All categories

3 years ago

The line with equation y=my+b is perpendicular to the line with equation y=16 - x/3. The value of m is ____?

Mathematics

1 answer:

sweet-ann [11.9K]3 years ago

8 0

Answer:

m=3

Step-by-step explanation:

Perpendicular lines intersect at 90 degrees or perpendicular angles. As such, their slopes are related. The slope of each line is the negative reciprocal of the other. For the equation, $y=16-\frac{x}{3}$ . The slope or $m=-\frac{1}{3}$ . This means the slope of the other line will be the negative reciprocal which is -(-3)=3

You might be interested in

Joshua's goal is to sell more than 20 items at a farmers' market. So far, he has sold 6 items. Each of his customers buys 2 item

amid [387]

Answer:

More than 7

Step-by-step explanation:

Given that:

Joshua's goal is to sell more than 20 items at a farmer's market.

Number of items already sold = 6

So, number of more items to be sold > Total number of items to be sold - Number of items already sold > 20 - 6 > 14

Given that each customer buys 2 items.

Let $c$ be the number of customers.

So, number of items bought be the customers = Number of items bought by each customer multiplied by the number of customers = $2c$

And as per the question statement,

Number of more items to be sold > 14 (as calculated in above step)

$2c>14\\\Rightarrow \bold{c>7}$

Therefore, the answer is: <em>More than 7 additional customers are required</em>.

3 0

3 years ago

Rockwell hardness of pins of a certain type is known to have a mean value of 50 and a standard deviation of 1.3. (Round your ans

Maurinko [17]

Answer:

0.0039 is the probability that the sample mean hardness for a random sample of 12 pins is at least 51.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 50

Standard Deviation, σ = 1.3

Sample size, n = 12

We are given that the distribution of hardness of pins is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

Standard error due to sampling =

$=\dfrac{\sigma}{\sqrt{n}} = \dfrac{1.3}{\sqrt{12}} = 0.3753$

P(sample mean hardness for a random sample of 12 pins is at least 51)

$P( x \geq 51) = P( z \geq \displaystyle\frac{51 - 50}{0.3753}) = P(z \geq 2.6645)$

$= 1 - P(z < 2.6645)$

Calculation the value from standard normal z table, we have,

$P(x \geq 51) = 1 - 0.9961= 0.0039$

0.0039 is the probability that the sample mean hardness for a random sample of 12 pins is at least 51.

3 0

3 years ago

Hii! I need some help, would anyone mind helping me?

Kisachek [45]

Step-by-step explanation:

${x}^{2} - 14x - 25 {y}^{2} + 100y = 76$

Factor by grouping,

$( {x}^{2} - 14x) - (25 {y}^{2} - 100y) = 76$

Complete the square, with the x variables,

$( {x}^{2} - 14x + 49) - (25 {y}^{2} - 100y) = 125$

Factor out 25 for the y variables

$( {x}^{2} - 14x + 49) - 25( {y}^{2} - 4y) = 125$

Complete the square

$( {x}^{2} - 14x + 49) - 25( {y}^{2} - 4y + 4) = 25$

Simplify the perfect square trinomial

$(x - 7) {}^{2} - 25(y - 2) {}^{2} = 25$

Make the right side be 1 so divide everything by 25.

$\frac{(x - 7) {}^{2} }{25} - (y - 2) {}^{2} = 1$

Here our center is (7,2).

8 0

2 years ago

Erica knits 18 squares on Monday. She knits 7 more squares each day for the rest of the week. How many squares does Erica have

Ne4ueva [31]

She knits 18 squares on Monday.
Then she knits 7 more squares each day:
Tuesday: +7, Wednesday: +7, Thursday: +7 and Friday: +7
18 + 7 * 4 = 18 + 28 = 46
Answer: She has 46 squares on Friday.

7 0

3 years ago

Im begging someone help me please

Tems11 [23]

Answer:

c. a: 4

b: 12

c: 9

4x² +12x+9=0

(2x+3)(2x+3)= 0

(2x+3)²=0 {square root both sides}

2x+3=0

2x=-3

x= -3/2

7 0

3 years ago