Answer:
6.1
Step-by-step explanation:
SOH-CAH-TOA
cos35=5/x
x=5/cos35
x=6.1m
Answer:
<u>The number is 67</u>
Step-by-step explanation:
<u>Equations</u>
Let's consider the number 83. The tens digit is 8 and the unit digit is 3. Note the tens digit's addition to the number is 80, and the unit's addition is 3. This means the tens digit adds 10 times its value, that is, 83 = 8*10 + 3.
Now, let's consider the number ab, where a is the tens digit, and b is the unit digit. It follows that
Number=10*a+b
The question gives us two conditions:
1) The sum of a two-digits number is 13.
2) The tens digit is 8 less than twice the units digit.
The first condition can be expressed as:
a + b = 13 [1]
And the second condition can be written as:
a = 2b-8 [2]
Replacing [2] into [1], we have:
2b-8 + b = 13
Operating:
3b = 13 + 8
3b = 21
Solving for b:
b = 21 / 3 = 7
Substituting into [2]:
a = 2*(7) - 8 = 6
Thus, the number is 67
Answer:
Step 3, because the solution should also include all the values for x between the two given values
Step-by-step explanation:
step 1
we have


step 2
The graph in the given problem
step 3
Identify the solution when 
so

using a graphing tool
The solution is the interval -----> [3,5]
see the attached figure
All real numbers greater than or equal to 3 and less than or equal to 5
therefore
The first step in which the student made an error is step 3
Answer:
X = 3, -1; B
Step-by-step explanation:
Use log properties, log 5 on both sides, log 5 of 25 is 2 that times the exponent, so 2*x = 2x, and on the other side, log 5 and base of 5 cancels. So 2x = x^2 -3, which can be solved using factoring:
x^2 -2x -3 = (x-3)(x+1) = 0, x=3,-1
Year New flowers
1 1200
2 300
3 75
There were 1200 wildflowers in the first year that the park started tracking them. Since then, there have been one fourth as many new flowers each year
Initially there are 1200 flowers and start decreasing by 
So first term is 1200 and common ratio is
.
Its a geometric sequence so summation becomes
i =1∑ ∞ 1200(
Now we find the sum
We use sum formula

Where a is the first term , a= 1200
r is the common ratio , r= 1/4


Sum = 1600 wildflowers