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zubka84 [21]
3 years ago
5

Justin is on a road trip. Over the past two days, he’s driven a total distance of 504 miles at an average speed of 56 miles/hour

. If Justin drove two hours today, he drove miles yesterday.
Mathematics
1 answer:
irakobra [83]3 years ago
8 0
Recall d  = rt, distance = rate * time.

now, he has a speed rate of 56 mph for a distance of 504

\bf d=rt\implies 504=56t\implies \cfrac{504}{56}=t\implies \stackrel{hours}{9}=t

so, at that speed the whole driving time is 9 hours then.  Ok, he drove 2 hours today, that means he drove 7 yesterday, 9 - 2.

how many miles is it for 7 hours at 56mph?  d = rt ---> d = 56 * 7

that many miles he drove yesterday.
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The function C(x)=−20x+1681 represents the cost to produce x items. What is the least number of items that can be produced so th
Reptile [31]

Answer:

<em>The least number of items to produce is 41</em>

Step-by-step explanation:

<u>Average Cost</u>

Given C(x) as the cost function to produce x items. The average cost is:

\displaystyle \bar C(X)=\frac{C(x)}{x}

The cost function is:

C(x) = -20x+1681

And the average cost function is:

\displaystyle \bar C(X)=\frac{-20x+1681}{x}

We are required to find the least number of items that can be produced so the average cost is less or equal to $21.

We set the inequality:

\displaystyle \frac{-20x+1681}{x}\le 21

Multiplying by x:

-20x+1681 \le 21x

Note we multiplied by x and did not flip the inequality sign because its value cannot be negative.

Adding 20x:

1681 \le 21x+20x

1681 \le 41x

Swapping sides and changing the sign:

41x \ge 1681

Dividing by 41:

x\ge 41

The least number of items to produce is 41

8 0
2 years ago
Forms of money in the United States consist of paper money, coins, and _____.
Maurinko [17]
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5 0
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This is a geometry question, i need something quickly :)
Marysya12 [62]

Answer:

hope it helps mark me brainlieast!

Step-by-step explanation:

<em>For triangle ABC with sides  a,b,c  labeled in the usual way, </em>

<em> </em>

<em>c2=a2+b2−2abcosC  </em>

<em> </em>

<em>We can easily solve for angle  C . </em>

<em> </em>

<em>2abcosC=a2+b2−c2  </em>

<em> </em>

<em>cosC=a2+b2−c22ab  </em>

<em> </em>

<em>C=arccosa2+b2−c22ab  </em>

<em> </em>

<em>That’s the formula for getting the angle of a triangle from its sides. </em>

<em> </em>

<em>The Law of Cosines has no exceptions and ambiguities, unlike many other trig formulas. Each possible value for a cosine maps uniquely to a triangle angle, and vice versa, a true bijection between cosines and triangle angles. Increasing cosines corresponds to smaller angles. </em>

<em> </em>

<em>−1≤cosC≤1  </em>

<em> </em>

<em>0∘≤C≤180∘  </em>

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<em>We needed to include the degenerate triangle angles,  0∘  and  180∘,  among the triangle angles to capture the full range of the cosine. Degenerate triangles aren’t triangles, but they do correspond to a valid configuration of three points, namely three collinear points. </em>

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<em>The Law of Cosines, together with  sin2θ+cos2θ=1 , is all we need to derive most of trigonometry.  C=90∘  gives the Pythagorean Theorem;  C=0  and  C=180∘  give the foundational but often unnamed Segment Addition Theorem, and the Law of Sines is in there as well, which I’ll leave for you to find, just a few steps from  cosC=  … above. (Hint: the Law of Cosines applies to all three angles in a triangle.) </em>

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<em>The Triangle Angle Sum Theorem,  A+B+C=180∘ , is a bit hard to tease out. Substituting the Law of Sines into the Law of Cosines we get the very cool </em>

<em> </em>

<em>2sinAsinBcosC=sin2A+sin2B−sin2C  </em>

<em> </em>

<em>Showing that’s the same as  A+B+C=180∘  is a challenge I’ll leave for you. </em>

<em> </em>

<em>In Rational Trigonometry instead of angle we use spreads, squared sines, and the squared form of the formula we just found is the Triple Spread Formula, </em>

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<em>4sin2Asin2B(1−sin2C)=(sin2A+sin2B−sin2C)2  </em>

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<em>true precisely when  ±A±B±C=180∘k , integer  k,  for some  k  and combination of signs. </em>

<em> </em>

<em>This is written in RT in an inverted notation, for triangle  abc  with vertices little  a,b,c  which we conflate with spreads  a,b,c,  </em>

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<em>(a+b−c)2=4ab(1−c)  </em>

<em> </em>

<em>Very tidy. It’s an often challenging third degree equation to find the spreads corresponding to angles that add to  180∘  or zero, but it’s a whole lot cleaner than the trip through the transcendental tunnel and back, which almost inevitably forces approximation.</em>

6 0
2 years ago
Find the value of x and y.
zysi [14]

Answer:

<em>x = 9</em>

<em>y = 36</em>

Step-by-step explanation:

<u>Lines and Angles</u>

Triangle CDE is isosceles. This means the two angles of the base DE are congruent (have the same measure):

7x + 1 = 4x + 28

Subtracting 4x + 1:

3x = 27

Dividing by 3:

x = 9

Substituting in the expression for the angles:

7x + 1 = 7*9 + 1 = 64°

The angles are 64° and 64°. The other internal angle at vertex C is 180°-64°-64°=52°. This angle is congruent with its vertical angle in the triangle ABC. We are given another angle of 43°. Thus the measure of angle A is 180°-52°-43°=85°

This last angle is equal to the expression of y:

-2(3 - y) + 19 = 85

Subtracting 19:

-2(3 - y) = 66

Removing the parentheses:

-6 + 2y = 66

Adding 6:

2y = 72

Dividing by 2:

y = 36

Final answer:

x = 9

y = 36

8 0
3 years ago
O. Find the distance between P (10,-7) and Q (7,- 10). Leave your answer in radical<br> form.
mr Goodwill [35]

Answer:

\sqrt{18} or 3\sqrt{2} units.

Step-by-step explanation:

To find the <em>distance between two points</em>, we can use the Distance Formula.

Distance Formula: d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

<u />

<u>Given:</u>

P (10, -7) ⇒ x₁ = 10, y₁ = -7

Q (7, -10) ⇒ x₂ = 7, y₂ = -10

Substitute the given values into the formula and simplify.

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The distance between points P and Q is \sqrt{18} or 3\sqrt{2} units.

Learn more here:

brainly.com/question/27991769

brainly.com/question/21095661

3 0
2 years ago
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