Answer:
Step-by-step explanation:
Okay, to do this we must understand what parallel means.
parallel means that that one line will NEVER touch the other. In order for this to happen they must be increasing (or decreasing) by the SAME rate. I.e the slope of your line must be the same as the lin in question thus our equation looks like,
.
Now lets find .
To do this, plug the point (3,6) into the equation
6=4(3)+C
6=12+C
-6=C
Thus now that we know C, our equaiton is
Answer:
k=14/5
Problem:
Three points have coordinates A (0 , 7) , B (8 , 3) and C (3k , k)
Find the value of the constant k for which C lies on the line that passes through A and B
Step-by-step explanation:
The slope of a line containing points (a,b) and (c,d) is found by computing (b-d)/(a-c). This is just the change in y divided by the change in x.
The slope of a line containing points (0,7) and (8,3) is (7-3)/(0-8)=4/-8=-1/2.
The slope of a line containing points (0,7) and (3k,k) and (8,3) is still -1/2 because it doesn't matter what two points on a line you use to calculate the slope. The slope will remain the same no matter the pair of points on the line you choose for it's calculation.
So lets pretend the question is now find the point (3k,k) such that a line with slope -1/2 goes through (3k,k) and (0,7).
We want to solve the equation:
(k-7)/(3k-0)=-1/2
Simplify denominator
(k-7)/(3k)=-1/2
Cross multiple
(k-7)(2)=(-1)(3k)
Distribute or multiply
2k-14=-3k
Subtract 2k on both sides
-14=-5k
Divide both sufes by -5
-14/-5=k
Simplifying fraction
14/5=k
Answer:
Step-by-step explanation:
(a + 7b)(a + 4b)
a^2 + 4ab + 7ab + 28b^2
a^2 + 11ab + 28b^2
<span>The correct answer is D. The number 7 is subtracted from the first term, 2x/3, but then an equal sum is added, and the two effectively cancel each other out. This means that the value of the first expression is essentially 2x/3, which is option D.</span>
Answer:
Step-by-step explanation:
Let the width of the pool deck be x.
- Dimensions of the pool are 12 + 2x and 24 + 2x.
- Total area is 1408 ft².
<u>We have equation:</u>
- (12 + 2x)(24 + 2x) = 1408
- 12*24 + 12*2x + 24*2x + (2x)² = 1408
- 288 + 72x + 4x² = 1408
- 4x² + 72x + 288 - 1408 = 0
- 4x² + 72x - 1120 = 0
- x² + 18x - 280 = 0
- x² - 10x + 28x - 280 = 0
- x(x - 10) + 28(x - 10) = 0
- (x - 10)(x + 28) = 0
1)
2)
- x + 28 = 0
- x = - 28 (discarded as negative)
Correct choice is B