Use elimination to solve the system for 4x + 7 y equals -14 + 8 x + 5 y equals 8 for x

Mathematics

1 answer:

olga2289 [7]2 years ago

4 0

9514 1404 393

Answer:

(x, y) = (3.5, -4)

Step-by-step explanation:

Elimination is easiest if one of the coefficients of a variable is a multiple of the other coefficient of the variable. Here, we have x-coefficients of 4 and 8, so it will be easiest to eliminate x.

Subtract the second equation from 2 times the first.

2(4x +7y) -(8x +5y) = 2(-14) -(8)

9y = -36 . . . . . simplify

y = -4 . . . . . . . divide by 9

4x +7(-4) = -14 . . . . substitute for y in the first equation

4x = 14 . . . . . . . add 28

x = 3.5 . . . . divide by 4

The solution is (x, y) = (3.5, -4).

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loris [4]

Answer:

7i) 140 7ii) 80 7iii) 60 8i) isosceles 8ii) 74 8iii) 60 8iv) 46 degrees 9i) 56

9ii) 80 9iii) 62 10) Angle c is 64 degrees. Angle d is 26 degrees

Step-by-step explanation:

7i) Add up all the interior angles. Since the triangle is isosceles, there are two 70 degree angles. The exterior angle is equal to the two 70 degree angles together, or 140 degrees.

7ii) Add up all the interior angles. Since the triangle is isosceles, there are two 40 degree angles. The exterior angle is equal to the two 40 degree angles together, or 80 degrees.

7iii) Add up all the interior angles. Since the left triangle is isosceles, there are two 30 degree angles. The exterior angle is equal to the two 30 degrees angles together, or 60 degrees.

8i) This is an isosceles triangle because two of the sides are the same length.

8ii) Since the triangle is isosceles, there are two 74 degree angles, and angle BDC is one of them.

8iii) Since the triangle is equilateral, all of the angles equal 60 degrees. This means that angle DAB is 60 degrees.

8iv) Add together 60 degrees from the equilateral and 74 degrees from the isosceles triangle and subtract that sum from 180. 180 - (60 + 74) = 46 degrees.

9i) Angles x and 56 are consecutive interior angles, which means they are the same measure.

9ii) Since the triangle is isosceles, two of the angles are 50 degrees, so subtract 100 from 180 to find the other angle. 180 - 100 = 80 Angles 80 and x are alternate interior angles, which means they are the same measure.

9iii) Angle is has a measure of 62 degrees because the two triangles are the same except for the size, which doesn't matter.

10) Since the left triangle is isosceles, there are two 58 degree angles, so subtract the sum of the two angles from 180. 180 - 116 = 64 degrees Looking at the triangle on the right, add together the 64 and 90 degree angles and subtract from 180 to find the measure of angle d. 180 - 154 = 26 degrees

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2 years ago

The waking time of a student under common conditions is normally distributed with mean of 30 hours and a standard deviation of 5

Elina [12.6K]

Answer:

If the walking time is greater than or equal to 38.225 hours, than it exceeds 95% probability that is lie in top 5%.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 30 hours

Standard Deviation, σ = 5 hours

We are given that the distribution of waking time is a bell shaped distribution that is a normal distribution.