Find the selling price of each item original plate price of gold fish at $7.65 discount 10%

Simplify each exponential expression using the properties of exponents and match it to the correct answer.

saveliy_v [14]

1) (2 $\times$ 3^-2)^3 (5 $\times$ 3^2)^2 / (3^-2)(5 $\times$ 2)^2 = 2

2) (3^3) (4^0)^2 (3 $\times$ 2)^-3 (2^2) = 1/2

3) (3^7 $\times$ 4^7) (2 $\times$ 5)^-3 (5)^2 / (12^7) (5^-1) (2^-4) = 2

4) (2.3)^-1 (2^0) / (2.3)^-1 = 1

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

Step 1 :

(2 $\times$ 3^-2)^3 (5 $\times$ 3^2)^2 / (3^-2)(5 $\times$ 2)^2

⇒ (2^3) (3^-6) (5^2) (3^4) / (3^-2) (10^2)

⇒ (2.2^2.5^2) (3^-6.3^4) / (3^-2) (10^2)

⇒ (2)(10^2) (3^-2) / (3^-2) (10^2)

⇒ 2

Step 2 :

(3^3) (4^0)^2 (3 $\times$ 2)^-3 (2^2)

Any number with power 'zero' is 1.

⇒ (3^3) (1^2) (3^-3) (2^-3) (2^2)

⇒ (2^(-3+2))

⇒ 2^-1 = 1/2

Step 3 :

(3^7 $\times$ 4^7) (2 $\times$ 5)^-3 (5)^2 / (12^7) (5^-1) (2^-4)

⇒ (12^7) (2^-3) (5^-3) (5^2) / (12^7) (5^-1) (2^-4)

⇒ (2^-3) (5^(-3+2)) / (5^-1) (2^-4)

⇒ (2^-3) (5^-1) / (5^-1) (2^-4)

⇒ 1 / (2^-1)

⇒ 2

Step 4 :

(2.3)^-1 (2^0) / (2.3)^-1

⇒ (2^0)

⇒ Any number with power 'zero' is 1

⇒ 1

8 0

3 years ago

Determine the quadrant when the terminal side of the angle lies according to the following conditions: cos (t) < 0, csc (t) &

Bess [88]

Answer:

The angle is in the second quadrant.

Step-by-step explanation:

The cosecant of an angle is the same as the reciprocal of the sine of that angle. In other words, as long as $\sin (t) \ne 0$ ,

$\displaystyle \csc t = \frac{1}{\sin t}$ .

Therefore, $\csc(t) > 0$ is equivalent to $\sin (t) > 0$ .

Consider a unit circle centered at the origin. If the terminal side of angle $t$ intersects the unit circle at point $(x,\, y)$ , then

$\cos (t) = x$ , and
$\sin(t) = y$ .

For angle $t$ ,

$x = \cos(t) < 0$ , meaning that the intersection is to the left of the $y$ -axis.
$y = \sin(t) > 0$ , meaning that the intersection is above the $x$ -axis.

In other words, this intersection is above and to the left of the origin. That corresponds to second quadrant of the cartesian plane.

6 0

2 years ago

if £5000 Is placed into a bank account that pays 2% compound interest per year, how much will be in the account after two years

timurjin [86]

Answer:

£5200

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 2%/100 = 0.02 per year,

then, solving our equation

I = 5000 × 0.02 × 2 = 200

I = £ 200.00

The simple interest accumulated

on a principal of £ 5,000.00

at a rate of 2% per year

for 2 years is £ 200.00.

5 0

2 years ago

Solve st + 3t = 6 for s

vaieri [72.5K]

st + 3t = 6 for s

Subtract 3t to both sides

st + 3t - 3t = 6 - 3t

Simplify

st = 6 - 3t

Divide both sides by t

st/t = (6-3t)/3

simplify

s = 6/3 - 3t/3

s = 2 - t

6 0

2 years ago

Let g(x) = 2x and h(x) = x2 + 4. Evaluate (h ∘ g)(−2).

kap26 [50]

Let g(x) = 2x and h(x) = x2 + 4. Evaluate (h ∘ g)(−2).

A. −12

the corrects answer is <em>B. −16 </em>

C. 20

D. 16

7 0

2 years ago

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Find the selling price of each item original plate price of gold fish at $7.65 discount 10%￼

Find the selling price of each item original plate price of gold fish at $7.65 discount 10%