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3 years ago

14

angle 3 and angle 4 form a linear pair. the measure of angle 3 is four more than three times the measure of angle 4. find the me

asure of each angle

1 answer:

lisabon 2012 [21]3 years ago

4 0

Since angles 3 and 4 form a linear pair, the sum of the measures of their angles must add up to 180.

We can define angle 3 as x, and angle 4 as (180-x).

x = 3 ( 180 - x ) + 4.

Solving for x, we get x=138. This is angle 3. Angle 4 is 180-138, so angle 4 is 42.

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Answer:

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Step-by-step explanation

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3 years ago

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3 years ago

A biology test is worth 100 points and has 36 questions.

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Answer:

(a) 7 essays and 29 multiple questions

(b) Your friend is incorrect

Step-by-step explanation:

Represent multiple choice with M and essay with E.

So:

$M + E= 36$ --- Number of questions

$2M + 6E = 100$ --- Points

Solving (a): Number of question of each type.

Make E the subject of formula in $M + E= 36$

$E = 36 - M$

Substitute 36 - M for E in $2M + 6E = 100$

$2M + 6(36 - M) = 100$

$2M + 216 - 6M = 100$

Collect Like Terms

$2M - 6M = 100 - 216$

$-4M = - 116$

Divide both sides by -4

$M = \frac{-116}{-4}$

$M = 29$

Substitute 29 for M in $E = 36 - M$

$E = 36 - 29$

$E = 7$

Solving (b): Can the multiple questions worth 4 points each?

It is not possible.

See explanation.

If multiple question worth 4 points each, then

$2M + 6E = 100$ would be:

$4M + xE = 100$

Where x represents the number of points for essay questions.

Substitute 7 for E and 29 for M.

$4 * 29 + x * 7 = 100$

$116 + 7x = 100$

Subtract 116 from both sides

$116-116 + 7x = 100 -116$

$7x = 100-116$

$7x = -16$

Make x the subject

$x = -\frac{16}{7}$

Since the essay question can not have worth negative points.

Then, it is impossible to have the multiple questions worth 4 points

<em>Your friend is incorrect.</em>

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3 years ago