Given that a || b, m∠2 = 63° and m∠9 = 105°.
Now, all the angles are as follows:
m∠5= m∠2 = 63° [vertically opposite angle]
m∠7= m∠9=105° [vertically opposite angle]
m∠8= 180°-m∠9=180°-105°=75° [Supplementry angles, m∠8+m∠9=180°]
m∠10= m∠8= 180° [vertically opposite angle]
m∠6= m∠8=75° [ Alternate angles]
m∠3= m∠6=75° [vertically opposite angle]
m∠1= 180°-(m∠2+m∠3)=180°-(63°+75°)=42° [as m∠1+m∠2+m∠3=180°]
m∠4= m∠1=42° [vertically opposite angle]
m∠11=m∠4=42° [ Alternate angles]
m∠13= m∠11=42° [vertically opposite angle]
m∠12= 180°-m∠11=180°-42°=138° [as m∠8+m∠9=180°]
m∠14 = m∠12=138° [vertically opposite angle]
Answer:
The length of the longest section x = 36 ft
Step-by-step explanation:
Total length of the wire = 51 ft
Let first section of wire = x
Second section of wire = y
Third section of wire = z
According to given data
x = 3 y & y = 4 z
Total length of the wire = x + y + z = 51
y = 12
x = 3 × 12 = 36
Therefore the length of the longest section x = 36 ft
Answer:
Step-by-step explanation:
3) Sales tax rate =
= 8.50
= 9%
4) Rate of commission =
= 5 %
5) Reduction =
=$ 1500
New price = 5000 - 1500
= $ 3500
22. B) $65,000,000 per year.
23. B) Education.
Step-by-step explanation:
Step 1; To find the average rate of change in annual budget between the two given years. We divide the difference in values for the two years by the period in between the two years. In 2008, the budget was $358,708,000 while in 2010 it was $488,106,000. The period in between was 2 years i.e 2009 and 2010.
The average rate of change = =
= $64,699,000 per year.
So the average rate of change was $64,699,000 which approximately equals option B. $65,000,000.
Step 2; To find the human resources program's 2007 to 2010 ratio we divide the value in 2007 to the value in 2010. To find the other similar ratio, we divide the value in 2007 to the value in 2010 for all the other programs and determine which is closest to the human resources program.
Human resources program ratio = = 0.6841,
Agricultural / natural resources ratio = = 0.766,
Education's ratio = = 0.7196,
General government's ratio = = 0.9749,
Highways and transportation's ratio = = 0.827,
Public safety's ratio = = 0.5675.
The Human resources' program ratio is 0.6841 and the closest is Education's ratio which is 0.7196. So education is the answer.