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2 years ago

(4x + 17) What is the measure of AC ? Enter your answer in the box. (4x – 3.5)

Mathematics

1 answer:

Natasha2012 [34]2 years ago

3 0

Answer: $AC=41\°$

Step-by-step explanation:

<h3> The complete exercise is attached.</h3>

For this exercise it is important to remember that, by definition, if an angle formed by two intersecting chords has its vertex on a circle, this is called an "Inscribed angle".

The following formula is used to calculate the measure of an Inscribed angle:

$Inscribed\ angle = \frac{1}{2}\ Intercepted\ Arc$

You can identify in the figure that:

$Inscribed\ angle=ABC=(4x -3.5)\\\\Intercepted\ Arc=AC=(4x + 17)$

Then you can substitute values into the formula and solve for "x":

$(4x -3.5)= \frac{1}{2}(4x + 17)\\\\8x-7=4x+17\\\\4x=24\\\\x=6$

Then, AC is:

$AC=(4(6)+ 17)\\\\AC=24+17\\\\AC=41\°$

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Suppose you have 5 riders and 5 horses, and you want to pair them off so that every rider is assigned one horse (and no horse is

maw [93]

There are 120 ways in which 5 riders and 5 horses can be arranged.

We have,

5 riders and 5 horses,

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We know that,

Now,

Using the arrangement formula of Permutation,

i.e.

The total number of ways $^nN_r = \frac{n!}{(n-r)!}$ ,

So,

For n = 5,

And,

r = 5

As we have,

n = r,

So,

Now,

Using the above-mentioned formula of arrangement,

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Substituting values,

We get,

$^5N_5 = \frac{5!}{(5-5)!}$

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The total number of ways of arrangement = 5! = 5 × 4 × 3 × 2 × 1 = 120,

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There are 120 ways to arrange horses for riders.

Hence we can say that there are 120 ways in which 5 riders and 5 horses can be arranged.

Learn more about arrangements here

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1 year ago

Which algebraic expression is a polynomial? Which term could be put in the blank to create a fully simplified polynomial written

kifflom [539]

Answer:

$x^3y$ and $x^2y^2$

Step-by-step explanation:

An algebraic expression is a polynomial if and only if the variables involve have positive integral indices or exponents.

The given polynomial is: $8x^3y^2----------+3xy^2$

We want to put one of the following polynomials in the blank space to create a fully simplified polynomial written in standard form.

$-4y^3$

$x^2y^2$

$x^3y$

$7x^2y$

$7x^0y^3$

A fully simplified polynomial written in standard form is obtained by writing the simplified polynomial in decreasing order according to degree.

Since the first term of $8x^3y^2----------+3xy^2$ having a degree of 5 and the last term is having a degree of 3.

The polynomial that goes into the blank must have a degree of 4.

This eliminates $-4y^3$ , $7x^2y$

and $7x^0y^3$

We are now left with $x^2y^2$ and $x^3y$

The required polynomial is therefore $8x^3y^2-x^2y^2+3xy^2$ or $8x^3y^2-x^3y+3xy^2$

These two polynomials are in standard form and cannot be simplified further.

The correct choices are;

$x^3y$ and $x^2y^2$

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2 years ago

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2 years ago

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A production line operation is designed to fill cartons with laundry detergent to a mean weight of 32 ounces. A sample of carton

Tema [17]

Answer:

See explanation below

Step-by-step explanation:

Given a mean of 32. The claim here is that the mean is 32.

Therefore, the null hypothesis and alternative hypothesis, would be:

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Ha: u ≠ 32

b) When we fail to reject null hypothesis, H0. This means that the mean weight, u = 32

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c) When null hypothesis, H0 is rejected. This means the mean weight, u ≠ 32.

Conclusion: There is enough evidence to conclude that overfilling or underfilling exists

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