A staircase is being constructed in a new house as displayed on the right. Each tread is 18 cm and each riser is 10cm. Determine the angle of inclination of the stairs.

Answer:

You need to use sohcahtoa to find your answer.

first you gotta identify what sides of the triangle you have.

You're missing the hypotenuse, and you have the value of the adjacent.

since you have the adjacent and need the hypotenuse, you're going to use cosine to find x

cos(65) = 16/x

x = 37.859

Answer:

x = 37.85

this is a standard "trig" question

it requires two pieces  of insight.

First that a triangle has 180° interior angles.

from that you can determine that the third angle is 25° because

90 + 65 + β = 180

the red symbol lets you know that it is 90°

the second think that will help is SOHCAHTOA

that is if you have a "right triangle" (one with a 90° angle)

in this problem (in your mind rotate the triangle so the 65° is at the bottom left and the two long sides are pointing up

in this case you have the 16 on the bottom (adjacent to the angle) and

the x is on the hypotenuse...

you have the A& H that is COS

thus you have cos(65) = [tex]\frac{16}{x}[/tex]

x = 37.85

Step-by-step explanation:

Answer:

Step-by-step explanation:

F(x)=2^x

[tex]F(-2)=2^{-2} =\frac{1}{2^2} =\frac{1}{4}[/tex]

Answer:

3

Step-by-step explanation:

u need to finish 4 assignments in 1 hour

Answer:

Let the number be x

Given that

⇒(x+

3

2

)×2=

3

16

⇒x+

3

2

=

3

8

⇒x=

3

8

−

3

2

⇒x=

3

6

⇒x=2

Thus the number is 2

Answer:

m = - 31

Step-by-step explanation:

Given

[tex]\frac{m-1}{2}[/tex] - [tex]\frac{m-2}{3}[/tex] = [tex]\frac{m-4}{7}[/tex]

Multiply through by 42 , the LCM of 2, 3 and 7 , to clear the fractions

21(m - 1) - 14(m - 2) = 6(m - 4) ← distribute parenthesis

21m - 21 - 14m + 28 = 6m - 24

7m + 7 = 6m - 24 ( subtract 6m from both sides )

m + 7 = - 24 ( subtract 7 from both sides )

m = - 31

340 x 0.03 = 10.2 (in state)

84 x 0.11 = 9.24 (out of state)

10.2 + 9.24 + 11.25

= $30.69 monthly charge

hope it helps :)

The total monthly charge for a customer is given as $30.69.

Simplifying allows us to test each process and strategy to determine which is the most efficient and best suited for its specific goal.

here,

A phone provider costs each customer $11.25 per month. Furthermore, it charges $0.03 per minute for in-state calls and $0.11 for out-of-state calls.

Charge within the boundary  of state for 340 minutes = 340 x 0.03 = 10.2

Charge beyond the boundary  of state for 84 minutes  = 84 x 0.11 = 9.24

Total monthly charge = 10.2 + 9.24 + 11.25

                                = $30.69 monthly charge

Thus, A customer's total monthly price is shown as $30.69.

Learn more about simplification here:

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#SPJ2

except for letter a. LIZM

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\boxed{\mathsf{4[30-(10-2)\times3]}}[/tex]

[tex]\huge\boxed{\rightarrow\mathsf{4[30 - (\bold{8}}) \times3]}[/tex]

[tex]\huge\boxed{\rightarrow \mathsf{4[30 - \bf 24]}}[/tex]

[tex]\huge\boxed{\rightarrow \mathsf{4(30) + 4(-24)}}[/tex]

[tex]\huge\boxed{\rightarrow \mathsf{\bf 120 - 96}}}[/tex]

[tex]\huge\boxed{\rightarrow\mathsf{\bf 24}}[/tex]

[tex]\huge\boxed{\rm{Answer: \mathsf{24}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

Step-by-step explanation:

Answer:

[tex]x=32[/tex]°

Step-by-step explanation:

The law of sines is a property of all triangles that relates the sides and angles of a triangle. This property states the following:

[tex]\frac{sin(a)}{A}=\frac{sin(b)}{B}=\frac{sin(c)}{C}[/tex]

Where side (A) is the side opposite angle (<a), side (B) is the side opposite angle (<b), and side (C) is the property opposite angle (<c).

