Hey guys! I need help with this question.

Are two lines parallel, perpendicular or neither 3x+7y=15 and 7x-3y=6

maw [93]

Answer:

The lines are perpendicular

Step-by-step explanation:

we know that

If two lines are parallel, then their slopes are equal

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

we have

$3x+7y=15$ ----> equation A

isolate the variable y

$7y=-3x+15$

Divide by 7 both sides

$y=-\frac{3}{7}x+\frac{15}{7}$

The slope of the line A is $m_A=-\frac{3}{7}$

$7x-3y=6$ ----> equation B

isolate the variable y

$3y=7x-6$

Divide by 3 both sides

$y=\frac{7}{3}x-2$

The slope of the line B is $m_B=\frac{7}{3}$

Compare the slope of both lines

$m_A=-\frac{3}{7}$

$m_B=\frac{7}{3}$

so

$m_A \neq m_B$ ----> the lines are not parallel

Find the product of the slopes

$-\frac{3}{7}(\frac{7}{3})=-1$ ----> the lines are perpendicular

4 0

3 years ago

4. Two cards are selected from a regular deck of cards. If the first was a ten, determine the probability that the second was a

ioda

Answer:

a) $P=\frac{1}{221}$

b) $P=\frac{4}{663}$

c) $P=\frac{4}{221}$

Step-by-step explanation:

Given : Two cards are selected from a regular deck of cards. If the first was a ten.

To determine : The probability that the second was a (a) ten, (b) jack, (c) picture card ?

Solution :

Total number of cards = 52 in which there are 4 sets of 13 cards with two different color.

We are drawing two card one after another without replacement.

Probability of drawn first card 10 is $P(T_1)=\frac{4}{52}=\frac{1}{13}$

a) Second card drawn is 10,

Probability of drawn second card 10 is $P(T_2)=\frac{3}{51}=\frac{1}{17}$

Total probability that first card was 10 and second card is 10,

$P=P(T_1)\times P(T_2)$

$P=\frac{1}{13}\times \frac{1}{17}$

$P=\frac{1}{221}$

b) Second card drawn is Jack,

Probability of drawn second card Jack is $P(J)=\frac{4}{51}$

Total probability that first card was 10 and second card is Jack,

$P=P(T_1)\times P(J)$

$P=\frac{1}{13}\times \frac{4}{51}$

$P=\frac{4}{663}$

c) Second card drawn is picture card,

Number of picture card is 4j's, 4Q's, 4K's = 12

Probability of drawn second card picture card is $P(p)=\frac{12}{51}=\frac{4}{17}$

Total probability that first card was 10 and second card is picture card,

$P=P(T_1)\times P(p)$

$P=\frac{1}{13}\times \frac{4}{17}$

$P=\frac{4}{221}$

7 0

3 years ago

Rewrite in simplest terms: 10(-8x+7)-9x

zloy xaker [14]

Answer:

Step-by-step explanation:

-80x+70-9x

-89x + 70

7 0

3 years ago

Read 2 more answers

What is the slope of the graph of y=-3x?<br> 1. -1/3<br> 2. 1/3<br> 3. 3<br> 4. -3

agasfer [191]

Answer:

4. -3

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

The highest point in California is Mount Whitney at 14,494 feet above sea level. The lowest point in California is in Death Vall

mariarad [96]

14,776 is the answer

6 0

3 years ago