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2 years ago

Determine the slope of a line that is perpendicular to a line with coordinates (4, -2) and (-1, 3).

Mathematics

1 answer:

LenaWriter [7]2 years ago

5 0

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the line above

$(\stackrel{x_1}{4}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{4}}} \implies \cfrac{3 +2}{-1 -4}\implies \cfrac{5}{-5}\implies \cfrac{1}{-1}\implies -1 \\\\[-0.35em] ~\dotfill$

$\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{1}{-1}} ~\hfill \stackrel{reciprocal}{\cfrac{-1}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{-1}{1}\implies 1}}$

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will the contents of a cylindrical can of soup with a 1.5-inch radius and a 5-inch height fit into a pan with a 4-inch radius an

Anna007 [38]

Answer:

Answer: The volume of the soup can is less that that of the pan, so the soup will fit in the pan.

Step-by-step explanation:

a. V = s3

V = (7 km)3

V = 7 km × 7 km × 7 km

V = 343 km3

b. V = s3

V = (11 yd.)3

V = 11 yd. × 11 yd. × 11 yd.

V = 1,331 km cu. yd.

a. V = l × w × h

V = 6 m × 2 m × 3 m

V = 36 m3

b. V = l × w × h

V = 5 ft. × 10 ft. × 8 ft.

V = 400 cu. ft.

a. V = πr2h

V = 3.14 × (3 in.)2 × 3 in.

V = 3.14 × 9 sq. in. × 3 in.

V = 84.78 cu. in.

b. V = πr2h

V = 3.14 × (1 m)2 × 4 m

V = 3.14 × 1 m2 × 4 m

V = 12.56 m3

V = s3

V = (2 ft.)3

V = 2 ft. × 2 ft. × 2 ft.

V = 8 cu. ft.

Answer: The capacity of the ice chest is 8 cubic feet.

V = πr2h

V = 3.14 × (1 ft.)2 × 3 ft.

V = 3.14 × 1 sq. ft. × 3 ft.

V = 9.42 cu. ft.

Answer: The volume of the trash can is 9.42 cubic feet.

Closet #1

V = l × w × h

V = 4 ft. × 5 ft. × 8 ft.

V = 160 cu. ft.

Closet #2

V = l × w × h

V = 6 ft. × 3 ft. × 8 ft.

V = 144 cu. ft.

Compare the size of the closets

160 cu. ft. > 144 cu. ft.

Answer: The first closet is larger.

Both the can and the pan are cylindrical shapes. Compare the volumes of the two objects.

Volume of Can

V = πr2h

V = 3.14 × (1.5 in.)2 × 5 in.

V = 3.14 × 2.25 sq. in. × 5 in.

V = 35.325 cu. in.

Volume of Pan

V = πr2h

V = 3.14 × (4 in.)2 × 3 in.

V = 3.14 × 16 sq. in.× 3 in.

V = 150.72 cu. in.

35.325 cu. in. soup can < 150.72 cu. in pan

Answer: The volume of the soup can is less that that of the pan, so the soup will fit in the pan.

3 0

3 years ago

Cathan and Jakove went out to eat, and the bill for their food was $24.50. If theyleft their server a 20% tip, what was the tota

Strike441 [17]

$\begin{gathered} \text{The total cost of the experience is } \\ Bill+(Bill\cdot\frac{20}{100}) \end{gathered}$ $\begin{gathered} \text{Then, the cost of the experience is } \\ 24.50+(24.50\cdot\frac{20}{100})=24.50+(24.50\cdot0.2) \\ =24.50+4.9 \\ =29.4 \end{gathered}$

And the cost is $29,40

6 0

1 year ago

Rita's family is moving to Grand Junction to Dallas. The moving van averages 60 miles each hour. About how many hours does the v

Eddi Din [679]

Answer:

16 hours and 20 minutes.

Step-by-step explanation:

Please consider the complete question.

Rita's family is moving to Grand Junction to Dallas, which is 980 miles. The moving van averages 60 miles each hour. About how many hours does the van take to reach Dallas?

To find the time taken by van to reach Dallas, we will divide total distance by speed.

$\text{Time}=\frac{\text{Distance}}{\text{Speed}}$

$\text{Time taken to reach Dallas}=\frac{980\text{ Miles}}{60\frac{\text{ Miles}}{\text{Hour}}}$

$\text{Time taken to reach Dallas}=\frac{980\text{ Miles}}{60}\times \frac{\text{ Hour}}{\text{Miles}}$

$\text{Time taken to reach Dallas}=\frac{98}{6}\text{ Hour}$

$\text{Time taken to reach Dallas}=16.3333\text{ Hour}$

Let us convert 0.3333 hours into minutes by multiplying 0.3333 by 60.

$0.3333\times 60=19.998\approx 20$

Therefore, it will take 16 hours and 20 minutes for the van to reach Dallas.

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3 years ago

Lower Quartile value (Q1) is: 41 42 46 48 54 56 57

Anettt [7]

The lower Quartile value should be from 42 to 48 i believe. I hope this help

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3 years ago

Read 2 more answers

What is the answer for this Problem?

geniusboy [140]

Answer:

Increasing on the interval(s) $-2\leq x\leq -4$

Decreasing on the interval(s) $-1\leq y\leq 1$

Step-by-step explanation:

Anytime the graph is going upward, the function is increasing. However, anytime the graph goes down, the function is decreasing. Look at the image below for further reference. Also, when the function is increasing, the slope is positive, and when the function is decreasing the slope is negative.

The increasing interval of the graph is -3

The decreasing interval of the graph is 0.5

Since the values are in the middle of the interval, it automatically becomes the answer.

5 0

3 years ago