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guajiro [1.7K]
3 years ago
8

Write the range of f(x) in all three notations if the domain is -2 < x < 6 . f(x)=x+3f(x)=x+3

Mathematics
1 answer:
julia-pushkina [17]3 years ago
3 0

Answer:

Interval notation: Range = (1,9)

Words notation: Range is between 1 and 9.

Inequality notation: Range = {f(x)| 1 < f(x) < 9}

Step-by-step explanation:

The given function is

f(x)=x+3

We need to find the range of f(x) for the domain -2 < x < 6 .

At x=-2,

f(-2)=-2+3=1

At x=6,

f(6)=6+3=9

So, the range of the function is 1 < f(x) < 9. It can be written as

Interval notation: Range = (1,9)

Words notation: Range is between 1 and 9.

Inequality notation: Range = {f(x)| 1 < f(x) < 9}

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Define equivalent expressions. Give an example of two equivalent expressions.
Tasya [4]

Answer:

Hello There!

Step-by-step explanation:

Equivalent expressions are expressions that work the same even though they look different.

Examples of two equivalent expressions are:

-4(x + 2) and 4x + 8

-2y+5y−5+8 and 7y+3

These are equivalent expressions as they have the same value.

hope this helps,have a great day!!

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3 0
3 years ago
Four years ago, Alex was twice as old as Jake. Four years from now,Jake will be 3/4 of Alex’s age. How old is Alex?
Vanyuwa [196]

Answer:Four years ago, Alex was twice as old as Jake. Four years from now, Jake will be 3/4 of Alex's age. How old is Alex? - Answer: 12.

Step-by-step explanation:

8 0
3 years ago
#7-9 please help with an explanation,, will mark brainliest
Mandarinka [93]

Answers:

<h2>7. 12</h2><h2>8. -√18</h2><h2>9. √220</h2>

Step-by-step explanation:

To find out which is greater, we must eliminate the radical symbol.

#7

\sqrt{88} = 9.38083151965

9.4 < 12

#8

-\sqrt{18} = -4.24264068712

-4.2 > -6

#9

\sqrt{220} = 14.8323969742

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8 0
3 years ago
52,300,000 in scientific rotation
tatiyna

Answer:

-5.230,0000

Step-by-step explanation:

Your number in decimal form is -52,300,000 . The negative sign remains unchanged. To get to "standard" scientific notation, we move the decimal point so there is only one non-zero digit in front of the decimal point. So, -52,300,000 becomes -5.230,0000

6 0
2 years ago
Read 2 more answers
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

7 0
2 years ago
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