The kite is symmetric about line segment BD.
Therefore
AB = BC
3x + 1 = 22
3x = 22 - 1 = 21
x = 21/3 = 7
Similarly,
AD = CD by symmetry
Therefore
4x = CD
4*7 = CD
28 = CD, the required line segment
Answer: 28
Answer:
$5564.87
Step-by-step explanation:
We are to determine the difference between the future values of each investment
The formula for calculating future value:
FV = P (1 + r)^mn
FV = Future value
P = Present value
R = interest rate
N = number of years
m = number of compounding
Madeline
P = Present value = 51,000
R = interest rate = 0.06125 / 365 = 0.000168
N = number of years = 13
m = number of compounding = 365
51,000 x (1.000168)^4745 = 113,070.20
Harper
51,000 x (1.004792)^156 = 107,505.33
Difference = 113,070.20 - 107,505.33 = $5,564.87
Answer:
The correct option is:
h = 1, k = 16
Step-by-step explanation:
y=4x^2-8x+20 =0
It is a quadratic formula in standard form:
ax^2+bx+c
where a = 4 , b = -8 and c=20
The vertex form is:
a(x − h)2 + k = 0
h is the axis of symmetry and (h,k) is the vertex.
Calculate h according to the following formula:
h = -b/2a
h= -(-8)/2(4)
h = 8/8
h = 1
Substitute k for y and insert the value of h for x in the standard form:
ax^2+bx+c
k = 4(1)^2+(-8)(1)+20
k = 4-8+20
k=-4+20
k = 16
Thus the correct option is h=1, k=16....
Answer:
3) 1 5/6 mi
4) a. 4 cm, 6 ft
b. 6.4 cm, 9.6 ft
c. same as part a
Step-by-step explanation:
3) Each of the given distances appears twice in the sum of side measures that is the perimeter. Hence by walking the perimeter twice, Kyle walks each of the given distances 4 times. His total walk is ...
4×1/3 + 4×1/8 = 4/3 + 4/8
= 1 1/3 + 1/2 = 1 2/6 + 3/6
= 1 5/6 . . . . . miles
___
4) Since the figure is rectilinear (all angles are right angles, and all sides are straight lines), the sum of partial dimensions in one direction is equal to the whole dimension in that direction.
a. 8 cm = 4 cm + x
8 cm - 4 cm = x = 4 cm
The distance in the room is ...
(4 cm)×(1.5 ft/cm) = 6 ft
b. 10.3 cm = 3.9 cm + y
10.3 cm - 3.9 cm = y = 6.4 cm
The distance in the room is ...
(6.4 cm)×(1.5 ft/cm) = 9.6 ft
c. The answer to part b was obtained in the same way as the answer to part a. The unknown dimension is the difference of given dimensions. The actual length in the room is the model length multiplied by the inverse of the scale factor.
Answer:
168 miles.
Step-by-step explanation:
5/7x+40+0.75x−118=x
Step 1: Simplify both sides of the equation.
5/7x+40+0.75x−118=x
5/7x+40+0.75x+−118=x
(5/7x+0.75x)+(40+−118)=x(Combine Like Terms)
1.464286x+−78=x
1.464286x−78=x
Step 2: Subtract x from both sides.
1.464286x−78−x=x−x
0.464286x−78=0
Step 3: Add 78 to both sides.
0.464286x−78+78=0+78
0.464286x=78
Step 4: Divide both sides by 0.464286.
0.464286x/0.464286=78/0.464286
x=168
