Answer:
The height of the trapezoid is 6.63 units
The perimeter of the trapezoid is 38 units
Step-by-step explanation:
Whenever a geometry problem is given, it is often useful if it is sketched out. A sketch of this problem can be found in the image attached.
A)
We can see that a right-angled triangle is formed between points BED, with line BE being the height, h.
To get the dimensions of the line EB, we subtract the dimensions of DC from AB. This will give 15 -5 = 10
hence the dimensions of the righ angled triangle are
DE= h
DB = 12 (diagonal)
EB = 10
From Pythagoras' theorem,
The height of the trapezoid is 6.63
B)
We can get the perimeter of the trapezoid by adding the dimensions of all four sides together.
This will be
AD + DC + CB + AB
However we can assume for this case that it is a symmetrical trapezoid, and hence AD = CB
Thus, perimeter =
2 (AD) + DC +AB
2(9) +5 +15 = 38.
The perimeter of the trapezoid is 38 units
How to solve your problem
x^{2}-21=100
Quadratic formula
Factor
1
Move terms to the left side
x^{2}-21=100
x^{2}-21-100=0
2
Subtract the numbers
x^{2}\textcolor{#C58AF9}{-21}\textcolor{#C58AF9}{-100}=0
x^{2}\textcolor{#C58AF9}{-121}=0
3
Use the quadratic formula
x=\frac{-\textcolor{#F28B82}{b}\pm \sqrt{\textcolor{#F28B82}{b}^{2}-4\textcolor{#C58AF9}{a}\textcolor{#8AB4F8}{c}}}{2\textcolor{#C58AF9}{a}}
Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.
x^{2}-121=0
a=\textcolor{#C58AF9}{1}
b=\textcolor{#F28B82}{0}
c=\textcolor{#8AB4F8}{-121}
x=\frac{-\textcolor{#F28B82}{0}\pm \sqrt{\textcolor{#F28B82}{0}^{2}-4\cdot \textcolor{#C58AF9}{1}(\textcolor{#8AB4F8}{-121})}}{2\cdot \textcolor{#C58AF9}{1}}
4
Simplify
Evaluate the exponent
Multiply the numbers
Add the numbers
Evaluate the square root
Add zero
Multiply the numbers
x=\frac{\pm 22}{2}
5
Separate the equations
To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.
x=\frac{22}{2}
x=\frac{-22}{2}
6
Solve
Rearrange and isolate the variable to find each solution
x=11
x=-11
Answer:
0.085 m
Step-by-step explanation:
change in displ. = change in velocity ÷ change in time
so,
x = v ÷ t
= -1.7 m/s ÷ 20s
=0.085 m
D. -4
sq rt of 3x+28-8=x
add 8 to both sides
sq rt of 3x+28 = x+8
square both sides of the equation
3x + 28 = x^2 + 16x + 64
subtract x^2+16x+64 from both sides
group common terms
-13x-36-x^2=0
rearrange and put in quadratic form
x= -13 +/- sq rt of 13^2-4(1)(36) over 2(1)
subtract 169 by 144
x= -12 +/- sq rt of 25 over 2
solve for both sides
x = -13+5 over 2
=-4
x= -13-5 over 2
= -9
now plug in x
sq rt of 3(-4)+28 -8=-4
sq rt of 3(-9)+28 -8= -9
-4 = -4
but
-7 does not = -9
so -4 is the solution
