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2 years ago

3. Given this quadratic equation, 2x2 - x - 28 = 0,

Mathematics

1 answer:

JulijaS [17]2 years ago

4 0

Answer:

a) (2x+7)(x-4)

b) x = -7/2 and x = 4

Step-by-step explanation:

a) (2x ?)(x ?)

set up the above and considered factors of 28 that, when paired with 2, would give me -1x and -28 → (1·28, 2·14, 4·7)

after trial-and-error, found that 4 and 7 worked (used un-FOIL)

b) 2x + 7 = 0

2x = -7

x = -7/2

*********

x-4 = 0

x = 4

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Can you help with this please

mojhsa [17]

Answer:

x = 81

Steps:

It says that y ~ √x

We have points (9, 18) as a guide.

We can write y = f(x) = a√x +b

Use points (9, 18) as a guide

18 = a√9 +b

18 = 3a + b

One solution might be a = 6, which means f(x) = 6√x

Thus when y = 54,

54 = 6√x

9 = √x

81 = x

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2 years ago

A large tank is filled to capacity with 600 gallons of pure water. brine containing 4 pounds of salt per gallon is pumped into t

nignag [31]

If $A(t)$ is the amount of salt in the tank at time $t$ , then the rate at which the amount of salt in the tank changes is given by

$\dfrac{\mathrm dA(t)}{\mathrm dt}=\dfrac{4\text{ lbs}}{1\text{ gal}}\dfrac{6\text{ gal}}{1\text{ min}}-\dfrac{A(t)\text{ lbs}}{600\text{ gal}}\dfrac{6\text{ gal}}{1\text{ min}}$
$\dfrac{\mathrm dA}{\mathrm dt}=24\dfrac{\text{lb}}{\text{min}}-\dfrac{A(t)}{100}\dfrac{\text{lb}}{\text{min}}$

Let's drop the units for now. We have

$\dfrac{\mathrm dA(t)}{\mathrm dt}+\dfrac{A(t)}{100}=24$
$e^{t/100}\dfrac{\mathrm dA(t)}{\mathrm dt}+e^{t/100}\dfrac{A(t)}{100}=24e^{t/100}$
$\dfrac{\mathrm d}{\mathrm dt}\left[e^{t/100}A(t)\right]=24e^{t/100}$
$e^{t/100}A(t)=\displaystyle24\int e^{t/100}\,\mathrm dt$
$e^{t/100}A(t)=2400e^{t/100}+C$
$A(t)=2400+Ce^{-t/100}$

We're given that the water is pure at the start, so $A(0)=0$ , giving

$A(0)=0=2400+Ce^{-0/100}\implies C=-2400$

So the amount of salt in the tank (in lbs) at time $t$ is

$A(t)=2400\left(1-e^{-t/100}\right)$

4 0

3 years ago

What is the slope of the line that contains the points (1,-1) and (-2,8)? (Also can you show me how you got it please?)

ArbitrLikvidat [17]

The answer is -3

You use the formula y1-y2
———
x1-x2
-1 and 8 are your y’s
1 and -2 are your x’s

Your equation should look like this
-1-8 -9
—— = —— = -3
1-(-2) 3

I plugged the y’s and x’s into the formula.
I hope this helps!!

3 0

3 years ago

What are you NOT able to do with an ATM card? Select the best answer from the choices provided. A. transfer money B. deposit mon

vesna_86 [32]

Answer:

Step-by-step explanation:

The rest of the options are possible using an atm card. but using it to deposit is not possible.

7 0

3 years ago

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What's the proportionality of y = 2x

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