answer.
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
Verdich [7]
2 years ago
11

Given: ΔABC, where AB = BC Prove: m∠BAC = m∠BCA Statement Reason 1. Let ΔABC be an isosceles triangle with AB = BC. given 2. Cre

ate point D on side so bisects ∠ABC. constructing an angle bisector 3. M∠ABD = m∠CBD definition of angle bisector 4. BD = BD Reflexive Property of Equality 5. ΔABD ≅ ΔCBD 6. M∠BAC = m∠BCA Corresponding angles of congruent triangles have equal measures. What is the reason for statement 5 in this proof? A. ASA B. SSS C. AAS D. SAS
Mathematics
1 answer:
weqwewe [10]2 years ago
4 0

Answer:

D. SAS

Step-by-step explanation:

Given: ΔABC

Bisecting <ABC to create point D implies that BD is a common side to  ΔABD and ΔCBD.

Also,

m<ABD = m<CBD (angle bisector)

BA = BC (given property of the isosceles triangle)

Therefore,

ΔABD ≅ ΔCBD (Side Angle Side)

The reason for statement 5 in this proof is that ΔABD ≅ ΔCBD by SAS (Side-Angle-Side) relations of the congruent triangles.

You might be interested in
The equation that represents the canned goods order is 24x + 64y = 384, where x = number of minutes spent producing fruit cans,
Lubov Fominskaja [6]
So wee need to find x

4 0
2 years ago
Read 2 more answers
Lucy wants to have a fun-filled day without spending too much money. The local zoo charges a $25 entry fee and a parking fee of
ehidna [41]

Answer:

The required system of equations is,

y=25+x

y=20+2x.

Step-by-step explanation:

Let the number of hours spent by Lucy = x

It is given that,

Local zoo charges initial fee $25 and per hour fee $1.

So, the equation representing the cost if Lucy stays 'x' hours is,

y=25+x in dollars.

Also, Local citcus charges initial fee $20 and per hour fee $2.

So, the equation representing the cost if Lucy stays 'x' hours is,

y=20+2x in dollars.

Since, the objective function for the situation is to 'minimize the cost'.

So, upon solving the equations, we will get the minimum value as,

25+x = 20+2x

i.e. x= 5

Thus,

y=25+x implies y=25+5 i.e. y= $30

y=20+2x implies y=20+2\times 5 i.e. y=20+10 i.e. y= $30

Thus, the minimum value is $30.

The required system of equations is,

y=25+x

y=20+2x.

8 0
2 years ago
What is 4 square root of 81 to the fifth power in exponential form
creativ13 [48]

Answer:

B is the answer.

Step-by-step explanation:

x^{\frac{m}{n} }  = \sqrt[n]{x^{m} }  

\sqrt[4]{81^{5} } =  81^{\frac{5}{4} }

5 0
2 years ago
The table shows the amount of money LaTasha charges customers to mow their lawns. The table represents a linear function.
sashaice [31]
It is b    Latasha charges 10 dollars before she begins to work

5 0
2 years ago
Read 2 more answers
6. Problems and Applications Q6 Consider an economy that produces only chocolate bars. In year 1, the quantity produced is 3 bar
natulia [17]

Answer:

Year 1 GDP Deflator is 100%

Year 2 GDP Deflator is 30%

Year 3 GDP Deflator is 14.29%

Inflation Rate between year 2 and year 3 is 50%

The Real GDP growth Rate for Year 2 and year 3 is 110%

Step-by-step explanation:

Year 1  

 Price of chocolate bar is $2 and 3 bars are sold that year so the real GDP is 3 x $2=$6 which we are also given that this year is the nominal base year so the nominal GDP is also $6. GDP is the sum of all market value produced products in an economy. Therefore that’s why we calculated as the price of a chocolate multiplied the number produced. To calculate the GDP Deflator will be as follows:

GDP Deflator= (nominal GDP/Real GDP) x 100

                      = ($6/$6) x 100

                       = 100%  

Year 2

Price of chocolate bars is $4 per bar and 5 bars were produced therefore Real GDP =$4 x 5 = $20, now we will calculate the GDP deflator as we have been told that year  is the nominal year therefore nominal GDP is $6.

GDP Deflator= (nominal GDP/Real GDP) x 100

                       = ($6/$20) x100

                        = 30%

Year 3

Price of chocolate bars is $6 per bar and 7 bars were produced therefore Real GDP =$6 x 7 =$42, now we calculate the GDP deflator as we have been told that year 1 is the nominal year therefore nominal GDP is $6.

GDP Deflator = (nominal GDP/ Real GDP) x 100

                      = ($6/$42)

                       =14.29%

Now we calculate the inflation rate between year 2 and year 3.we use the CPI (consumer price index to get the inflation rate for year 2 ad 3)

Consumer Price Index = (Current price of bar/previous price of bar) x 100 formula for CPI

                      = ($6/$4) x 100= 150%-100%

                         = 50% is the inflation rate as the consumer price gave us a positive value.

Now we compute the real GDP growth rate between year 2 and year 3

Real GDP growth rate = [  (current Real GDP- Previous Real GDP)/Previous Real GDP] x 100

                                      = ($42-$20)/$20

                                       = 110% so real GDP grew by 110% from year 2 to year 3.

8 0
2 years ago
Other questions:
  • Helena needs 3.5 cups of flour per loaf of bread and 2.5 cups of flour per batch of muffins. She also needs 0.75 cup of sugar pe
    6·1 answer
  • A country is considering two income tax rates. Geoffrey is comparing what his tax bill would be under each plan. Under plan A, h
    9·2 answers
  • Sam has $1,000 to be distributed among two groups equally. Later the first part is divided among five children and second part i
    5·1 answer
  • What is the value of the discriminant for the quadratic equation 0 = 2x2 + x – 3?
    15·2 answers
  • 82.25% of the employees at Industrial Mechanics are college graduates. If 254 employees are college graduates, what is the total
    13·1 answer
  • 489 to the nearest ten​
    12·2 answers
  • Which graph represents the function f(x) =three-halves(2)x?
    10·2 answers
  • Temperature can be measured in two different common units: degrees Celsius and degrees Fahrenheit. fff represents the temperatur
    9·1 answer
  • 8. Which of the numbers in each pair is farther to the left on the number line?
    5·1 answer
  • After school, Carlos helps his mom at her cake shop, Love and Lace Cakes. Today, he is helping her bake a 3-layer wedding cake.
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!