Answer:
131
Step-by-step explanation:
Using proportion,
If Out of 550 calculators = 6 are defective,
Then out of 12000 calculators = ? are defective
![\frac{12000 calculators}{550calculators} * 6](https://tex.z-dn.net/?f=%5Cfrac%7B12000%20calculators%7D%7B550calculators%7D%20%2A%206)
= 21.8 * 6
= 130.8 ≈ 131
∴ Approximately 131 calculators are defective
Answer:
They are skew lines.
Step-by-step explanation:
Which statement is true about lines a and b?
They are parallel lines.
They are perpendicular lines.
They are skew lines.
They will intersect.
As they both are in different directions they are skew lines .
Skew lines are not parallel neither they .They are also not co planar i.e they lie in different planes.
We have two plane Q and R . We have two line a and b on the different planes Q and R. Both planes are parallel but the lines a and b are in different directions. Therefore they are skew lines . They do not intersect and are also not parallel neither co planar.
Answer:
Therefore, Michael concludes option C)
C)![(DA)^{2}=(DG)^{2}+(AG)^{2}](https://tex.z-dn.net/?f=%28DA%29%5E%7B2%7D%3D%28DG%29%5E%7B2%7D%2B%28AG%29%5E%7B2%7D)
Step-by-step explanation:
Given:
1. DG = 3 and the area of square DEFG is 9.
2. AG = 4 and the area of square GHIA is 16.
3. DA = 5 and the area of square ABCD is 25.
So we have,
![(DG)^{2}=3^{2}=9\\ \\(AG)^{2}=4^{2}=16\\\\(DA)^{2}=5^{2}=25\\](https://tex.z-dn.net/?f=%28DG%29%5E%7B2%7D%3D3%5E%7B2%7D%3D9%5C%5C%20%5C%5C%28AG%29%5E%7B2%7D%3D4%5E%7B2%7D%3D16%5C%5C%5C%5C%28DA%29%5E%7B2%7D%3D5%5E%7B2%7D%3D25%5C%5C)
Now Add DG² and AG² we get
![(DG)^{2}+(AG)^{2}=9+16=25=(DA)^{2}](https://tex.z-dn.net/?f=%28DG%29%5E%7B2%7D%2B%28AG%29%5E%7B2%7D%3D9%2B16%3D25%3D%28DA%29%5E%7B2%7D)
Which is also called as Pythagoras theorem i.e
![(\textrm{Hypotenuse})^{2} = (\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}](https://tex.z-dn.net/?f=%28%5Ctextrm%7BHypotenuse%7D%29%5E%7B2%7D%20%3D%20%28%5Ctextrm%7BShorter%20leg%7D%29%5E%7B2%7D%2B%28%5Ctextrm%7BLonger%20leg%7D%29%5E%7B2%7D)
Therefore, Michael concludes option C)
C)![(DA)^{2}=(DG)^{2}+(AG)^{2}](https://tex.z-dn.net/?f=%28DA%29%5E%7B2%7D%3D%28DG%29%5E%7B2%7D%2B%28AG%29%5E%7B2%7D)
Answer:
![m=-\frac{4}{5}](https://tex.z-dn.net/?f=m%3D-%5Cfrac%7B4%7D%7B5%7D)
Step-by-step explanation:
We can take 2 arbitrary points in the graph and solve for slope using the formula shown below.
<u>Note:</u> we will use the 2 points (2,-3) & (-3,1)
Where x_1 = 2, y _1 = -3 and x _ 2 = -3 and y _ 2 = 1
The formula:
![m=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Let's plug the numbers and find the slope:
![m=\frac{1-(-3)}{-3-2}\\m=\frac{4}{-5}\\m=-\frac{4}{5}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B1-%28-3%29%7D%7B-3-2%7D%5C%5Cm%3D%5Cfrac%7B4%7D%7B-5%7D%5C%5Cm%3D-%5Cfrac%7B4%7D%7B5%7D)
Hence, thsi is the slope.
Algebraically that would be expressed as 2r + 11
The product of 2 and r is 2r.
The sum of 2r and 11 is 2r + 11