What is (34-23)+5? answer

The angle θ 1 is located in Quadrant IV, and cos ⁡ ( θ 1 ) = 9/ 19 , theta, start subscript, 1, end subscript, right parenthesis

Firdavs [7]

Answer:

$sin\theta_1 = - \frac{2\sqrt{70}}{19}$

Step-by-step explanation:

We are given that $\theta_1$ is in fourth quadrant.

$cos\theta_1$ is always positive in 4th quadrant and

$sin\theta_1$ is always negative in 4th quadrant.

Also, we know the following identity about $sin\theta$ and $cos\theta$ :

$sin^2\theta + cos^2\theta = 1$

Using \theta_1 in place of \theta:

$sin^2\theta_1 + cos^2\theta_1 = 1$

We are given that $cos\theta_1 = \frac{9}{19}$

$\Rightarrow sin^2\theta_1 + \dfrac{9^2}{19^2} = 1\\\Rightarrow sin^2\theta_1 = 1 - \dfrac{81}{361}\\\Rightarrow sin^2\theta_1 = \dfrac{361-81}{361}\\\Rightarrow sin^2\theta_1 = \dfrac{280}{361}\\\Rightarrow sin\theta_1 = \sqrt{\dfrac{280}{361}}\\\Rightarrow sin\theta_1 = +\dfrac{2\sqrt{70}}{19}, -\dfrac{2\sqrt{70}}{19}$

$\theta_1$ is in 4th quadrant so $sin\theta_1$ is negative.

So, value of $sin\theta_1 = - \frac{2\sqrt{70}}{19}$

6 0

3 years ago

2x-5) = 2(x-5) One Solution Infinitely Many Solutions No Solution 5x + 4) = 5(1-6) 5(x + 4) = 3(x-6) 4x - 2) = 4(x + 2) x + 2(x-

Gekata [30.6K]

9514 1404 393

Answer:

top down: ∞, 0, 1, 0, ∞

Step-by-step explanation:

The equation will have infinite solutions when the left side and right side simplify to the same expression. This is the case for the first and last expressions listed.

2(x -5) = 2(x -5) . . . . expressions are already identical

x +2(x -5) = 3(x -2) -4 ⇒ 3x -10 = 3x -10 . . . the same simplified expression

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The equation will have no solutions when the x-coefficients are the same, but there are different added constants.

5(x +4) = 5(x -6) ⇒ x +4 = x -6 . . . not true for any x

4(x -2) = 4(x +2) ⇒ x -2 = x +2 . . . not true for any x

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The equation will have one solution when coefficients of x are different.

5(x +4) = 3(x -6) ⇒ 2x = -38 ⇒ x = -19

4 0

3 years ago

What is the GCF of h4 and h8

Naily [24]

The greatest common factor is to h4 and h8 is 4

7 0

3 years ago

MANUFACTURING A shoe manufacturer spends $2.50 to make sandals and $4 to make running shoes. During a typical month, they spend

jonny [76]

Answer:

200 pairs of sandals

Step-by-step explanation:

Represent the sandals with x and the running shoes with y.

In a typical month:

$Total = 2500$

In April

$Total = 3000$

Required

The number of sandals in a typical month

In a typical month:

If 1 sandal costs 2.50, then x costs 2.50x

If 1 running shoe costs 4, then y costs 4y

The total is:

$2.50x + 4y = 2500$

In April:

If 1 sandal costs 2.50, then 2x costs 5x ---- we used 2x because the pairs is doubled

If 1 running shoe costs 4, then y costs 4y

The total is:

$5x + 4y = 3000$

The equations are:

$5x + 4y = 3000$

$2.50x + 4y = 2500$

Subtract

$5x - 2.50x + 4y - 4y = 3000 - 2500$

$2.50x = 500$

$x = \frac{500}{2.50}$

$x = 200$

8 0

3 years ago

Right triangle ABC is on a coordinate plane. Segment AB is on the line y = 2 and is 3 units long. Point C is on the line x = -1.

IgorLugansk [536]

Answer:

The possible y-coordinate of point C is 6

Step-by-step explanation:

The coordinate of a point is given by (x,y) where x is the horizontal distance from the origin on the x axis and y is the vertical distance from the origin.

Given Segment AB is on the line y = 2 and is 3 units long and Segment AB is on the line y = 2 and is 3 units long. The area of triangle ABC is 6 square units.

The area of a triangle = 1/2 × base × height

6 = 1/2 × 3 × height

height = (2 × 6) / 3 = 4 units

Since point C is perpendicular to line y = 2, they coordinates is either 2 + 4 = 6 or 2 - 4 = -2

The coordinate of point C is either (-1, 6) or (-1, -2)

7 0

3 years ago