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2 years ago

Please help me asap!!

Mathematics

1 answer:

Bess [88]2 years ago

3 0

Answer:

x = 14

Step-by-step explanation:

The polygon given has 6 sides

Sum of interior angles of a 6-sided polygon = 180(n - 2)

substitute n = 6 into 180(n - 2)

Sum of the polygon = 180(6 - 2) = 720°

Thus:

10x + 8x - 16 + 12x - 8 + 7x + 2 + 9x + 4 + 6x + 10 = 720

Add like terms

52x - 8 = 720

52x = 720 + 8

52x = 728

x = 728/52

x = 14

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the coordinates of the vertex of a parabola in the xy-plane are (-4,k). If the y-intercept of the parabola is 12 and the parabol

svp [43]

The value of k is (A) 20/3.

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To find the value of k:

y - b = c (x - a)²

Where (a, b) is the vertex and c is the constant.

(a, b) = (-4, k)
y - k = c (x - (- 4))²
y - k = c (x + 4)²

So,

x = 0, y = 12
12 - k = 16c
k = 12 - 16c ...... (1)

Then,

(-3, 7) = (x, y)
7 - k = c (1)²
k = 7 - c ...... (2)

Now,

12 - 16c = 7 - c
12 - 7 = 16c - c
5 = 15c
c = 5/15 = 1/3

So, the value of k:

k = 12 - 16 (1/3) = 12 - 16/3 = 36-16/3 = 20/3

Therefore, the value of k is (A) 20/3.

Know more about a parabola here:

brainly.com/question/4061870

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The complete question is given below:

The coordinates of the vertex of a parabola in the XY plane are (-4,k). If the y-intercept of the parabola is 12 and the parabola passes through the point (-3,7), then what is the value of k?

(A) 20/3

(B) 16/5

(D) 12/5

5 0

1 year ago

The average systolic blood pressure was found to be 140 mm for people who have high responsibility jobs, specifically investment

defon

Answer:

t = -1.428

Step-by-step explanation:

Average blood pressure among people with high responsibility jobs = u = 140 mm

Number of people sampled for the study = n = 51

Average blood pressure of the sample = x = 139 mm

Standard deviation of the sample = s = 5 mm

The claim is that practicing yoga decreases the blood pressure. So we have to test that after practicing yoga, the average blood pressure will be lesser than 140. Based on this we can formulate the null and alternate hypothesis as:

Null Hypothesis: $\mu \geq 140$

Alternate Hypothesis: $\mu < 140$

Since population standard deviation is not known, we cannot use z-distribution for this test. We are given the value of sample standard deviation, so t-test will be used for this case.

Test statistic is calculated as:

$t=\frac{x-u}{\frac{s}{\sqrt{n} } }$