Answer:
a. The value of the constant k is 21
b. The equation is y = k * x, where k is the proportionality constant, "x" is the number of terraced houses and "y" is the width of a row of identical houses.
Step-by-step explanation:
a.
<em>A proportional relationship satisfies the equation y = k * x, where k is a positive constant and is called a proportionality constant. In this case "x" is the number of terraced houses and "y" is the width of a row of identical houses.
</em>
The data you have is that the width of 5 townhouses are 105 feet. This means that the value of "x" is 5 houses and the value of "y" is 105 feet. By replacing in the equation y = k * x and isolating the constant k, you get:
<em>105=k*5
</em>
<em>k=21
</em>
<u><em>So the value of the constant k is 21.</em></u>
b.
<em>As mentioned, the equation is y = k * x, where k is the proportionality constant, "x" is the number of terraced houses and "y" is the width of a row of identical houses.</em>
This means that just as "x" increases, "y" increases. And that if "x" decreases, "y" will decrease. And this relationship between "x" e "and" will always be the same, determined by the value of the constant "k".
Answer:
The second option is the incorrect:
2) 4d3 – 4d2 – 9d + 9 = (d – 1)(2d – 3)^2
Step-by-step explanation:
Let's check each one of the factorizations:
1) x3 + 5x2 + 4x + x2 + 5x + 4 = (x + 4)(x + 1)^2
(x + 4)(x + 1)^2 = (x + 4)(x2 + 2x + 1) = x3 + 6x2 + 9x + 4
x3 + 5x2 + 4x + x2 + 5x + 4 = x3 + 6x2 + 9x + 4
This one is correct.
2) 4d3 – 4d2 – 9d + 9 = (d – 1)(2d – 3)^2
(d – 1)(2d – 3)^2 = (d - 1)(4d2 - 12d + 9) = 4d3 - 16d2 + 21d - 9
4d3 – 4d2 – 9d + 9 = 4d3 - 16d2 + 21d - 9
This one is incorrect.
3) 27h3 – 8k3 = (3h – 2k)(9h2 + 6hk + 4k2 )
(3h – 2k)(9h2 + 6hk + 4k2 ) = 27h3 - 8k3
This one is correct.
4) 64 – 9t2 = (8 + 3t)(8 – 3t)
(8 + 3t)(8 – 3t) = 64 - 9t2
This one is correct.
So the incorrect option is the second one.
42,500x0.09 should get you your commission
Answer: The correct answer is the last choice.
In the first segment of the trip, the car goes from 0 to 2 hours and the line is moving up. Therefore, it traveled for 2 hours.
In the second segment, the line went straight horizontal for 1 hour. That means the distance didn't change, in other words it didn't move.
In the last segment, it moved up again for 2 hours.
Answer:
See below for answers (in bold) and explanations
Step-by-step explanation:
Part A: (h+t)(x) = h(x) + t(x) = (2x-5) + (6x+4) = 2x - 5 + 6x + 4 = 8x - 1
Part B: (h*t)(x) = h(x) * t(x) = (2x-5) * (6x+4) = (2x)(6x) + (2x)(4) + (-5)(6x) + (-5)(4) = 12x² + 8x - 30x - 20 = 12x² - 22x - 20
Part C: h(t(x)) = h(6x + 4) = 2(6x + 4) - 5 = 12x + 8 - 5 = 12x + 3
