What two numbers multiply to -15 and can also add up to -7

1 answer:

8 0

Let the numbers be x and y
According to the data : xy=-15 and x+y=-7
xy=-15
x+y=-7

y=-7-x
x(-x-7)=-15

y=-7-x
-x^2-7x=-15

y=-7-x
x^2+7x-15=0

y=-7-x
x=(-7±sqrt(7*7+4*15))/2

y=-7-x
x=(-7±sqrt(109))/2

Goes to two systems.
1)
y=-7-x
x=(-7+sqrt(109))/2


y=-7+3.5-sqrt(109))/2
x=(-7+sqrt(109))/2

y=-3.5-sqrt(109))/2
x=(-7+sqrt(109))/2

2)
y=-7-x
x=(-7-sqrt(109))/2

y=-7+3.5+sqrt(109))/2
x=(-7-sqrt(109))/2

y=-3.5+sqrt(109))/2
x=(-7-sqrt(109))/2

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In 1-5, given: Two similar cylinders with heights of 8 and 5 respectively.

lana66690 [7]

Answer:

1. The ratio of their diameters is 8/5 = 8 : 5

2. The ratio of their surface area is (8/5)²

3. The ratio of their volume is (8/5)³

4.The area of the base of the larger cylinder is 128 cm²

Step-by-step explanation:

Given that the two cylinders are similar, we have;

Two cylinders are similar when the ratio of their heights is equal to the ratio of their radii

Therefore, we have;

1. The ratio of the height of the two cylinders = 8/5 = The radio of their radii = r₁/r₂

The ratio of their diameter = D₁/D₂ = 2·r₁/2·r₂ = r₁/r₂ = 8/5

The ratio of their diameters D₁/D₂ = 8/5 = 8 : 5

2. The surface area of the cylinders = 2·π·r·h + 2·π·r²

Therefore, we have;

(2·π·r₁·h₁ + 2·π·r₁²)/(2·π·r₂·h₂ + 2·π·r₂²) = (r₁·h₁ + r₁²)/(r₂·h₂ + r₂²)

h₁ = h₂ × 8/5

r₁ = r₂ × 8/5

= (8/5)²(r₂·h₂ + r₂²)/(r₂·h₂ + r₂²) = (8/5)²

The ratio of their surface area = (8/5)²

3. The volume of the cylinder = π·r²·h

∴ The ratio of the volume = (π·r₁²·h₁)/(π·r₂²·h₂) = (8/5)³ × (π·r₂²·h₂)/(π·r₂²·h₂) = (8/5)³

The ratio of their volume = (8/5)³

4. The ratio of the area of the base of the larger cylinder to the area of the base of the smaller cylinder is (8/5)²

Therefore if the area of the base of the smaller cylinder is 50 cm², the area of the base of the larger cylinder = 50 cm² × (8/5)² = 128 cm²

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What is the median value of the data set shown on the line plot? Enter your answer in the box. A line plot with twenty-two data

Bogdan [553]

Answer: the median is 6.

Please see the picture attached.

A line plot shows the number of occurrences (crosses) of each number of a data set.

The median is the central value, the middle number, of a data set ordered from least to greatest. When there are two middle numbers, the median will be the mean between the two.

In order to find the median, look at the line plot: count how many values you have (22), then add 1 (23) and divide by two (11.5). Since we have an even number of values, we will have two middle numbers, which will be in the eleventh and twelfth position.

Count the crosses from the left, the eleventh and twelfth crosses both correspond to the number 6, therefore the median is 6.

You can also write all the numbers in increasing order and divide them into two equal groups:
1, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6 | 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 11

The median will be the average between the two central numbers, therefore 6 (again).