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2 years ago

A paper company needs to ship paper to a large printing business. The paper will be

Mathematics

1 answer:

Kryger [21]2 years ago

5 0

Answer:

x = 8

y = 11

Step-by-step explanation:

Total small box weight = 50x [x being the number of small boxes]

Total large box weight = 80y [y being the number of large boxes]

Total boxes = x+y = 19

Total weight = 1280

Determine x and y.

You know 2 equations. One for weight and another for number of boxes each.

1280 = 50x +80y
x+y = 19

Rewrite second equation:

x+y=19

y=19-x

You have to plug in one into another.

1280 = 50x + 80(19-x)

Solve for x

1280 = 50x + 1520 - 80x

-240 = -30x

x = 8

Solve for y by plugging in x into one of the equations:

8+y = 19

y = 11

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Find the equation of the line that is parallel to the given line and passes through the given point

Sati [7]

Answer:

$\huge\boxed{y=-\dfrac{1}{4}x-1\to x+4y=-4}$

Step-by-step explanation:

$\text{Let}\ k:y=m_1x+b_1;\ l:y=m_2x+b_2\\\\l\ ||\ k\iff m_1=m_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\==========================\\\\\text{We have}\ x+4y=-6.\\\text{Convert to the slope-intercept form:}\\\\x+4y=-6\qquad\text{subtract}\ x\ \text{from both sides}\\\\4y=-x-6\qquad\text{divide both sides by 4}\\\\y=\dfrac{-x}{4}-\dfrac{6}{4}\\\\y=-\dfrac{1}{4}x-\dfrac{3}{2}\to m_1=-\dfrac{1}{4}$

$\text{Lines are to be parallel. Therefore}\ m_2=-\dfrac{1}{4}.\\\\\text{We initially have the form equation}\ y=-\dfrac{1}{4}x+b.\\\\\text{The line passes through the point}\ (9,\ -3).\\\\\text{Substitute the coordinates of the point to the equation of a line:}\\\\x=9,\ y=-3\\\\-3=-\dfrac{1}{4}(9)+b\\\\-3=-\dfrac{9}{4}+b\qquad\text{add}\ \dfrac{9}{4}\ \text{to both sides}\\\\-\dfrac{12}{4}+\dfrac{9}{4}=b\to b=-\dfrac{3}{4}$

$x=8,\ y=-3\\\\-3=-\dfrac{1}{4}(8)+b\\\\-3=-2+b\qquad\text{add 2 to both sides}\\\\-1=b\to b=-1$

$\text{Therefore the equation is:}\ y=-\dfrac{1}{4}x-1.\\\\\text{Convert to the standard form}\ Ax+By=C:\\\\y=-\dfrac{1}{4}x-1\qquad\text{multiply both sides by 4}\\\\4y=-x-4\qquad\text{add}\ x\ \text{to both sides}\\\\x+4y=-4$

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3 years ago

Find f(-2) for f(x) = 3x +4.

Bingel [31]

Answer:

f(- 2) = - 2

Step-by-step explanation:

To evaluate f(- 2) substitute x = - 2 into f(x)

f(- 2) = 3(- 2) + 4 = - 6 + 4 = - 2

5 0

2 years ago

Subtract 715 from the sum of 810 and 189

hodyreva [135]

810+189-715= 284. the answer is 284

3 0

2 years ago

Read 2 more answers

Lucy is on her way home in her car. She has driven 22 miles so far, which is one-half of the way home. What is the total length

Ket [755]

Answer:

Step-by-step explanation:

if 22 miles = 1/2

then, 22 times 2 = 44 miles

ANSWER= 44 miles

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2 years ago

Montraie is driving on a long road trip. He currently has 13 gallons of gas in his car.

dedylja [7]

Answer:

7 gallons

Step-by-step explanation:

Montraie is driving on a long road trip

He currentlyhase 13 gallons of fuel in his car

Each hour that he drives, he uses up 1 gallon of fuel

Therefore the amount of gas that would be left after 6 hours can be calculated as follows

= 13-6

= 7

Hence there will be 7 gallons of fuel left

6 0

3 years ago