1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
liq [111]
3 years ago
14

In Exercises 37– 40, BD ⃗ bisects ∠ABC. Find m∠ABD,m∠CBD, and m∠ABC.

Mathematics
1 answer:
MrRissso [65]3 years ago
3 0

Answer:

37,  ABD = CBD = 44 degrees, and ABC = 88 degrees

38.  ABD = CBD = 24 degrees, and ABC = 48 degrees

39.  ABD = CBD = 65 degrees, and ABC = 130 degrees

40.  ABD = CBD =67 degrees, and ABC = 134 degrees

Step-by-step explanation:

Recall that when a segment bisects an angle, the angle is divided in equal parts then we have:

37.  

6 x + 14 = 3 x + 29

3 x = 19 - 14 = 15

x = 15/3

x = 5

then ABD = 6 (5) + 14 = 30 + 14 = 44 degrees

CBD must equal ABD , so CBD = 44 degrees

And the total angle ABC = 88 degrees

38.

3 x + 6 = 7 x - 18

24 = 4 x

x = 24/4 = 6

Then ABD = 3 (6) + 6 = 24 degrees. Also CBD = 24 degrees and ABC = 48 degrees

39.

- 4 x + 33 = 2 x + 81

- 6 x = 81 - 33

-6 x = 48

x = - 48/6

x = -8

Then ABD = -4 (-8) + 33 = 32 + 33 = 65 degrees

The also CBD = 65 degrees, and ABC = 130 degrees

40.

8 x + 35 = 11 x + 23

35 - 23 = 11 x - 8 x

12 = 3 x

x = 12/3

x = 4 degrees

Therefore:

ABD = 8 (4) + 35 = 32 + 35 = 67 degrees.

Then also CBD = 67 degrees, and ABC = 134 degrees

You might be interested in
A teacher has a box of pens and pencils. There are 8 more pencils than pens. After the students take 1 pen and 5 pencils from th
crimeas [40]
Let no. of pens be x.

Pens : x
Pencils: x+8

Total: 2x+8

Student takes 1 pen and 5 pencils.

Remainder: 2x+8 - 5 -1 = 2x+2
2x+2 = 26
2x= 24
x = 12 (original no. of pens)
x+ 8 = 20 (original no of pencils)

There are 12 pens at first and 20 pencils.
After 1 pen is taken, 11 pens are left.
After 5 pencils are taken, 20-5=15 pencils are left.
5 0
3 years ago
Read 2 more answers
Lia must work at least 5 hours per week in her family’s restaurant for $8 per hour. She also does yard work for $12 per hour. Li
Fittoniya [83]

Answer:

(a)

r\geq  5

r+y\leq 15

8r+12y\geq 120

y\geq 0

(c)Maximum number of hours Lia can work at the restaurant and still meet her earnings goal = 15 hours

(d)Maximum Earning = $160

Step-by-step explanation:

Let r be the number of hours worked at the restaurant.

Let y be the number of hours of yard work,

Lia must work at least 5 hours per week in her family’s restaurant for $8 per hour.

r\geq  5

Since she does yard work, y\geq 0

Lia’s parents allow her to work a maximum of 15 hours per week overall.

r+y\leq 15

Lia’s goal is to earn at least $120 per week.

The restaurant, r pays $8 per hour

Yard work, y pays $12 per hour.

Therefore:

8r+12y\geq 120

The system of inequalities that represent this problem is therefore:

r\geq  5

r+y\leq 15

8r+12y\geq 120

y\geq 0

(b)The graph of the inequality is attached below

(c)When the graph is plotted, the vertices of the feasible region are:

  • (5,10)
  • (5, 6.7)
  • (15,0)

Where the first term is for the number of hours worked in the restaurant.

The maximum value of r possible is 15 from the three points.

Therefore, she can work at the restaurant for 15 hours and still meet her earning goal.

(d)Maximum Amount Lia can earn in 1 Week

  • At (5,10), Earning=(5X8)+(10X12)=40+120=$160
  • At (5, 6.7), Earning=(5X8)+(6.7X12)=40+80.4=$120.4
  • At (15,0) Earning=(15X8)+(0X12)=$120

Since she has to work at least 5 hours at the restaurant, the maximum amount possible is $160.

8 0
3 years ago
Find the quotient if the sum of 3/5 and 7/10 is divided by the difference between 7/12 and 3/10
Serggg [28]

3/5 + 7/10 / 7/12 - 3/10

13/10 / (35/60 - 18/60=)17/60

10/13 x 60/17 = 78/17 = 4 10/17

8 0
3 years ago
The price of a technology stock has dropped to $9.79 yesterday. Today. the price fell to $9.68. Find the percentage decrease.
Citrus2011 [14]
The answer is 1.12% decrease
Explanation in image

4 0
3 years ago
If a+ar=b+r, the value of a in terms of b and r can be expressed as
nikdorinn [45]
A + ar = b + r
a(1 + r) = b + r
a = (b + r) / (1 + r)

Its c
4 0
3 years ago
Other questions:
  • A butcher is dividing a round of beef into 3 equal sized roasts. If each roast weighs 7.9 pounds, and there are 1.4 pounds of be
    14·2 answers
  • There are 3 inches of snow on the ground when it begins to snow 0.5 inches per hour.
    12·2 answers
  • Lee drove 348 miles on Monday and 135 miles on Tuesday. is 313 miles a reasonable answer for how much farther Lee drove on Monda
    5·2 answers
  • How many units? What is e value of a?
    5·1 answer
  • Water weighs about 8.34 pounds per gallon
    9·1 answer
  • 1 A large bottle holds 250% as much water as a small bottle. If the small bottle holds 12 ounces of water, how many ounces of wa
    11·1 answer
  • 4x-3+x=7x-3 solve x and show work easy to undertand please. Really appreciate it ^^
    6·2 answers
  • Which set of ordered pairs does not represent a function?
    9·1 answer
  • Solve pls brainliest
    14·2 answers
  • A/4 - 5/6 = -1/2 whats a help (;
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!