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2 years ago

I need help figuring out the answers for this

Mathematics

1 answer:

Gennadij [26K]2 years ago

6 0

<h2>Step-by-step explanation:</h2>

Interest, is an additional money paid for borrowing money. it could be simple or compound interest.

simple interest= p×T×R/100

when interest is compounded annually

F= p(1+r)^t

F= future value

p= principal

r= rate

t= time

compound interest is calculated based on the initial and accumulated interest.

<h2>interest Linda earns</h2><h3>fist year</h3>

F= p(n+r)^n

F= 10000(1+0.02)^1

F= 10000×1.02= $10200

interest= 10200-10000

interest = $200

second year

F = 10200(1+0.02)^1

F=10200×1.02= $10404

Interest= 10404-10200

interest= $204

third year

F= 10404(1+0.02)^1

F= 10404(1.02)

F = $10612.08

interest= 10612.08-10404

interest= $208.08

<h2>Bob's interest</h2><h2>I= p×t×R/100</h2>

first year

I=10000×1×0.02/100

interest= $2

second year

I= 10000×2×0.02/100

interest= $4

for the third year

I =10000×3 × 0.02/100

interest= $6

<h2>check answer above for final computation</h2>

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3 years ago

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3 years ago

A youth soccer field has an perimeter of 120 meters. The length of the field is

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3 years ago

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 <em>11 units to the left:</em>

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

Then translating<em> 5 units down:</em>

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

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

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

SECOND.

Translating <em>8 units to the right:</em>

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

Then translating<em> 1 unit down:</em>

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

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

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

7 0

3 years ago