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3 years ago

Explain why the value of sine ratio for an acute angle of a right triangle must always be a positive value less than 1

Mathematics

2 answers:

kotykmax [81]3 years ago

5 0

Answer:

Step-by-step explanation:

The sine ratio is the length of the side opposite a given acute angle divided by the length of the hypotenuse. Because the hypotenuse is the side opposite the largest angle, the 90° angle, it has to be the longest side. Thus, the ratio will have a denominator that is larger than the numerator, and the ratio will be less than 1.

weqwewe [10]3 years ago

4 0

Answer: See below.

The sine ratio is the ratio of the opposite side over the hypotenuse in a right triangle. The hypotenuse is always the largest side of a triangle.

Therefore, the denominator will always be the largest. If the denominator is larger than the numerator, it will be a number less than one.

And it will be positive because it is an acute angle so the triangle when plotting in the unit circle would only be in the first quadrant. All values in the first quadrant are positive.

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Solve the linear system by graphing y=x+2 and y=-6x+9

skelet666 [1.2K]

Answer:

(1, 3)

General Formulas and Concepts:

Algebra I

Coordinates (x, y)
Reading a Cartesian (Rectangular) plane
Solving systems of equations by graphing

Step-by-step explanation:

Where the 2 lines intersect will be the solution set to the systems of equations.

If the lines are parallel, they will have no solution.

If the lines are the same, they will have infinite amount of solutions.

6 0

3 years ago

Which equation is y = –6x^2 + 3x + 2 rewritten in vertex form? y = negative 6 (x minus 1) squared + 8 y = negative 6 (x + one-fo

mart [117]

Answer:

$y = -6(x - \frac{1}{2})^2 -\frac{7}{2}$

Step-by-step explanation:

Given:

$y = -6x^2 + 3x + 2$

Required

Rewrite in vertex form

The vertex form of an equation is in form of: $y = a(x - h)^2+ k$

Solving: $y = -6x^2 + 3x + 2$

Subtract 2 from both sides

$y - 2 = -6x^2 + 3x + 2 - 2$

$y - 2 = -6x^2 + 3x$

Factorize expression on the right hand side by dividing through by the coefficient of x²

$y - 2 = -6(x^2 + \frac{3x}{-6})$

$y - 2 = -6(x^2 - \frac{3x}{6})$

$y - 2 = -6(x^2 - \frac{x}{2})$

Get a perfect square of coefficient of x; then add to both sides

------------------------------------------------------------------------------------

Rough work

The coefficient of x is $\frac{-1}{2}$

It's square is $(\frac{-1}{2})^2 = \frac{1}{4}$

Adding inside the bracket of $-6(x^2 - \frac{x}{2})$ to give: $-6(x^2 - \frac{x}{2} + \frac{1}{4})$

To balance the equation, the same expression must be added to the other side of the equation;

Equivalent expression is: $-6(\frac{1}{4})$

------------------------------------------------------------------------------------

The expression becomes

$y - 2 -6(\frac{1}{4})= -6(x^2 - \frac{x}{2} + \frac{1}{4})$

$y - 2 -\frac{6}{4}= -6(x^2 - \frac{x}{2} + \frac{1}{4})$

$y - 2 -\frac{3}{2}= -6(x^2 - \frac{x}{2} + \frac{1}{4})$

Factorize the expression on the right hand side

$y - 2 -\frac{3}{2}= -6(x - \frac{1}{2})^2$

$y - (2 +\frac{3}{2})= -6(x - \frac{1}{2})^2$

$y - (\frac{4+3}{2})= -6(x - \frac{1}{2})^2$

$y - (\frac{7}{2})= -6(x - \frac{1}{2})^2$

$y +\frac{7}{2} = -6(x - \frac{1}{2})^2$

Make y the subject of formula

$y = -6(x - \frac{1}{2})^2 -\frac{7}{2}$

Solved

7 0

3 years ago

Read 2 more answers

A grocer bought n eggs at $x each. He marked up the price of each egg by $y and sold all of them. Find the sales amount, express

Alex777 [14]

Answer:

Sales = n $\times$ ($x + $y)

Step-by-step explanation:

The basic simple sales equation is

Quantity $\times$ Price = Sales

Here in the given question,

Total quantity of sales = n

Price = Cost + markup

(Markup refers to the profit added to cost)

Thus price = $x (cost) + $y (markup)

Sales = n $\times$ ($x + $y)

Sales amount is the total amount received from sales of products, total quantity at some price provided.

4 0

2 years ago

A national organization has been working with utilities throughout the nation to find sites for large wind machines that generat

kap26 [50]

Answer:

B) At alpha = 0.01, there is insufficient evidence to conclude the true mean wind speed at the site exceeds 25 mph.

Step-by-step explanation:

P-value of the test:

The p-value of the test is the probability of finding a sample mean above 25.

We are using the t-distribution, with test statistic t = 1.25 and 43 - 1 = 42 degrees of freedom. This probability is a right-tailed test.

With the help of a calculator, this p-value is of 0.1091.

Since the p-value of the test is 0.1091 > 0.01, at $\alpha = 0.01$ there is insufficient evidence to conclude the true mean wind speed at the site exceeds 25 mph, and the correct answer is given by option B.