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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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Answer:

The area of the rectangle is increasing at a rate of 84 square centimeters per second.

Step-by-step explanation:

The area for a rectangle is given by the formula:

A=w\ell

Where <em>w</em> is the width and <em>l</em> is the length.

We are given that the length of the rectangle is increasing at a rate of 6 cm/s and that the width is increasing at a rate of 5 cm/s. In other words, dl/dt = 6 and dw/dt = 5.

First, differentiate the equation with respect to <em>t</em>, where <em>w</em> and <em>l</em> are both functions of <em>t: </em>

\displaystyle \frac{dA}{dt}=\frac{d}{dt}\left[w\ell]

By the Product Rule:

\displaystyle \frac{dA}{dt}=\frac{dw}{dt}\ell +\frac{d\ell}{dt}w

Since we know that dl/dt = 6 and that dw/dt = 5:

\displaystyle \frac{dA}{dt}=5\ell + 6w

We want to find the rate at which the area is increasing when the length is 12 cm and the width is 4 cm. Substitute:

\displaystyle \frac{dA}{dt}=5(12)+6(4)=84\text{ cm}^2\text{/s}

The area of the rectangle is increasing at a rate of 84 square centimeters per second.

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Answer:

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Answer:

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Step-by-step explanation:

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X \sim Binom(n=8, p=0.9)  

The probability mass function for the Binomial distribution is given as:  

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P(X \geq 7) = P(X=7) +P(X=8)

And we can find the individual probabilities using the probability mass function

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And replacing we got:

P(X \geq 7) = P(X=7) +P(X=8)=0.3826 +0.4305=0.8131

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Answer:

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Step-by-step explanation:

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Hence,

Length of diagonal of picture = 15.30 inches

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