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3 years ago

Can someone please help me with this math question .

Mathematics

1 answer:

Alona [7]3 years ago

5 0

No, Yes, No, Yes

using the laws of exponents

(1)

( $4^{3}$ )³ = $4^{9}$

4³ × 4³ = $4^{6}$

$4^{9}$ ≠ $4^{6}$ → No

(2)

( $3^{4}$ )^4 = $3^{16}$

$3^{8}$ × $3^{8}$ = $3^{16}$ → Yes

(3)

$18^{8}$ = (6 × 3 )^8 = $6^{8}$ × $3^{8}$ ≠ $6^{4}$ × $3^{4}$ → No

(4)

$20^{3}$ = (4 × 5 )³ = 4³ × 5³ → Yes

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\sqrt{2x+\cfrac{4369}{25}}-\cfrac{2}{5}=t$

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A) $f(t)=6-\frac{2}{3}t$

B) The value of f(-3) is 8

C) The value of t is 6

Step-by-step explanation:

* Lets explain how to solve the problem

- The relation is 3r + 2t = 18

- To change the relation as a function of f(t) you must to find r in terms

of t that means put r in one side and the others in the second side

∵ 3r + 2t = 18

- Subtract 2t from both sides

∴ 3r = 18 - 2t

- Divide each side by 3

∴ r = 18/3 - 2t/3

∴ r = 6 - 2/3 t

- Change the equation to a function by using the function notation

∵ r = f(t)

∴ $f(t)=6-\frac{2}{3}t$

- To evaluate f(-3) substitute t by -3 in f(t)

∵ $f(t)=6-\frac{2}{3}t$

∴ $f(-3)=6-\frac{2}{3}(-3)=6-(-2)=6+2=8$

∴ f(-3) = 8

* The value of f(-3) is 8

- Solve f(t) = 2 means find the value of t when r = 2

∵ $f(t)=6-\frac{2}{3}t$

∵ f(t) = 2

∴ $2=6-\frac{2}{3}t$

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- Multiply both sides by 3

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