Determine the taxi distance from point C(2, 4) to point D(1, 7).

Janet Woo decided to retire to Florida in 6 years. What amount should Janet invest today so she can withdraw $51,500 at the end

Elina [12.6K]

Answer:

$293,562.707

Step-by-step explanation:

As for the provided details we know,

Janet needs $51,500 from end of 7th year for upcoming 20 years.

The present value of 20 installments of $51,500 shall be @ 6% from year 7 to year 8.0858

Thus total value = $51,500 $\times$ 8.0858 = $416,418.7

Now the compound interest factor for 6 year @ 6 % = 1.4185

Thus, value to be invested today = $416,418.70/1.4185 = $293,562.707

As this when compounded annually will provide the balance as required at the end of 6 years.

7 0

3 years ago

\angle B=∠B=angle, B, equals ^\circ ∘ degrees Round your answer to the nearest hundredth.

Irina18 [472]

Answer:

<B is 53.13degrees

Step-by-step explanation:

Find the diagram attached

Given

Opposite side= 4 (side facing <B)

Adjacent side = 3

Required

<B

According to SOH CAH TOAS identity

tan theta = opp/adj

tan<B = 4/3

<B = arctan(4/3)

<B = arctan(1.3333)

<B = 53.13 degrees

Hence the angle <B is 53.13degrees based on the diagram

3 1

3 years ago

Read 2 more answers

1/2log25-2log3+log8

Schach [20]

Answer:

log base 10 of 40/9, log(40/9), or 0.6478

Step-by-step explanation:

Easiest and fastest way to do this is to plug it into the calc because the log base 10 of those numbers given will be nasty decimals.

4 0

4 years ago

Convert 0.31 into a fraction.

fenix001 [56]

Answer:

Step-by-step explanation:

Hello friend !!!

0.31 as a fraction is $\frac{31}{100}$

Hope this helps

plz mark as brainliest!!!!!!!

4 0

4 years ago

Read 2 more answers

If the parent function f(x) = x^2 is fatter translated 11 units to the left, then translated 5 units down, write the resulting f

nikklg [1K]

The quadratic function given by:

$f(x)=a(x-h)^2+k, \ \ \ a\neq 0$

is in vertex form. The graph of $f$ is a parabola whose axis is the vertical line $x=h$ and whose vertex is the point $(h, k)$ . So:

To translate the graph of a function to the right, left, upward or downward we have:

$For \ a \ positive \ real \ number \ c. \ \mathbf{Vertical \ and \ horizontal \ shifts} \\ in \ the \ graph \ of \ y=f(x) \ are \ represented \ as \ follows:\\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{upward}: \\ g(x)=f(x)+c \\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{downward}: \\ g(x)=f(x)-c \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ \mathbf{right}: \\ g(x)=f(x-c) \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ \mathbf{left}: \\ g(x)=f(x+c)$

By knowing this things, we can solve our problem as follows:

FIRST.

Translating 11 units to the left:

$g(x)=f(x+11) \\ \\ \therefore g(x)=(x+11)^2$

Then translating 5 units down:

$g(x)=f(x)-c \\ \\ \therefore g(x)=(x+11)^2-5$

Since the new function is fatter, the factor we need to multiply the term $(x+11)^2$ must be less than 1, to make the graph fatter. So, according to our options, there are two factors 1/2 and 2.

Therefore, the right answer is b. f(x) = 1/2(x + 11)^2 - 5

SECOND.

Translating 8 units to the right:

$g(x)=f(x-8) \\ \\ \therefore g(x)=(x-8)^2$

Then translating 1 unit down:

$g(x)=f(x)-c \\ \\ \therefore g(x)=(x-8)^2-1$

As explained in the previous case, there are two factors 1/3 and 3, so we choose the first one.

Therefore, the right answer is a. g(x) = 1/3(x - 8)^2 - 1

7 0

3 years ago