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natulia [17]
3 years ago
13

Use a system of equations to solve this problem.

Mathematics
1 answer:
emmainna [20.7K]3 years ago
6 0
We have to set up 2 equations:
A) x + y = 10 liters
B) .05x + .25y = 10 * .10

Multiply equation B) by -4
B) -.2x  - y = -4 then add to equation A)
A) x + y = 10 liters
.8x = 6 liters
x = 7.5 liters of 5%
y = 2.5 liters of 25%

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What is the value of x? <br><br> Enter your answer in the box.<br><br> X =
melamori03 [73]

Answer:

x=54

Step-by-step explanation:

2x + 2 = 3x - 52

subtract 2x from both sides, now u have:

2 = x - 52

add 52 from both sides, now u have

54 = x

7 0
3 years ago
Free points help me​
geniusboy [140]
The answer is d your welcome
3 0
3 years ago
Read 2 more answers
PLEASE HELP ASAP! I don’t recall how to do this!
MakcuM [25]

Answer:

Step-by-step explanation:

For a. we start by dividing both sides by 200:

(1.05)^x=1.885

In order to solve for x, we have to get it out from its position of an exponent.  Do that by taking the natural log of both sides:

ln(1.05)^x=ln(1.885)

Applying the power rule for logs lets us now bring down the x in front of the ln:

x * ln(1.05) = ln(1.885)

Now we can divide both sides by ln(1.05) to solve for x:

x=\frac{ln(1.885)}{ln(1.05)}

Do this on your calculator to find that

x = 12.99294297

For b. we will first apply the rule for "undoing" the addition of logs by multipllying:

ln(x*x^2)=5

Simplifying gives you

ln(x^3)=5

Applying the power rule allows us to bring down the 3 in front of the ln:

3 * ln(x) = 5

Now we can divide both sides by 3 to get

ln(x)=\frac{5}{3}

Take the inverse ln by raising each side to e:

e^{ln(x)}=e^{\frac{5}{3}}

The "e" and the ln on the left undo each other, leaving you with just x; and raising e to the power or 5/3 gives you that

x = 5.29449005

For c. begin by dividing both sides by 20 to get:

\frac{1}{2}=e^{.1x}

"Undo" that e by taking the ln of both sides:

ln(.5)=ln(e^{.1x})

When the ln and the e undo each other on the right you're left with just .1x; on the left we have, from our calculators:

-.6931471806 = .1x

x = -6.931471806

Question d. is a bit more complicated than the others.  Begin by turning the base of 4 into a base of 2 so they are "like" in a sense:

(2^2)^x-6(2)^x=-8

Now we will bring over the -8 by adding:

(2^2)^x-6(2)^x+8=0

We can turn this into a quadratic of sorts and factor it, but we have to use a u substitution.  Let's let u=2^x

When we do that, we can rewrite the polynomial as

u^2-6u+8=0

This factors very nicely into u = 4 and u = 2

But don't forget the substitution that we made earlier to make this easy to factor.  Now we have to put it back in:

2^x=4,2^x=2

For the first solution, we will change the base of 4 into a 2 again like we did in the beginning:

2^2=2^x

Now that the bases are the same, we can say that

x = 2

For the second solution, we will raise the 2 on the right to a power of 1 to get:

2^x=2^1

Now that the bases are the same, we can say that

x = 1

5 0
3 years ago
I need the answer in 1 minute
Varvara68 [4.7K]

Answer:

4 Units.

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
The smallest natural number divisible by 2,3,4,5,6,8 and 9 is____.
SVETLANKA909090 [29]

Answer:

360

Step-by-step explanation:

You will need 2 * 2 * 2 for the smallest number to be divisible by 8 with all the others.

You will need 3 * 3  for the smallest number to be divisible by 9 with all the others.

Finally you will need 1 five

The smallest number divisible by all of these is 2*2*2*3*3*5 = 360

  • 360/2 = 180 works
  • 360/3 = 120 works
  • 360/5 = 72   works
  • 360/6 = 60 works
  • 360/8 = 45 works
  • 360/9 = 40 works.

There is no smaller number below 360 which will work.

7 0
3 years ago
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