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3 years ago

Identify each pair of angles as corresponding, Alternate interior, alternate exterior, or consecutive interior and solve for X

Mathematics

1 answer:

-BARSIC- [3]3 years ago

4 0

Answer:

Step-by-step explanation:

19). Angles measuring 90° and (21x + 6)° are Alternate exterior angles.

Therefore, 21x + 6 = 90

2x = 90 - 6

2x = 84

x = 42

21). Angles measuring 60° and (8x - 4)° are Alternate interior angles,

8x - 4 = 60

8x = 60 + 4

x = $\frac{64}{8}$

x = 8

23). Since, angles measuring (-1 + 14x)° and (12x + 17)° are Alternate exterior angles

Therefore, (-1 + 14x) = (12x + 17)

14x - 12x = 17 + 1

2x = 18

x = 9

25). Both the angles (x + 96)° and (x + 96)° are consecutive interior angles.

Therefore, (x + 96)° + (x + 96)° = 180° [Property of consecutive interior angles]

2x + 192 = 180

2x = 180 - 192

2x = -12

x = -6

Now measure of (x + 96)° = -6 + 96

= 90°

26). Both the angles (20x + 5)° and (24x - 1)° are consecutive interior angles.

Therefore, (20x + 5)° + (24x - 1)° = 180°

44x + 4 = 180

44x = 176

x = 4

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Find the distance between each pair of integers. 9 and –1

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3 years ago

Walt grew 10 cm in 1 year. He is now 1.6 m tall. How tall was he 1 year ago?

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3 years ago

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3 years ago

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An arena receives $1,700 per event for 12 concerts. If the costs for this sponsorship total $14,000, what is the profit margin f

miss Akunina [59]

Answer:

total profit margin for all 12 concert is $6,400.

profit margin for all one concert is $533.33

Step-by-step explanation:

Amount of money received for one event = $1700

Total no of concert = 12

Total money received for 12 event = Amount of money received for one event * Total no of concert

Total money received for 12 event = $1700 *12 = $20,400

Total cost of sponsorship = $14,000

Profit margin is the difference money invested and money earned.

here total investment is $14,000

Total money earned is $20,400

Therefore profit margin = money earned - total investment

= $20,400 - $14,000 = $6,400

Therefore total profit margin for all 12 concert is $6,400.

However to calculate profit margin for one concert we can simply divide the total profit margin for all 12 concert by no of concert (i.e 12)

profit margin for one concert = total profit margin for all 12 concert/total no of concert = $6,400/12 = $533.33

profit margin for all one concert is $533.33

6 0

3 years ago

ANSWER QUICKLY!!!!!

Paul [167]

Answer:

1. The possible roots are ±1, ±2, ±3, ±6. These are the factors of the trailing constant (6) divided by the factors of the leading coefficient (1). When the leading coefficient is 1, the possible roots are the factors of the constant

2. The polynomial is easier to evaluate when it is written in Horner form:

f(x) = ((x -4)x +1)x +6

To show that 2 is a zero, we want to find f(2):

f(2) = ((2 -4)2 +1)2 +6 = (-4 +1)2 +6 = -6 +6 = 0

f(2) = 0, so 2 is one of the zeros of this function

3. Using synthetic division (attached) or polynomial long division, we can divide the given polynomial by (x-2) to find the remaining factors. This division gives (x^2 -2x -3), which can be factored as (x -3)(x +1), so the three actual roots are ...

x = 2 (from above), x = 3, x = -1 (from our factorization)

4. In factored form, the polynomial can be written ...

f(x) = (x +1)(x -2)(x -3)

The first factor was found from the fact that 2 was given as a zero of the function. For any zero "a", a factor of the polynomial is (x-a).

The remaining factors were found by factoring the quadratic trinomial that resulted from the division of f(x) by x-2. That trinomial is x^2 -2x -3.

There are a number of methods that can be used to factor x^2 -2x -3. Again, the rational root theorem can help. It suggests that ±1 and ±3 are possible roots.

4 0

2 years ago