A 5-lb box of soap powder costs $ 4.65. A 10-lb box of the same powder costs $ 8.90. Which is the better price?
1 answer:
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Answer:
Step-by-step explanation:
We can use the trigonometric formula for the area of a triangle:
Where a and b are the side lengths, and C is the angle <em>between</em> the two side lengths.
As demonstrated by the line, ABCD is the sum of the areas of two triangles: a right triangle ABD and a scalene triangle CDB.
We will determine the area of each triangle individually and then sum their values.
Right Triangle ABD:
We can use the above area formula if we know the angle between two sides.
Looking at our triangle, we know that ∠ADB is 55 DB is 10.
So, if we can find AD, we can apply the formula.
Notice that AD is the adjacent side to ∠ADB. Also, DB is the hypotenuse.
Since this is a right triangle, we can utilize the trig ratios.
In this case, we will use cosine. Remember that cosine is the ratio of the adjacent side to the hypotenuse.
Therefore:
Solve for AD:
Now, we can use the formula. We have:
Substituting AD for a, 10 for b, and 55 for C, we get:
Simplify. Therefore, the area of the right triangle is:
We will not evaluate this, as we do not want inaccuracies in our final answer.
Scalene Triangle CDB:
We will use the same tactic as above.
We see that if we can determine CD, we can use our area formula.
First, we can determine ∠C. Since the interior angles sum to 180 in a triangle, this means that:
Notice that we know the angle opposite to CD.
And, ∠C is opposite to BD, which measures 10.
Therefore, we can use the Law of Sines to determine CD:
Where A and B are the angles opposite to its respective sides.
So, we can substitute 98 for A, 10 for a, 38 for B, and CD for b. Therefore:
Solve for CD. Cross-multiply:
Divide both sides by sin(98). Hence:
Therefore, we can now use our area formula:
We will substitute 10 for a, CD for b, and 44 for C. Hence:
Simplify. So, the area of the scalene triangle is:
Therefore, our total area will be given by:
Approximate. Use a calculator. Thus:
Answer:
<h2>The answer is option C</h2>Step-by-step explanation:
To find an equation of a line in point slope form when given the slope and a point we use the formula
where
m is the slope
( x1 , y1) is the point
From the question the point is (1,2) and the slope is 6
The equation of the line in point slope form is
<h2>Hope this helps you
Answer:
<em>The probability is 0.89 or 89%</em>
Step-by-step explanation:
<u>Probability</u>
There are n=27 students in a certain Algebra 2 class. 18 out of them play basketball and 16 of them play baseball.
We also know 3 students play neither sport. This leaves 27-3=24 students playing sports.
The probability that a randomly chosen student plays basketball or baseball is:
Simplifying:
The probability is 0.89 or 89%