0.85 is between 0.8 and 0.9
Answer:
Step-by-step explanation:
Usimg formula for calculating compound interest.
A = P(1+r/n)^nt
P is the principal =$250
r is the rate = 5%
t is the time = 25years
n = 1/4(compounded quarterly)
Substituting to get the amount A.
A = 250(1+5/25)^25/4
A = 250(1+0.2)^6.25
A = 250(1.2)^6.25
A = 250(3.125)
A = $781.31
Hence the accumulated amount in Jessica's annuity after 25 years is $781.31
The answer to the question is
20/30. 24/30,. 21/30
Answer:
x = ± - 3
Explanation:
I'm assuming you want the solutions to that equation, so here goes! (If not, please comment.)
(x-3)(x+9)=27
Let's FOIL this all out and expand. (Remember: First, Outer, Inner, Last.)
x^2 + 9x - 3x - 27
(first+ inner + outer + last)
x^2 + 9x - 3x - 27 = 27
Combine like terms, and add 27 to both sides.
x^2 + 6x - 27 + 27 = 27 + 27
x^2 + 6x = 54
Let's complete the square, because factoring doesn't work, and because it's good practice.
x^2 + 6x + ___ = 54 + ____
In the blank we will put b/2 ^2 = 6/2 ^2 = 3^2 = 9 to complete the square.
x^2 + 6x + 9 = 54 + 9
Now we've got a perfect square factor:
(x + 3)^2 = 63
sqrt(x+3)^2 =
x + 3 = ±
x = ± - 3
Answer:
Part A:
Hence proved that Vector= ai + bj is perpendicular to the line ax + by = c.
Part B:
Slope of vector =
Step-by-step explanation:
Condition for perpendicular is:
Part A:
Consider the vector v = ai + bj
x component of vector=a
y component of vector=b
Slope of vector=
Consider the line ax + by = c:
Rearranging the equation:
ax+by=c
by=c-ax
y=
According to general equation of line:
Where m is the slope
In our case the slope of above line is:
According to the condition of perpendicular:
Hence proved that Vector= ai + bj is perpendicular to the line ax + by = c.
Part B:
Slope of vector is also calculated above.
Since the slope of vector is negative reciprocal of the slope of the given line:
According to equation of line ax + by = c
y=
According to general equation of line:
Where m is the slope
Slope of given line=m=
negative reciprocal of the slope of the given line =
Slope of vector =