Step-by-step explanation:
You have 3/5 of an apple pie" means you have 3 pieces of the 5-piece pie
"You divide the remaining pie into 5 equal slices." means
(3/5 pie) / 5
The math:
(3/5 pie) / 5
is also
(3/5 pie) * (1/5) [to divide by fraction 5/1, invert to 1/5 and multiply]
is also (1/5) * (3/5 pie)
[This means 1/5 of the 3/5 of a pie that is left of"]
So,
each slice is (1/5)*(3/5) pie = 3/25 pie [multiply numerators and denominators]
These ones always feel weird. But we will read the problem directly and do what it says.
So it is 3/5 divided by 5.
Or 3/5/5.
But that looks really weird, so lets think of it like multiplying by 1/5 instead (which is the same as dividing by 5)
So, (3/5) * (1/5) which equals 3/25.
Everyone gets 3 twenty fifths of a pie.
The sum of the interior angles in a triangle is 180 degrees. Therefore, if we add up all of these angles, they must be equal to 180.
64 + 85 + (4x + 27) = 180
176 + 4x = 180
4x = 4
x = 1
Let's check our answer!
4(1) + 27 = 31
31 + 85 + 64 = 180
180 = 180
Hope this helps!! :)
Answer:
-x³ + 3x² - 14x + 12
Step-by-step explanation:
Area of outer rectangle = (x² + 3x - 4) * (2x - 3)
= (x² + 3x - 4) * 2x + (x² + 3x - 4) * (-3)
=x²*2x + 3x *2x - 4*2x + x² *(-3) + 3x *(-3) - 4*(-3)
=2x³ + 6x² - 8x - 3x² - 9x + 12
= 2x³ + <u>6x² - 3x²</u> <u>- 8x - 9x</u> + 12 {Combine like terms}
= 2x³ + 3x² - 17x + 12
Area of inner rectangle = (x² - 1)* 3x
= x² *3x - 1*3x
= 3x³ - 3x
Area of shaded region = area of outer rectangle - area of inner rectangle
= 2x³ + 3x² - 17x + 12 - (3x³ - 3x)
= 2x³ + 3x² - 17x + 12 -3x³ + 3x
= 2x³ - 3x³ + 3x² - 17x + 3x + 12
= -x³ + 3x² - 14x + 12
Answer:
2. a and b only.
Step-by-step explanation:
We can check all of the given conditions to see which is true and which false.
a. f(c)=0 for some c in (-2,2).
According to the intermediate value theorem this must be true, since the extreme values of the function are f(-2)=1 and f(2)=-1, so according to the theorem, there must be one x-value for which f(x)=0 (middle value between the extreme values) if the function is continuous.
b. the graph of f(-x)+x crosses the x-axis on (-2,2)
Let's test this condition, we will substitute x for the given values on the interval so we get:
f(-(-2))+(-2)
f(2)-2
-1-1=-3 lower limit
f(-2)+2
1+2=3 higher limit
according to these results, the graph must cross the x-axis at some point so the graph can move from f(x)=-3 to f(x)=3, so this must be true.
c. f(c)<1 for all c in (-2,2)
even though this might be true for some x-values of of the interval, there are some other points where this might not be the case. You can find one of those situations when finding f(-2)=1, which is a positive value of f(c), so this must be false.
The final answer is then 2. a and b only.
Answer:
The required equation is .
Step-by-step explanation:
Consider the provided information.
Write a division equation that has a solution of 12.
The required division equation is shown below:
Solve the above equation a shown.
Now check this with algebraic method.
The required tape diagram is shown below:
Which is true, Hence 12 is the correct answer.