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3 years ago

F(x) = 4x2–2x + 1 i need help solving this problem and the steps

Mathematics

1 answer:

Shkiper50 [21]3 years ago

3 0

F(x)=2x+3
assuming the problem is 4 times 2 minus 2x plus 1
you add like variables

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Simplify 3-(4x-5)+6.

Leviafan [203]

3 + -4x = 5(x +6)

Re-order the terms:

3 + -4x = 5(6 + x)
3 + -4x = (6 . 5 + x . 5)
3 + -4x = (30 + 5x)

Solving:

3 + -4x = 30 + 5x

Solving for variable "x"

Move all terms containing "x" to the left, all the other terms to the right.

Add "-5x" to each side of the equation.
3 + -4x + -5x = 30 + 5x + -5x

Combine like terms: -4x + -5x = -9x
3 + -9x = 30 +5x + -5x

Combine like terms: 5x + -5x = 0
0 + -9x = 30 +0
3 + -9x = 30

Add "-3" to each side of the equation.
3 + -3 + -9x = 30 + 3

Combine like terms: 3 + -3 = 0
0 + -9x = 30 + -3
-9x = 30 + -3

Combine like terms: 30 + -3 = 27
-9x = 27

Divide each side by "-9".
x = -3

Simplifying:
x = -3

6 0

4 years ago

Read 2 more answers

3The frequency (in Hz) of a vibrating violin string is given by f = 1 2L s T rho where L is the length of the string (in meters)

bagirrra123 [75]

Answer:

(i) $\dfrac{df}{dL}=-\dfrac{1}{2L^2}\sqrt{\dfrac{T}{\rho}}$

(ii) $\dfrac{df}{dT}=\dfrac{1}{4L\sqrt{T\rho}}$

(iii) $\dfrac{df}{d\rho}=-\dfrac{\sqrt{T}}{4L\rho^{-\frac{3}{2}}}}$

Step-by-step explanation:

Let as consider the frequency (in Hz) of a vibrating violin string is given by

$f=\dfrac{1}{2L}\sqrt{\dfrac{T}{\rho}}$

(i)

Differentiate f with respect L (assuming T and rho are constants).

$\dfrac{df}{dL}=\dfrac{d}{dL}\dfrac{1}{2L}\sqrt{\dfrac{T}{\rho}}$

Taking out constant terms.

$\dfrac{df}{dL}=\dfrac{1}{2}\sqrt{\dfrac{T}{\rho}}\dfrac{d}{dL}\dfrac{1}{L}$

$\dfrac{df}{dL}=\dfrac{1}{2}\sqrt{\dfrac{T}{\rho}}(-\dfrac{1}{L^2})$

$\dfrac{df}{dL}=-\dfrac{1}{2L^2}\sqrt{\dfrac{T}{\rho}}$

(ii)

Differentiate f with respect T (assuming L and rho are constants).

$\dfrac{df}{dT}=\dfrac{d}{dT}\dfrac{1}{2L}\sqrt{\dfrac{T}{\rho}}$

Taking out constant terms.

$\dfrac{df}{dT}=\dfrac{1}{2L}\sqrt{\dfrac{1}{\rho}}\dfrac{d}{dT}\sqrt{T}}$

$\dfrac{df}{dT}=\dfrac{1}{2L}\sqrt{\dfrac{1}{\rho}}(\dfrac{1}{2\sqrt{T}})$

$\dfrac{df}{dT}=\dfrac{1}{4L\sqrt{T\rho}}$

(iii)

Differentiate f with respect rho (assuming L and T are constants).

$\dfrac{df}{d\rho}=\dfrac{d}{d\rho}\dfrac{1}{2L}\sqrt{\dfrac{T}{\rho}}$

Taking out constant terms.

$\dfrac{df}{d\rho}=\dfrac{\sqrt{T}}{2L}\dfrac{d}{d\rho}(\rho)^{-\frac{1}{2}}}$

$\dfrac{df}{d\rho}=\dfrac{\sqrt{T}}{2L}(-\dfrac{1}{2}(\rho)^{-\frac{3}{2}}})$

$\dfrac{df}{d\rho}=-\dfrac{\sqrt{T}}{4L\rho^{-\frac{3}{2}}}}$

4 0

3 years ago

Which is the better buy? 13-pint jug of juice for $12.74 3-gallon jug of juice for $30.48

Ainat [17]

Answer: second one

13 pint = 1.625 gallons, so 1.625 gallons =$12.74.

3 gallons = 24 pint. so 24 pints = 30.48

now if we divide 13 and 24.= 1.84615384615

3 divided by 1.625 =1.84615384615

This is equaled the same now we need to divide the money so 30.48 divided by 12.74 = 2.39246467818 and now you got 2.39 so the answer is the second one

Step-by-step explanation:

7 0

3 years ago

A number cube is rolled 10 times. An even number comes up 6 times. What is the experimental probability of an even number coming

FromTheMoon [43]

Answer:

Step-by-step explanation:

Experimental probability is the ratio of the number of times an event occurs to the total number of trials or times the activity is performed.

A number cube is rolled 10 times, so

Number of trials or times the activity is performed = 10.

An even number comes up 6 times, so

Number of times an event occurs = 6.

Hence, the experimental probability is

$P=\dfrac{6}{10}=\dfrac{3}{5}.$

5 0

3 years ago

Suppose a graduate student receives a non-subsidized student loan of $12,000 for each of the 4 years the student pursues a PhD.

AnnyKZ [126]

Answer:

Monthly Payment $ 515.92

Step-by-step explanation:

First we calculate the value of the loan after the four years:

We will calcualte that using the future value of an annuity of $12,000 for 4 years at 4%

$C \times \frac{(1+r)^{time} -1}{rate} = FV\\$

C 12000

time 4

rate 0.04

$12000 \times \frac{(1+0.04)^{4} -1}{0.04} = FV\\$

FV $50,957.57

Now we have to calculate the cuota of a 10 years loan with this value as the principal.

$PV \div \frac{1-(1+r)^{-time} }{rate} = C\\$

PV $50,957.57

time 10 years x 12 months per year = 120

rate4% per year / 12 months = monthly rate = 0.00333

$50957.57 \times \frac{1-(1+0.00333)^{-120} }{0.00333} = C\\$

C $ 515.92

6 0

3 years ago