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3 years ago

Mon wants to make 5 lbs of the sugar syrup. How much water and how much sugar does he need to make 1.5% syrup?

Mathematics

1 answer:

Alona [7]3 years ago

6 0

Answer:

He needs 0.075 lbs of sugar and 4.925 lbs of water.

Step-by-step explanation:

Let x lbs be the amount of sugar in the syrup. Then 5-x lbs is the amount of water in this syrup.

Note

5 lbs - 100%

x lbs - 1.5%

Write a proportion:

$\dfrac{5}{x}=\dfrac{100}{1.5}$

Cross multiply:

$100x=5\cdot 1.5\\ \\100x=7.5\\ \\x=\dfrac{7.5}{100}=0.075$

So, he needs 0.075 lbs of sugar and 5 - 0.075 = 4.925 lbs of water.

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67. The line contains the point (4,0) and is parallel to the line defined by 3x = 2y.

olganol [36]

Answer:

$y=\frac{3}{2} x-6$

Step-by-step explanation:

Hi there!

What we need to know:

Linear equations are typically organized in slope-intercept form:

$y=mx+b$ where m is the slope of the line and b is the y-intercept (the value of y when the line crosses the y-axis)

Parallel lines will always have the same slope but different y-intercepts.

1) Determine the slope of the parallel line

Organize 3x = 2y into slope-intercept form. Why? So we can easily identify the slope, m.

$3x = 2y$

Switch the sides

$2y=3x$

Divide both sides by 2 to isolate y

$\frac{2y}{2} = \frac{3}{2} x\\y=\frac{3}{2} x$

Now that this equation is in slope-intercept form, we can easily identify that $\frac{3}{2}$ is in the place of m. Therefore, because parallel lines have the same slope, the parallel line we're solving for now will also have the slope $\frac{3}{2}$ . Plug this into $y=mx+b$ :

$y=\frac{3}{2} x+b$

2) Determine the y-intercept

$y=\frac{3}{2} x+b$

Plug in the given point, (4,0)

$0=\frac{3}{2} (4)+b\\0=6+b$

Subtract both sides by 6

$0-6=6+b-6\\-6=b$

Therefore, -6 is the y-intercept of the line. Plug this into $y=\frac{3}{2} x+b$ as b:

$y=\frac{3}{2} x-6$

I hope this helps!

7 0

3 years ago

If f(x) = 3x + 10 and g(x) = 2x - 4, find (f - g)(x).

torisob [31]

<h3>Answer: Choice A) x+14</h3>

=======================================

Work Shown:

(f-g)(x) = f(x) - g(x)

(f-g)(x) = (f(x)) - (g(x))

(f-g)(x) = (3x+10) - (2x-4)

(f-g)(x) = 3x+10 - 2x+4

(f-g)(x) = (3x-2x) + (10+4)

(f-g)(x) = x+14

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3 years ago

Find the Net Pay: 40 hours worked, $7.85 an hour. Deductions: Federal tax $32.24, Social Security $24.02, Other $24.53 Answer $3

Trava [24]

For the answer to the question on what is the net pay if you are 40 hours worked, $7.85 an hour. Deductions: Federal tax $32.24, Social Security $24.02, Other.

The answer to this question is the last one which is $233.21

I hope my answer helped you.

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3 years ago

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MakcuM [25]

Step-by-step explanation:

$\sqrt{3 x - \sqrt{2x = 4} }$