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3 years ago

Find the measure of angle y

Mathematics

1 answer:

chubhunter [2.5K]3 years ago

5 0

<h2><u>ISOSCELES TRIANGLE</u></h2>

An isosceles triangle is a triangle that has two sides of equal length. In this exercise, we see small lines on two of the sides. This means that those sides are equal.

‎ ‏‏‎

Equalize the expressions:

Add 23 to both sides of the equation:

6x - 23 + 23 = 4x + 9 + 23

‎ ‏‏‎‎ ‏‏‎‎ 6x = 4x + 32

Substract 4x from both sides:

6x - 4x = 4x - 4x + 32

‏‏‎‎ 2x = 32

Finally, divide both sides by 2:

$\mathsf{\dfrac{2x}{2} = \dfrac{32}{2}}$

$\large{\boxed{\mathsf{x = 16}}}$

‎ ‏‏‎

Now, let's find the measures of the angles:

(6x - 23)° = 6(16) - 23 = 96 - 23 = 73°
(4x + 9)° = 4(16) + 9 = 64 + 9 = 73°

‎ ‏‏‎

Remember: The sum of the three angles of any triangle is equal to 180 degrees. Let's find the measure of the angle Y:

73° + 73° + Y = 180°

146° + Y = 180°

Y = 180° - 146°

Y = 34°

‎ <u>‏‏‎</u>

<h3><u>Answer</u>. m∠Y = 34°</h3>

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3 years ago

Match the confidence level with the confidence interval for the population mean. type the correct letter in each box. equation e

Ainat [17]

Answer:

$\bar X \pm 1.96 \frac{\sigma}{\sqrt{n}}$

"=1-2*(1-NORM.DIST(1.96,0,1,TRUE))"

And we got 95%

$\bar X \pm 1.645 \frac{\sigma}{\sqrt{n}}$

"=1-2*(1-NORM.DIST(1.645,0,1,TRUE))"

And we got 90%

$\bar X \pm 2.575 \frac{\sigma}{\sqrt{n}}$

"=1-2*(1-NORM.DIST(2.575,0,1,TRUE))"

And we got 99%

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

For this case we have the following cases:

$\bar X \pm 1.96 \frac{\sigma}{\sqrt{n}}$

And for this case we can find the % of confidence with the following excel code:

"=1-2*(1-NORM.DIST(1.96,0,1,TRUE))"

And we got 95%

For the other case:

$\bar X \pm 1.645 \frac{\sigma}{\sqrt{n}}$

And for this case we can find the % of confidence with the following excel code:

"=1-2*(1-NORM.DIST(1.645,0,1,TRUE))"

And we got 90%

For the other case:

$\bar X \pm 2.575 \frac{\sigma}{\sqrt{n}}$

And for this case we can find the % of confidence with the following excel code:

"=1-2*(1-NORM.DIST(2.575,0,1,TRUE))"

And we got 99%

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3 years ago

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2 years ago

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Archy [21]

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3 years ago

1. The sum of x and -45 is at most 35

Lorico [155]

Answer:

The given set of equation are: x+ (-45) ≤ 35 , x - (-45) ≥ 35

For the given equality to be true, x ≤ 35

Step-by-step explanation:

Here, given the first number = x

Second number = -45

Now, Sum of x and - 45 is at most 35.

⇒ x+ (-45) ≤ 35

Also, The difference of x and -45 is at least 35.

⇒ x - (-45) ≥ 35

Now, simplifying the given set of equations:

x - 45 ≤ 35 ⇒ -x - (-45) > - 35 ( as 3 < 4 ⇒ -3 > -4)

or, -x + 45 > - 35

and second equation is x + 45 ≥ 35

Now, solving both the equations by not taking sign of inequality in to the consideration, we get

x - 45 = 35

x + 45 = 35

Adding both equations,we get: ⇒ 2x = 70

or x = 35

Hence for the given equality to be true, x ≤ 35

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3 years ago