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2 years ago

Find angle E if angle E and angle F are supplementary, angle E= 2x + 5 and angle F= 5x - 38

Mathematics

1 answer:

Bingel [31]2 years ago

4 0

Answer:

About 65.86 degrees

Step-by-step explanation:

A supplementary angle means that the angles add to 180 degrees.

Angle E + Angle F = 180 degrees.

You can then plug in the given equations for E and F.

2x + 5 + 5x - 38 = 180

Combine like terms:

2x + 5x = 7x

5 - 38 = -33

New equation: 7x-33=180

Remove the -33 from the left side of the equation by adding 33 to each side

7x-33+33 = 180+33 ---> 7x = 213

Divide by 7 on each side

7x/7 = 213/7 ---> x = about 30.43

You can then plug this into your equation for E and solve

2(30.43) + 5 = 65.86 Degrees

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Which is bigger, 7/8" or 9/16"?

Iteru [2.4K]

7/8 and 9/16

7*2/8*2 = 14/16

14/16 and 9/16

Now since we have a common denominator, we can compare the numerators.

14/16 is greater, so 7/8 is greater than 9/16

Answer: 7/8 is bigger

5 0

3 years ago

Read 2 more answers

Line g passes through points (5, 9) and (3, 2). Line h passes through points (9, 10) and (2, 12). Are line g and line h parallel

icang [17]

For this case we find the slopes of each of the lines:

The g line passes through the following points:

$(x_ {1}, y_ {1}) :( 3,2)\\(x_ {2}, y_ {2}) :( 5,9)$

So, the slope is:

$m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {9-2} {5-3} = \frac {7} {2}$

Line h passes through the following points:

$(x_ {1}, y_ {1}) :( 9,10)\\(x_ {2}, y_ {2}) :( 2,12)$

So, the slope is:

$m = \frac {y_ {2} -y_ {1}}{x_ {2} -x_ {1}} = \frac {12-10} {2-9} = \frac {2} {- 7} = - \frac {2} {7}$

By definition, if two lines are parallel then their slopes are equal. If the lines are perpendicular then the product of their slopes is -1.

It is observed that lines g and h are not parallel. We verify if they are perpendicular:

$\frac {7} {2} * - \frac {2} {7} = \frac {-14} {14} = - 1$

Thus, the lines are perpendicular.

Answer:

The lines are perpendicular.

8 0

2 years ago

Please solve step by step

Bingel [31]

Please report the picture, it is cut off :)

8 0

2 years ago

Read 2 more answers

Element X decays radioactively with a half life of 12 minutes. If there are 200 grams of Element X, how long, to the nearest ten

Semenov [28]

Answer:

It would take 24 minutes for the element to decay to 50 grams

Step-by-step explanation:

The equation for the amount of the element present, after t minutes, is:

$Q(t) = Q(0)e^{-rt}$

In which Q(X) decays radioactively with a half life of 12 minutes.(0) is the initial amount and r is the rate it decreases.

Half life of 12 minutes

This means that $Q(12) = 0.5Q(0)$

$Q(t) = Q(0)e^{-rt}$

$0.5Q(0) = Q(0)e^{-12r}$

$e^{-12r} = 0.5$

$\ln{e^{-12r}} = \ln{0.5}$

$-12r = \ln{0.5}$

$12r = -\ln{0.5}$

$r = -\frac{\ln{0.5}}{12}$

$r = 0.05776$

If there are 200 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 50 grams?

This is t when Q(t) = 50. Q(0) = 200.

$Q(t) = Q(0)e^{-rt}$

$50 = 200e^{-0.05776t}$

$e^{-0.05776t} = 0.25$

$\ln{e^{-0.05776t}} = \ln{0.25}$

$-0.05776t = \ln{0.25}$

$0.05776t = -\ln{0.25}$

$t = -\frac{\ln{0.25}}{0.05776}$

$t = 24$

It would take 24 minutes for the element to decay to 50 grams

6 0

3 years ago

Happy Hound Pet Store sells dog food in 25-pound bags for $15.80. Pampered Pet Store sells dog food in 18-pound bags for $11.59.

AveGali [126]

Answer: c

Step-by-step explanation:it is lower price and its only 7 pounds of so the smaller bag will last you a long time about a few months

7 0

2 years ago