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Andreyy89
3 years ago
8

What is the solution of log4(2x-6)=2

Mathematics
1 answer:
Flauer [41]3 years ago
3 0

Answer: x=11

Step-by-step explanation:

Remembert that, by definition:

log_b(x)=y → b^y=x

Then, you can rewrite log_4(2x-6)=2 in exponential form:

4^2=2x-6

Now you can solve for the variable "x":

Add 6 to both sides of the equation:

4^2+6=2x-6+6

22=2x

And finally you must divide both sides of the equation by 2, then:

\frac{22}{2}=\frac{2x}{2}\\\\x=11

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If you launch the cannonball from the ground instead (hi=0), what does that change in the original equation?
ikadub [295]

Answer:

  the value of hi changes from 58 to 0:

  h(t) = -4.9t^2 +19.8t

Step-by-step explanation:

If the initial height changes, then the term in the equation that represents that height will change. The initial height term is hi, so it changes from 58 to 0.

  h(t)=-4.9t^2+19.8t+0\\\\\boxed{h(t)=-4.9t^2+19.8t}

7 0
2 years ago
Alexis wants to make a paperweight at pottery class. He designs a pyramid-like model with a base area of 100 square centimeters
chubhunter [2.5K]

Answer:

1 g/cm³

Step-by-step explanation:

Volume of the model:

V=1/3bh= 1/3*100*6= 300 cm³

Density= weight/volume= 300 g/300 cm³= 1 g/cm³

The lowest density is 1 g/cm³

7 0
3 years ago
Simplify 4( x - 6) ^2 / ( x - 6)​
Leno4ka [110]

Answer:

4x - 24

Step-by-step explanation:

\frac{4(x - 6 {)}^{2} }{(x - 6)}

4(x - 6) = 4x - 4 \times 6 = 4x - 24

4x - 24

5 0
2 years ago
Read 2 more answers
The school uses between 300 and 400 sheets of paper per school day. If paper costs the school $2.00 per 100 sheets, approximatel
Nady [450]

Answer:

  • Option A. $140.00

Explanation:

<u>1. Using the minimun number of sheets  of paper in the interval [300, 400]</u>

a) Cost: $ 2.00 / 100 sheets

b) 300 sheets / day × $ 2.00 / 100 sheets = $ 6.00 / day

c) Approimately 20 school days per month:

  • $ 6.00 / day × 20 day = $ 120.00

<u>2. Using the maximum number of sheets of paper in the interval [300, 400]</u>

a) Cost: $ 2.00 / 100 sheets

b) 400 sheets / day × $ 2.00 / 100 sheets = $ 8.00 / day

c) Approimately 20 school days per month:

  • $8.00 / day × 20 day = $ 160.00

<u>3. Middle value:</u>

Calculate the middle value between $160.00 and $120.00

  • [$120.00 + $160.00] / 2 = $140.00

Thus, the answer is the option A.

7 0
3 years ago
________________________
xenn [34]

✩ Answer:

 ✧・゚: *✧・゚:*✧・゚: *✧・゚:*✧・゚: *✧・゚:*  

 \bold{Hello!}\\\bold{Your~answer~is~below!}  

✩ Step-by-step explanation:

 ✧・゚: *✧・゚:*✧・゚: *✧・゚:*✧・゚: *✧・゚:*

✺ Divide both sides by −3. Since −3 is negative, the inequality direction is changed:

  • -3 ÷ -3 = Cancels Out
  • Turns into: \frac{-9}{-3} >5x-2

✺ Divide −9 by −3 to get 3. Since they are both negatives it turns into a positive:

  • -9 ÷ -3 = 3
  • Turns into: 3 > 5x - 2

✺ Swap sides so that all variable terms are on the left hand side. This changes the sign direction once more:

  • Turns into: 5x-2

✺ Add 2 to both sides:

  • Turns into: 5x

✺ Add 3 and 2 to get 5:

  • 3 + 2 = 5
  • Turns into: 5x

✺ Divide both sides by 5. Since 5 is positive, the inequality direction remains the same:

  • 5 ÷ 5 = Cancels Out
  • Turns into: x

✺ Divide 5 by 5 to get 1:

  • 5 ÷ 5 = 1

✺  So your answer is B, \boxed{x.

(Number line is below.)

Hope~this~helps~and,\\Best~of~luck!\\\\~~~~~-TotallyNotTrillex

5 0
3 years ago
Read 2 more answers
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