Find an explicit rule for the nth term of the sequence. 9, 36, 144, 576, ...

Final answer:

The net change in temperature over the day is 0 degrees. After increasing by 17 degrees in the afternoon, the temperature fell by 17 degrees by nightfall, returning it to the starting temperature.

Explanation:

The student has asked about calculating the net change in temperature over the course of a day starting at 48 degrees. By 3:00 p.m., the temperature increased by 17 degrees, making it 65 degrees. But by nightfall, the temperature decreased by the same amount, falling back down to 48 degrees. The calculation of net change in this scenario is simple: subtract the starting temperature from the final temperature after all changes have occurred. In this case, the starting temperature was 48 degrees, it went up to 65 degrees, and then back to 48 degrees.

The net temperature change is therefore 48 degrees (final temperature) - 48 degrees (starting temperature), which equals 0 degrees. This means there was no net change in temperature over the course of the day. It is important to recognize that even though there was a temporary increase and subsequent decrease, the net effect cancels out, leaving the temperature the same as it started.

Answer:

The equation of the line is [tex]y=\frac{-1}{2}x+1[/tex]

Step-by-step explanation:

1. The equation of the line that passes through two points can be expresed as:

[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex] (Eq.1)

where [tex]x_{1}[/tex], [tex]x_{2}[/tex], [tex]y_{1}[/tex] and [tex]y_{2}[/tex] are the given points.

2. Name the points:

[tex]x_{1}[/tex]=-6

[tex]x_{2}[/tex]=-2

[tex]y_{1}[/tex]=4

[tex]y_{2}[/tex]=2

3. Replace the points in the Eq.1:

[tex]\frac{y-4}{x-(-6)}=\frac{2-4}{-2-(-6)}[/tex]

[tex]\frac{y-4}{x+6}=\frac{2-4}{-2+6}[/tex]

[tex]\frac{y-4}{x+6}=\frac{-2}{4}[/tex]

[tex]\frac{4(y-4)}{x+6}=-2[/tex]

[tex]4(y-4)=-2(x+6)[/tex]

[tex]4y-16=-2x-12[/tex]

[tex]4y=-2x-12+16[/tex]

[tex]4y=-2x+4[/tex]

[tex]y=\frac{-2x+4}{4}[/tex]

[tex]y=\frac{-2x}{4}+\frac{4}{4}[/tex]

[tex]y=\frac{-1}{2}x+1[/tex]

Answer:

degenerate hyperbola

pair of intersecting lines

Step-by-step explanation:

Answer:

Step-by-step explanation:

Notice that this situation models a right triangle, when the height, which is a leg of the triangle, is 6 meters.

Also, we know the angle between the ladder and the ground, which is 72°.

To find the distance from A to B, which from the bottom of the ladder to the bottom of the wall, we just need to use trigonometric reasons.

[tex]tan(72\°)=\frac{opposite \ leg}{adjacent \ leg}[/tex]

Why we use tangent? Because it relates both legs where we just need to find the adjacent one.

[tex]tan(72\°)=\frac{6}{AB}\\AB=\frac{6}{tan(72\°)} \\AB \approx \frac{6}{3} \\AB \approx 2 \ m[/tex]

Therefore, the best approximation of AB is 2 meters.

Compound interest formula is  [tex]A = P(1+r)^t[/tex]

Where P is the principal amount

r is the rate of interest

t is number of years

Brian invests $10,000 in an account earning 4% interest, compounded annually for 10 years

P = 10,000  , r= 4% = 0.04 , t =10

Plug in all the values

[tex]A = 10000(1+0.04)^{10}[/tex] = 14,802.44

Chris invests $10,000 in an account earning 7% interest, compounded annually for 5 years.

P = 10,000  , r= 7% = 0.07 , t =5

Plug in all the values

[tex]A = 10000(1+0.07)^5[/tex] = 14,025.52

Brian balance  after the interest period = $ 14,802.44

Chris balance  after the interest period = $ 14,025.52

Balance in Brian's account is more than Chris account

Answer:

Input of the function are -8,2,4,6

Step-by-step explanation:

Input of a function are the domain .

Domain is the values of x. So inputs are the value of x in the table

Input of the table is x and output is f(x)

Input are the values that gives the output f(x)

From the table the x values are -8,2,4 and 6

Input of the function are -8,2,4,6

(3, -2)

Given equations are

d+e=1

-d+e=-5

We need to find d and e.

