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3 years ago

In Triangle ABC, Sin B= 9/38. What is the value of the hypotenuse in the triangle?

Mathematics

1 answer:

Montano1993 [528]3 years ago

8 0

The definition of sine is "opposite / hypotenuse".
So, it is safe to assume that hypotenuse = 38.

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Solve for x & y. 30x−42y=−6 and 5x−7y=−1

vladimir1956 [14]

Um.. Both of those equations are the exact same. Divide both sides of the first equation by 6. You get:

$\frac{30x - 42y}{6} = \frac{-6}{6} \\ 5x - 7y = -1$

That is the exact same as the second equation. This system has an infinite number of solutions. 5x - 7y = -1 is a line, so basically every point on that line is a solution to the system.

For example, $x = 0$ and $y = \frac{1}{7}$ would work, but so would $x = 1$ and $y = \frac{6}{7}$

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2 years ago

(5×^2-4x-1)-(4x^2-4) how do i simplify this

castortr0y [4]

Simplify whatever is in the parenthesis:

(5×^2-4x-1) and <span>(4x^2-4)

after that subtract the numbers you got from both </span>parenthesis after simplifying

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2 years ago

AB contains points (2, 1) and (-1, -8). What is the equation of the line parallel to AB that contains point (0, 2)?

Iteru [2.4K]

For this case we have that by definition, the equation of a line in the slope-intersection form is given by:

$y = mx + b$

Where:

m: It's the slope

b: It is the cut-off point with the y axis

We have two points that belong to the AB line:

$(x_ {1}, y_ {1}) :( 2,1)\\(x_ {2}, y_ {2}): (- 1, -8)$

We can find the slope:

$m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {-8-1} {- 1-2} = \frac {-9} {- 3} = 3$

By definition, if two lines are parallel then their slopes are equal. Thus, a line parallel to AB will have slope $m = 3$ , then the equation will be of the form:

$y = 3x + b$

We substitute the given point and find b:

$(x, y) :( 0,2)\\2 = 3 (0) + b\\2 = b$

Finally, the equation is:

$y = 3x + 2$

Answer:

$y = 3x + 2$

7 0

2 years ago

3a - 17 < 34<br><br> Solve the following inequality

Dafna11 [192]

3a = 34 + 17
a = 51/3 = 17

Plz replace the equal sign with less than sign

8 0

2 years ago

A square is inscribed in a circle as shown. If the radius of the circle is 9, what is the area of the shaded region, rounded to

djyliett [7]

Answer:

Area of shaded region is:

A = 92.41

Step-by-step explanation:

(As the diagram is not shown, consider the diagram attached below.)

r = 9

Diagonal of the square = 2r = 18

As all angles of square are of 90°

The diagonal is dividing the angles into 2 halves of 45° at point where diagonal is joining the corner.

Taking sine:

$sin\theta=\frac{perpendicular}{hypotenuse}\\perpendicular = s\\hypotenuse = 2r = 18\\\theta = 45^\circ\\Substitute:\\sin45=\frac{s}{18}\\sin45\cdot18=s\\s=12.73$

<h3>Area of Circle:</h3>

$A=\pi{r}^2\\A=\pi{9}^2\\A=254.34$

<h3>Area of Square:</h3><h3> $Area = s\cdot{s}\\Area=12.73\cdot12.73\\Area = 161.93$ </h3><h3>Area of Shaded Region:</h3>

Area of circle - Area of square

$A = 254.34-161.93\\A=92.41$

3 0

3 years ago