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2 years ago

If the first term in an arithmetic sequence is –3 and the tenth term is 15, what is the common difference?

Mathematics

1 answer:

Triss [41]2 years ago

6 0

Given that the First term of the Arithmetic sequence = -3

⇒ a = -3

We know that nth term of a Arithmetic sequence is : Tn = a + (n - 1)d

where a is the first term and d is the common difference

Given that 10th term is 15

⇒ T₁₀ = -3 + (10 - 1)d

⇒ -3 + (10 - 1)d = 15

⇒ 9d = 18

⇒ d = 2

⇒ Common difference of given Arithmetic Sequence is 2

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Simply the expression given below (3x^3+4x^2+4x-12)+(-5x^3+9x^2-9x+20)

Svet_ta [14]

Answer:

1. Simplify: (4x2 - 2x) - (-5x2 - 8x).

Solution:

(4x2 - 2x) - (-5x2 - 8x)

= 4x2 - 2x + 5x2 + 8x.

= 4x2 + 5x2 - 2x + 8x.

= 9x2 + 6x.

= 3x(3x + 2).

Answer: 3x(3x + 2)

Step-by-step explanation:

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2 years ago

Pregnant women metabolize some drugs at a slower rate than the rest of the population. The half-life of caffeine is about 4 hour

UkoKoshka [18]

Answer:

Husband:

The husband will have 16.35 mg of caffeine in his body at 7 pm.

Woman:

The pregnant woman will have 51.33 mg of caffeine in her body at 7 pm.

Step-by-step explanation:

The amount of caffeine in the body can be modeled by the following equation:

$C(t) = C(0)e^{rt}$

In which C(t) is the amount of caffeine t hours after 8 am, C(0) is how much coffee they took and r is the rate the the amount of caffeine decreases in their bodies.

110 mg of caffeine at 8 am,

So $C(0) = 110$

Husband

Half life of 4 hours. So

$C(4) = 0.5C(0) = 0.5*110 = 55$

$C(t) = C(0)e^{rt}$

$55 = 110e^{4r}$

$e^{4r} = 0.5$

Applying ln to both sides

$\ln{e^{4r}} = \ln{0.5}$

$4r = \ln{0.5}$

$r = \frac{\ln{0.5}}{4}$

$r = -0.1733$

So for the husband

$C(t) = 110e^{-0.1733t}$

At 7 pm

7 pm is 11 hours after 8 am, so this is C(11)

$C(t) = 110e^{-0.1733t}$

$C(11) = 110e^{-0.1733*11} = 16.35$

The husband will have 16.35 mg of caffeine in his body at 7 pm.

Pregnant woman

Half life of 10 hours. So

$C(10) = 0.5C(0) = 0.5*110 = 55$

$C(t) = C(0)e^{rt}$

$55 = 110e^{10}$

$e^{10r} = 0.5$

Applying ln to both sides

$\ln{e^{10r}} = \ln{0.5}$

$10r = \ln{0.5}$

$r = \frac{\ln{0.5}}{10}$

$r = -0.0693$

At 7 pm

7 pm is 11 hours after 8 am, so this is C(11)

$C(t) = 110e^{-0.0693t}$

$C(11) = 110e^{-0.0693*11} = 51.33$

The pregnant woman will have 51.33 mg of caffeine in her body at 7 pm.

7 0

3 years ago

The lengths of the legs of a right triangle are 6 cm and 8 cm. What is the length of the hypotenuse?

Svetllana [295]

You require the Pythagorean Theorem: in a right triangle, the sum of the squares of the legs equals the square of the hypotenuse.In this case 6^2 + 8^2 = 36 + 64 = 100 = 10^2
the hypotenuse is 10.

6 0

3 years ago

Read 2 more answers

What is a termites favorite breakfast 1 9m 6m find x

Nitella [24]

Is that 19m or 9 m ?

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2 years ago

Kennedy and Olivia go to the movie theater and purchase refreshments for their friends.

Anvisha [2.4K]

Answer:

6x + y = 38.75

x + 2y = 17

price of drink is $5.75

Step-by-step explanation:

Let the price of popcorn be x

Let the price of drink be y.

price of 12 bags of popcorn will be 12x

price of 2 drinks will be 2y

it is given that "Kennedy spends a total of $77.50 on 12 bags of popcorn and 2 drinks."

thus

12x + 2y = 77.50

dividing LHS and RHS by 2 we have

12x/2 + 2y/2 = 77.50/2

=> 6x + y = 38.75 _________(1)

__________________________________________________

price of 3 bags of popcorn will be 3x

price of 6 drinks will be 6y

it is given that "Olivia spends a total of $51.00 on 3 bags of popcorn and 6 drinks."

thus

3x + 6y = 51.00

dividing LHS and RHS by 3 we have

3x/3 + 6y/3 = 51/3

=> x + 2y = 17 _____________(2)

__________________________________________________

Thus we have two equation

6x + y = 38.75 _________(1)

x + 2y = 17

=> x = 17 - 2y

putting this value of x in equation 1 we have

6( 17 - 2y) + y = 38.75

=> 102 - 12y + y = 38.75

=> 102 - 11y = 38.75

=> -11y = 38.75 -102

=> -11y = -63.25

=> y = -63.25/-11 = 5.75

as we have x = 17 - 2y

using 5.75 in place of y

x = 17 - 2(5.75 )

=> x = 17 - 11.5

=> x = 5.5

Thus, system of equations are

6x + y = 38.75

x + 2y = 17

price of drink is $5.75

3 0

3 years ago