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Lapatulllka [165]
3 years ago
12

(-6, -2) and (5, 1) find the distance between these two points using the distance formula

Mathematics
2 answers:
Paha777 [63]3 years ago
6 0

Answer:

The answer is 11.401754

Setler79 [48]3 years ago
6 0

Answer: Approximately 11.4 units

================================================

Work Shown:

(x1,y1) is the first point (-6,-2)

(x2,y2) is the second point (5,1)

Apply the distance formula

d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\\\\d = \sqrt{(-6-5)^2+(-2-1)^2}\\\\d = \sqrt{(-11)^2+(-3)^2}\\\\d = \sqrt{121+9}\\\\d = \sqrt{130}\\\\d \approx 11.4017542509913\\\\d \approx 11.4\\\\

The distance between the two points is roughly 11.4 units.

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box with a square base and open top must have a volume of 4,000 cm3. Find the dimensions of the box (in cm) that minimize the am
Naya [18.7K]

Answer:

Hence the width, length is 20 cm and height is 10 cm

Step-by-step explanation:

Since the box has a square base, let length = width = x. Also, let the height = y, therefore:

The volume of box = width * length * height

4000 = x * x * y

4000 = x²y

y=4000/x²

The surface area (SA) = area of the base + sum of the area of each side

SA = x² + xy + xy + xy + xy

SA = x² + 4xy

substitute y = 4000/x²

SA = x² + 4x(4000/x²)

SA = x² + 16000/x

Taking the derivative:

SA' = 2x - 16000/x²

making SA' = 0:

0 = 2x - 16000/x²

2x = 16000/x²

2x³ = 16000

x³ = 8000

x = 20 cm

y = 4000 / x² = 4000 / 20² = 10 cm

Hence the width, length is 20 cm and height is 10 cm

6 0
3 years ago
What happens to the width of a confidence interval for a population mean if the level of confidence is increased without changin
natulia [17]

Answer: If the level of confidence is increased without changing the sample size then<em> </em><u><em>The margin of error will decrease because the critical value will decrease. The decreased margin of error will cause the confidence interval to be narrower.</em></u>

where;

<em>Margin of error = Critical value × Standard deviation</em>

<em>Here, it can be duly noted that Margin of error has a positive relation with critical value, i.e </em><u><em>The margin of error will decrease because the critical value will decrease.</em></u>

<u><em>whereas;</em></u>

The confidence interval is  <em>the value  ±  the margin of error.</em>

<em>Therefore, </em><u><em>the decreased margin of error will cause the confidence interval to be narrower.</em></u>

7 0
4 years ago
Last year, a lighting supplier called Bright Idea shipped a total of 37,220 lamps to its distributors. This year, the supplier s
fredd [130]

Answer:

25%

Step-by-step explanation:

Given data

Last years shipment= 37220  lamps

These years shipment= 29776 lamps

% Decrease= Initial-Final/Initial*100

% Decrease= 37220-29776/29776*100

% Decrease= 7444/29776*100

% Decrease= 0.25*100

% Decrease= 25%

Hence the decrease is 25%

7 0
3 years ago
Use the elimination method to
IrinaK [193]

Answer:

5x + 3y = 2

5x - 3y = -22

Step-by-step explanation:yes

3 0
3 years ago
Right triangle XYZ is shown. Y (2,6) (1, 2) 6 х 7 Z Rounded to the nearest hundredth of a unit, what is the length of the hypote
Dmitriy789 [7]

Answer:

8.12

Step-by-step explanation:

We obtain the distance between x and y

d = sqrt[(x2 - x1)² + (y2 - y1)²]

d = sqrt[(1 - 2)² + (2 - 6)²]

d = sqrt[1 + 16)

d = sqrt(17)

d² = 17

From Pythagoras rule;

Hypotenus = sqrt(Adjacent² + opposite²)

Hence,

Hypotenus = sqrt(17 + 7²)

Hypotenus = sqrt(17+ 49)

Hypotenus = sqrt(66)

Hypotenus = 8.124

Hypotenus = 8.12

7 0
3 years ago
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