Find the exact solution to the equation. Show your work. 4^(12-4x) = 256
(I know the answer is 2, the thing I don't know how to do correctly is showing my work)

Answers

Answer 1

Answer: Hello,

$4^(12-4x)=256\n ==\ \textgreater \ \ 2^(24-8x)=2^8\n ==\ \textgreater \ \ 24-8x=8\n ==\ \textgreater \ 8x=16\n ==\ \textgreater \ x=2$

Answer 2

Answer: Hi

4^(12-4x) =256
First we need to take log of both sides
log(4^-4x+12) = log (256)
(-4x + 12)(log(4)) = log(256)
so now we have
-4x + 12 = log(256)/log(4)
-4x + 12 = 4
-4x = 4 - 12
-4x = -8
x = -8/-4
x= 2

I hope that's help :)

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Solving need help in don't get it

Answers

$√(3x-5)-2=0$
add 2 to both sides
$√(3x-5)=2$
square both sides
3x-5=4
add 5 to both sides
3x=9
divide 3
x=3

a nswer is B

The ticket price for the ice hockey match was £14.50. The price has increased by 7%. How much is a ticket after the increase?

Answers

7%= $\frac {7}{100}$ = 0.07
14.5 × 0.07 = 1.015
Add this number to the original:
14.5+1.015 = £15.515

There is another way, whenever they give us an increased Percentage, they provide us with a hint!
we add that increased percent to 100
100+7=107%
107%= $(107)/(100)$ = 1.07
14.5×1.07= £15.515, it can also be rounded to 15.52
£15.515≈£15.52

A triangle has sides with lengths of 5x - 2, 4x - 4, 6x - 8. What is the perimeter of the triangle?

Answers

Answer:

(15x - 4) units

Step-by-step explanation:

5x-2 + 4x-4 + 6x - 8

15x - 14

There is a 0.23 probability that a typical convenience store customer buys gasoline. The probability that a customer buys groceries is 0.76 and the conditional probability of buying groceries given that the customer buys gasoline is 0.85.a) Find the probability that a typical customer buys both gasoline and groceries.

Answers

Answer:

The probability that a typical customer buys both gasoline and groceries, P(Ga n Gr) = 0.1955

Step-by-step explanation:

Let the probability that a customer guys groceries be represented by P(Gr) and that of buying gasoline be P(Ga)

Given

P(Gr) = 0.76

P(Ga) = 0.23

P(Gr|Ga) = 0.85

For mutually exclusive events,

P(B|A) = (P(B n A))/P(A)

P(Gr|Ga) = (P(Gr n Ga))/P(Ga)

P(Gr n Ga) = P(Gr|Ga) × P(Ga)

P(Gr n Ga) = 0.85 × 0.23 = 0.1955

Hope this Helps!!!!

Work out 5/8−2/5 Give your answer in its simplest form.

Answers

$(5)/(8) - (2)/(5)$

First, find the LCD (least common denominator) of the two fractions.
List the multiples of each denominator and find the one that is common.
Multiples of 8: 8, 16, 24, 32, 40
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40
40 is your LCD.

Second, what can you divide by to make the denominators of each fraction '40'? Whatever you do to the bottom you must do to the top.
$(5*5)/(8*5) - (2*8)/(5*8)$

Third, multiply.
$(25)/(40) - (16)/(40)$

Fourth, since the denominators are the same now, we can combine them.
$(25-16)/(40)$

Fifth, subtract '25 - 16' to get 9.
$(9)/(40)$

Since $(9)/(40)$ is already in the simplest form, it is your answer.

Answer as fraction: $(9)/(40)$
Answer as decimal: $0.225$

Point Mis on line segment LN. Given LN = 9, MN. = 4x, andLM = 5x, determine the numerical length of MN.