Answer:
1296
Step-by-step explanation:
Simple interest is
I = PRT where I is the interest P is the principle, r is the rate and t is the time
I = 1350 * .08 * 12
I = 1296
Answer:
![(\frac{1}{2},\frac{-1}{2},\frac{1}{2})](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B2%7D%2C%5Cfrac%7B-1%7D%7B2%7D%2C%5Cfrac%7B1%7D%7B2%7D%29)
Step-by-step explanation:
We have been given the intersection coordinates:
(7,1,-6) and perpendicular to the line x=-1+t ,y=-2+t and z=-1+t
From the condition of perpendicularity we know:
![(7,1,-6)(x,y,z)](https://tex.z-dn.net/?f=%287%2C1%2C-6%29%28x%2Cy%2Cz%29)
![\Rightarrow 7x+y-6z=0](https://tex.z-dn.net/?f=%5CRightarrow%207x%2By-6z%3D0)
Now, we have given x=-1+t , y=-2+t and z= -1+t
![7(-1+t)+(-2+t)-6(-1+t)=0](https://tex.z-dn.net/?f=7%28-1%2Bt%29%2B%28-2%2Bt%29-6%28-1%2Bt%29%3D0)
![-7+7t-2+t+6-6t=0](https://tex.z-dn.net/?f=-7%2B7t-2%2Bt%2B6-6t%3D0)
![\Rightarrow -3+2t=0](https://tex.z-dn.net/?f=%5CRightarrow%20-3%2B2t%3D0)
![2t=3](https://tex.z-dn.net/?f=2t%3D3)
![t=\frac{3}{2}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B3%7D%7B2%7D)
Now, substituting t in the given coordinates x,y and z we get:
![x=-1+\frac{3}{2}=\frac{1}{2}](https://tex.z-dn.net/?f=x%3D-1%2B%5Cfrac%7B3%7D%7B2%7D%3D%5Cfrac%7B1%7D%7B2%7D)
![y=-2+\frac{3}{2}=\frac{-1}{2}](https://tex.z-dn.net/?f=y%3D-2%2B%5Cfrac%7B3%7D%7B2%7D%3D%5Cfrac%7B-1%7D%7B2%7D)
And ![z=-1+\frac{3}{2}=\frac{1}{2}](https://tex.z-dn.net/?f=z%3D-1%2B%5Cfrac%7B3%7D%7B2%7D%3D%5Cfrac%7B1%7D%7B2%7D)
Answer:
<em>The measure of the angle ∠ABC is 108°</em>
Step-by-step explanation:
<em>An isosceles triangle has two equal sides and two equal angles</em>
<em>In this problem</em>
<em>∠BDA=∠BAD= 66° ----> the angles of the base are equals</em>
<em>Find the measure of the vertex angle</em>
<em>∠ABD = 180° - 2×66° = 48° (the sum of the internal angles of a triangle is equal to 180°)</em>
<em>then. Find the measure of the angle ∠CBD in the equilateral triangle we know that</em>
<em>The measure of the internal angle in a equilateral triangle is 60° so</em>
<em>∠CBD= 60°</em>
<em>Then find the measure of the angle ∠ABC</em>
<em>∠ABC=∠ABD+∠DBC</em>
<em>substitute the values</em>
<em>∠ABC= 48°+60° = 108°</em>
<em>The answer is 108°</em>
<em>The measure of the angle ∠ABC is 108°</em>