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ipn [44]
3 years ago
15

An experienced carpenter can frame a house twice as fast as an apprentice. Working together, it takes the carpenters 2 days. How

long would it take the apprentice working alone?
Mathematics
1 answer:
AleksAgata [21]3 years ago
4 0

Answer:

<em>6 days</em>

<em></em>

Step-by-step explanation:

Let the time taken by Carpenter working alone = C days

Then time taken by apprentice alone = Twice as that of taken by Carpenter = 2C days

Time taken working together = 2 days

Work done in one day working together = \frac{1}{2}

Work done in one day by Carpenter working alone = \frac{1}{C}

Work done in one day by apprentice working alone = \frac{1}{2C}

Work done in one day by Carpenter working alone + Work done in one day by Carpenter working alone =  \frac{1}{C}+\frac{1}{2C} = Work done in one day working together = \frac{1}{2}

\dfrac{1}{C}+\dfrac{1}{2C}=\dfrac{1}{2}\\\Rightarrow \dfrac{2+1}{2C}=\dfrac{1}{2}\\\Rightarrow C = 3\ days

Time taken by Carpenter alone to complete the work = 3 days

Time taken by Apprentice alone to complete the work = 3 \times 2= <em>6 days</em>

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Need help step by step plz
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I'm assuming D is the center of the circle.  See the new figure.

Angle BDC = 106 degrees, that's the definition of arc measure.

Triangle BDC is isosceles (two radii make congruent sides) so the two remaining angles in BDC are equal, DBC=DCB=(180-106)/2=37 degrees.

Angle BAC = 106/2 = 53 degrees, subtending the arc of 106 degrees.

Angle CAD = 53/2 = 26.5 degrees because AD is a bisector, the shared hypotenuse of congruent right triangles AED and AFD.

AFD is also congruent to CFD, so angle DCA is also 26.5 degrees

Angle ACB is the sum of DCA and DCB, ACB = 26.5 + 37 = 63.5 degrees

The angle subtends the arc we seek, whose measure must be double:

10x - 23 = 2(63.5) = 127 degrees

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3 years ago
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Colt1911 [192]

Answer:

  • angle list = measure
  • 2, 4 = 35°
  • 3, 7, 9 = 52°
  • 11 = 87°
  • 1, 5, 10, 12 = 93°
  • 6, 8 = 128°

Step-by-step explanation:

As with a lot of math, it helps to understand the vocabulary. That helps you understand what is being said when the words are used to form a thought.

A "transversal" is a line that cuts across two parallel lines. At each intersection, 4 angles are formed. The angles are given different names, so we can talk about pairs of them being congruent.

The four angles between the parallel lines are called <em>interior</em> angles. The four angles outside the parallel lines are called <em>exterior</em> angles. When the angles are on opposite sides of the transversal, they are <em>alternate</em> angles.

In the diagram, we can identify the following pairs in each category:

  • alternate interior: {3, 9}, {5, 10}
  • alternate exterior: {1, 12}, {7, 52°}

When interior angles are on the same side of the transversal, they are called <em>same-side</em> or <em>consecutive</em> interior angles. Exterior angles cannot be consecutive. Here are some in that category:

  • consecutive interior: {3, 6}, {5, 87°}

Angles created by a ray extending from a line are a <em>linear pair</em>. Angles of a linear pair are supplementary, that is, their sum is 180°. Angles formed by two intersecting lines, sharing only the same vertex, are called <em>vertical</em> angles. Vertical angles are both supplementary to the other angle of the linear pair of which they are a part. Since they are supplementary to the same angle, they are congruent (have the same measure). Here are some linear pairs and some vertical angles in the figure:

  • linear pairs: {6, 7}, {7, 8}, {8, 9}, {6, 9}, {10, 87°}, {10, 11}, {11, 12}, {12, 87°}
  • vertical angles: {1, 5}, {2, 4}, {3, 52°}, {6, 8}, {7, 9}, {10, 12}, {11, 87°}

<em>Corresponding</em> angles are ones that are in the same direction from the point of intersection. Some of those pairs are ...

  • corresponding angles: {1, 10}, {5, 12}, {3, 7}, {9, 52°}

Here are the relations that help you work this problem:

  • alternate interior angles are congruent
  • alternate exterior angles are congruent
  • vertical angles are congruent
  • corresponding angles are congruent
  • a linear pair is supplementary
  • consecutive interior angles are supplementary

__

So far, we haven't mentioned much about the angles where lines j, k, l all meet. Transversal j cuts some of the angles created by transversal k, and vice versa. So, there are some angle sum relations that also apply to corresponding angles:

  • ∠1+∠2≅∠6
  • ∠2+52°≅87°
  • ∠3+∠4≅∠11
  • ∠4+∠5≅∠8

_____

With an awareness of all of the above, you can figure the measures of all of the angles in the diagram.

  ∠1 ≅ ∠5 ≅ ∠10 ≅ ∠12 = 180° -87° = 93°

  ∠2+52° = 87°  ⇒  ∠2 ≅ ∠4 = 87° -52° = 35°

  ∠3 ≅ ∠7 ≅ ∠9 ≅ 52°

  ∠6 ≅ ∠8 = 180° -∠7 = 128°

  ∠11 ≅ 87°

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