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Amanda [17]
3 years ago
12

Tell whether each triangle with the given side lengths is a right triangle.

Mathematics
1 answer:
azamat3 years ago
3 0

should be 60 cm if not it's 11

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Read the following statement. If a number is divisible by 2,then it is even what is the inverse of this statement?
Lapatulllka [165]

Answer:

If it is an even number, then it is divisible by 2

Step-by-step explanation:

You flip the order of statements.  One statement is "a number is divisible by 2", the other is "it is even" is the other.  

7 0
3 years ago
7) PG & E have 12 linemen working Tuesdays in Placer County. They work in groups of 8. How many
BabaBlast [244]

Part A

Since order matters, we use the nPr permutation formula

We use n = 12 and r = 8

_{n}P_{r} = \frac{n!}{(n-r)!}\\\\_{12}P_{8} = \frac{12!}{(12-8)!}\\\\_{12}P_{8} = \frac{12!}{4!}\\\\_{12}P_{8} = \frac{12*11*10*9*8*7*6*5*4*3*2*1}{4*3*2*1}\\\\_{12}P_{8} = \frac{479,001,600}{24}\\\\_{12}P_{8} = 19,958,400\\\\

There are a little under 20 million different permutations.

<h3>Answer: 19,958,400</h3>

Side note: your teacher may not want you to type in the commas

============================================================

Part B

In this case, order doesn't matter. We could use the nCr combination formula like so.

_{n}C_{r} = \frac{n!}{r!(n-r)!}\\\\_{12}C_{8} = \frac{12!}{8!(12-8)!}\\\\_{12}C_{8} = \frac{12!}{4!}\\\\_{12}C_{8} = \frac{12*11*10*9*8!}{8!*4!}\\\\_{12}C_{8} = \frac{12*11*10*9}{4!} \ \text{ ... pair of 8! terms cancel}\\\\_{12}C_{8} = \frac{12*11*10*9}{4*3*2*1}\\\\_{12}C_{8} = \frac{11880}{24}\\\\_{12}C_{8} = 495\\\\

We have a much smaller number compared to last time because order isn't important. Consider a group of 3 people {A,B,C} and this group is identical to {C,B,A}. This idea applies to groups of any number.

-----------------

Another way we can compute the answer is to use the result from part A.

Recall that:

nCr = (nPr)/(r!)

If we know the permutation value, we simply divide by r! to get the combination value. In this case, we divide by r! = 8! = 8*7*6*5*4*3*2*1 = 40,320

So,

_{n}C_{r} = \frac{_{n}P_{r}}{r!}\\\\_{12}C_{8} = \frac{_{12}P_{8}}{8!}\\\\_{12}C_{8} = \frac{19,958,400}{40,320}\\\\_{12}C_{8} = 495\\\\

Not only is this shortcut fairly handy, but it's also interesting to see how the concepts of combinations and permutations connect to one another.

-----------------

<h3>Answer: 495</h3>
5 0
2 years ago
Please Help.<br> Write the equation of linear Inequalities to represent each graph.
DerKrebs [107]

Green Line:

This is a horizontal line at x = 0, so it would be:

x ? 0      

Since the shaded area is going to the left of 0 (this means x is negative):

x ≤ 0


Blue Line:

The shaded area is below the line, so:

y ≤ mx + b

When x = 0, y is -5.

y ≤ mx - 5

From each point, you go up 3 units, and to the right 4 units, so the slope is \frac{3}{4}.


y\leq \frac{3}{4}x-5

7 0
3 years ago
A standard clock has a 1-cm hour hand and a 2-cm minute hand. At 12 pm, they are both pointing in the same direction and the dis
Levart [38]

Answer:

The distance between the hands is √(3)cm ≈ 1.73cm.

Step-by-step explanation:

In a standard clock, the angle between every number is 30°, therefore the angle between 12 and 2 will be 30° x 2 = 60°.

Looking at the diagram, to find c we can make use of our cosine formula

c² = a² + b² –2abCos(C°)

a = 2, b = 1 and C° = 60°

Therefore we have:

c² = 2² + 1² –2 x 2 x 1 x cos(60°) =

c² = 4 + 1 – 4 x 0.5 =

c² = 5 – 2 =

c² = 3

c = √(3) ≈ 1.73

Therefore, the distance between the hands is √(3)cm ≈ 1.73cm.

8 0
2 years ago
Suzanne has a student loan balance of $25,904 with an average interest rate of 6.8 percent. Use the student loan repayment calcu
Alex_Xolod [135]

Since the problem is requiring us to use the loan repayment calculator and here is what the calculator gave:


Loan Balance: $25,506.00


Adjusted Loan Balance: $25,506.00


Loan Interest Rate: 6.80%


Loan Fees: 0.00%


Loan Term: 10 years


Minimum Payment: $0.00


Monthly Loan Payment: $293.52


Number of Payments: 120 months


Cumulative Payments: $35,223.07


Total Interest Paid: $9,717.07


It is projected that you will need an annual salary of a minimum $35,222.40 to be capable to have enough money to repay this loan. This approximation assumes that 10% of your gross monthly income will be keen to repaying your student loans. This resembles to a debt-to-income ratio of 0.7. If you use 15% of your gross monthly income to repay the loan, you will need an annual salary of only $23,481.60, but you may experience some financial difficulty. This corresponds to a debt-to-income ratio of 1.1.


8 0
3 years ago
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