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3 years ago

Find the fourth term of the

Mathematics

1 answer:

garik1379 [7]3 years ago

6 0

Answer:

The fourth term of the geometric sequence is 512.

Step-by-step explanation:

To find the geometric sequence of the nth term we will use the formula:

An = a×r^(n-1)

As, we have to find the fourth term,

A4 = 8×(4)^4-1

A4 = 8×64

A4 = 512.

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Sam drove 754 miles in 13 hours, at the same rate how many miles would he drive in 9 hours

VARVARA [1.3K]

Divide 754 by 13 and you get 58
Now multiply by 9 and you get 522 miles.

8 0

3 years ago

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The sum of 2 times a number and 8 is 7

My name is Ann [436]

Answer:

The number is -1/2

Step-by-step explanation:

Let x be the number

2x+8 = 7

Subtract 8 from each side

2x+8-8 = 7-8

2x = -1

Divide each side by 2

2x/2 =-1/2

x = -1/2

The number is -1/2

8 0

3 years ago

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A culture started with 3000 bacteria. After 2 hours it grew to 3300 bacteria. Predict how many bacteria will be present after 16

bixtya [17]

Answer:

$6,430\ bacteria$

Step-by-step explanation:

we have a exponential function of the form

$y=a(1+r)^{x}$

where

y is the population of bacteria

a is the initial value

r is the rate of growth

x is the number of hours

we have

a=3,000 bacteria

$y=3,000(1+r)^{x}$

For x=2, y=3,300

substitute

$3,300=3,000(1+r)^{2}$

$(3,300/3,000)=(1+r)^{2}$

Apply square root both sides

$1+r=\sqrt{3.3/3}$

$r=\sqrt{3.3/3}-1$

$r=0.0488$

$r=4.88\%$

substitute in the equation

$y=3,000(1+0.0488)^{x}$

$y=3,000(1.0488)^{x}$

<u><em>Predict how many bacteria will be present after 16 hours</em></u>

For x=16 hours

substitute

$y=3,000(1.0488)^{16}$

$y=6,430\ bacteria$

6 0

3 years ago

Write an equation for a line parallel to y=3x-3 and passing through the point (4,15)

Andrews [41]

Hello!

To find the equation of a line parallel to y = 3x - 3 and passing through the point (4, 15), we need to know that if two lines are parallel, then their slopes are equivalent.

This means that we create a new equation in slope-intercept form, which includes the original slope, which is equal to 3.

In slope-intercept form, we need a y-intercept. So, we would substitute the given ordered pair into the new equation with the same slope and solve.

Remember that slope-intercept form is: y = mx + b, where m is the slope and b is the y-intercept.

y = 3x + b (substitute the ordered pair (4, 15))

15 = 3(4) + b (simplify)

15 = 12 + b (subtract 12 from both sides)

3 = b

Therefore, the equation for the line parallel to the line y = 3x - 3, and passing through the point (4, 15) is y = 3x + 3.

8 0

3 years ago

The quadratic function g(x) = a.ca + bx+c has the

Mumz [18]

<em>The value of b is 14 and the value of c is 65</em>

<h2>Explanation:</h2>

The quadratic function is a function of the form:

$f(x)=ax^2+bx+c$

Here we know that the leading coefficient $a=1$ so we reduce our equation to:

$g(x)=x^2+bx+c$

The roots are those values at which $g(x)=0$

So:

$x^2+bx+c=0 \\ \\ First \ root: \\ \\ (-7+4i)^2+b(-7+4i)+c=0 \\ \\ (-7)^2-2(7)(4i)+(4i)^2-7b+4bi+c=0 \\ \\ 49-56i+16i^2-7b+4bi+c=0 \\ \\ \\ Simplifying: \\ \\ 49-56i+16(-1)-7b+4bi+c=0 \\ \\ 49-56i-16-7b+4bi+c=0 \\ \\ 33-56i-7b+4bi+c=0 \\ \\ \\$

$Second \ root: \\ \\ (-7-4i)^2+b(-7-4i)+c=0 \\ \\ (-1)^2(7+4i)^2+b(-7-4i)+c=0 \\ \\ (7)^2+2(7)(4i)+(4i)^2-7b-4bi+c=0 \\ \\ 49+56i+16i^2-7b-4bi+c=0 \\ \\ \\ Simplifying: \\ \\ 49+56i+16(-1)-7b-4bi+c=0 \\ \\ 49+56i-16-7b-4bi+c=0 \\ \\ 33+56i-7b-4bi+c=0$

So we have:

$(1) \ 33-56i-7b+4bi+c=0 \\ \\ (2) \ 33+56i-7b-4bi+c=0 \\ \\ \\ Subtract \ 2 \ from: \\ \\ 33-56i-7b+4bi+c-(33+56i-7b-4bi+c)=0 \\ \\ 33-56i-7b+4bi+c-33-56i+7b+4bi-c=0 \\ \\ \\ Combine \ like \ terms: \\ \\ 33-33-56i-56i-7b+7b+4bi+4bi+c-c=0 \\ \\ -112i+8bi=0 \\ \\ Isolating \ b: \\ \\ b=\frac{112i}{8i} \\ \\ \boxed{b=14}$

Finding c from (1):

$33-56i-7b+4bi+c=0 \\ \\ \\ Substituting \ b: \\ \\ 33-56i-7(14)+4(14)i+c=0 \\ \\ 33-56i-98+56i+c=0 \\ \\ -65+c=0 \\ \\ \boxed{c=65}$

<h2>Learn more:</h2>

Complex conjugate: brainly.com/question/2137496

#LearnWithBrainly

5 0

3 years ago