Answer:
10.63.
Step-by-step explanation:
First we need to understand pythagorean theorem that is,
Hypotenuse^2=perpendicular^2+base^2.
=7^2+8^2.
=49+64
=113.
Hypotenuse^2=113.
Square root both sides.
Hypotenuse=10.63.
On the first question, the formula would be m=\frac{y2-y1}{x2-x1} and the value we got is -4/3, so D.
On the second quesiton, the slope in the given equation of the line is -2, its negative reciprocal is 1/2, so A.
On the third question, use the slope formula above and the value you would get is zero, so A.
On the fourth question, the equation of the line perpendicular to line QR is y=2x+b, to find b, just substitute the point (5,6) to the equation. That would make b = -4. the final equation of the line would be: y=2x-4, so D.
On the fifth question, the equation of the line parallel to line QR is y = -2x + b. substitute the point (4,5) to the equation, and you'll get b = 13. the final equation of the line would be y=-2x+13, so A.
Answer:
= 1 5/16
[/tex] 1 \frac{5}{16}[/tex]
Step-by-step explanation:
![\frac{8}{5} (2x + 13) - 3 = 22](https://tex.z-dn.net/?f=%20%5Cfrac%7B8%7D%7B5%7D%20%282x%20%2B%2013%29%20-%203%20%3D%2022)
Expand
![\frac{16}{5} x + \frac{104}{5} - 3 = 22 \\ \frac{16}{5} x + \frac{89}{5} = 2](https://tex.z-dn.net/?f=%20%5Cfrac%7B16%7D%7B5%7D%20x%20%2B%20%20%5Cfrac%7B104%7D%7B5%7D%20%20-%203%20%3D%2022%20%5C%5C%20%20%5Cfrac%7B16%7D%7B5%7D%20x%20%2B%20%20%5Cfrac%7B89%7D%7B5%7D%20%20%3D%202)
Collect like terms and simplify
![\frac{16}{5} x = 22 - \frac{89}{5} \\ \frac{16}{5} x = \frac{21}{5}](https://tex.z-dn.net/?f=%20%5Cfrac%7B16%7D%7B5%7D%20x%20%3D%2022%20-%20%20%5Cfrac%7B89%7D%7B5%7D%20%20%5C%5C%20%20%5Cfrac%7B16%7D%7B5%7D%20x%20%3D%20%20%5Cfrac%7B21%7D%7B5%7D%20)
Cross Multiply
![80x = 105](https://tex.z-dn.net/?f=80x%20%3D%20105)
Divide both sides of the equation by 80
![\frac{80x}{80} = \frac{105}{80} \\ x = \frac{21}{16}](https://tex.z-dn.net/?f=%20%5Cfrac%7B80x%7D%7B80%7D%20%20%3D%20%20%5Cfrac%7B105%7D%7B80%7D%20%20%5C%5C%20x%20%3D%20%20%5Cfrac%7B21%7D%7B16%7D%20)
360=x+x+(2x+3)+(2x+3)
we have 360=2x+2x+2x+6
360-6=6x
354=6x
x=354/6=59
x=59
Answer:
Step-by-step explanation:
Let us first find the hypotenuses of the right triangle.
![c=\sqrt{12^2+9^2} =\sqrt{225} = 15](https://tex.z-dn.net/?f=c%3D%5Csqrt%7B12%5E2%2B9%5E2%7D%20%3D%5Csqrt%7B225%7D%20%3D%2015)
![sin(theta) = 12/15 = 4/5\\cos(theta) = 9/15 = 3/5\\tan(theta) = 12/9 = 4/3\\csc(theta) = sin(theta)^{-1} = 5/4\\sec(theta) = cos(theta)^{-1} = 5/3\\cot(theta) = tan(theta)^{-1} = 3/4](https://tex.z-dn.net/?f=sin%28theta%29%20%3D%2012%2F15%20%3D%204%2F5%5C%5Ccos%28theta%29%20%3D%209%2F15%20%3D%203%2F5%5C%5Ctan%28theta%29%20%3D%2012%2F9%20%3D%204%2F3%5C%5Ccsc%28theta%29%20%3D%20sin%28theta%29%5E%7B-1%7D%20%20%3D%205%2F4%5C%5Csec%28theta%29%20%3D%20cos%28theta%29%5E%7B-1%7D%20%3D%205%2F3%5C%5Ccot%28theta%29%20%3D%20tan%28theta%29%5E%7B-1%7D%20%3D%203%2F4)