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2 years ago

Triangles ΔABC ≅ ΔBAD so that C and D lie in the opposite semi-planes of segment AB. Prove that segment CD bisects segment AD.

Mathematics

1 answer:

kolbaska11 [484]2 years ago

6 0

Answer:

See explanation

Step-by-step explanation:

Triangles ΔABC and ΔBAD are congruent. So,

AB ≅ BA;
AC ≅ BD;
BC ≅ AD;
∠ABC ≅ ∠BAD;
∠BCA ≅ ∠ADB;
∠CAB ≅ ∠DBA.

Consider triangles AEC and BED. In these triangles,

AC ≅ BD;
∠EAC ≅ ∠EBD (because ∠CBA ≅ ∠BAD);
∠AEC ≅ ∠BED (as vertical angles).

So, ΔAEC ≅ ΔBED. Thus,

AE ≅ EB.

This means that segment CD bisects segment AD.

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You and a friend have a hula hoop competition. you win 3 out of every 7 trials. your friend wins 5 more trials than you. how man

Ivenika [448]

Answer:

Total number of trials is 35.

Step-by-step explanation:

Given : Me and my friend have a hula hoop competition. I win 3 out of every 7 trials. My friend wins 5 more trials than me.

To find : How many trials are in the competition?

Solution :

Probability of my winning is 3 out of 7 trials $=\frac{3}{7}$

and probability of my friend's winning is $=1-\frac{3}{7}=\frac{4}{7}$

Let there be n numbers of trials.

Therefore, my score after n trials $=\frac{3n}{7}$

and my friend's score after n trials $=\frac{4n}{7}$

Now, the number of trials my friend won more than me is

$\frac{4n}{7}-\frac{3n}{7}=\frac{n}{7}$

We know, that my friend won 5 more trials than me so comparing the actual and given we get,

$\frac{n}{7}=5\\n=7\times5=35$

Therefore, total number of trials is 35.

We can also verify our answer by placing value of n,

After 35 trials I will win $\frac{3\times 35}{7}=15$ trials

and my friend will win $\frac{4\times 35}{7}=20$ trials.

Hence, my friend won 5 more trials than me.

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2 years ago

If the price of attending Big Benefits University is $42,000 a year, including tuition, fees, books, and foregone earnings, what

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Answer:

$229673.215

Step-by-step explanation:

Given : The price of attending Big Benefits University is $42,000 a year, including tuition, fees, books, and foregone earnings

To Find : what is the marginal cost of attending, if it takes you 5 years to graduate, and you assume a 3% annual inflation rate?

Solution:

Principal = $42000

Time = 5 years

Rate = 3% = 0.03

Formula : $A=P(1+r)^t$

$A_1=42000(1+0.03)^1$

$A_1=43260$

$A_2=42000(1+0.03)^2$

$A_2=44557.8$

$A_3=42000(1+0.03)^3$

$A_3=45894.534$

$A_4=42000(1+0.03)^4$

$A_4=47271.370$

$A_5=42000(1+0.03)^4$

$A_5=48689.511$

So , Marginal cost = 43260+44557.8+45894.534+47271.370+48689.511

Marginal cost = $229673.215

Hence the marginal cost of attending, if it takes you 5 years to graduate, and you assume a 3% annual inflation rate is $229673.215

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Answer:

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