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3 years ago

Analyze the diagram below and complete the instructions that follow.

Mathematics

2 answers:

earnstyle [38]3 years ago

8 0

When you have a right triangle with 45 degrees as shown
the hypotenuse would be the length of the side times sqrt(2)

so the side length for this would be 4

topjm [15]3 years ago

3 0

The value of x is $\boxed{4{\text{ units}}}.$ Option (B) is correct.

Further explanation:

The Pythagorean formula can be expressed as,

$\boxed{{H^2} = {P^2} + {B^2}}.$

Here, H represents the hypotenuse, P represents the perpendicular and B represents the base.

The formula for sin of angle a can be expressed as

$\boxed{\sin a = \frac{P}{H}}$

The formula for cos of angle a can be expressed as

$\boxed{\cos a = \frac{B}{H}}$

The formula for tan of angle a can be expressed as

$\boxed{\tan a = \frac{P}{B}}$

Given:

The options are as follows,

(A). $\frac{{4\sqrt 2 }}{2}$

(B).4

(C). $4\sqrt 2$

(D). $4\sqrt 3$

Explanation:

The hypotenuse of the triangle is $4\sqrt 2.$

The perpendicular of the triangle is x.

Consider the base of triangles as y.

The value of x can be calculated as follows,

$\sin {45^ \circ }=\dfrac{x}{{4\sqrt 2 }}$

The value of $\sin {45^\circ } \:{\text{is}\:\dfrac{1}{{\sqrt 2 }}.$

$\begin{aligned}\frac{1}{{\sqrt 2 }}&=\frac{x}{{4\sqrt 2 }}\\\frac{{4\sqrt 2 }}{{\sqrt 2 }}&= x\\4&=x\\\end{aligned}$

The value of x is $\boxed{4{\text{ units}}}.$ Option (B) is correct.

Option (A) is not correct.

Option (B) is correct.

Option (C) is not correct.

Option (D) is not correct.

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Trigonometry

Keywords: perpendicular bisectors, sides, right angle triangle, triangle, altitudes, hypotenuse, on the triangle, hypotenuse, trigonometric functions.

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In one year the perseid metor shower had a metor appear every 1/5 5 minutes on average That same year the Leonid metor shower ha

olga55 [171]

In one year, the Perseid meteor shower had a meteor appear every 1 1/5 minutes on average. That same year, the Leonid meteor shower had a meteor appear every 4 2/3 minutes on average. How many more meteors fell during the Perseid meteor shower?

Answer:

325,452 meteors

Step-by-step explanation:

We all know that :

We have 365 days in a year and in each day there are 24 hours, Likewise an hour has 60 minutes

SO, the total number of minutes in a year is :

365 × 24 × 60 = 525600 minutes

For Perseid meteor:

$1 + \frac{1}{5} \\ \\ = 1 + 0.2 \\ \\ = 1.2$

So one meteor fall at 1.2 minutes interval Thus, in a year, we will have :

1 meteor - 1.2 minutes.

x meteor - 525600 minutes.

1.2x = 525600

$x = \frac{525600}{1.2}$

x = 438000

∴ 438,000 meteors fell during the Perseid shower.

For Leonid meteor shower:

$4 + \frac{2}{3} = 4.67$

So one meteor fall at 4.67 minutes interval Thus, in a year, we will have :

1 meteor - 4.67 minutes.

x meteors - 525600 minutes.

$4.67x = 525600$

$x = \frac{525600}{4.67}$

x = 112548

112,548 meteors fell during the Leonid Shower.

Finally , the numbers of more meteors that fell during the Perseid meteor shower is calculated by the difference in the number of Perseid meteor shower and Lenoid meteor shower. i.e

438,000 - 112,548 = 325,452

325,452 more meteors fell during the Perseid meteor shower

5 0

3 years ago

How can you evaluate this expression using the distributive property? 5×(7+6)

Sveta_85 [38]

Answer:

35+30=65

Step-by-step explanation:

3 0

4 years ago

Read 2 more answers

8/x-5 - 9/x-4 = 5/x^2-9x+20

adelina 88 [10]

If you're using the app, try seeing this answer through your browser: brainly.com/question/2752942

_______________

Solve the equation:

$\mathsf{\dfrac{8}{x-5}-\dfrac{9}{x-4}=\dfrac{5}{x^2-9x+20}\qquad\qquad(x\ne 5~and~x\ne 4)}$

Reduce the fractions at the left side so that they have the same denominator:

$\mathsf{\dfrac{8(x-4)}{(x-5)(x-4)}-\dfrac{9(x-5)}{(x-4)(x-5)}=\dfrac{5}{x^2-9x+20}}\\\\\\
\mathsf{\dfrac{8x-32}{x^2-4x-5x+20}-\dfrac{9x-45}{x^2-4x-5x+20}=\dfrac{5}{x^2-9x+20}}\\\\\\
\mathsf{\dfrac{8x-32}{x^2-9x+20}-\dfrac{9x-45}{x^2-9x+20}=\dfrac{5}{x^2-9x+20}}\\\\\\
\mathsf{\dfrac{8x-32-(9x-45)}{x^2-9x+20}=\dfrac{5}{x^2-9x+20}}$

Numerators must be equal:

$\mathsf{8x-32-(9x-45)=5}\\\\
\mathsf{8x-32-9x+45=5}\\\\
\mathsf{8x-9x=5+32-45}\\\\
\mathsf{-x=-8}\\\\
\mathsf{x=8}\quad\longleftarrow\quad\textsf{this is the solution.}$

I hope this helps. =)

Tags: rational equation fraction solution algebra

7 0

3 years ago

The cost of a circular table is directly proportional to the square of the radius. A circular table with a radius of 50cm costs

Lana71 [14]

Answer:

£135 is the correct answer.

Step-by-step explanation:

Let C be the cost of table.

And let R be the radius of table.

Cost of table is directly proportional to square of radius.

As per question statement:

$C\propto R^{2}$ or

$C=a\times R^2 ....... (1)$

where $a$ is the constant to remove the $\propto sign$ .

It is given that

$C_1 =$ £60 and $R_1 = 50\ cm$

$C_2 = ?$ when $R_2= 75\ cm$

Putting the values of $C_1$ and $R_1$ in equation (1):

$60=a \times 50^2 ....... (2)$

Putting the values of $C_2$ and $R_2$ in equation (1):

$C_2=a \times 75^2 ....... (3)$

Dividing equation (2) by (3):

$\dfrac{60}{C_2}= \dfrac{a \times 50^2}{a \times 75^2}\\\Rightarrow \dfrac{60}{C_2}= \dfrac{50^2}{75^2}\\\Rightarrow \dfrac{60}{C_2}= \dfrac{2^2}{3^2}\\\Rightarrow \dfrac{60}{C_2}= \dfrac{4}{9}\\\Rightarrow C_2 = 15 \times 9 \\\Rightarrow C_2 = 135$

So, £135 is the correct answer.

7 0

3 years ago

3 more than the quotient of 18 and x

melisa1 [442]

Answer:

18/x + 3

Step-by-step explanation:

This can be written algebraically as 18/x +3. This question is a little unclear, but I think it’s asking to write it as an equation

6 0

2 years ago