Substitute each of the sides and respective angles into the formula, and solve for the unknown angle (<x). Please note that a triangle with two congruent sides (referred to as an isosceles triangle) has a property called the base angles theorem. This states that the angles opposite the congruent sides in an isosceles triangle are congruent. Therefore, there can be two (<x)'s in this triangle.

[tex]\frac{sin(a)}{A}=\frac{sin(b)}{B}=\frac{sin(c)}{C}[/tex]

[tex]\frac{sin(x)}{10}=\frac{sin(116)}{17}=\frac{sin(x)}{10}[/tex]

One can shorten the equation so it only holds the parts that will play a role in solving this equation,

[tex]\frac{sin(x)}{10}=\frac{sin(116)}{17}[/tex]

Now take the cross product in this equation to simplify it further,

[tex]\frac{sin(x)}{10}=\frac{sin(116)}{17}[/tex]

[tex]17(sin(x))=10(sin(116))[/tex]

Inverse operations, solve this equation for (x),

[tex]17(sin(x))=10(sin(116))[/tex]

[tex]sin(x)=\frac{10(sin(116))}{17}[/tex]

[tex]x=sin^-^1(\frac{10(sin(116))}{17})[/tex]

[tex]x=31.91782...[/tex]

[tex]x\approx32[/tex]

Answer:

hello,

Step-by-step explanation:

the triangle is isocele,

x+x+116=180

x=(180-116)/2

x= 32° (thirty-two , trente-deux in french)

Answer:

y = 2x+4

Step-by-step explanation:

First find the slope

m = ( y2-y1)/(x2-x1)

    = ( 12-6)/(4-1)

   = 6/3

    = 2

The slope intercept form is

y = mx+b where m is the slope and b is the y intercept

y = 2x+b

Using a point from the table

10 = 2(3)+b

10 = 6+b

10-6 = b

4=b

y = 2x+4

Answer:

75 degrees

Step-by-step explanation:

From the first part of the diagram,

vertically opposite angles are equal,

hence we have

125° + (4x-5)° + 125° + (4x-5)° = 360°

(Angles about a point equals 360°)

4x – 5 + 4x – 5 + 125 + 125 = 360

8x + 250 – 10 = 360

8x = 360–250 + 10

8x = 120

x = 15°

Now we have (5x)° in the second part.

5x = 5 × 15 = 75°

1 is vertically opposite to angle 75°

hence it is equal to 75 degrees.

Answer:75

Step-by-step explanation:

Answer:

x = 14

[tex]h^2 = p^2 + b^2\\h^2 = 7^2 + 12^2\\x^2 = 49 + 144\\x^2 = 193\\so, x = 13.89\\so, x = 14[/tex]

Answer:

2^0

Step-by-step explanation:

When you are dividing 2 exponents with the same base (in this case, 2) you subtract them. 2^5 ➗ 2^5 => 2^(5-5) = 2^0 => which is equal to 1, but the answer here would be 2^0.

There are two ways to go about this problem.

The first way, the generic way, is to know that,

[tex]\frac{a^n}{a^m}=a^{n-m},a\neq0[/tex].

So,

[tex]\frac{2^5}{2^5}=2^{5-5}=\boxed{2^0}[/tex].

The second way is to realise that both numerator and denominator are equal and when diving two equal numbers you obtain 1. (except when diving zeros) aka,

[tex]\frac{a}{a}=1, a\neq0[/tex]

And 1 equals to any number raised to the power of zero,

[tex]a^0=1,a\neq0[/tex]

So we just have to say that the 1 we got is rewritten as some base to the power of zero.

Since our base needs to be 2, we just simply say,

[tex]2^0[/tex].

