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3 years ago

What is the solution to the equation below?

Mathematics

1 answer:

Harman [31]3 years ago

7 0

Answer:

$\frac{38}{7}$

Step-by-step explanation:

Using the properties of logarithms,

$\log(7)+\log(x-4)=1\\\log(7(x-4))=1\\\log(7x-28)$

Now think about what this is asking. The log function say 10 to the power of whats on the other side of the equals sign, equals whats in the parenthesis. So, this means whats is the parenthesis is equal to $10^1$ or just 10.

We can now solve to x.

$7x-28 = 10\\7x=38\\x=\frac{38}{7}$

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Solve the compound inequality n-4 > 5 AND 2 > n + 3

Papessa [141]

Get n by itself in both inequalities

(This program doesn't allow for regular less than or greater than signs, so for the purposes of this problem I will be using less than or equal to (≤) and greater than or equal to (≥) signs)

Inequality 1:
$n-4 \geq 5 \\ n \geq 9$

Inequality 2:
$2 \geq n+3 \\ -1 \geq n$

Now that you have both of the n's by themselves, you can put the two inequalities together, like this
$-1 \geq n \geq 9$

Just keep in mind that these are supposed to be regular less than signs

5 0

3 years ago

Ella has 0.5 lbs of sugar. How much water should she add to make the following concentrations? Tell Ella how much syrup she will

olya-2409 [2.1K]

Answer:

1. 20% - add 2 lbs of water to get 2.5 lbs of syrup

2. 25% - add 1.5 lbs of water to get 2 lbs of syrup

3. 1.5% - add 32.833 lbs of water to get 33.333 lbs of syrup

Step-by-step explanation:

Ella has 0.5 lbs of sugar. Let x lbs be the amount of water Ella should add to get the syrup.

1. 20% syrup:

0.5 lbs - 20%

x+0.5 lbs - 100%

Write a proportion:

$\dfrac{0.5}{x+0.5}=\dfrac{20}{100}\\ \\0.5\cdot 100=(x+0.5)\cdot 20\\ \\50=20x+10\\ \\20x=50-10\\ \\20x=40\\ \\x=2\ lbs$

To get 20% syrup Ella should add 2 lbs of water. The total weight of strup is 2.5 lbs.

2. 25% syrup:

0.5 lbs - 25%

x+0.5 lbs - 100%

Write a proportion:

$\dfrac{0.5}{x+0.5}=\dfrac{25}{100}\\ \\0.5\cdot 100=(x+0.5)\cdot 25\\ \\50=25x+12.5\\ \\25x=50-12.5\\ \\25x=37.5\\ \\x=1.5\ lbs$

To get 25% syrup Ella should add 1.5 lbs of water. The total weight of strup is 2 lbs.

3. 1.5% syrup:

0.5 lbs - 1.5%

x+0.5 lbs - 100%

Write a proportion:

$\dfrac{0.5}{x+0.5}=\dfrac{1.5}{100}\\ \\0.5\cdot 100=(x+0.5)\cdot 1.5\\ \\50=1.5x+0.75\\ \\1.5x=50-0.75\\ \\1.5x=49.25\\ \\x=\dfrac{49.25}{1.5}\approx 32.833\ lbs$

To get 1.5% syrup Ella should add 32.833 lbs of water. The total weight of strup is 33.333 lbs.

7 0

3 years ago

The temperature is 0 degrees, every hr it's dropping 3 degrees the temperature is -6 degrees at a certain time. How mush did the

mariarad [96]

Answer:

i think 2

Step-by-step explanation:

4 0

3 years ago

Gabby is an aspiring country artist. She has a record contract that pays her a base rate of $200 a month and an additional $12 f

Rus_ich [418]

Answer:

From the formula above, you see that your slope would be the $12.

Step-by-step explanation:

So, from this problem the base rate is the y-intercept because it is fixed. The slope of the is the additional fee because it's changing by the number of albums sold. Below is the equation that should have been created using the slope intercept formula.

220 + 12x = 644

You will need the slope intercept form, y = mx + b

m is the slope

b is the y-intercept

5 0

3 years ago

Y=6x 2x+3y=-20. (Solving by substitution)

almond37 [142]

Y=6x, 2x+3y=-20
Substitution means just plugging in another equation equal to a single variable in order to solve for the other variable, and then the first. In this case, the equation being plugged in is y=6x, so 6x will be put in place of y in the equation 2x+3y=-20.
2x+3(6x)=-20
2x+18x=-20
20x=-20
x=-1
And then x=-1 can be plugged into the original equation to find y. (And, if you wish, into the y= equation to check it.)
2(-1)+3y=-20
-2+3y=-20
3y=-20+2
3y=-18
y=-6
And to check it, we plug the two into the original y= equation.
y=6x
-6=6(-1)
-6=-6
They are equal, so both check out.
x=-1, y=-6

7 0

3 years ago

Read 2 more answers