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mart [117]
3 years ago
6

Solve for x given that

%7D%20" id="TexFormula1" title=" {64}^{2x - 1} = {32}^{x + 1} " alt=" {64}^{2x - 1} = {32}^{x + 1} " align="absmiddle" class="latex-formula">
​
Mathematics
1 answer:
marissa [1.9K]3 years ago
8 0

Answer:

x = \frac{11}{7}

Step-by-step explanation:

note that 64 = 2^{6} and 32 = 2^{5} , thus

(2^{6}) ^{2x-1} = (2^{5}) ^{x+1} , that is

2^{6(2x-1)} = 2^{5(x+1)}

2^{12x-6} = 2^{5x+5}

Since the bases on both sides are equal, then equate the exponents

12x - 6 = 5x + 5 ( subtract 5x from both sides )

7x - 6 = 5 ( add 6 to both sides )

7x = 11 ( divide both sides by 7 )

x = \frac{11}{7}

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Paper plates cost $8 per package and plastic utensils cost $5 per package. Your supplier delivers 15 packages for a total cost o
Fittoniya [83]
To find the total of what you sold for each package, you'll need to write two equations. Know that x = paper plate packages and y = utensil packages.
First, x + y = 15 shows that there has to be fifteen packages, and 8x + 5y = 90 shows the $ made from selling a certain number of packages.
Next, you can solve by substitution, so change x + y = 15 to y = 15 - x.

To find our x, substitute the y in 8x + 5y = 90 to get
8x + 5(15 - x) = 90
Distribute: 8x + 75 - 5x = 90
Combine the X's and subtract the 75: 3x = 15
Divide the 3: x = 5

Now with our x, we can put 5 into the original equation x + y = 15 to get 5 + y = 15. Subtracting the 5, we get y = 10.

So, you have delivered 5 paper plate packages and 10 utensil packages.
8 0
3 years ago
Does anyone know how to solve this?
Bezzdna [24]

Use this version of the Law of Cosines to find side b:

b^2 = a^2 + c^2 − 2ac cos(B)

We want side b.

b^2 = (41)^2 + (20)^2 - 2(41)(20)cos(36°)

After finding b, you can use the Law of Sines to find angles A and C or use other forms of the Law of Cosines to find angles A and C.

Try it....

6 0
3 years ago
Quien puede resolver solo el problema 59 , porfavor!!<br>si no van a responder bien , no respondan
RideAnS [48]

Answer:

number 58 es...

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6 0
3 years ago
0.2(12x-10)-3x+2=0<br> what's the answer?
lina2011 [118]

Answer:

im not sure but i think its -25

Step-by-step explanation:

hope im not wrong:)

hope you have a great day and god loves you:))

8 0
3 years ago
Read 2 more answers
6000 is deposited into a fund at the annual rate of 9.5%. Find the time required for the investment to double if the interest is
Anna [14]

Answer: 7.58 years

Step-by-step explanation:

When it comes to finding out how long it will take for an investment to double, one can use the Rule of 72.

The Rule of 72 estimates the amount of time it will take to double an investment when you divide 72 by the interest rate:

= 72 / r

= 72 / 9.5

= 7.58 years

3 0
2 years ago
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