Answer:
She has enough sugar.
Step-by-step explanation:
Let x = cups of sugar needed
eggs/cups of sugar = 2/4 = 1/2
12 eggs/x = 1/2
24 = x
Since she as 25 cups available and she needs 24 cups, it looks like she has enough sugar with 1 cup left over. I hope she is making chocolate chip cookies.
Answer:
When f(x) is replaced by f(x+5), it will shift the parent function '5 units' to the left.
Step-by-step explanation:
- We know that when we add a number 'a' to the input of the function, it would move the parent function 'a' units to the left.
In other words, the rule is:
- f(x + a) will shift the parent function 'a units' to the left.
Given the function
Thus, when f(x) is replaced by f(x+5), it will shift the parent function '5 units' to the left.
- The effect on the graph of the linear parent function is shown in the attached diagram.
In the graph, the red line is representing the parent function f(x) and the blue line is representing the effect on the graph i.e. f(x+5).
Answer:
Chuck's speed is 37 mi/h
.
Step-by-step explanation:
We're asked to find the speed, Chuck, with some given information.
To do this, let's first recognize the simplified velocity equation:
speed = distance/time
or, rearranging to solve for time:
time = distance/speed
let's write this using symbols to simplify things:
time = s/v
s= distance
v= velocity
we're given that
1. s
Chuck
=
185 mi
2. sDana= 160 mi
3. vDana= x
4. vChuck= x+5
Let's plug these values in for two separate equations for each person:
Chick: t = 185/x+5
Dana: t = 160 mi/x
We're asked to find Chuck's speed given that the time intervals are equal, so what we can do is set these two equations (which are solved for the time,t
), equal to each other:
chuck Dana
Now, we solve for x
(which would be Dana's speed):
Cross-multiply:
185x= 160(x+5)
distribute :
185x= 160z+800
subtract 160x from both sides:
25x=800
divide both sides by 25:
x=32 mi/h
Remember that Chuck's speed is:
v
Chuck
=
x
+
5
so
vChuck = 32mi/h+5mi/h= 37 mi/h
Because
has real coefficients, you know the complex root occurs along with its conjugate. That is, both
are roots to
.
This means that dividing through by both factors yields another polynomial with no remainder:
This means the last root (there are only three according to the fundamental theorem of algebra) is
.