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lidiya [134]
3 years ago
12

Solve for x 27^(2x+4)=1/9^(x-46)

Mathematics
1 answer:
lys-0071 [83]3 years ago
8 0
27^{2x+4}=(\frac{1}{9})^{x-46} \\
(3^3)^{2x+4}=(3^{-2})^{x-46} \\
3^{3(2x+4)}=3^{-2(x-46)} \\
3^{6x+12}=3^{-2x+92} \\
6x+12=-2x+92 \\
6x+2x=92-12 \\
8x=80 \\
x=10
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The number 64 has the property that it is divisible by its units digit. How many whole numbers between 10 and 50 have this prope
sineoko [7]

Answer:

\large \boxed{17}

Step-by-step explanation:

Let's call the numbers "<em>tu</em>", where<em> t</em> is the tens digit and <em>u</em> is the units digit.

We can solve this by the "brute force" method —  examining each number to see if it satisfies the conditions.

\begin{array}{cccl}\mathbf{u}&\mathbf{tu}& \textbf{Divisible by u} & \\0 &20, 30, 40 & 0 & \text{Division by zero is impossible}\\1 & 11, 21, 31, 41 & 4& \text{All numbers are divisible by one}\\2 & 12, 22, 32, 42 & 4 & \text{All even numbers are divisible by two}\\3 & 13,  23, 33, 43 & 1 &\text{Only 33 is divisible by three}\\4 & 14, 24, 34, 44 & 2 & \text{Only 24 and 44 are divisible by four}\\5 & 15, 25, 35, 45 & 4 & \text{Numbers ending in 5 are divisible by five}\\\end{array}

\begin{array}{cccl}6 & 16, 26, 36, 46 & 1 & \text{Only 36 is divisible by six}\\7 & 17, 27, 37, 47 & 0 & \text{None of the numbers is divisible by seven}\\8 & 18, 28, 38, 48 & 1 & \text{Only 48 is divisible by eight}\\9 & 19, 29, 39, 49 & 0 & \text{None of the numbers is divisible by nine}\\& \textbf{TOTAL =} &\mathbf{17}& \\\end{array}\\\text{$\large \boxed{\mathbf{17}}$ numbers between 10 and 50 are divisible by their units digit}

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3 years ago
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7 0
3 years ago
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A pyramid has a regular hexagonal base with side lengths of 4 and a slant height of 6. Find the total area of the pyramid.
CaHeK987 [17]
Area of the Base = 6 * side^2 / 4 * tan (180/6)
Area of the Base = 6 * 16 / 4 * 0.57735
Area of the Base = 96 / <span> <span> <span> 2.3094 </span> </span> </span>
Area of the Base = <span> <span> <span> 41.5692387633 </span> </span> </span>

Area of 1 Face = 2 * 6 = 12
Area of 6 Faces = 72

<span> <span> Total Area = 41.5692387633 </span> + 72</span>
Total Area = 113<span>.5692387633</span>


6 0
3 years ago
Read 2 more answers
There is $500 in Holly's bank account. She takes out $50 from her account each month but doesn't put money back in. What is the
galina1969 [7]

Answer:

The rate of change or slope m  = -50

Step-by-step explanation:

The slope-intercept form of the line equation

y = mx+b

where

  • m is the rate of change or slope
  • b is the y-intercept

Given that there is $500 in Holly's bank account.

Thus, the y-intercept b = 500

It is stated that she takes out $50 from her account each month but doesn't put money back in.

It means the rate of change or slope is decreasing.

Thus, the rate of change or slope m  = -50

<u>EXTRA BONUS!</u>

We can also determine the line equation by substituting m = -50 and b = 500 in the slope-intercept form

y = mx+b

y = -50x + 500

Here:

The slope m = -50

The y-intercept = 500

3 0
3 years ago
To make concrete it takes 8 parts crushed gravel, 7 parts water and 5 parts cement mix. A worker needs to make 220kg of concrete
Alika [10]
A) 8 + 7 + 5 = 20 parts
b) 220 kg ÷ 20 = 11
c) <span> 8 parts crushed gravel: 8 x 11 = 88 kg
     7 parts water: 7 x 11 = 77 kg
     5 parts cement: 5 x 11 = 55 kg</span>
8 0
3 years ago
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