tex]82r^{4}-82 = r^{8}-1\\r^{8}-82r^{4}+81 = 0\\r^{8}-81r^{4}-r^{4}+81 = 0\\(r^{4}-81)( r^{4}-1) =0[/tex](r=1 is not possible so neglect [tex]( r^{4}-1) =0[/tex] )

So, r=3 Now Put this value in [tex]S_{4} = {\frac{a(r^{4-1)} }{r-1}}[/tex] We get a=6 .

Answer:

to use the money when in an emergency

Answer:

Step-by-step explanation:

FORMULA= P(A)=

NUMBER OF FAVORABLE OUTCOMES

-------------------------------------------------------------

NUMBER OF POSSIBLE OUTCOMES

GIVEN: 12 Guitars, 10 Bass, 9 Drums, 12 Keyboards

WANT: The probality a seventh grader chosen at randome will play drums

add all the instruments

12+10+9+12=33

there are 9 drums

FOLLOW THE FORMULA

9 3

---- = ---- SIMPLIFIES FORM

33 11

Answer:

[tex]7,500[/tex]

Step-by-step explanation:

Let's solve this problem step-by-step. The library had 1,500 books in 2011. The ratio of books in 2011 and in 2012 is 1:2. Therefore, let the number of books in 2012 be [tex]x[/tex].

We have the following proportion:

[tex]\frac{1}{1,500}=\frac{2}{x},\\x=2\cdot 1,500=3,000[/tex]

Therefore, there were 3,000 books in 2012. The ratio of books in 2012 and in 2013 is 2:5. Let the number of books in 2013 be [tex]y[/tex].

We have:

[tex]\frac{2}{3,000}=\frac{5}{y},\\2y=5\cdot 3,000,\\2y=15,000\\y=\boxed{7,500}[/tex]

Therefore, there were 7,500 books in 2013.

Answer:

7,500 books

Step-by-step explanation:

Answer:

The value of x is 9.

Step-by-step explanation:

55°

(3 x + 23)

75°

The sum of all the angles of triangle is 180°.

55 + 3 x + 23 + 75 = 180

3 x = 27

x = 9

So, the value of x is 9.

Step-by-step explanation:

In interval form, the domain of f is (−∞,∞).

Answer:

hundredths

Step-by-step explanation:

Numbers after the decimal start with

tenth

hundredth

Answer:

x=3

Step-by-step explanation:

Answer:

B. x² + 4x - 4

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

f(x) = 4x + 1

g(x) = x² - 5

(f + g)(x) = f(x) + g(x)

Step 2: Find

Answer:

B  

Step-by-step explanation:  6  18  11  18

f(x)=4x+1 and g(x)=x^2 -5

f(x)=     4x+1

g(x)=x^2 -5      just add these two equations

(f+g)(x)  =  x² + 4x +1 - 5

(f+g)(x)  =  x² + 4x - 4     B

Answer:

Option B

Step-by-step explanation:

Look.......Polynomial is something which has more than 3 term..So, as you can see option B has more than three.

Answer:

[tex]= \frac{2x-3\sqrt{x} }{x-1}[/tex]

Step-by-step explanation:

Given the expression

[tex]\frac{(\sqrt{x} +1)^{2} +(\sqrt{x} -1)^{2} )}{(\sqrt{x} +1)(\sqrt{x} -1)} -\frac{3\sqrt{x} +1}{x-1}[/tex]

Expand

[tex]\frac{(\sqrt{x} +1)^{2} +(\sqrt{x} -1)^{2} )}{(\sqrt{x} +1)(\sqrt{x} -1)} -\frac{3\sqrt{x} +1}{x-1}\\= \frac{x+2\sqrt{x}+1+(x-2\sqrt{x} +1) }{x-1}- \frac{3\sqrt{x} +1}{x-1}\\= \frac{2x+1}{x-1} - \frac{3\sqrt{x} +1}{x-1}\\= \frac{2x+1-(3\sqrt{x} +1)}{x-1}\\= \frac{2x-3\sqrt{x} +1-1}{x-1}\\= \frac{2x-3\sqrt{x} }{x-1}[/tex]

This gives the simplified form

Answer:

To convert a meter measurement to a foot measurement, multiply the length by the conversion ratio. The length in feet is equal to the meters multiplied by 3.28084.

Step-by-step explanation:

Answer:

A; C.

Step-by-step explanation:

B. not correct: the graph can have no interception; one interception or two interception;

D. not correct: the graph can have no interception; one interception or two interception.

Answer:

20 % increase in Area

Step-by-step explanation:

1.  Original Rectangle Area = 150cm ²

2. 20% of 15 is 3

3. Increased length is equal to 18

4. Increased Rectangle Area = 180cm ²

5. Ten percent of 150 = 15.

6. 15x2(ten percent) = 30. Which give us 150+30 equal to 180.

7. 2 ten percent equals 20%

8. Answer is 20%.

Answer:

$13 - senior

$6 - child

Step-by-step explanation:

set up a system of equations:

s = senior tickets price

c = child tickets price

4s + 2c = 64; you can simplify this by dividing through by 2 to get:

2s + c = 32

12s + 8c = 204; you can simplify this by dividing through by 4 to get:

3s + 2c = 51

we can say that 'c' = 32-2s' and substitute that for 'c' in the second equation:

3s + 2(32-2s) = 51

3s + 64 - 4s = 51

-s = -13

s = 13

now find 'c' by substituting 13 for 's':

2(13) + c = 32

26 + c = 32

c = 6

Answer:

A

Step-by-step explanation:

multiple across

5 * 6 = 30

2x+1 * x = 2x^2 + x

Answer:

The Number of Zeroes In The Results is Always equal To the Powers of 10.

Step-by-step explanation:

Example:-

345*[tex]10^{2}[/tex] = 34500

345*[tex]10^{5}[/tex] = 34500000

345*[tex]10^{7}[/tex] = 3450000000

345*[tex]10^{8}[/tex] = 34500000000

(In the Above examples, There is All The Numbers of Zeroes In The Results is equal To the Powers of 10)

Answer:

70

Step-by-step explanation:

the fraction 7/10 turns into 70% which means 70 out of 100 tickets were sold.

Answer:

70 tickets sold

Step-by-step explanation:

Multiply the number of tickets by the fraction of tickets sold

100 *7/10

Rewriting

100/10 * 7

10*7

70