Answer:
n = 59
Step-by-step explanation:
I find it easiest to work problems of this kind using a graphing calculator. That way, extraneous solutions can be avoided. It seems to work well to rewrite the problem, so you're looking for a value of n that makes the result zero. Here, that would mean you want ...
... f(n) = √(n+5) -√(n-10) -1
_____
The solution by hand involves eliminating the root symbols. You do that by squaring the equation:
... n +5 -2√((n+5)(n-10)) + n -10 = 1
Now, we isolate the remaining root and square again.
... 2n -6 = 2√((n+5)(n-10)) . . . collect terms, add 2√( ) -1
... n -3 = √(n²-5n-50) . . . . . . . divide by 2
... n² -6n +9 = n² -5n -50 . . . . square both sides
... 59 = n . . . . . . . . . . . . . . . . . add 50 +6n -n²
Answer: A. There all 90 degrees
Step-by-step explanation:
Given: Three parallel lines are cut by a transversal and one angle is measured to be 90 degrees.
We know that if two lines cut by transversal the following pairs are equal:
- Vertically opposite angles.
- Corresponding angles.
- Alternate interior angles.
- Alternate exterior angles.
If one angles measures 90°, then its supplement would be 90°.
Then by using above properties , we will get measure of all angles as 90°.
A number cube has 6 different numbers.
A coin can have 2 outcomes ( heads or tails.)
Total out comes = 6 x 2 x 2 = 24
Answer:
2 touchdowns, 3 field goals
Step-by-step explanation:
The number of touchdowns cannot be more than 3, so it is relatively easy to find the solution by trial and error.
23 is not divisible by 3, so 0 touchdowns is not a solution
23 -7 = 16 is not divisible by 3, so 1 touchdown is not a solution
23 -14 = 9 is divisible by 3, so 2 touchdowns and 3 field goals is a solution
21 -21 = 2 is not divisible by 3, so there is only one solution.
Answer:
-7
Step-by-step explanation:
Lets assume the number Peggy is thinking of be "x".
Now as given, when twice the number is added to three times one more than the number. We can write it as
∴ 
--- Equation 1
Again, it is given that Peggy gets the same result as when she multiplies four times one less than the number.
∴ 
-- equation 2
Next, we can equate both the equation 1 and 2 as it is given that result is same.
Let´s distribute 3 into 
and 4 into 
⇒ 
⇒ 
Subtract both side by 4x and 3
∴ 
∴ Peggy was thinking of -7
