F a triangle has a side length of 10, 12 and 15 units respectively, what type of triangle is it acute right obtuse or no solution

Acute.

Step-by-step explanation:

Using the Triangle Inequality Theorem you know that the sum of the lengths of two sides of a triangle are greater than the length of the third side.

Using this we can narrow it down that this DOES have a solution, since 10+12>15.

Now, we can determine if this triangle is a right triangle using the Pythagorean Theorem. C is the longest length.

If c^2= a^2+b^2, then it is a right triangle.

If c^2< a^2+b^2 then it is an acute triangle.

If c^2>a^2+b^2 then it is an obtuse triangle.

We can now substitute. (A and B are interchangeable, but C is the longest length.

A=10

B=12

C=15

A^2=100

B^2=144

C^2=255

We can now figure out that this triangle is acute because A^2+ B^2 (244) < C^2 (255).

Hope this helps!

answer: all of the odd numbers were opened

the first person was the one that was opening all of the lockers. since one is odd, this causes all of the odd number lockers to be opened in the end.

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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