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sineoko [7]
3 years ago
15

Find the volume of the prism

Mathematics
1 answer:
miskamm [114]3 years ago
8 0
The answer is 654 square
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10(2^×) + 7(3^×) = 6^× + 70​
Mkey [24]

Answer:

x = 2.81 and 2.096

Step-by-step explanation:

Given the expression

10(2^x) + 7(3^x) = 6^x + 70​

This can also be expressed as;

10(2^x) + 7(3^x) = (2*3)^x + 70

10(2^x) + 7(3^x) = 2^x*3^x + 70

Let a  = 2^x and b = 3^x

10a + 7b = ab + 70

10a + 7b - ab = 70

10a-ab + 7b - 70 = 0

a(10-b)+7(b-10) = 0

a(10-b)-7(10-b) = 0

a-7 = 0 and 10-b = 0

a = 7 and b = 10

Since a = 2^x

7 = 2^x

log 7 = log2^x

log7 = xlog2

x = log7/log2

x = 2.81

Similarly

10 = 3^x

log 10 = log 3^x

log 10 = xlog3

x = log 10/log 3

x = 1/0.4771

x = 2.096

Hence the values of x that satisfies the equation are 2.81 and 2.096

8 0
2 years ago
A new online music service has a collection of 1,500 songs. It expects to triple the number of songs each year for the next few
Rzqust [24]

Answer: y = (3^(x-1))*1500

Step-by-step explanation:

We want the relationship

y = f(x)

where y is the number of songs, and x is the number of years.

We know that in the first year, x = 1, the site has 1,500 songs.

The next year, x = 2, the number of songs is tripled, then we will have:

1,500*3 = 4500 songs.

The next year, x = 3, we will have: 3*(3*1500) = (3^2)*1500.

when x = 4, the number is tripled again:

3*(3^2)*1500 = (3^3)*1500

We already can see the pattern, for the year x, the site will have:

y = (3^(x-1))*1500 songs.

This is the equation we are looking for.

7 0
3 years ago
Gabby is buying flowers for a friend. She can choose daisies, carnations, or sunflowers. She can put the flowers in a clear, red
In-s [12.5K]

Answer:

Daisies: Clear vase

Carnations: Red vase

Sunflowers: Blue vase

Step-by-step explanation:

Your using all the objects and is is in all the combinations.

8 0
3 years ago
Read 2 more answers
A company that has 350000 shares declares an annual gross profit of $2450665, pays 18.5% of this in tax, and reinvests 25% of th
podryga [215]

Gross profit, G = $2450665

Tax, t=18.5%

reinvestment, r = 25%


Total dividends

= G(1-t)(1-r)

=2450665*(1-0.185)(1-0.25)

=1497968.98


Dividend per share

=1497968.98/350000

=4.280


Earnings per share

EPS = Net profit / number of shares

= 2450665(1-0.185)/350000

=5.7065


Current price = 43.36


P/E ratio

= Current price/EPS

= 43.36/5.7065

= 7.598

=7.6 to one decimal place.



8 0
2 years ago
Veronica’s velocity was measured as 4.3 m/s. She displaced 20 meters in 4.7 seconds. Which piece of information is missing for t
telo118 [61]

We are given displacement = 20 meters.

Time given = 4.7 seconds.

Velocity = 4.3 m/s.

Please note : Velocity is a vector quantity. A vector quantity depends on magnitude and direction as well.

We are given magnitude of displacement = 20 meter and time 4.7 seconds but the direction is missing there.

If it would be in forward direction it would be positive and if it would be in backward direction, it would be of negative.

Therefore, <u>"B)the direction"</u> is correct option.

4 0
3 years ago
Read 2 more answers
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