9514 1404 393
Answer:
1, 2
Step-by-step explanation:
1. The area of a parallelogram is the product of length and width. The given statement is FALSE.
2. The angles formed by the diagonals are linear pairs, so supplementary. The given statement is FALSE.
3. TRUE
4. TRUE
5. TRUE
__
Statements 1 and 2 are not true.
Answer:
Step-by-step explanation:
Area of shape A = 
= 
= 10 square units
Area of shape B = Length × width
= 4×2
= 8 square units
Area of shape C = 5 square units
Area scale factor = 
Area scale factor = (Scale factor)²
If scale factor = 2
Area scale factor = 2² = 4
Rule for the dilation,
Area of image = Area scale factor × Area of preimage
Therefore, area of figure A after dilation = 4×10 = 40 square feet
Area of figure B after dilation = 4×8 = 32 square feet
Area of figure C after dilation = 4×5 = 20 square feet
Similarly, we can get areas by different scale factors given in the table.
Scale factor Area of shape A Area of shape B Area of shape C
2 40 32 20
3 90 72 45
10 1000 800 500
2.5 2 1.25
x 10x² 8x² 5x²
Answer:
The Answer is D.
Step-by-step explanation:
To solve this question we should use the process of elimination.
We can clearly see that the function f(x) increases as x increases so we can rule out options A and C.
Now we have to decide between B and D.
So the format for a quadratic function is 
The format for an exponential function is 
So let's try exponential first:
at x = 0 we solve for a and b:

so we find b when x =5
![12201.9 =10000b^5\\b^5=\frac{12201.9}{10000} \\b^5=1.22019\\b=\sqrt[5]{1.22019} \\](https://tex.z-dn.net/?f=12201.9%20%3D10000b%5E5%5C%5Cb%5E5%3D%5Cfrac%7B12201.9%7D%7B10000%7D%20%5C%5Cb%5E5%3D1.22019%5C%5Cb%3D%5Csqrt%5B5%5D%7B1.22019%7D%20%5C%5C)
b = 1.04060
Then we evaluate the value as x=10
![14888.64=10000b^10\\b^10=14888.64/10000\\b^10=1.488864\\b=\sqrt[10]{1.488864} \\b=1.04060](https://tex.z-dn.net/?f=14888.64%3D10000b%5E10%5C%5Cb%5E10%3D14888.64%2F10000%5C%5Cb%5E10%3D1.488864%5C%5Cb%3D%5Csqrt%5B10%5D%7B1.488864%7D%20%5C%5Cb%3D1.04060)
As can be seen from both cases b is the same. This is a key chareteristic of an exponential function. So the Answer is D.
Answer:
2 hrs 13 mins
Step-by-step explanation:
If Richard can paint the living room in 4 hrs, then in 1 hour he can paint 1/4 of the living .
If Vanessa can paint the living room in 5 hours, then in one hour, she can paint 1/5 of the living room.
In one hour Richard and Vanessa can paint 1/4 + 1/5 = 1/y
y is the number of hours it will take both Richard and Vanessa to paint the living room. 1/y is how much of the house they can paint in one hour.
1/4 + 1/5 = 1/y
(5 + 4)/20. ( find the LCM)
9/20 = 1/y
9y= 20
y = 20/9
y = 2.22hrs
y = 2 hrs 13 mins
X - 9/3 = 2
Simplify 9/3, 9/3 = 3
x - 3 = 2
Add 3 on both sides
x = 5