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3 years ago

Adele is 5 years older than Timothy. In three years, Timothy will be of Adele’s age. What is Adele’s current age?

Mathematics

1 answer:

lyudmila [28]3 years ago

8 0

Answer:

Step-by-step explanation:

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Identify the function that contains the data in the following table: x -2 0 2 3 5 f(x)

Veseljchak [2.6K]

Answer:

f(x) = |x - 2| + 1

Step-by-step explanation:

When x = -2, then f(-2) = 5

The first function gives the relation equation as f(x) = |x| + 1

So, f(-2) = |-2| + 1 = 2 + 1 = 3 ≠ 5

{Since the definition of |x| is given by

|x| = x, when x ≥ 0 and |x| = - x, when x < 0}

Again, the second function gives the relation equation as f(x) = |x - 2|.

So, f(-2) = |-2 - 2| = |-4| = 4 ≠ 5

Now, the third function gives the relation equation as f(x) = |x - 2| - 1.

So, f(-2) = |-2 - 2| - 1 = |-4| - 1 = 4 - 1 = 3 ≠5

Again, the fourth function gives the relation equation as f(x) = |x - 2| + 1.

Hence, f(-2) = |-2 - 2| + 1 = |-4| + 1 = 4 + 1 = 5

Therefore, the fourth function f(x) = |x - 2| + 1 contains the given data table.

For further clarity we can check f(0) = 3, f(2) = 1, f(3) = 2 and f(5) = 4. (Answer)

6 0

3 years ago

Read 2 more answers

Write the point-slope form of the line that passes through (-8, 2) and is parallel to a line with a slope of -8. Include all of

Verizon [17]

Parallel lines have the same slope, so since you want a line that is parallel to a line with slope -8, your line will also have slope -8.

The slope-intercept form of the equation of a line is

y = mx + b

where m is the slope, and b is the y-intercept.

You already know you have a slope of -8, so m = -8, and you have

y = -8x + b

Now you need to find the value of b.

Use the point you know and substitute it in for x and y, and solve for b.

y = -8x + b

Use x = -8, and y = 2.

2 = -8(-8) + b

2 = 64 + b

-62 = b

b = -62

Now replace b with -62.

y = -8x + b

y = -8x - 62

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3 years ago

The class collected $1690, if there were only 13 students that collected money,what is the average amount each student collected

Svet_ta [14]

Divide 1690 by 13, and you get 130, so $130.

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4 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.

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3 years ago

Six different second-year medical students at Bellevue Hospital measured the blood pressure of the same person. The systolic re

Sauron [17]

Answer:

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