She has run 21 miles already. Let t be the number of additional miles added on.
In total, she has run t+21 miles
This is going to be set greater than 38 since "Ann will run more than 38 miles"
So we have this inequality
t+21 > 38
we solve for t by subtracting 21 from both sides
t+21 > 38
t+21-21 > 38-21
t+0 > 17
t > 17
The final answer is t > 17
which means that the possible additional number of miles she could run is anything larger than 17. So t = 18 is one possibility.
The slope of the line is -1/7, so the perpendicular line has a slope of 7
#16: Let's clear the fraction on the way to solving this inequality for x. By mult. the given inequality by 2, we'll get -2 (is greater than) x+4. We want x to be positive. So, leave it where it is. Subtract 4 from both sides of this inequality. We end up with -6 (is greater than) x, which is the same thing as x (is less than) -6. What would the graph of that simple inequality look like?
Graph it. (Hint: The graph is a straight dashed line, and you must shade one side of it, but not the other side.
Answer:
B) The maximum y-value of f(x) approaches 2
C) g(x) has the largest possible y-value
Step-by-step explanation:
f(x)=-5^x+2
f(x) is an exponential function.
Lim x→∞ f(x) = Lim x→∞ (-5^x+2) = -5^(∞)+2 = -∞+2→ Lim x→∞ f(x) = -∞
Lim x→ -∞ f(x) = Lim x→ -∞ (-5^x+2) = -5^(-∞)+2 = -1/5^∞+2 = -1/∞+2 = 0+2→
Lim x→ -∞ f(x) = 2
Then the maximun y-value of f(x) approaches 2
g(x)=-5x^2+2
g(x) is a quadratic function. The graph is a parabola
g(x)=ax^2+bx+c
a=-5<0, the parabola opens downward and has a maximum value at
x=-b/(2a)
b=0
c=2
x=-0/2(-5)
x=0/10
x=0
The maximum value is at x=0:
g(0)=-5(0)^2+2=-5(0)+2=0+2→g(0)=2
The maximum value of g(x) is 2
Answer:
x = 129.8 degrees, y = 50.2 degrees, x + y = 180
Step-by-step explanation:
Let's say you have 2 supplementary angles, x and y
So x + y = 180
if x is 79.8 degrees less than the measure of a supplementary angle, then x = y - 79.8
Putting this into our x + y = 180 equation, we get
(y - 79.8) + y = 180
2y - 79.8 = 180
2y = 180 + 79.8
2y = 259.8
y = 259.8/2 = 129.9 degrees.
so x = 129.9 - 79.6 = 50.3 degrees.
See if it worked. x = 129.9 degrees, y = 50.3 degrees, x + y = 180 so we found the correct two angles! :-)
