In rectangle abcd measure of angle d =(3x+15) measure b =(6x-42) find measure of angle a
1 answer:
5) So for parallelogram ABCD, ∠B ≅ ∠D, and ∠A ≅ ∠C. Further, ∠B and ∠A are supplementary (i.e., their sum is 180°), and ∠D and ∠C are also supplementary.
So, we have that m∠B = m∠D. Therefore,
Now, let's substitute for x back into the expression for either ∠B or ∠D to find it's angle measure.
m∠B =
Now, remember that ∠B or ∠D are supplements of ∠A.
So, m∠B + m∠A = 180°.
That means m∠A = 180° – 72° = 108°.
That seems reasonable, because A appears to be an obtuse angle.
So, we have that m∠B = m∠D. Therefore,
Now, let's substitute for x back into the expression for either ∠B or ∠D to find it's angle measure.
m∠B =
Now, remember that ∠B or ∠D are supplements of ∠A.
So, m∠B + m∠A = 180°.
That means m∠A = 180° – 72° = 108°.
That seems reasonable, because A appears to be an obtuse angle.
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The profit function is the difference between the cost and the revenue functions.
The true statement is (a) If material 2 is used, Carrie will earn a profit if she sells chairs for more than $150 each.
<h3>How to determine the true profit functions</h3>From the complete questions, the profit functions are calculated as follows:
<u>Material 1</u>
<u>Material 2</u>
<u>Material 3</u>
Next, we test the options
Option 1: When material 2 is used
A price is greater than $150 is $151.
Calculate P(151) using
So, we have:
P(151) is greater than 0; this represents a profit
Hence, option (1) is true
Option 2: When material 1 is used
A price is less than $50 is $49.
Calculate P(49) using
So, we have:
P(49) is less than 0; this represents loss
Hence, option (2) is false
Option 3: When material 3 is used
Calculate P(45) and P(160) using
So, we have:
P(45) is less than 0; this represents loss
Hence, option (3) is false
Option 1: When material 2 is used
Calculate P(30) and P(120) using
So, we have:
P(30) is less than 0; this represents a loss
Hence, option (4) is false
Option 2: When material 1 is used
Calculate P(40) and P(70) using
So, we have:
P(49) is less than 0; this represents loss
Hence, option (5) is false
The above means that:
The true statement is (a) If material 2 is used, Carrie will earn a profit if she sells chairs for more than $150 each.
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