A 6
B 9
C 12
D 18
Answer:
length: 6 inches
width: 7 inches
Step-by-step explanation:
Let n represent the number. Then the length is (n+2) and the width is (2n-1). The product of these dimensions is the area:
42 = (n+2)(2n -1) = 2n^2 +3n -2
2n^2 +3n -44 = 0 . . . . subtract 42
(n -4)(2n +11) = 0 . . . . . factor
n = 4 . . . . . . . . we aren't interested in the negative solution
Length = 4+2 = 6 . . . inches
Width = 2·4 -1 = 7 . . . inches
The dimensions of the rectangle given that its area is 42 square inches, the length is 2 inches more than a number, and the width is 1 inch less than twice the same number, are 6 inches by 7 inches.
To solve this problem, let's define the unknown number as
x. According to the problem, the length of the rectangle is 2 inches more than x (so it's x + 2), and the width is 1 inch less than twice the number x (which makes it 2x - 1).
Now, we'll use the formula for the area of a rectangle, which is length times width: (x + 2) * (2x - 1) = 42.
Solve this equation by expanding the parentheses (2x^2 + 4x - x - 2 = 42), simplifying (2x^2 + 3x - 2 - 42 = 0), and rearranging (2x^2 + 3x - 44 = 0).
Using the quadratic formula, we find that the possible values of x are 4 and -5.5. However, a negative size doesn't make sense in this context, so x = 4 inches. That makes the length = 4 + 2 = 6 inches, and the width = 2*4 - 1 = 7 inches. Therefore, "the dimensions of the rectangle are 6 inches by 7 inches".
#SPJ3
If f(1) = 1 that means c is -2 because when you substitute x = 1 and when c = -2, you'll get f(1) = -2(1)+3 = -2+3 = 1
So the constant c is -2 and that means the value of f(-4) is
f(-4)=-2(-4)+3=8+3=11
Thus, the value of f(-4) is 11.
About why does "c" have to be -2, here's the proof.
Given y = f(x), therefore.
y=cx+3
Since when x = 1 and y = 1, then Substitute x = 1 and y = 1, thus 1 = c+3
1 - 3 = c and therefore, -2 = c #
So this is the proof that c = -2
Answer:
11
Step-by-step explanation:
To find the 4th term, you simply put 4 in for n because n denotes which term:
The answer is thus 11.
Answer:
QRU and VUR
Step-by-step explanation:
Alternative interior angles are angles that have the same degrees, but different locations. In this case, you can see QRU has the same degree of angle as VUR; They are only in different locations.
- Hope that helps! Please let me know if you need further explanation.
Answer:
QRU and VUR
Step-by-step explanation:
Hope this helps!