Answer:
B. 7(6x – 1) and 42x – 7 is equivalent
Step-by-step explanation:
A. –3(3x + 5) and –9x + 5
=–3(3x + 5)=-9x-15 not equivalent
B. 7(6x – 1) and 42x – 7
7(6x – 1)=42x-7 equivalent
C. –6(4x – 3) and –6x
=–6(4x – 3)=-24+18 not equivalent
D. 5(2x + 3y) and 25xy
=5(2x + 3y)=10x+15y not equivalent.
Answer:
Step-by-step explanation:
We have the equations
4x + 3y = 18 where x = the side of the square and y = the side of the triangle
For the areas:
A = x^2 + √3y/2* y/2
A = x^2 + √3y^2/4
From the first equation x = (18 - 3y)/4
So substituting in the area equation:
A = [ (18 - 3y)/4]^2 + √3y^2/4
A = (18 - 3y)^2 / 16 + √3y^2/4
Now for maximum / minimum area the derivative = 0 so we have
A' = 1/16 * 2(18 - 3y) * -3 + 1/4 * 2√3 y = 0
-3/8 (18 - 3y) + √3 y /2 = 0
-27/4 + 9y/8 + √3y /2 = 0
-54 + 9y + 4√3y = 0
y = 54 / 15.93
= 3.39 metres
So x = (18-3(3.39) / 4 = 1.96.
This is a minimum value for x.
So the total length of wire the square for minimum total area is 4 * 1.96
= 7.84 m
There is no maximum area as the equation for the total area is a quadratic with a positive leading coefficient.
The answer is b. It cannot be c cause the answer would be a negative number. It cannot be a because there would be more than 100 lollipops altogether. And it cannot be d because the answer would be a fraction. There was 29 lollipops altogether. Hope this helps!
Answer:
Each fraction is greater than the previous fraction.
Explanation:
The bigger the denominator, the smaller the fraction.
Answer: 810
<u>Step-by-step explanation:</u>
There are 10 numbers to choose from. Since the 2nd digit and 3rd digit cannot repeat the number before it, they only have 9 numbers to choose from.
1st digit and 2nd digit and 3rd digit
10 choices x 9 choices x 9 choices = 810
