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emmainna [20.7K]
3 years ago
5

Which of the following terms best describes the set of all points in a plane for which the difference between the distances of a

given point to two fixed foci equals a certain constant?

Mathematics
1 answer:
Gnoma [55]3 years ago
6 0

Answer:

HYPERBOLA

Step-by-step explanation:

We have the statement,

'The set of all points in a plane for which the difference between the distances of a given point to two fixed foci equals a certain constant'.

We know that,

Hyperbola is the set of points such that for point P anywhere on the curve, the absolute distance to the two fixed points is a constant.

i.e. From the figure, we see that, the difference of the distance of P from F_{1} and F_{2} is equal to constant 2a.

Thus, the term representing the given statement is HYPERBOLA.

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The amount of water inside each of these things is proportional to the volume of the tank the tropical fish tank has a volume of
k0ka [10]

Answer:

1920 gallons of water

Step-by-step explanation:

From the question; the amount of water is proportional to volume of the tank

i.e amount of water = volume of the tank

in a tropical fish;

3000 gallons of water = 12.5 m³     ----- Equation (1)

However, in the  measurement of  shark tank, we have

length = 20cm = 0.2 meters

width = 4 meters

Height = 10 meters

How many gallons of water can the shark tank hold?

From the measurement of  shark tank, we can calculate the volume;

The volume of the tank = Length × width × height

Volume of the tank = 0.2 × 4 × 10 = 8 m³

since, the amount of water is proportional to volume of the tank

y ( Gallons of water ) = 8 m³    -------- Equation (2)

Equating equation 1 and 2; we have:

3000 gallons of water = 12.5 m³  

y ( Gallons of water ) = 8 m³    

y ( Gallons of water ) ×  12.5 m³  = 3000 gallons of water × 8 m³  

y ( Gallons of water )  = \frac{3000 gallons of water * 8 m^3  }{12.5m^3}

y ( Gallons of water )  = \frac{24000}{12.5}

y ( Gallons of water )  = 1920 gallons of water

Thus, the shark tank can hold 1920 gallons of water

6 0
3 years ago
Read 2 more answers
Tell whether the ordered pair (1,1) is a solution of the system of inequalities.
Dmitry [639]

Since 0 < y < 1.5, hence the coordinate (1,1) is a solution

<h3>A solution to the system of inequality</h3>

Given the following inequality expression

y>0

y< 2.5x - 1

Wee are to check if (1, 1) is a solution to the systen of equation

If x = 1

y < 2.5(1) - 1

Y < 2.5 - 1

y < 1.5

Since 0 < y < 1.5, hence the coordinate (1,1) is a solution

Learn more on inequality here: brainly.com/question/24372553

8 0
2 years ago
The height of adult males on a given South Pacific Island is approximately normally distributed with mean 65 inches and standard
zvonat [6]

Answer:

a) 0.59871

b) 0.22663

e) 0.95994

Step-by-step explanation:

The height of adult males on a given South Pacific Island is approximately normally distributed with mean 65 inches and standard deviation of 4 inches.

We solve using z score

z = (x-μ)/σ, where

x is the raw score

μ is the population mean = 65 inches

σ is the population standard deviation = 4 inches

a). Taller than 64 inches

This means x > 64

Hence,

64 - 65/4

=- 1/4 = -0.25

P-value from Z-Table:

P(x<64) = 0.40129

P(x>64) = 1 - P(x<64) = 0.59871

b.) shorter than 62 inches

Hence,

62 - 65/4

=- 3/4 =- 0.75

P-value from Z-Table:

P(x<62) = 0.22663

c.) between 64 inches and 68 inches

Hence,

for 64 inches

64 - 65/4

=- 1/4 = -0.25

P-value from Z-Table:

P(x = 64) = 0.40129

For 68 inches

Hence,

68 - 65/4

= 3/4= 0.75

P-value from Z-Table:

P(x = 68) = 0.77337

d.) between 58 and 68 inches

e.) taller than 58 inches

Hence,

58 - 65/4

= -6/4 = -1.5

P-value from Z-Table:

P(x<58) = 0.040059

P(x>58) = 1 - P(x<58) = 0.95994

7 0
3 years ago
Solve the system using elimination.
expeople1 [14]

Answer:

(- 9, - 9)

Step-by-step explanation:

Given the 2 equations

3x - 4y = 9 → (1)

- 3x + 2y = 9 → (2)

Adding (1) and (2) will eliminate the term in x

(1) + (2) term by term

(3x - 3x) + (- 4y + 2y) = (9 + 9)

0 - 2y = 18

- 2y = 18 ( divide both sides by - 2 )

y = - 9

Substitute y = - 9 into (1) or (2) and evaluate for x

(1) → 3x + 36 = 9 ( subtract 36 from both sides )

3x = - 27 ( divide both sides by 3 )

x = - 9

Solution is (- 9, - 9)

3 0
3 years ago
How much larger is 0.30 than 0.3
Xelga [282]
They are both equal because in decimals you can add thousands of zeros and it's still equal.
4 0
3 years ago
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