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Minchanka [31]
3 years ago
15

Lines a and b are parallel. line c is perpendicular to both line a and line B. Which statement about lines a,b and C is not true

?

Mathematics
2 answers:
7nadin3 [17]3 years ago
7 0

When lines are parallel, they have the same slope, so the statement "line a and line b have the same slope" is TRUE


When lines are perpendicular, the slopes are opposites (the sign and number is flipped)

For example:

slope is 2

perpendicular line's slope is -1/2

slope is -1

perpendicular line's slope is 1/1 or 1

slope is 4/5

perpendicular line's slope is -5/4


When you multiply(the product) perpendicular slopes together, they equal -1. Since line c is perpendicular to line a and line b, the product of their slopes is -1.(so this is true)


The statement "the sum of the slopes of line a and b is 0" is false because if they have the same slope, when added together the result would not be 0. The slopes of line a and line b is -2/3, so the sum would be -4/3.

Paha777 [63]3 years ago
7 0

Answer:

Option A) The sum of slopes of a and b is zero

Step-by-step explanation:

We are given the following:

Line ~a \parallel Line ~b

Line ~c \perp Line ~a\\Line ~c \perp Line ~b

We have to find the false statement.

a) The sum of slopes of a and b is zero

The given statement is false as the parallel lines have same slope and their sum can only be zero if the slopes of both the parallel lines is zero.

b) Lines a and b have same slope

The statement is true. Parallel lines have same slope.

c) The product of slopes of line a and line c is -1

The statement is true.

As two perpendicular lines with slope m_1, m_2 respectively, satisfies the property:

m_1 \times m_2 = -1

d) The product of slopes of line b and line c is -1

The statement is true.

Again, as two perpendicular lines with slope m_1, m_2 respectively, satisfies the property:

m_1 \times m_2 = -1

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kirill115 [55]

Answer:

0.60 - 1.96\sqrt{\frac{0.60(1-0.60)}{1019}}=0.570

0.60 + 1.96\sqrt{\frac{0.60(1-0.60)}{1019}}=0.630

The 95% confidence interval for the true proportion would be given by (0.570;0.630) .

And if we convert this into % we got (57.0%, 63.0%)

Step-by-step explanation:

The information given we have the following info given:

n = 1019 represent the sampel size

\hat p=0.6 represent the sample proportion of interest

The confidence level is 95%, our significance level would be given by \alpha=1-0.95=0.05 and \alpha/2 =0.025. And the critical value would be given by:

z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96

The confidence interval for the mean is given by the following formula:  

\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}

Replacing the info given we got:

0.60 - 1.96\sqrt{\frac{0.60(1-0.60)}{1019}}=0.570

0.60 + 1.96\sqrt{\frac{0.60(1-0.60)}{1019}}=0.630

The 95% confidence interval for the true proportion would be given by (0.570;0.630) .

And if we convert this into % we got (57.0%, 63.0%)

7 0
2 years ago
Find the limit, if it exists (picture below)
valentinak56 [21]

Answer:

c. \frac{1}{2 \sqrt{7} }

Step-by-step explanation:

When plugging in zero into the given equation:

\lim_{x \rightarrow 0}    \frac{\sqrt{x + 7} -  \sqrt{7}  }{x} =  \frac{0}{0}

Answer is in indeterminate form = use L'Hospital's Rule:

(Derivative of the top / Derivative of the bottom)

\lim_{x \rightarrow 0}  \frac{ \frac{1}{2} (x + 7)^{ \frac{-1}{2}} - 0 }{1}

Rearranged equation:

\lim_{x \rightarrow 0}  \frac{1}{2 \sqrt{x + 7} }

Plug zero back into equation:

\lim_{x \rightarrow 0}  \frac{1}{2 \sqrt{x + 7} }  =  \frac{1}{2 \sqrt{0 + 7} } =  \frac{1}{2 \sqrt{7} }

Answer:

\lim_{x \rightarrow 0}    \frac{\sqrt{x + 7} -  \sqrt{7}  }{x} = \frac{1}{2 \sqrt{7} }

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3 years ago
Thomas finished the 200-meter race in 25.7 seconds while Mikah finished in 28.1 seconds. How much faster did Thomas run the race
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Answer:

2.4 seconds

Step-by-step explanation:

We can use subtraction to solve this problem.

28.1 - 25.7 = 2.4 seconds

[] Fun Fact: For men, the world record in the 200-meter dash is by Usain Bolt with a time of 19.30 seconds

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

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Answer:

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Step-by-step explanation:

41,000 x 1.2 = 49,200

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