If AJKL - ARST, which congruences are true by CPCTC? Check all that apply.

(SAT Prep) If the lengths of two sides of a triangle are 5 and 9 which would be length of the third side?

julia-pushkina [17]

The length of third side of triangle is 4 or 14.

According to the statement

we have given that the two sides of the triangle which are 5 and 9 and we have to find the length of the third side of triangle.

So, For this purpose, we know that the

If we had a triangle with sides a, b and c, then we can say

b-a < c < b+a

where b is larger than 'a'. This is the triangle inequality theorem

In this case, a = 5 and b = 9 so,

b-a < c < b+a

9-5 < c < 9+5

4 < c < 14

Telling us that c is some number between 4 and 14, not including either endpoint. If c is a whole number, then c could be any value from this set.

And

We see that the numbers 4 and 14 are in this set. The values 2 and 7 are not in the set.

So, The length of third side of triangle is 4 or 14.

Learn more about Triangle here

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7 0

1 year ago

All 231 students in math club went on a field trip some rode in vans that held 7 people and some rode on buses that held 25 peop

MariettaO [177]

Answer:

8 vans

7 buses

Step-by-step explanation:

Let there be "b" buses

and "v" vans

Since 7 people is the capacity of vans, the total capacity is

7v

Also, since 25 people is the capacity of 1 bus, the total capacity is

25b

In total 231 people, so we can write our first equation as:

7v + 25b = 231

Now, we know there are 15 vehicles (bus + vans) in total, so we can write our 2nd equation as:

v + b = 15

Now, we solve for v and b. Let's solve the 2nd equation for v and substitute that into 1st and solve for b first:

v + b = 15

v = 15 - b

Now,

$7v + 25b = 231\\7(15-b) + 25b = 231\\105-7b+25b=231\\18b=126\\b=7$

Hence, there are 7 buses

Since 15 vehicles in total, the number of vans is:

15 - 7 = 8 vans

So,

8 vans

7 buses

8 0

4 years ago

The selling price of a chair is N14 000. The trader gives a 25% discount for cash. What is the cash price?

True [87]

Answer:N10500

Step-by-step explanation:

10%of 14000=1400

20%=1400x2=2800

5%=1400 divided by 2=700

25%=2800+700=3500

14000-3500=10500

hope this helps

5 0

4 years ago

Cynthia completed 2/3 of the items on her to - do listin the morning and finished 1/6 of the items during her lunch break. Wht f

adell [148]

She finished 5/6 of her work and still has 1/6 do to.

4 0

3 years ago

Read 2 more answers

A manufacturer buys large quantities of certain fuel pumps. He finds that his cost depends on the number of cases, q, bought at

ruslelena [56]

Answer:

The correct option is <u>c) $17.50/case</u>.

Step-by-step explanation:

Note: The data in the question are merged. The data are therefore sorted and the whole question is represented before answering the question. Please, see the attached pdf file for the sorted data and the represented question.

The explanation of the answer is now given as follows:

Marginal cost refers to the cost incurred in order to produce one more unit of a product.

Therefore, marginal cost is the change in the total cost that is caused by a one-unit increase in the quantity of a commodity that is produced.

From the table in the question, the marginal cost at q = 108 can be calculated as follows:

Change in total quantity at 180 cases = 108 - Number of cases immediately before 108 = 180 - 104 = 4

Change in total cost at 180 cases = Total cost at 108 cases - Total cost immediately before 108 cases = 1990 - 1920 = 70

Marginal cost at 108 cases = Change in total cost at 180 cases / Change in total quantity at 180 cases = 70 / 4 = 17.50 per case

Therefore, the correct option is <u>c) $17.50/case</u>.

Download pdf

4 0

3 years ago