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3 years ago

For f(x)=2|x+3|-5, name the type of function and describe each of the three transformations from the parent function f(x)=|x|

Mathematics

1 answer:

Vadim26 [7]3 years ago

8 0

Answer:

Function: absolute value function

Transformations: Vertical stretch by a factor of 2, horizontal shift three units to the left, and vertical shift five units down.

Let me know if this helps!

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Alona [7]

Answer: I didn't understand

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2 years ago

Kelly inherits land which had a basis to the decedent of $95,000 and a fair market value of $50,000 on August 4, 2018, the date

Degger [83]

Answer:

The correct option is;

Her recognized <u>loss </u>is ($1,000)

Step-by-step explanation:

The given information are;

The basis of the land to the decedent = $95,000

The land's market value on 4th of August 2018 when the decedent died = $50,000

The alternate valuation date = 6 months + The date of death of the decedent = 4th February, 2019

The value filed by the executor on the tax return using the alternate valuation date = The market value of the estate on 4th of February 2019

The market value of the land on 4th of February 2019 = $45,000

∴ The value filed by the executor on the tax return using the alternate valuation date = $45,000

The value of the land on November 12, 2018 when the executor distributed the land to Kelly = $49,000

The value at which Kelly sells the land on June 10, 2019 = $48,000

Given that, recognized gain is the profit made from selling an asset based on the value of the asset when it was obtained, we have;

Kelly's recognized gain or loss = (The value at which Kelly sells the land) - (The value of the land when the executor distributed the land to Kelly)

Kelly's recognized gain or loss = $48,000 - $49,000 = -$1,000 = ($1,000)

Therefore, Kelly's recognized loss = ($1,000).

6 0

3 years ago

A tank contains 60 kg of salt and 1000 L of water. Pure water enters a tank at the rate 6 L/min. The solution is mixed and drain

MissTica

Answer:

(a) 60 kg; (b) 21.6 kg; (c) 0 kg/L

Step-by-step explanation:

(a) Initial amount of salt in tank

The tank initially contains 60 kg of salt.

(b) Amount of salt after 4.5 h

$\text{Let A = mass of salt after t min}\\\text{and }r_{i} = \text{rate of salt coming into tank}\\\text{and }r_{0} =\text{rate of salt going out of tank}$

(i) Set up an expression for the rate of change of salt concentration.

$\dfrac{\text{d}A}{\text{d}t} = r_{i} - r_{o}\\\\\text{The fresh water is entering with no salt, so}\\ r_{i} = 0\\r_{o} = \dfrac{\text{3 L}}{\text{1 min}} \times \dfrac {A\text{ kg}}{\text{1000 L}} =\dfrac{3A}{1000}\text{ kg/min}\\\\\dfrac{\text{d}A}{\text{d}t} = -0.003A \text{ kg/min}$

(ii) Integrate the expression

$\dfrac{\text{d}A}{\text{d}t} = -0.003A\\\\\dfrac{\text{d}A}{A} = -0.003\text{d}t\\\\\int \dfrac{\text{d}A}{A} = -\int 0.003\text{d}t\\\\\ln A = -0.003t + C$

(iii) Find the constant of integration

$\ln A = -0.003t + C\\\text{At t = 0, A = 60 kg/1000 L = 0.060 kg/L} \\\ln (0.060) = -0.003\times0 + C\\C = \ln(0.060)$

(iv) Solve for A as a function of time.

$\text{The integrated rate expression is}\\\ln A = -0.003t + \ln(0.060)\\\text{Solve for } A\\A = 0.060e^{-0.003t}$

(v) Calculate the amount of salt after 4.5 h

a. Convert hours to minutes

$\text{Time} = \text{4.5 h} \times \dfrac{\text{60 min}}{\text{1h}} = \text{270 min}$

b.Calculate the concentration

$A = 0.060e^{-0.003t} = 0.060e^{-0.003\times270} = 0.060e^{-0.81} = 0.060 \times 0.445 = \text{0.0267 kg/L}$

c. Calculate the volume

The tank has been filling at 6 L/min and draining at 3 L/min, so it is filling at a net rate of 3 L/min.

The volume added in 4.5 h is

$\text{Volume added} = \text{270 min} \times \dfrac{\text{3 L}}{\text{1 min}} = \text{810 L}$

Total volume in tank = 1000 L + 810 L = 1810 L

d. Calculate the mass of salt in the tank

$\text{Mass of salt in tank } = \text{1810 L} \times \dfrac{\text{0.0267 kg}}{\text{1 L}} = \textbf{21.6 kg}$

(c) Concentration at infinite time

$\text{As t $\longrightarrow \, -\infty,\, e^{-\infty} \longrightarrow \, 0$, so A $\longrightarrow \, 0$.}$

This makes sense, because the salt is continuously being flushed out by the fresh water coming in.

The graph below shows how the concentration of salt varies with time.

3 0

3 years ago

A rectanglar swimming pool is three times as long as it is wide. If the perimeter of the soccer feild is 300 yards, what are the

fredd [130]

Answer:

The dimension of the rectangular pool is $112.5\times 37.5$

Step-by-step explanation:

Given : A rectangular swimming pool is three times as long as it is wide. If the perimeter of the soccer field is 300 yards.

To find : What are the dimensions?

Solution :

Let the width of the rectangular pool be 'x'.

A rectangular swimming pool is three times as long as it is wide.

The length of the pool be '3x'

The perimeter of the rectangular swimming pool is $P=2(l+w)$

The perimeter of the soccer field is 300 yards.

Substitute the value in the formula,

$300=2(3x+x)$

$300=2\times 4x$

$300=8x$

$x=\frac{300}{8}$

$x=37.5$

The width of the pool is x=37.5 unit

The length of the pool is $3x=3(37.5)=112.5$

Therefore, The dimension of the rectangular pool is $112.5\times 37.5$

4 0

3 years ago

What is the first step when solving this equation: 2(x-4)+6=3x+19

Delicious77 [7]

Solve the parenthesis

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3 years ago

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