Answer:
12 inches
Step-by-step explanation:
Let b represent the base
h represents the height
area of the parallelogram = base * height = 216 square inches
From the question'
b = 18 + 3h
Slot in the value of b
216 = (18 + 3h) * h
expand
216 = 18h + 3h^2
subtract 216 from both sides
0 = 18h + 3h^2 - 216
rearrange
3h^2 + 18h - 216 = 0
divide through by 3
h^2 + 6h - 72 = 0
Now, lets solve!
h^2 + 6h - 12h - 72 = 0
h( h + 6 ) - 12(h + 6) = 0
(h - 12) (h + 6) = 0
h - 12 = 0
h = 12
and
h + 6 = 0
h = - 6
Taking the positive value of h
Hence, the height is 12 inches
Lets check
when h = 12 inches
Area of the parallelogram = 18* 12 = 216 square inches .... correct
when h = -6inches
A = 18 * -6 ≠ 216 square inches
So height is 12 inches
The opposite side pairs in a rectangle are congruent, so basically QT would be congruent to RS when you draw the rectangle and label the points.
4x+10=30
4x=20
x=5
Answer:
The system of equations has a one unique solution
Step-by-step explanation:
To quickly determine the number of solutions of a linear system of equations, we need to express each of the equations in slope-intercept form, so we can compare their slopes, and decide:
1) if they intersect at a unique point (when the slopes are different) thus giving a one solution, or
2) if the slopes have the exact same value giving parallel lines (with no intersections, and the y-intercept is different so there is no solution), or
3) if there is an infinite number of solutions (both lines are exactly the same, that is same slope and same y-intercept)
So we write them in slope -intercept form:
First equation:
second equation:
So we see that their slopes are different (for the first one slope = -6, and for the second one slope= -3/2) and then the lines must intercept in a one unique point. Therefore the system of equations has a one unique solution.
Answer:
The slope of the line is 2.
This means that Jan runs 2 laps every 1 minute.
Answer:
a = 1 b = -1.
Step-by-step explanation:
Suppose the quotient when you divide x^4+x^3+ax+b by x^2 + 1 is
x^2 + ax + b then expanding we have:
(x^2 + 1)(x^2 + ax + b)
= x^4 + ax^3 + bx^2 + x^2 + ax + b
= x^4 + ax^3 + (b + 1)x^2 + ax + b Comparing this with the original expression:
x^4 + x^3 + 0 x^2 + ax + b Comparing coefficients:
a = 1 and b+ 1 = 0 so b = -1.
