The word in the problem that indicates that a negative sign should be used is "descend"
<h3>
</h3><h3>How many meters did he descend?</h3>
We know that he stops for water breaks four times, and between each water break, he descends 15 meters.
The written equation is:
4*(-15)m = -60m
Why the negative sign is used?
The negative sign is used because the hiker is descending, so its height is decreasing. The word in the problem that indicates that a negative sign should be used is "descend"
If you want to learn more about signs:
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Answer:
D
Step-by-step explanation:
Consider the equation:
Use distributive property in both sides:
Separate terms with x into the left part and terms without x into the right part:
Since you get true equality 0 = 0, the equation is true for all real values of x. So, the equation has infinitely many solutions.
Let's solve your system by substitution.
y
=
−
2
x
+
7
;
y
=
5
x
−
7
Step: Solve
y
=
−
2
x
+
7
for y:
y
=
−
2
x
+
7
Step: Substitute
−
2
x
+
7
for
y
in
y
=
5
x
−
7
:
y
=
5
x
−
7
−
2
x
+
7
=
5
x
−
7
−
2
x
+
7
+
−
5
x
=
5
x
−
7
+
−
5
x
(Add -5x to both sides)
−
7
x
+
7
=
−
7
−
7
x
+
7
+
−
7
=
−
7
+
−
7
(Add -7 to both sides)
−
7
x
=
−
14
−
7
x
−
7
=
−
14
−
7
(Divide both sides by -7)
x
=
2
Step: Substitute
2
for
x
in
y
=
−
2
x
+
7
:
y
=
−
2
x
+
7
y
=
(
−
2
)
(
2
)
+
7
y
=
3
(Simplify both sides of the equation)
Answer: x=2 and y=3
We are given the two functions
and
. Since the question is asking us for the value of x when f(x) is equal to g(x), all we need to do is equate the respective expressions together. This is what the result should be:
Now, just solve for x. If you want to save some time, you can use logic and then algebra. To do this, look at the square root. We cannot have an imaginary number, so we can rule out the first two options. Now, we are left with x = 2 and x = 4. When we plug in each x-value to the equation, only 4 works out with a result of 0.5 = 0.5. Therefore, the solution to f(x) = g(x) is
D) x = 4. Hope this helps and have a great day!