MATHEMATICAL CONNECTIONS What value of x makes the quadrilateral a parallelogram?
1 answer:
Answer:
x = 5 (check the diagram included)
Step-by-step explanation:
The question is incomplete, I have included a diagram to aid the understanding of the question
Parallelograms are quadrilaterals which have their opposite sides parallel and equal. This also means that the opposite angles in a parallelogram are equal
From the attached figure, we have:
|FG| = 3x + 10, |HE| = 7x - 30
To calculate for the value of x that makes the quadrilateral a parallelogram, we have:
Remember the opposite sides of a parallelogram are equal
3x + 10 = 7x - 30
3x - 7x = 10 - 30
-4x = -20
x = 20 ÷ 4
x = <u>5</u>
x = 5 makes the quadrilateral a parallelogram
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3 + 5(c + 3) = -17
First, subtract 3 from both sides. / Your problem should look like:
Second, simplify -17 - 3 to get -20. / Your problem should look like:
Third, divide both sides by 5. / Your problem should look like:
Fourth, simplify
to 4. / Your problem should look like: 
Fifth, subtract 3 from both sides. / Your problem should look like:
Sixth, simplify -4 - 3 to get -7. / Your problem should look like:
Answer: c = -7
First, subtract 3 from both sides. / Your problem should look like:
Second, simplify -17 - 3 to get -20. / Your problem should look like:
Third, divide both sides by 5. / Your problem should look like:
Fourth, simplify
Fifth, subtract 3 from both sides. / Your problem should look like:
Sixth, simplify -4 - 3 to get -7. / Your problem should look like:
Answer: c = -7
Answer:
1a) p-hat=0.38
1b) P=0.08
1c) The null hypothesis is not rejected
2a) p-hat=0.64
2b) P=0.0027
2c) The null hypothesis is rejected
3a) p-hat=0.55
3b) P=0.153
3c) The null hypothesis is not rejected
Step-by-step explanation:
(1) H0: p = 0.3 vs Ha: p ≠ 0.3. In their survey, they had a count of 38 using a sample size n=100.
1a) The p-hat is p-hat=38/100=0.38.
1b) The standard deviation is
The sample size is n=100.
The z-value is:
As it is a two-sided test, the p-value considers both tails of the distribution.
The p-value for this |z|=1.74 is P=0.08.
1c) The null hypothesis is not rejected.
(2) H0: p = 0.7 vs Ha: p ≠ 0.7. In their survey, they had a count of 320 using a sample size n=500.
2a) The p-hat is p-hat=320/500=0.64.
2b) The standard deviation is
The sample size is n=500.
The z-value is:
As it is a two-sided test, the p-value considers both tails of the distribution.
The p-value for this |z|=3 is P=0.0027.
2c) The null hypothesis is rejected.
(3) H0: p = 0.6 vs Ha: p < 0.6. In their survey, they had a count of 110 using a sample size n=200.
2a) The p-hat is p-hat=110/200=0.55.
2b) The standard deviation is
The sample size is n=200.
The z-value is:
As it is a two-sided test, the p-value considers both tails of the distribution.
The p-value for this |z|=1.43 is P=0.153.
2c) The null hypothesis is not rejected.