Answer:
B
Step-by-step explanation:
The equation of the line is given by
y = mx + c
where m is the gradient of the line
c is where the line cuts the y-axis
x & y represent coordinates on the line.
The gradient m can be obtained as follows:
m = (5 - 8) / (5 - - 10) = (-3) / (15) = - 1/5
To obtain c, we use any known coordinate on the line and substitute it as well as the gradient in the general equation for the line.
Taking coordinates (5,5)
5 = (- 1/5)(5) + c
5 = - 1 + c
c = 6
Hence, the equation for this line is
y = -x/5 + 6
The answer would be D. It says the length is 10 millimeters less than TWICE the width, so it would be 10 millimeters greater than the original width.
Answer:
First triangle:
, second triangle: ![c = \frac{8\sqrt{3}}{3}](https://tex.z-dn.net/?f=c%20%3D%20%5Cfrac%7B8%5Csqrt%7B3%7D%7D%7B3%7D)
Step-by-step explanation:
In the first triangle, the value of
is equal to the following trigonometric relation:
![a = \frac{5}{\cos 45^{\circ}}](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7B5%7D%7B%5Ccos%2045%5E%7B%5Ccirc%7D%7D)
![a = \frac{5}{\frac{\sqrt{2}}{2} }](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7B5%7D%7B%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%20%7D)
![a = \frac{10}{\sqrt{2}}](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7B10%7D%7B%5Csqrt%7B2%7D%7D)
![a = \frac{10\sqrt{2}}{2}](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7B10%5Csqrt%7B2%7D%7D%7B2%7D)
![a = 5\sqrt{2}](https://tex.z-dn.net/?f=a%20%3D%205%5Csqrt%7B2%7D)
In the second triangle, we obtain the value of
is equal to the following trigonometric relation:
![c = 8\cdot \tan 30^{\circ}](https://tex.z-dn.net/?f=c%20%3D%208%5Ccdot%20%5Ctan%2030%5E%7B%5Ccirc%7D)
![c = 8 \cdot \left(\frac{\sin 30^{\circ}}{\cos 30^{\circ}} \right)](https://tex.z-dn.net/?f=c%20%3D%208%20%5Ccdot%20%5Cleft%28%5Cfrac%7B%5Csin%2030%5E%7B%5Ccirc%7D%7D%7B%5Ccos%2030%5E%7B%5Ccirc%7D%7D%20%5Cright%29)
![c = 8\cdot \left(\frac{\frac{1}{2} }{\frac{\sqrt{3}}{2} } \right)](https://tex.z-dn.net/?f=c%20%3D%208%5Ccdot%20%5Cleft%28%5Cfrac%7B%5Cfrac%7B1%7D%7B2%7D%20%7D%7B%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%20%7D%20%5Cright%29)
![c = \frac{8}{\sqrt{3}}](https://tex.z-dn.net/?f=c%20%3D%20%5Cfrac%7B8%7D%7B%5Csqrt%7B3%7D%7D)
![c = \frac{8\sqrt{3}}{3}](https://tex.z-dn.net/?f=c%20%3D%20%5Cfrac%7B8%5Csqrt%7B3%7D%7D%7B3%7D)