See attachment

then we add 7 and 5 and divide that by 2, which gives you 6 (x-coordinate)
and add 10 and -8 and divide that by 2, which gives you 1 (y-coordinate)

the answer is (6, 1)

justification
so midpoint is basically the middle point of 2 points
that's why we have to add the two x coordinates first then divide it by 2
or add the two y coordinates then divide it by 2

8 0

3 years ago

If 180°<α<270°, cos ⁡α= −8/17, 270°<β<360°, and sin β= −4/5, what is sin⁡(α+β)?

mars1129 [50]

Answer:

$\sin(\alpha+\beta) = -0.153$

Step-by-step explanation:

Let determine the angles behind each trigonometric expression:

$\cos \alpha = -\frac{8}{17}$

$\alpha = \cos^{-1}\left(-\frac{8}{17} \right)$

Given that $180^{\circ}< \alpha < 270^{\circ}$ , the value of $\alpha$ is:

$\alpha \approx 241.928^{\circ}$

$\sin \beta = -\frac{4}{5}$

$\beta = \sin^{-1}\left(-\frac{4}{5} \right)$

Given that $270^{\circ}< \beta$ , the value of $\beta$ is:

$\beta \approx 306.870^{\circ}$

The sine function of the sum of angles can be determined by the following identity:

$\sin(\alpha + \beta)=\sin \alpha \cdot \cos \beta + \sin \beta \cdot \cos \alpha$

If $\alpha \approx 241.928^{\circ}$ and $\beta \approx 306.870^{\circ}$ , then:

$\sin (241.928^{\circ}+306.870^{\circ}) = (\sin 241.928^{\circ}) \cdot (\cos 306.870^{\circ}) + (\sin 306.870^{\circ})\cdot (\cos 241.928^{\circ})$ $\sin(241.928^{\circ}+306.870^{\circ}) = -0.153$

7 0

4 years ago

Separate the number 219 into three parts. The second number is two less than 5 times the first number, and the third number is 4

Sav [38]

Let us assume the first number = x
Then the second number = 5x -2
The third number = x + 4
The total number that needs to be divided into three parts is 219
Then we can write the equation as
x + 5x - 2 + x + 4 = 219
7x + 2 = 219
7x = 219 - 2
7x = 217
x = 217/7
= 31
Then
First number = 31
Second number = 5x - 2
   = (5 * 31) - 2
   = 155 -2
= 153
Third number = x + 4
   = 31 + 4
   = 35
So the three numbers are 31, 153 and 35.

4 0

3 years ago