Et Viola.

Hope this helps.

Answer:

-5x = 26 is 5.2

x/2 = 4 is -8

3/2x=6 is 4

x/-7.2=4 is 28.8

Answer:

Step-by-step explanation:

The function [tex]g(x) =|x + 1| - 7[/tex] decreases at interval [tex](-\infty, -1)[/tex]

The parent function is given as:

[tex]f(x) =|x|[/tex]

The transformed function is given as:

[tex]g(x) =|x + 1| - 7[/tex]

Both functions are absolute value functions, and an absolute value function is represented as:

[tex]y=a| x-h |+k[/tex]

Where, the vertex of the function is:

[tex]Vertex = (h,k)[/tex]

By comparing [tex]y=a| x-h |+k[/tex] and [tex]g(x) =|x + 1| - 7[/tex], we have:

[tex](h,k) = (-1,-7)[/tex]

[tex]a= 1[/tex]

Because (a) has a positive value (i.e. 1) and (h) is negative, then the vertex represents a minimum.

This also means that, the function will decrease from infinity, till it gets to the x-coordinate of the vertex.

Hence, the function [tex]g(x) =|x + 1| - 7[/tex] decreases at interval [tex](-\infty, -1)[/tex]

Read more about transformation at:

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Answer:

Hello,

3842

Step-by-step explanation:

[tex]a=4-\sqrt{15} \\\\\dfrac{1}{a} =\dfrac{1}{4-\sqrt{15}} \\\\=\dfrac{4+\sqrt{15}}{(4-\sqrt{15})*(4+\sqrt{15})}\\\\=\dfrac{4+\sqrt{15}}{16-15} \\\\=4+\sqrt{15}\\\\[/tex]

[tex]a+\dfrac{1}{a} =4-\sqrt{15}+4+\sqrt{15}=8\\\\[/tex]

[tex](a+\dfrac{1}{a} )^2=a^2+\dfrac{1}{a^2} +2\\\\a^2+\dfrac{1}{a^2} =8^2-2=62\\[/tex]

[tex](a+\dfrac{1}{a} )^3=a^3+\dfrac{1}{a^3} +3*\dfrac{a^2}{a} +3*\dfrac{a}{a^2} \\\\8^3=a^3+\dfrac{1}{a^3} +3(a+\dfrac{1}{a} )\\\\a^3+\dfrac{1}{a^3} =8^3-3*8=488\\[/tex]

[tex](a+\dfrac{1}{a} )^4=a^4+\dfrac{1}{a^4} +4*\dfrac{a^3}{a} +6*\dfrac{a^2}{a^2} +4*\dfrac{a}{a^3}\\\\a^4+\dfrac{1}{a^4}=(a+\dfrac{1}{a} )^4-4*a^2-4*\dfrac{1}{a^2} -6\\a^4+\dfrac{1}{a^4} =8^4-4*62-6\\\\=4096-248-6\\\\=3842\\\boxed{a^4+\dfrac{1}{a^4} =3842}\\[/tex]

Using a calculator:

[tex]a=4-\sqrt{15}=0,1270166537925831148207346002176....\\\\a^4= 2,6028112122495108436170792979303e-4\\\\\dfrac{1}{a} =4+\sqrt{15} =7,8729833462074168851792653997824...\\\\\dfrac{1}{a^4}=3841,9997397188787750489156382921....\\\\a^4+\dfrac{1}{a^4} \\\\= 2,6028112122495108436170792979303e-4+3841,9997397188787750489156382921....\\\\=3842\\[/tex]

Answer:

554,000

Step-by-step explanation:

that is the answer

Emma earns $554,064.80  in total in the first 11 years of her career

We are to determine the future value of $39,000 each year for 11 years given the growth rate of 5%

The formula for calculating future value:

FV = P (1 + r)^n

Where :