A system of equations is a set of one or more equations involving a number of variables

The system of equations are

d+e=1....(1)

-d+e=-5....(2)

d=1-e (from 1)

Substitute d in (2)

-(1-e)+e=-5

-1+e+e=-5

-1+2e=-5

2e=-5+1

2e=-4

e=-2

Now substitute value of e in (1)

d-2=1

d=1+2

d=3

Therefore the ordered pair for d + e = 1 and −d + e = −5 is (3, -2)

i.e value of d=3 and e=-2

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Answer: [tex]\frac{1}{5}[/tex]

Step-by-step explanation:

From the given picture, the total number of cards = 5

The number of red card = 2

Thus, the probability of drawing a red card P(red)=[tex]\frac{2}{5}[/tex]

Also, total number of digits on spinner = 8

Number of 1's=4

Thus, the probability of  spinning a 1 P( spinning 1)=[tex]\frac{4}{8}=\frac{1}{2}[/tex]

Since both the events of drawing a red card and spinning a 1 are independent events, therefore, the probability of drawing a red card and then spinning a 1=[tex]\text{ P(red)}\times\text{P( spinning 1)}=\frac{2}{5}\times\frac{1}{2}=\frac{1}{5}[/tex]

1. The secant is defined as the inverse function of co-secant or cos function

Hence when the cosine is 0, the secant is 1/0 which is undefined. So, when cosine is 0, secant is undefined

Cos 30 = [tex] \sqrt{3} /2 [/tex]

Cos 45 = [tex] 1/\sqrt{2} [/tex]

Cos 180 = -1

cos 270 =0

Since cos 270 is 0, secant of 270 is undefined

Answer is d: 270

2. cosec (-x) = - cosec (180 -x)

We have cosec(-166) = - cosec (180-14) = -cosec (14)

Alternatively we can confirm this as csc (-166) = -4.133565 and -csc(14) = -4.133565; Hence, we can reconfirm that the answer arrived at is right

Therefore csc (-166) = -csc(14) (Option B) is the right answer

Arranging the numbers in ascending order is: √99 < 6π - 6 < π³

Arranging numbers in ascending order simply means arranging them from smallest to the biggest.

Now, the given numbers are:

6π - 6

π³

√99

Let us simplify the numbers to get:

6π - 6 = 6(3.14) - 6 = 12.85

π³ = 3.14³= 31

√99 = 9.95

Thus, arranging in ascending order is:

√99 < 6π - 6 < π³

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To find the sum of the squares of the lengths of the legs of a triangle, use the distance formula to calculate the length of each leg and then square these lengths, summing the squares of the two legs that do not form the hypotenuse.

To find the sum of the squares of the lengths of the legs of a triangle with vertices A=(-6,11), B=(2,8), and C=(-1,0), we first calculate the length of each leg using the distance formula, which is √((x2-x1)² + (y2-y1)²). For AB, AC, and BC we find distances:

Then, we square each leg's length:

Finally, we sum up the squares of AB and AC because they represent the legs of the triangle:

The sum of the squares of the lengths of the legs has now been found.

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The 12th term of the sequence 3, -9, 27, -81, 243, ... is 177,147.

The given sequence is: 3, -9, 27, -81, 243, ...

To find the 12th term, we can observe that the sequence alternates between positive and negative, and each term is obtained by multiplying the previous term by -3. Starting with 3 as the first term, we can find the 12th term using the formula:

an = a1 * (-3)n-1

Substituting the values, we have:

Final answer:

The 12th term of the geometric sequence is -531441, found by using the formula for the nth term of a geometric series with a first term of 3 and a common ratio of -3.

Explanation:

The sequence given is geometric with each term being multiplied by -3 to obtain the next term. To find the 12th term of the sequence, we can use the formula for the nth term of a geometric sequence: Tn = a * rn-1, where a is the first term, r is the common ratio, and n is the term number.

For the given sequence, the first term a is 3 and the common ratio r is -3. The 12th term is found by placing these values into the formula:

T12 = 3 * (-3)12-1

T12 = 3 * (-3)11

T12 = 3 * (-177147)

T12 = -531441

Therefore, the 12th term of the sequence is -531441.

The correct answer to this problem C.)7/3

Answer:

Face value of bond = $ 6000

Rate of interest =7.25 %

The Bond will mature in 5 years.

If the interest is semiannually , the rate of interest will reduce to half.

So, new rate of interest will be [tex]\frac{7.25}{2}=3.625[/tex]

Formula for simple interest

[tex]=\frac{\text{Principal}\times Rate \times time}{100}[/tex]

   Interest after 6 months will be

   [tex]=\frac{6000 \times 3.625 \times 1}{100}\\\\=60 \times 3.625\\\\=217.5[/tex]

So, interest that Randall will receive after six months = $ 217.50

Answer:

It's B

Step-by-step explanation:

Solution:

we have been asked to find the equation of the line that passes through (7, 4) and (4, -2).

First we will find the slope of the line using the formula

[tex] m=\frac{y_2-y_1}{x_2-x_1} [/tex]

Plugin the given values we get

[tex] m=\frac{-2-4}{4-7}=\frac{-6}{-3}=2 [/tex]

Now using the point slope form of a straight line

[tex] (y-y_1)=m(x-x_1) [/tex]

Plugin the values

[tex] (y-4)=2(x-7)\\
\\
y=2x-14+4\\
\\
y=2x-10\\ [/tex]

Hence the correct option is a.