All categories

3 years ago

Find w and y without a calculator, will give brainliest for the correct answer

Mathematics

1 answer:

love history [14]3 years ago

6 0

Answer: w=4, y=4

Step-by-step explanation:

For this problem, we can use the 30-60-90 triangle to find out what the length of w and y are. 30-60-90 triangle is a special triangle. The hypotenuse is 2x in length. It is directly opposite the right angle. The leg opposite of 60° is x√3 in length. The leg opposite of 30° is x. For all 3 legs, wherever you see x, you plug in the same number.

We can look at the figure as 2 separate triangles.

For the triangle on the right, we can see the hypotenuse is 8. Since we know the length of the hypotenuse is 2x, we can plug in 8 for 2x to find x.

2x=8

x=4

Now that we know x=4, we can directly plug it into the lengths above.

W is across from 30°. Above, we have established that the leg across from 30° has the length of x. Since x=4, w=4.

Since w=4, we can use this information to find the length of y by looking on the left triangle. Now, y is across from 30°. In the first paragraph, we stated that the leg across from 30° is x. Since we know x, we can directly plug it into this. After we plug it in, y=4.

You might be interested in

According to the MIT Airline Data Project, American Airlines controlled 15.5% of the domestic market during a recent year. A ran

andrey2020 [161]

Answer:

$P(20$

And we can use the z score given by:

$z = \frac{x-\mu}{\sigma}$

And if we find the z score for 20 and 25 we got:

$z = \frac{20-19.375}{4.046}=0.154$

$z = \frac{25-19.375}{4.046}=1.390$

And we have the probability given by:

$P(20$

And we can find this probbaility with this difference:

$P(0.154< Z$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=125, p=0.155)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

We need to check the conditions in order to use the normal approximation.

$np=125*0.155=19.375 \geq 10$

$n(1-p)=125*(1-0.155)=105.625 \geq 10$

So we see that we satisfy the conditions and then we can apply the approximation.

If we appply the approximation the new mean and standard deviation are:

$E(X)=np=125*0.155=19.375$

$\sigma=\sqrt{np(1-p)}=\sqrt{125*0.155(1-0.155)}=4.046$

So then we can approximate the random variable like this:

$X\sim N(\mu = 19.375 , \sigma=4.046)$

And we are interested on this probability:

$P(20$

And we can use the z score given by:

$z = \frac{x-\mu}{\sigma}$

And if we find the z score for 20 and 25 we got:

$z = \frac{20-19.375}{4.046}=0.154$

$z = \frac{25-19.375}{4.046}=1.390$

And we have the probability given by:

$P(20$

And we can find this probbaility with this difference:

$P(0.154< Z$

4 0

3 years ago

The graphs below have the same shape.What is the equation of the red graph?

Alika [10]

$\bf ~\hspace{10em}\textit{function transformations} \\\\\\ \begin{array}{llll} f(x)= A( Bx+ C)^2+ D \\\\ f(x)= A\sqrt{ Bx+ C}+ D \\\\ f(x)= A(\mathbb{R})^{ Bx+ C}+ D \end{array}\qquad \qquad \begin{array}{llll} f(x)=\cfrac{1}{A(Bx+C)}+D \\\\\\ f(x)= A sin\left( B x+ C \right)+ D \end{array} \\\\---------------------------------$

$\bf \bullet \textit{ stretches or shrinks horizontally by } A\cdot B\\\\ \bullet \textit{ flips it upside-down if } A\textit{ is negative}\\ ~~~~~~\textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if } B\textit{ is negative}\\ ~~~~~~\textit{reflection over the y-axis} \\\\ \bullet \textit{ horizontal shift by }\frac{ C}{ B}\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is negative, to the right}$

$\bf ~~~~~~if\ \frac{ C}{ B}\textit{ is positive, to the left}\\\\ \bullet \textit{ vertical shift by } D\\ ~~~~~~if\ D\textit{ is negative, downwards}\\\\ ~~~~~~if\ D\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{ B}$

keeping that template in mind, the g(x) function is just a translated version of f(x), it is translated upwards by 2 units, namely D = 2.

$\bf f(x)=3-x^4\implies f(x)=\stackrel{A}{-1}(\stackrel{B}{1}x+\stackrel{C}{0})^4+\stackrel{D}{3}\implies \stackrel{\textit{shifted upwards by 2 units}}{f(x)=\stackrel{A}{-1}(\stackrel{B}{1}x+\stackrel{C}{0})^4+\stackrel{D}{3+2}} \\\\\\ f(x)=-1(1x+0)^4+5\implies f(x)=-x^4+5\implies f(x)=5-x^4=g(x)$

3 0

3 years ago

Read 2 more answers

Anita, Byron, Carlos, and Dominique buy a gift for their grandmother. They split the cost equally and each pay $14.62. Which equ

Natasha_Volkova [10]

$14.62 = d / 4

Here is one variation of an equation that satisfies your request. You could also put the amount of people as a variable, or the total amount paid.

8 0

3 years ago

Read 2 more answers

The rectangle below represents the base of a rectangular prism.

ki77a [65]

Answer:

its 2. 20cm³ or 3. 32cm³

Step-by-step explanation:

I'm dont know if im right because the picture is asking for something different then the question

4 0

3 years ago

Read 2 more answers

Part A: Explain why x = 5 makes 4x - 1 3 19 true but not 4x - 1 19

Olenka [21]

Answer:

Part A: Explain why x = 5 makes 4x - 1 ≤ 19 true but not 4x - 1 < 19

Part B: x=9

Step-by-step explanation:

Part A: Because the first one is less than or equal to 19 and the other is just less than.

x = 5

TRUE: 4x - 1 ≤ 19 = 20-1 ≤ 19 = 19 ≤ 19

19 is less than or equal to 19 so its true

FALSE: 4x - 1 < 19 = 19 < 19

19 is not greater than 19

Part B:

5x + 2 = 47 subtract 2 from both sides

5x = 45 divide both sides by 5

x = 9

To check we can plug it back in

5x + 2 = 47

5(9) + 2 = 47

45 + 2 = 47

47 = 47

TRUE

5 0

3 years ago