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mina [271]
3 years ago
7

Marco takes 12 mins to drive his car down the hill to the movies and 24 mins to drive up the hill from the movies he goes to the

movies Monday through Friday.How many mins does he spend driving his car to and from the movies in two weeks ?Wrote an equation to model your work
Mathematics
1 answer:
Shtirlitz [24]3 years ago
7 0

Answer:

360 minutes

Step-by-step explanation:

Given that:

Driving down the hill (d) = 12 minutes

Driving up the hill (u) = 24 minutes

Days = Monday - Friday = 5days

For 2 weeks : 2 * 5 = 10

Total time taken to drive up and down daily (T) : (12 + 24) minutes = 36 minutes

For the two weeks :

10(T)

= 10(36)

= 360 minutes

Model:

Let number of days = n

Number of minutes :

n(u + d)

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Determine the most precise name for ABCD (parallelogram, rhombus, rectangle, or square). Explain how you determined your answer.
Sonja [21]
<h3>Answer:  Rhombus</h3>

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

Reason:

Let's find the distance from A to B. This is equivalent to finding the length of segment AB. I'll use the distance formula.

A = (x_1,y_1) = (3,5) \text{ and } B = (x_2, y_2) = (7,6)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(3-7)^2 + (5-6)^2}\\\\d = \sqrt{(-4)^2 + (-1)^2}\\\\d = \sqrt{16 + 1}\\\\d = \sqrt{17}\\\\d \approx 4.1231\\\\

Segment AB is exactly \sqrt{17} units long, which is approximately 4.1231 units.

If you were to repeat similar steps for the other sides (BC, CD and AD) you should find that all four sides are the same length. Because of this fact, we have a rhombus.

-------------------------

Let's see if this rhombus is a square or not. We'll need to see if the adjacent sides are perpendicular. For that we'll need the slope.

Let's find the slope of AB.

A = (x_1,y_1) = (3,5) \text{ and } B = (x_2,y_2)  = (7,6)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{6 - 5}{7 - 3}\\\\m = \frac{1}{4}\\\\

Segment AB has a slope of 1/4.

Do the same for BC

B = (x_1,y_1) = (7,6) \text{ and } C = (x_2,y_2)  = (6,2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{2 - 6}{6 - 7}\\\\m = \frac{-4}{-1}\\\\m = 4\\\\

Unfortunately the two slopes of 1/4 and 4 are not negative reciprocals of one another. One slope has to be negative while the other is positive, if we wanted perpendicular lines. Also recall that perpendicular slopes must multiply to -1.

We don't have perpendicular lines, so the interior angles are not 90 degrees each.

Therefore, this figure is not a rectangle and by extension it's not a square either.

The best description for this figure is a <u>rhombus</u>.

4 0
1 year ago
Read 2 more answers
Find two positive numbers satisfying the given requirements.
Umnica [9.8K]

Answer:

8 and 19

Step-by-step explanation:

To some this, let's first list all the factors of 152. They are;

1, 2, 4, 8, 19, 38, 76, 152.

Now, let's arrange them to reflect being multiplied to get 152.

Thus;

1 × 152 = 152

2 × 76 = 152

4 × 38 = 152

8 × 19 = 152

Also, let's do the same for their sum;

1 + 152 = 153

2 + 76 = 78

4 + 38 = 42

8 + 19 = 27

Looking at the figures above, the ones that their product is 152 but have the least sum are 8 and 19

8 0
2 years ago
An isosceles triangle △ABC with the base BC is inscribed in a circle. Find the measures of angles of the triangle, if measure of
____ [38]

Answer:

  • angle at A: 51°
  • base angles: 64.5°

Step-by-step explanation:

The measure of the inscribed angle BAC is half the measure of the intercepted arc BC, so is 102°/2 = 51°.

The base angles  at B and C are the complement of half this value, or ...

  90° -(51°/2) = 64.5°

The angle measures in the triangle are ...

  ∠A = 51°

  ∠B = ∠C = 64.5°

6 0
3 years ago
Which of the following should you do first when solving the equation 2x-7=3x-2(x+8)
Georgia [21]

Answer:

multiply 3x-2(x+8)

Step-by-step explanation:

PEMDAS

also you must simplify both sides to solve this problem and that's the first step to simplifying this side (the other one is simplified)

3 0
2 years ago
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How can the common difference between 375-315=30
Firlakuza [10]
Hello :
in the arithemitic sequence  : an = an-1 + 30
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