Answer:
Given: A triangle ABC and a line DE parallel to BC.
To prove: A line parallel to one side of a triangle divides the other two sides proportionally.
Proof: Consider ΔABC and DE be the line parallel to Bc, then from ΔABC and ΔADE, we have
∠A=∠A (Common)
∠ADE=∠ABC (Corresponding angles)
Thus, by AA similarity, ΔABC is similar to ΔADE, therefore
AB/AD= AC/AE
⇒AD+DB/AD = AE+EC/AE
⇒1+DB/AD = 1+ EC/AE
⇒DB/AD = EC/AE
Therefore, a line parallel to one side of a triangle divides the other two sides proportionally.
⇒Therefore Proved
Hope this helps!!!
Answer
Social security tax amount = $3348
Medicare tax amount = $743
Step by step explanation
The amount earned by Marcus = $54000
Social security tax = 6.2% = 6.2/100 = 0.062
Social security tax amount = 54000*0.062
Social security tax amount = $3348
Medicare tax = 1.45% = 1.45/100 = 0.0145
Medicare tax amount = 54000*0.0145
Medicare tax amount = $743
Hope this will help you.
Work the information to set inequalities that represent each condition or restriction.
2) Name the
variables.
c: number of color copies
b: number of black-and-white copies
3)
Model each restriction:
i) <span>It
takes 3 minutes to print a color copy and 1 minute to print a
black-and-white copy.
</span><span>
</span><span>
3c + b</span><span>
</span><span>
</span><span>ii) He needs to print
at least 6 copies ⇒
c + b ≥ 6</span><span>
</span><span>
</span><span>iv) And must have
the copies completed in
no more than 12 minutes ⇒</span>
3c + b ≤ 12<span />
4) Additional restrictions are
c ≥ 0, and
b ≥ 0 (i.e.
only positive values for the number of each kind of copies are acceptable)
5) This is how you
graph that:
i) 3c + b ≤ 12: draw the line 3c + b = 12 and shade the region up and to the right of the line.
ii) c + b ≥ 6: draw the line c + b = 6 and shade the region down and to the left of the line.
iii) since c ≥ 0 and b ≥ 0, the region is in the
first quadrant.
iv) The final region is the
intersection of the above mentioned shaded regions.v) You can see such graph in the attached figure.
Answer:
Step-by-step explanation:
The area of solutions of the first inequality lies above an orange straight line.
The area of solutions of the second inequality lies below a blue straight line.
These areas are crossed in the yellow field.
The green field does not meet a condition of the second inequality and therefore does not enter the area of the solution of a system of inequalities
The first one is 13 points and the 2nd one is 8. I'm pretty sure, hope this helps! :)
