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2 years ago

8.

Mathematics

1 answer:

kakasveta [241]2 years ago

8 0

Step-by-step explanation:

i just answered this.

the average change rate is the change of the functional result in a given interval relative (= divided by) to the length of the interval of the input variable.

in short

( f (interval upper limit) - f (interval lower limit) ) /

(interval upper limit) - (interval lower limit)

upper limit = 0

lower limit = -2

the functional values (y) are 6 and 10 at these points.

so, we get

(6 - 10) / (0 - -2) = -4 / 2 = -2

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<img src="https://tex.z-dn.net/?f=%5Cfrac%7Ba%5E%7B2%7D-1%7D%7B2-5a%7D%20times%20%5Cfrac%7B15a-6%7D%7Ba%5E%7B2%7D%2B5a-6%7D" id=

stepan [7]

$\bf \cfrac{a^2-1}{2-5a}\times \cfrac{15-6}{a^2+5a-6}\\\\
-----------------------------\\\\
recall\quad \textit{difference of squares}
\\ \quad \\
(a-b)(a+b) = a^2-b^2\qquad \qquad 
a^2-b^2 = (a-b)(a+b)\\\\
thus\quad a^2-1\iff a^2-1^2\implies (a-1)(a+1)
\\\\\\
now\quad a^2+5a-6\implies (a+6)(a-1)\\\\
-----------------------------\\\\
thus
\\\\\\
\cfrac{a^2-1}{2-5a}\times \cfrac{15-6}{a^2+5a-6}\implies \cfrac{(a-1)(a+1)}{2-5a}\times \cfrac{3(5a-2)}{(a+6)(a-1)}\\\\
-----------------------------\\\\
$

$\bf now\quad 3(5a-2) \iff -3(2-5a)\\\\
-----------------------------\\\\
thus
\\\\\\
\cfrac{\underline{(a-1)}(a+1)}{\underline{2-5a}}\times \cfrac{-3\underline{(2-5a)}}{(a+6)\underline{(a-1)}}\implies \cfrac{-3(a+1)}{a+6}$

6 0

3 years ago

You earned 1008 in interest by keeping your money in the bank for 7 years at a rate of 4.5.What was your initial deposit?

8090 [49]

Answer:

The principal required to accumulate interest of $ 1,008.00 on a rate of 4.5% per year for 7 years is $ 3200.

Step-by-step explanation:

Given:

Interest I = $ 1008

Time period t = 7 years

Rate of Interest per year r = 4.5% = 4.5/100 = 0.045

To determine:

Initial deposit P = ?

Using the simple interest formula

I = Prt

P = I / rt

P = 1008 / ( 0.045 × 7 )

P = $ 3200

Therefore, the principal required to accumulate interest of $ 1,008.00 on a rate of 4.5% per year for 7 years is $ 3200.

6 0

3 years ago

Need help quickly! Thanks

Rzqust [24]

Answer:

y = $-2^x$

Step-by-step explanation:

If the equation of a function is in the form of y = h(x)

When the graph of this function is reflected across x-axis,

Transformed function will be,

y = -h(x)

Further reflected across y-axis, then the transformed function will be,

y = -h(-x)

By this rule,

Given equation when reflected across x-axis,

y = $-(\frac{1}{2})^{x}$

Further reflected across y-axis,

y = $-(\frac{1}{2})^{-x}$

y = $-(2^{-1})^x$

y = $-2^x$

5 0

3 years ago

Suppose that a leatherback turtle swam 7.5 kilometers in 3 hours at a constant speed. At this rate, how long would it take the t

mario62 [17]

Answer: It would take the turtle a total of 4 hours to swim 10 kilometers

Step-by-step explanation:

3 × 10 = 30

30 ÷ 7.5 = 4

3 0

3 years ago

The area of a square is equal to twice the perimeter of the square. Find the area of the square. 8 units2 64 units2 16 units2 32

Aloiza [94]

The answer is 249 square units

8 0

4 years ago

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