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GREYUIT [131]
3 years ago
6

The sum of two consecutive even integers is at most seven more than half the sum of the next two consecutive even integers

Mathematics
1 answer:
Pavel [41]3 years ago
7 0

The sum of two consecutive even integers is at most seven more than half the sum of the next two consecutive even integers

two consecutive even integers: n, n+2

next two consecutive even integers n+4, n+6

n+(n+2) >= 7+1/2(n+4 +n+6)

combine like terms

2n+2 >= 7 +1/2(2n+10)

distribute 1/2

2n+2 >= 7+n+5

2n+2>= n+12

subtract n from each side

n+2>= 12

subtract 2 from each side

n>10

4 integers : 10, 12 ,14, 16

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0<br> -3 &lt; n &lt; 1<br> n is an integer.<br> Write down the possible values of n.
n200080 [17]

Answer:

-2,-1,0

Step-by-step explanation:

the integers between -3 and 1, not including -3 and 1 are

-2,-1,0

4 0
2 years ago
In order for this ratio of volumes to be true, what measurements would have to be equal in all 3 solids?
Neporo4naja [7]

The measurements of the figures that should be equal in order for the ratio of volumes between the volumes of the cone, sphere, and cylinder of 1:2:3 to be true is; The radius and the height

<h3>What is a ratio?</h3>

A ratio is a comparison between the magnitudes or measurements of items, expressing the number of times one item in the ratio is contained within another item in the ratio.

The formula for the volume of a cone, V_p is, V_p = (1/3)·π·r₁²·h₁

The formula for the volume of a sphere, V_s, is V_s = (4/3)·π·r₂³

The formula for the volume of a cylinder, V_c, is V_c = π·r₃²·h₃

The ratio of the volumes in the question is 1:2:3

Therefore; The volume of the sphere is twice the volume of the cone, and the volume of the cylinder is three times the volume of the cone, which indicates;

(4/3)·π·r₂³ = 2 × (1/3)·π·r₁²·h₁...(1)

π·r₃²·h₃ = 3 × (1/3)·π·r₁²·h₁...(2)

Equation (1) indicates that we have;

(4/3)·π·r₂³ = 2 × (1/3)·π·r₁²·h₁

Where, h₁ = 2·r₂, we get;

(4/3)·π·r₂³ = 2 × (1/3)·π·r₁²·(2·r₂) = (4/3)·π·r₁²·r₂

Therefore; r₁ = r₂, and the diameter of the sphere is equal to the height of the cone

The radius of the cone is equal to the radius of the sphere

Equation (2) indicates;

π·r₃²·h₃ = 3 × (1/3)·π·r₁²·h₁ = π·r₁²·h₁

Therefore;

r₃²·h₃ = r₁²·h₁

r₃ = r₁

h₃ = h₁

The radius of the cone = The radius of the cylinder

The height of the cone = The height of the cylinder

  • The ratio of the volumes, 1 : 2 : 3 is true when the measurements of the radius and the height are equal for all three solids.

Learn more about the volume of regular solids here:

brainly.com/question/15316195

#SPJ1

4 0
1 year ago
Complete the square for the expression
melamori03 [73]

Answer:

x^2 + 14x + 49 = 0

Step-by-step explanation:

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In addition to the facts in the diagram, which statement is necessary to prove that the two triangles are congruent by the SAS c
nasty-shy [4]
The best answer to go with is b
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A text font fits 12 characters per inch. Using the same font, how many characters can be expected per yard of text? There are 12
kirza4 [7]

Answer:

Step-by-step explanation:

12 X 36 = 432 Characters

6 0
2 years ago
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