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2 years ago

Find the values for k so that the intersection of x = 2k and 3x + 2y = 12 lies in the first quadrant.

Mathematics

2 answers:

RUDIKE [14]2 years ago

5 0

Answer:

0 < k < 2

Step-by-step explanation:

The intersection will lie in the first quadrant when the solution has the characteristics: x > 0, y > 0.

For x > 0, we require ...

x = 2k

x > 0

2k > 0 . . . . substitute for x

k > 0 . . . . . divide by 2

For y > 0, we require ...

y = (12 -3x)/2

y = (12 -3(2k))/2 = 6 -3k . . . . . substituted for x and simplify

y > 0

6 -3k > 0 . . . . . . substitute for y

2 -k > 0 . . . . . . . divide by 3

k < 2 . . . . . . . . . add k

So, the values of k that result in the intersection being in the first quadrant are ...

0 < k < 2

RUDIKE [14]2 years ago

3 0

Answer:

0 < k < 2

Step-by-step explanation:

In the first quadrant both of x and y get positive values, so

x > 0 and y > 0

x = 2k, k > 0

And replacing x with 2k in the second equation:

3x + 2y = 12
3*2k + 2y = 12
2y= 12 - 6k
y = 6 - 3k

Since y > 0:

6 - 3k> 0
2 - k > 0
k < 2

Combining both k > 0 and k < 2, we get:

0 < k < 2

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Which shows two triangles that are congruent by ASA

Ksenya-84 [330]

The four options are attached below

Answer:
Second attachment is the correct choice

Explanation:
ASA (angle-side-angle) means that two angles and the included side between them in the first triangle are congruent to the corresponding two angles and the included side between them in the second triangle

Now, let's check the choices:
First attachment:
It shows that two sides and the included angle between them in the first triangle is congruent to the corresponding two sides and the included angle between them in the second one. This is congruency by SAS. Therefore, this option is incorrect

Second attachment:
It shows that two angles and the included side between them in the first triangle is congruent to the corresponding two sides and the included angle between them in the second triangle. This is congruency by ASA. Therefore, this option is correct

Third attachment:
It shows that the three angles in the first triangle are congruent to the corresponding three angles in the second one. This is not enough to prove congruency. Therefore, this option is incorrect

Fourth attachment:
It shows that the three sides in the first triangle are congruent to the corresponding three sides in the second one. This is congruency by SSS. Therefore, this option is incorrect.

Based on the above, the second attachment is the only correct one

Hope this helps :)

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2 years ago

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A scientist measures a substance to be 0.8 grams. Calculate the percent of error in the measurement. Show all work for full cred

Volgvan

You'll need to give a bit more information for the question to be answered. You can only calculate the percentage of error if you know what the mass of the substance *should be* and what you've *measured* it to be.

In other words, if a substance has a mass of 0.55 grams and you measure it to be 0.80 grams, then the percent of error would be:

percent of error = { | measured value - actual value | / actual value } x 100%

So, in this case:

percent of error = { | 0.80 - 0.55 | / 0.55 } x 100%
percent of error = { | 0.25 | / 0.55 } x 100%
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2 years ago

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Tpy6a [65]

Check the tree diagram, of all the possible scenarios and the probabilities.

All the possible scenarios are:

1st.non defective, 2nd.non defective
1st.non defective, 2nd. defective
1st. defective, 2nd. non defective
1st. defective, 2nd. defective

consider the case 1st.non defective, 2nd.non defective

the probability that the first one is non defective is 8/10, since 8 out of 10 are non defective.

In this scenario, the second one is non defective as well. The probability for this to happen is 7/9, since now we have 7 non defective pots, and 9 in total.

This means that the probability of the first to be non defective, and the second non-defective is (8/10) * (7/9)=0.622

similarly we calculate the other cases, as shown in the picture.

P(at least one is defective)=
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1 year ago

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