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3 years ago

Which function describes this graph?

Mathematics

2 answers:

Aleksandr [31]3 years ago

6 0

Answer:

C. y = x2 + 8x + 12

Step-by-step explanation:

To find x intercept/zero, substitute y = 0

0 = x^2 + 8x + 12

x^2 += 8x + 12 = 0

x^2 + 8x + 12 = 0

Solve the quadratic equation

ax^2 + bx + c = 0 using x = -b± $\sqrt{b^2 -4ac$ / 2a
x = -8± $\sqrt{8^2 -4(1)(12)$ / 2(1)

x = -8± $\sqrt{8^2 -4(12)$ / 2(1)

any expression multiplied by 1 remains the same

x= -8± $\sqrt{8^2 - 4(12)$ / 2(1)

Evaluate the power

8^2

write the exponentiation as a multiplication

8(8)

multiply the numbers

x = -8± $\sqrt{64 - 4(12)$ / 2(1)

multiply the numbers

x = -8± $\sqrt{64 - 48$ / 2(1)

any expression multiplied by q remains the same

x = -8± $\sqrt{64-48$ /2

subtract the numbers

x = -8± $\sqrt{16$ / 2

calculate the square root

x= -8± 4 / 2

x= -8 + 4 / 2

x= -8 - 4 / 2

simplify the expression

x = -2

x = -8 - 4 / 2

x = -2

x = -6

final solutions are

x1 = -6, x 2 = -2

solmaris [256]3 years ago

6 0

Answer:

y=x^2+8x+12

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Nick has $7.00. Bagels cost $0.75 each and a small container of cream cheese costs $1.29. Write an inequality to find the number

stepladder [879]

.75x+1.29y < $7.00
x represents how many bagels he can buy
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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

F(x) =2x^2+4x+5 Find: f(a)

MA_775_DIABLO [31]

Answer:

F(a) =2a^2+4a+5

Step-by-step explanation:

just put x= a

5 0

4 years ago

Find AC I'd appreciate any help!

Digiron [165]

5

Explanation:
2 - (-3) = 5

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3 years ago

What are the coordinates of (-4,-2) rotating 90° counterclockwise?

RUDIKE [14]

Answer:

(2, -4)

Step-by-step explanation:

The rotation of an object turns the object around a fixed point called the center of rotation.

A rotation of 90° counterclockwise means:

A 90° rotation counterclockwise with the origin (0, 0) as the center of rotation.

The rule for a counterclockwise rotation of 90° about the origin is:

(x, y) → (-y, x)

Therefore:

(-4, -2) → (2, -4)

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2 years ago