Answer:
Step-by-step explanation:
A fraction can only be simplified if the values on the numerator and denominator share a common factor
In this case the only common factor that 186 and 35 share is 1
When this is the case then the fraction is in simplest form
Answer:
5 + 11/35
Step-by-step explanation:
Our task is to simplify this fraction:
Let's look for common factors that both 186 and 35 have.
Is it 5? No. 186 doesn't end in 5 or 0, so it can't be divisible by 5.
Is it 7? No. 7 does not go into 186 evenly.
Apparently, 185/35 can't be reduced, because it already is in its lowest terms.
The only thing we can do is we can write it as a mixed number.
The denominator stays the same.
How many times does 35 go into 186? 5 times.
So far we have:
Then we multiply 5 times 35 - that gives us 175.
Then we subtract 186 - 175. That gives us 11.
That's the numerator of our fraction, so we have:
B)100 + 20x ≥ 250. They can boat for 8 hours.
C)100 + 20x ≤ 250. They can boat for 8 hours.
D)100 + 20x ≥ 250. They can boat for 7 hours.
Answer:
$2.55
Step-by-step explanation:
If you Multiply $85 by 0.03 you get your answer because you have to turn the 3% into a decimal which you have to move the decimal two places to the left.
1. y = - (x + 4)2
2. y = - (x + 2)2 - 2
3. y = (x - 2)2
4. y = 2 - (x + 2)2
5. y = -x2
6. y = (x + 2)2
A. Reflected across the x-axis and the y-axis
B. Translated right by 2 units
C. Translated up by 2 units
D. Reflected across the x-axis
E. Translated left by 2 units
F. Translated down by 2 units
Always remember general rules of transformation.
1) Vertical Shift:
y= f(x)+k ; shifts the graph of f up k units if k>0, shifts it down |k| units if k<0.
2) Horizontal Shift:
y=f(x+h) ; shifts the graph of f left h units if h>0, shifts it right |h| units if h<0.
3) Reflection across x-axis
y= - f(x) ; reflect the graph of f across the x-axis.
Now,
The parent function is y= -(x+2)²
1. y= -(x+4)²
In this question +2 is added with x+2 and becomes y= -(x+2+2)²=-(x+4)²
So, according to rule 2 it will shift the parent function to the left by 2 units.
E is the correct option.
2. y = - (x + 2)² - 2
In this question, -2 is added to the parent function and we get y= - (x + 2)² - 2
So, according to rule 1, it will shift the graph down by 2 units.
F is the correct option.
3. y=(x - 2)²
In this question, two operations are performed on the parent function.
First one, -4 is added with x+2 so we get x+2-4= x-2
Second one, -1 is multiplied with parent function.
By performing the two operations at a time we get a new function which is
y=-(-(x+2-4)²)=(x-2)²
The first operation will translate the parent function 4 units right (according to rule 2).
The second operation will reflect the graph across x-axis(according to rule 3).
D and translation 4 units to right is correct option.
4. y= 2 -(x+2)²
In this question, we add +2 to the parent function so according to rule 1 it will shift the graph up by 2 units.
C is the correct option.
5. y= -x²
In this question, we add -2 to x+2 so we get a new function y= -(x+2-2)²=-x²
So, according to rule 2 it will shift the graph right by 2 units.
B is the correct option.
6. y= (x+2)²
In this question, -1 is multiplied with parent function and we get
y= -(-(x+2)²)= (x+2)²
So, according to rule 3 , graph is reflected across x-axis.
D is the correct answer.
The graph of parent function and question no. 1,2,3 are attached separately, while question no. 4,5,6 are attached in combined form(due to space limit).
Answer:
30
Step-by-step explanation:
Assuming your parallelogram looks like the one in the attached image.
The area of a parallelogram is base x height, .
The base is 10; the height is 3, so A = 10 x 3 = 30.
Answer:
30
Step-by-step explanation: