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Fofino [41]
1 year ago
12

Find the distance between the following points using the Pythagorean theorem: (-5, 4) and (8, -3)

Mathematics
1 answer:
3241004551 [841]1 year ago
5 0

First, draw a diagram to visualize the situation:

As we can see, the difference between the x-coordinates of the points is the length of one leg of a right triangle, and the difference between the y-coordinates is the length of the other leg.

Then, for the given points (-5,4) and (8,-3), the distance given by the Pythagorean Theorem is:

\begin{gathered} d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\  \\ =\sqrt{(8--5)^2+(-3-4)^2} \\  \\ =\sqrt{(13)^2+(-7)^2} \\  \\ =\sqrt{169+49} \\  \\ =\sqrt{218} \\  \\ \approx14.7648... \end{gathered}

Therefore, the distance between the points (-5,4) and (8,-3) is: √218.

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Write the given differential equation in the form L(y) = g(x), where L is a linear differential operator with constant coefficie
Greeley [361]

Answer:

The differential equation will be like the one shown below

Step-by-step explanation:

Data:

Let the equation be given as:

y(4) + 8y' = 6

The equation will be expressed linearly as follows:

y(4) + 8\frac{dy}{dx}  = 6

8\frac{dy}{dx}+ 4y = 6

This is the linear form of the differential equation.

5 0
3 years ago
Read 2 more answers
If the ratio of the purple flowers to black flowers is 4 to 8 and there are a total of 108 flowers, how many of the flowers are
tankabanditka [31]
There would be 36 purple flowers.
7 0
3 years ago
I wasn't in class so I need help solving the inequality 7/10n+14<49
NikAS [45]

Answer:

n<50

Step-by-step explanation:

7/2*5n + 14<49

7n/2*5+14<49

(7n)+(2*5)14/2*5 <49

7n+10*14/2*5 <49

7n+140/2*5 <49

7n+140/10 <49

7n+140 < 10*49

7n+140 < 490

(7n+140)+(-140)<490+(-140)

7n+140-140<490-140

7n<350

7n/7 < 350/7

n<2*5^2*7/7

n<2*5^2

n<2*25

n<50

8 0
2 years ago
Angelo and Deborah are landscapers. Angelo charges a one time fee of $50 plus $15 per hour. Deborah charges a one time fee of $2
Tems11 [23]

Answer:

5 hours

Step-by-step explanation:

Step one:'

given data

Angelo charges a one time fee of $50 plus $15 per hour

let the total charge be y

and the number of hours be x

y= 50+15x----------------1

Deborah charges a one time fee of $25 plus $20 per hour

y= 25+20x----------------2

equate 1 and 2 to find x

50+15x=25+20x

collect like terms

50-25= 20x-15x

25= 5x

divide both sides by 5

x= 25/5

x= 5 hours

4 0
3 years ago
The answer to the problem
frez [133]

Could you take a better picture please?

6 0
3 years ago
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