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Mathematics

1 answer:

AlladinOne [14]2 years ago

8 0

Answer:

Car C

Step-by-step explanation:

Car A: 40/4=10 km/L

Car B: 110/10 = 11 km/L

Car C: 48/4 = 12 km/L

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The length of a rectangle is 5 centimeters less then twice it's width. The perimeter of the rectangle is 26 cm. What are the dim

Sedaia [141]

Answer:

The dimensions of the rectangle are length = 7cm and width = 6cm.

Step-by-step explanation:

In order to solve for the dimensions, you will need to set up two equations in order to solve for the missing variable. Given the information that the length is 5 cm less then twice it's width, using 'L' for length and 'w' for width we get the following equation: L = 2w - 5. Perimeter is the sum of all the sides, or in the case of a rectangle P = 2w + 2L. We can then use our expression for 'L' in our perimeter formula: 26 = 2w + 2(2w - 5). First, using the distributive property we get: 26 = 2w + 4w - 10. Next, we combine like terms: 26 = 6w - 10. Then, we use inverse operations to isolate the variable: 26 + 10 = 6w - 10 + 10 to get 36 = 6w, divide both sides by 6 to get w = 6. Lastly, plug in the value of 'w' to 'L': L = 2(6) - 5 or L = 7.

3 0

3 years ago

Solve the given triangles by finding the missing angle and other side lengths.

coldgirl [10]

Answer:

a ≈ 27.65; B = 28°; c ≈ 19.17
a ≈ 163.30; B = 120°; c ≈ 59.77
A = 13°; b ≈ 0.3874; c ≈ 1.3737

Step-by-step explanation:

As long as you're seeking outside help, the use of a suitable tool is appropriate. Many graphing calculators, apps, and web sites are available for solving triangles.

Here, you're given two angles and a side. The third angle is the difference from 180° of the sum of the other two. For example, in the first problem, ...

B = 180° -A -C = 28°

The missing sides are found using the law of sines. Since you are given a side, use that as the reference, and its opposite angle as the reference angle. Then you have ...

side = sin(opposite angle)×<em>((reference side)/sin(reference angle))</em>

Note that the factor in italics remains the same for both remaining sides.

In the first problem, this becomes ...

a = sin(112°)·14/sin(28°) ≈ 27.65

c = sin(40°)·14/sin(28°) ≈ 19.17

The remaining problems are worked in similar fashion.

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<em>Comment on triangle solutions</em>

These are straightforward because you're given two angles. If you're given two sides and an angle, the solution method varies depending on which angle you're given (opposite the long side, the short side, or the unknown side). In the last case, the law of cosines is involved. In the second case, there are likely two solutions. Once you have two angles, you can proceed as above.