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vlada-n [284]
3 years ago
6

you have a large container of olive oil. You have used 22 1/2 quarts of oil. Twenty- five percent of the oil remain. How many qu

arts of olive oil remain
Mathematics
1 answer:
Alex Ar [27]3 years ago
3 0
Answer:

7.5 quarts of olive oil remain.

Explanation:

Let

q = quarts of olive oil remain

<span>25%</span> of olive oil remains means that <span>75%</span> has been used.

22<span>12</span> quarts = 22.5 quarts used

<span><span>22.5.75</span>=<span>q.25</span></span>

Multiply both sides by .25 to isolate q.

<span><span>22.5.75</span><span>(.25)</span>=<span>q.25</span><span>(.25)</span></span>

<span><span>5.625.75</span>=q</span>

<span>7.5=<span>q</span></span>

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From base camp, a hiker walks 3.5 miles west and 1.5 miles north. Another hiker walks 2 miles east and 0.5 miles south. To the n
levacccp [35]

Answer:

The hikers are 5.9 miles apart.

Step-by-step explanation:

Let O represents the base camp,

Suppose after walking 3.5 miles west, first hiker's position is A, then after going 1.5 miles north from A his final position is B,

Similarly, after walking 2 miles east, second hiker's position is C then going towards 0.5 miles south his final position is D.

By making the diagram of this situation,

Let D' is the point in the line AB,

Such that, AD' = CD

In triangle BD'D,

BD' = AB + AD' = 1.5 + 0.5 = 2 miles,

DD' = AC = AO + OC = 3.5 + 2 = 5.5 miles,

By Pythagoras theorem,

BD^2 = BD'^2 + DD'^2

BD = \sqrt{2^2 + 5.5^2}=\sqrt{4+30.25}=\sqrt{34.25}\approx 5.9

Hence, the hikers are 5.9 miles apart.

8 0
2 years ago
Passing through (-2,1 ) and perpendicular to<br> 4x + 7y + 3 = 0.
Lunna [17]

Answer:

<h2>7x - 4y + 18 = 0</h2>

Step-by-step explanation:

The slope-intercept form of an equation of a line:

y=mx+b

m - slope

b - y-intercept

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

Let

k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2

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

We have the equation of a line in a general form (Ax + By + C = 0)

Convert it to the slope-intercept form:

4x+7y+3=0             <em>subtract 7y from both sides</em>

4x+3=-7y         <em>divide both sides by (-7)</em>

-\dfrac{4}{7}x-\dfrac{3}{7}=y\to m_1=-\dfrac{4}{7}

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m_2=-\dfrac{1}{-\frac{4}{7}}=\dfrac{7}{4}

We have the equation:

y=\dfrac{7}{4}x+b

Put the coordinates of the point (-2, 1) to the equation, and solve for <em>b</em> :

1=\dfrac{7}{4}(-2)+b

1=-\dfrac{7}{2}+b     <em>multiply both sides by 2</em>

2=-7+2b           <em>add 7 to both sides</em>

9=2b            <em>divide both sides by 2</em>

[te]x\dfrac{9}{2}=b\to b=\dfrac{9}{2}[/tex]

Finally:

y=\dfrac{7}{4}x+\dfrac{9}{2} - <em>slope-intercept form</em>

Convert to the general form:

y=\dfrac{7}{4}x+\dfrac{9}{2}         <em>multiply both sides by 4</em>

4y=7x+18      <em>subtract 4y from both sides</em>

0=7x-4y+18

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