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KengaRu [80]
3 years ago
11

Point Tis on line segment SU. Given ST = 4x – 4,

Mathematics
2 answers:
blondinia [14]3 years ago
4 0

Answer:

3

Step-by-step explanation:

Vladimir79 [104]3 years ago
3 0

Answer:

TU=10\ units

Step-by-step explanation:

we know that

Point T is on line segment SU (between point S and point U)

so

SU=ST+TU-----> by addition segment postulate

substitute the given values and solve for x

5x+1=(4x-4)+(4x-10)

5x+1=8x-14

8x-5x=1+14

3x=15

x=5

<u><em>Find the length of TU</em></u>

TU=4x-10

substitute the value of x

TU=4(5)-10

TU=10\ units

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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
In a recent year, 33.6% of all registered doctors were female. If there were 44,500 female registered doctors that year, what wa
Ronch [10]

Answer:

132,440

Step-by-step explanation:

In order to find out the total number of doctors, we must divide 44,500 by 33.6%. This will give you the total number of doctors from this specific data set.  

6 0
3 years ago
What’s 22,000 - 407% of 60?
DENIUS [597]

Answer:

21,755.8

Step-by-step explanation:

To solve this equation, we must first find 407% of 60.

To do this, place the percent over 100 (fraction form), then, multiply it by the number you're finding the percentage of.

407/100 x 60/1 = 24,420/100

24420 / 100 = 244.2

244.2 is 407% of 60.

Lastly, you subtract 244.2 from 22,000.

22,000 - 244.2 = 21,755.8

4 0
3 years ago
Chris can drive 41 miles for every 3 gallons of gas. At this
maks197457 [2]

Answer:

27 gallons

Step-by-step explanation:

If for every 41 miles, 3 gallons are needed. Using what we know, 369 ÷ 41 = 9. This means, to get 369 miles, we need to times the first amoiyng of gallons needed to drive 41 miles, which is 3, and times it by 9. (3×9=27) Therefore, 27 gallons of gas is needed.

5 0
3 years ago
Can someone please help me this is due in 10 mins
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7 0
3 years ago
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