The triangle inequality states that in a triangle, any two of the side lengths must add up to a length that is greater than the third. That is, if you have a triangle with sides a, b, and c, then a+b>c, a+c>b, and b+c>a.
In this case, we are given two lengths of a triangle. Let's call those two values a and b, where a>b.
Then we have that c
Now we can also use another inequality, a
Now we can apply these limits to all the individual questions.
1) 13 - 10 < c < 13 + 10. This simplifies down to 3 < c < 23
2) 12 - 5 < c < 12 + 5. This simplifies down to 7 < c < 17
3) 11 - 4 < c < 11 + 4. This simplifies down to 7 < c < 15
Hope it help!
Distance biked before lunch = 1
km (the number is written in mixed fraction)
⇒ Distance biked before lunch = 
Distance biked after lunch = 6
km (the number is written in mixed fraction)
⇒ Distance biked after lunch = 
We need to determine how much farther does Hallie bike after lunch than before lunch
Extra distance biked after lunch vs. before lunch =
- 
⇒ Extra distance biked after lunch vs. before lunch = 
⇒ Extra distance biked after lunch vs. before lunch = 
⇒ Extra distance biked after lunch vs. before lunch = 4
(in mixed fraction)
Hence, Hallie biked 4
km extra after lunch vs. before lunch.
Answer:
-6
Step-by-step explanation:
Given that :
we are to evaluate the Riemann sum for
from 2 ≤ x ≤ 14
where the endpoints are included with six subintervals, taking the sample points to be the left endpoints.
The Riemann sum can be computed as follows:

where:

a = 2
b =14
n = 6
∴



Hence;

Here, we are using left end-points, then:

Replacing it into Riemann equation;






Estimating the integrals, we have :

= 6n - n(n+1)
replacing thevalue of n = 6 (i.e the sub interval number), we have:
= 6(6) - 6(6+1)
= 36 - 36 -6
= -6
Answer:
13.9
Step-by-step explanation:
7^2 + 12^2 = c^2
49 + 144 = 193
square root 193
and it’s 13.9
Answer:
$16
Step-by-step explanation:
This method is probbaly working backwards. I'm not sure.
12 - 4 = 8 (How much she was left with if she didn't wash the car for 4 dollars)
8 x 2 = 16 (They mentioned she spent half of her weekly allowance)