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3 years ago

How do I do this qn?

Mathematics

1 answer:

denis-greek [22]3 years ago

3 0

You can take the log of the left and right hand side, and then apply the logarithm rules:

log(aˣ) = x·log(a)
log(ab) = log(a) + log(b)

log(9^(x-1) * 2^(2x+2)) = log(6^(3x))
log(9^(x-1)) + log(2^(2x+2)) = 3x log(6)
(x-1) log(9) + (2x+2) log(2) - 3x log(6) = 0
x(log9 + 2log2 - 3log6) = log9 - 2log2
x = (log9 - 2log2) / (log9 + 2log2 - 3log6)

simplifying by writing log9 = 2log3 and log6 = log2+log3

x= 2(log3 - log2) / (2log3 + 2log2 - 3log2 - 3log3) =
x= -2(log3 - log2) / (log3 + log2) = -2 log(3/2) / log(6)

So 6^x = 4/9

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Given that the measurement is in centimeters, find the area of the circle to the nearest tenth. (Use 3.14 for π) the radius is 3

Fofino [41]

Answer:

Area of the circle = $28.26cm^2$

Step-by-step explanation:

Radius of the circle= 3 cm

Area of the circle= $\pi *r^2$

As,

$\pi =\frac{22}{7}=3.14$

Putting the values in the formula:

Area of the circle= $3.14*3*3$

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The area of the circle is $28.26cm^2$

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krek1111 [17]

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Step-by-step explanation:

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3 years ago

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Is there enough information to prove each quadrilateral is a parallelogram? Explain.

omeli [17]

Answer:

1. yes

2, no

3. yes

4. yes

Step-by-step explanation:

1. yes

If both sets of opposite sides are congruent, the quadrilateral is a parallelogram.

2. no

We know two side lengths. We know nothing about the other 2 sides and also nothing about all 4 angles.

3. yes

The missing angle must be 102°. With both pairs of opposite angles congruent, it must be a parallelogram.

4. yes

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3 years ago

PLEASE HELP ILL GIVE 49 POINTS! THANKS! Show work

NemiM [27]

Answer:

y = -2x+11

Step-by-step explanation:

If we have a slope and a line, we can use the slope intercept form of a line

y-y1 = m(x-x1)

where (x1,y1) is the point and m is the slope.

Substitute in what we know

y-5 = -2 (x-3)

We want it in slope intercept form which is y = mx+b

Distribute the -2

y-5 = -2x+6

Add 5 to each side

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Here is the complete question

A nominal interest rate of 5%

A real interest rate of 5%

A real interest rate of 3%

A nominal interest rate of 3%

Answer:

A real interest rate of 5%

Step-by-step explanation:

A real interest rate of 5% is the best option for oscar. The nominal rate of interest is a type of interest rate that shows the increase in in percentage of money without the depreciation discount that is usually caused by inflation or the payment of tax.

The real rate of interest shows the real increase in the money that has been paid for an investment. This is after inflation has been discounted and all forms of taxes have been paid.

So oscar should invest his $4000 on a savings account whose real interest rate is 5% per year

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