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Svetlanka [38]
3 years ago
11

Let f(x) = |x|, ????????(x) = f(x − 3), and h(x) = f(x + 2), where x can be any real number.

Mathematics
1 answer:
ra1l [238]3 years ago
5 0

Answer:

g(x)= |x-3|

h(x) = |x+2|

Step-by-step explanation:

1. Let g(x)=f(x-3), we can write the function in terms of |x| as:

g(x)= |x-3|

2. Let h(x)=f(x+2), the function can be rewrite in terms of |x| as:

h(x) = |x+2|

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The triangles are similar.
Liula [17]

Answer:

x=16

Step-by-step explanation:

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3 0
2 years ago
Numerical expression for the phrase and simplify <br> -5 and 7 added to 4
slavikrds [6]

The Numerical expansion for the phrase is Negaquinary and Balanced Septenary added to Balanced Quaternary.

Simplification Answer : 6(Senary)

Step-by-step explanation:

  • The Numerical expression for the -5 is Negaquinary.
  • The Numerical expression for the +7 is Balanced Septenary.
  • The Numerical expression for the +4 is Balanced Quaternary.
  • STEP 1 : -5+7 = +5
  • STEP 2 : +5+4 = 6.
  • The Numerical expression for the 6 is Senary.

7 0
3 years ago
coffee maker has the shape of a cone 10cm high with a radius of 6 cm at the top. The coffee maker is filled with water, and the
andrezito [222]

Answer: the rate of the water level in the cone falling when it is 5cm from the bottom of the cone is -0.1768 cm/sec

Step-by-step explanation:

Given the data in the question;

H/h = R/r

10/5 = 6/r

r 1 = 30/10 = 3

Also

10/h = 6/r

r2 = 6h/10 = 3/5 × h

Volume = 1/3πr²h

V = 1/3 × π × (3/5 × h)² × h

V =  1/3 × π × 9/25 × h³

V = 3π/25 × h³

Now

dv/dt = 3π/25 × 3 × h² × dh/dt

-5 = 3π/25 × 3 × 25 × dh/dt

-5 = 3π × 3 × dh/dt

-5 = 9π × dh/dt

dh/dt = -5/9π

dh/dt = -0.1768 cm/sec

therefore, the rate of the water level in the cone falling when it is 5cm from the bottom of the cone is -0.1768 cm/sec

4 0
3 years ago
for a certain type of heater, the increase in gas bills is directly proportional to the temperature setting (in fahrenheit). if
erica [24]

Answer:

The gas bill increases by $50

Step-by-step explanation:

We know that the increase in gas bills is directly proportional to the temperature setting. Let's take the increase in gas bills as g and increase in temperature setting as t. Thus, this can be written as:

g ∝ t

In every proportionality, there is a constant k, so it will be:

g = kt

It is mentioned that when the temperature setting increases by 4, the gas bill increases by $20, so in terms of the constant, we can write it as:

20 = k 4

We don't know the value of the constant, so we have to first find it out.

k = 20 ÷ 4

k = 5

Thus,

g = 5t

Now that we know the value of the constant, we can find by how much the gas bill will increase if the temperature setting increases by 10.

g = 5 × 10

g = <u>50</u>

∴ the gas bill increases by $50 when the temperature setting increases by 10 degrees Fahrenheit.

7 0
2 years ago
Smallest four digit number which is a perfect square
Daniel [21]
1024 is the smallest number which is a perfect square root.

32 times 32 is 1024
8 0
3 years ago
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