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Nuetrik [128]
3 years ago
10

Find the length of side x in the simplest radical form with a rational denominator

Mathematics
1 answer:
chubhunter [2.5K]3 years ago
3 0

Answer:

The value of x = 1

Step-by-step explanation:

Given

  • hypotenuse = √2
  • angle Ф = 45°

To determine

x = ?

Using the trigonometric ratio

cos Ф = adjacent / hypotenuse

here

Ф = 45°

adjacent of 45° = x

hypotenuse = √2

so substituting Ф = 45°  adjacent = x and hypotenuse = √2  in the equation

cos Ф = adjacent / hypotenuse

\cos \left(45^{\circ \:}\right)=\frac{x}{\sqrt{2}}

switch sides

\frac{x}{\sqrt{2}}=\cos \left(45^{\circ \:}\right)

Multiply both sides by 2

\frac{2x}{\sqrt{2}}=2\cos \left(45^{\circ \:}\right)

\sqrt{2}x=\sqrt{2}             ∵  \cos \left(45^{\circ \:}\right)=\frac{\sqrt{2}}{2}

Divide both sides by √2

\frac{\sqrt{2}x}{\sqrt{2}}=\frac{\sqrt{2}}{\sqrt{2}}

x=1

Therefore, the value of x = 1

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The answer is 56%
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3 years ago
The value of a car decreases by 15% for each year the car is leased. If the original price of
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Answer:

Around 7830 dollars

Step-by-step explanation

Times 15,000 by 0.85, you'll get 12,750. Times each product by 0.85 and you'll get around 7830 dollars

6 0
2 years ago
A hardware store rents vacuum cleaners that customers may use for part or all of a day, up to 12 hours, before returning. The st
jek_recluse [69]

The flat fee that the store charges is $14 and the cost for 7 hours is $56

A linear equation is on the form:

y = mx + b

where y, x are variables, m is the rate of change and b is the initial value of y.

let f for the total rental cost of a vacuum cleaner for x hours

Using the points (1, 20) and (3, 32) from the table:

f-f_1=\frac{f_2-f_1}{x_2-x_1} (x-x_1)\\\\f-20=\frac{32-20}{3-1} (x-1)\\\\f(x)=6x+14

The flat fee that the store charges is $14

The reasonable domain is 1 ≤ x ≤ 12

The cost for 7 hours is:

f(7) = 6(7) + 14 = 46

Find out more on linear equation at: brainly.com/question/14323743

4 0
2 years ago
Simplify the following expression 6.187-0.36
yKpoI14uk [10]
To put add plus sign and minus sign, and it gives too negative 0.36, and the answer is equal to 5.827.

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6 0
3 years ago
Alison is learning how to walk. 50% of the time that she takes a step she falls down. Her older brother wants to design a simula
MissTica

Answer with explanation:

Alison is learning how to walk.50% of times she takes a step she falls down.

Probability of falling down in next step =\frac{50}{100}=\frac{1}{2}

Probability of not falling down in next step =\frac{50}{100}=\frac{1}{2}

From ,the four option given,we have to find the best simulation which her older brother wants to design a simulation to find the probability that she will fall down 5 out of the next 7 times she tries to take step.

While Simulating the Probability of falling down should be =\frac{5}{7}

And , probability of not falling down1-\frac{5}{7}=\frac{2}{7}

→→⇒F=Falling, NF=Non Falling

A) Roll a die letting 1 represent Alison falling and 2-6 represent Alison not falling. Roll the die five times.

P(F)=\frac{1}{6},P(NF)=\frac{5}{6}

Incorrect option,probabilities of falling and non falling does not match with Actual probability of falling and non falling.  

B) Roll a die letting 1 represent Alison falling and 2-6 represent Alison not falling. Roll the die seven times.

P(F)=\frac{1}{6},P(NF)=\frac{5}{6}

Incorrect option,probabilities of falling and non falling does not match with Actual probability of falling and non falling.

C) Let Heads represent Alison falling down and Tails representing Alison not falling down. Flip the coin five times.

P(F)=\frac{1}{2},P(NF)=\frac{1}{2}

Simulation is done only five times , that is coin has been flipped only five times.it must have been flipped seven times.Incorrect option.  

D) Let Heads represent Alison falling down and Tails representing Alison not falling down. Flip the coin seven times.

P(F)=\frac{1}{2},P(NF)=\frac{1}{2}

Simulation is done seven times , that is coin has been flipped seven times.So,she should fall 5 times that is head should appear 5 out of seven times, and tail should appear 2 out of seven times.correct option.

Option D

4 0
3 years ago
Read 2 more answers
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