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:
Sequence: Reflection over the y-axis, then 1 to the right and 2 down to get the triangle ABC to A'B'C.
Step-by-step explanation:
Have a nice day!
Answer:
The answer is H.
Step-by-step explanation:
There is no "b" in this y = mx + b, so it has to go through zero, eliminating the bottom two. If we insert y = 2(1), the point should be at (1, 2), and if when looking at the possible answers, we can go with letter H.
The first one includes both
Answer:
The area of the shaded figure is:
Step-by-step explanation:
To obtain the area of the shaded figure, first, you must calculate this as a rectangle, with the measurements: wide (4 units), and long (6 units):
- Area of a rectangle = long * wide
- Area of a rectangle = 6 * 4
- Area of a rectangle = 24 units^2
How the figure isn't a rectangle, you must subtract the triangle on the top, so, now we calculate the area of that triangle with measurements: wide (4 units), and height (2 units):
- Area of a triangle =
- Area of a triangle =
- Area of a triangle =
- Area of a triangle = 4 units^2
In the end, you subtract the area of the triangle to the area of the rectangle, to obtain the area of the shaded figure:
- Area of the shaded figure = Area of the rectangle - Area of the triangle
- Area of the shaded figure = 24 units^2 - 4 units^2
- <u>Area of the shaded figure = 20 units^2</u>
I use the name "units" because the exercise doesn't say if they are feet, inches, or another, but you can replace this in case you need it.
