Answer:
(10, -29)
Step-by-step explanation:
I assume you are looking for the solution to this system of equations.
Plug them both into a graphing calculator. The point where they cross is:
(10, -29)
X=35 and y= 130.
similar triangles have at least 2 congruent angles.
ABC = 130, 35 and 15
DEF = 130, 35 and 15
so B) the triangles are similar because y=130 and there are 3 pairs of congruent angles.
Answer: x intercept= (-10,0) y intercept = (0,-40)
Just look at where the line hits the x axis for the x intercept, then those coordinates are your x intercept. Then for the y intercept, look at where the line meets the y axis and then that point's coordinates are your y intercept.
Hope this helps!
Answer:
Therefore,
![BC=a=10\ units\\\\AC=b=13.66\ units](https://tex.z-dn.net/?f=BC%3Da%3D10%5C%20units%5C%5C%5C%5CAC%3Db%3D13.66%5C%20units)
Step-by-step explanation:
Consider a Δ ABC with
m∠ A = 45°
m∠ C = 30°
AB = c = 5√2
To Find:
BC = a = ?
AC = c = ?
Solution:
Triangle sum property:
In a Triangle sum of the measures of all the angles of a triangle is 180°.
![\angle A+\angle B+\angle C=180\\\\45+30+\angle B=180\\\ttherefore m\angle B =180-75=105\°](https://tex.z-dn.net/?f=%5Cangle%20A%2B%5Cangle%20B%2B%5Cangle%20C%3D180%5C%5C%5C%5C45%2B30%2B%5Cangle%20B%3D180%5C%5C%5Cttherefore%20m%5Cangle%20B%20%3D180-75%3D105%5C%C2%B0)
We know in a Triangle Sine Rule Says that,
In Δ ABC,
![\frac{a}{\sin A}= \frac{b}{\sin B}= \frac{c}{\sin C}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7B%5Csin%20A%7D%3D%20%5Cfrac%7Bb%7D%7B%5Csin%20B%7D%3D%20%5Cfrac%7Bc%7D%7B%5Csin%20C%7D)
substituting the given values we get
![\frac{a}{\sin 45}= \frac{b}{\sin 105}= \frac{5\sqrt{2} }{\sin 30}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7B%5Csin%2045%7D%3D%20%5Cfrac%7Bb%7D%7B%5Csin%20105%7D%3D%20%5Cfrac%7B5%5Csqrt%7B2%7D%20%7D%7B%5Csin%2030%7D)
∴ ![\frac{a}{\sin 45}= \frac{5\sqrt{2} }{\sin 30}\\\\a=\sin 45\times \frac{5\sqrt{2} }{\sin 30}\\\\a=\frac{1}{\sqrt{2} }\times \frac{5\sqrt{2} }{0.5} \\\\\\a=\frac{5}{0.5} =10\\\therefore BC = a = 10\ units](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7B%5Csin%2045%7D%3D%20%5Cfrac%7B5%5Csqrt%7B2%7D%20%7D%7B%5Csin%2030%7D%5C%5C%5C%5Ca%3D%5Csin%2045%5Ctimes%20%5Cfrac%7B5%5Csqrt%7B2%7D%20%7D%7B%5Csin%2030%7D%5C%5C%5C%5Ca%3D%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%20%7D%5Ctimes%20%5Cfrac%7B5%5Csqrt%7B2%7D%20%7D%7B0.5%7D%20%5C%5C%5C%5C%5C%5Ca%3D%5Cfrac%7B5%7D%7B0.5%7D%20%3D10%5C%5C%5Ctherefore%20BC%20%3D%20a%20%3D%2010%5C%20units)
Similarly for 'b',
![\frac{b}{\sin 105}= \frac{5\sqrt{2} }{\sin 30}\\\frac{b}{0.9659}= \frac{5\sqrt{2} }{0.5}\\\\b=0.9659\times \frac{5\sqrt{2} }{0.5}\\\\b=\frac{6.8301}{0.5} \\\\b=13.66\\\therefore AC = b =13.66\ units\\](https://tex.z-dn.net/?f=%5Cfrac%7Bb%7D%7B%5Csin%20105%7D%3D%20%5Cfrac%7B5%5Csqrt%7B2%7D%20%7D%7B%5Csin%2030%7D%5C%5C%5Cfrac%7Bb%7D%7B0.9659%7D%3D%20%5Cfrac%7B5%5Csqrt%7B2%7D%20%7D%7B0.5%7D%5C%5C%5C%5Cb%3D0.9659%5Ctimes%20%5Cfrac%7B5%5Csqrt%7B2%7D%20%7D%7B0.5%7D%5C%5C%5C%5Cb%3D%5Cfrac%7B6.8301%7D%7B0.5%7D%20%5C%5C%5C%5Cb%3D13.66%5C%5C%5Ctherefore%20AC%20%3D%20b%20%3D13.66%5C%20units%5C%5C)
Therefore,
![BC=a=10\ units\\\\AC=b=13.66\ units](https://tex.z-dn.net/?f=BC%3Da%3D10%5C%20units%5C%5C%5C%5CAC%3Db%3D13.66%5C%20units)
The correct answer to the question what is 35 million divided by 12 is 2,916,666.666666