FV = Future value  

P = Present value  

R = interest rate  

N = number of years

First year =  $39,000

Second year = 39,000 x (1.05) = $40,950

Third year = 39,000 x (1.05)^2 = $42,997.50

Fourth year = 39,000 x (1.05)^3 = $45,147.38

Fifth year = 39,000 x (1.05)^4 = $47,404.75

Sixth year = 39,000 x (1.05)^5 = $49,774.99

seventh year = 39,000 x (1.05)^6 = $52,263.74

eighth year = 39,000 x (1.05)^7 = $54,876.93

ninth year = 39,000 x (1.05)^8 = $57,620.78

tenth year = 39,000 x (1.05)^9 = $60,501.82

eleventh year = 39,000 x (1.05)^10 = $63,526.91

Sum of the earnings for the first eleven years = $554,064.80

To learn more about the future value of income, please check : https://brainly.com/question/19407218?referrer=searchResults

It's rational because of the repeating digits.

We have

x = 2.732343434…

Then

1,000x = 2,732.343434…

and

100,000x = 273,234.343434…

Subtracting these makes the fractional part go away, leaving you with

100,000x - 1,000x = 273,234.343434… - 2,732.343434…

100,000x - 1,000x = 273,234 - 2,732

99,000x = 270,502

x = 270,502/99,000 = 135,251/49,500

which is clearly a rational number.

Answer:

vertex of 4 is 2

Step-by-step explanation:

cuh cuh uchuch uch uch uch

Answer:

17 and 19

Step-by-step explanation:

Let n denote the first odd integer.

If the two integers are consecutive and odd, then the second number is n+2.

Hence, n+n+2=36

=2n=34

Divide both sides by 2

=n=17

Therefore, the numbers are 17 and 19.

Answer:

y>17

Step-by-step explanation:

[tex]x + y = 30 \\ 13 + y = 30 \\ y = 17 \\ for \: x < 13 \\ y > 17[/tex]

Answer:

y>17

Step-by-step explanation:

x+y=30

x<13

What + 13 is 30?

17. So if x+y=30. Because x will be less than 13, y must make up the differnce by being greater than 17.

Ex: x=12

y+12=30

y=18

18 is greater than 17.

This is a great way to check because if your not sure, it elimates the other options!

Hope this helps!

Answer:

V = 180 ft^3

Step-by-step explanation:

The volume of a cone is found by

V = 1/3 pi r^2 h  where r is the radius and h is the height

The diameter is 12 so the radius is 1/2 the diameter or 1/2(12) = 6

The height is 5 and we are using 3 for pi

V = 1/3 (3) *6^2 *5

V = 180 ft^3

Answer:

The Polynominal is not shown. So how can i answer???

Step-by-step explanation:

Thank You! Hope it helps! Please Mark me brainliest!

Answer:

The p is 4

Step-by-step explanation:

Answer:

B) Multiply by 3/2 on both sides of the equation by the multiplication property of equality

Answer:

72

The result is rational because it can be written as the ratio of two integers and its decimal expansion can terminate or repeat.

Answered by GAUTHMATH

Answer:

0.5 = 50% probabilidad de que apruebe el estudiante B dado que el estudiante A aprueba.

Step-by-step explanation:

La probabilidad condicional :

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

En el cual:

P(B|A) es la probabilidad de que ocurra el evento B, dado que A sucedió.  

[tex]P(A \cap B)[/tex] es la probabilidad de que ocurran tanto A como B.  

P(A) es la probabilidad de que ocurra A.

En esta pregunta :

Evento A: Estudiante A aprueba.

Evento B: Estudiante B aprueba.

La probabilidad de que el estudiante A apruebe un examen de MM-100 es 0.6

Entonces [tex]P(A) = 0.6[/tex]

La probabilidad de que ambos estudiantes aprueben es 0.3

Entonces [tex]P(A \cap B) = 0.3[/tex]

¿Cual es la probabilidad de que apruebe el estudiante B dado que el estudiante A aprueba.?

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.3}{0.6} = 0.5[/tex]

0.5 = 50% probabilidad de que apruebe el estudiante B dado que el estudiante A aprueba.