Find the formula for the nth term of the following sequence:

648, 108, 18, 3...

Include "n=" in your answer, and do not use any spaces.

Answer:

a

Step-by-step explanation:

The dimensions of the rectangle are 4 ft by 5 ft.

Given that the length of a rectangle is 3 ft less than twice the width, and the area of the rectangle is 44 sq.ft. We have to find the dimensions of the rectangle. Let's consider the width of the rectangle as x ft.Length of the rectangle = (2x - 3) ftArea of the rectangle = Length x Width44 = (2x - 3) x x44 = 2x^2 - 3x44 = x (2x - 3)2x^2 - 3x - 44 = 0To solve for x, we will factorize the equation by splitting the middle term.2x^2 - 8x + 5x - 20 = 0Factorize2x(x - 4) + 5(x - 4) = 0(x - 4) (2x + 5) = 0x = 4 ft (since the width of a rectangle can't be negative)or 2x = -5This gives us an invalid value, so x = 4 ftNow that we have the width of the rectangle, we can calculate the length as follows:Length of the rectangle = (2x - 3) ftLength of the rectangle = (2 * 4) - 3Length of the rectangle = 8 - 3Length of the rectangle = 5 ft.

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The only solution for the equation 8 tan^2 θ = 3 cos^2 θ in the given Range is θ ≈ 19.47 degrees.

a) We are given the equation 8 tan θ = 3 cos θ.

Dividing both sides of the equation by cos θ, we have:

8 tan θ / cos θ = 3

Using the identity tan θ = sin θ / cos θ, we can substitute it into the equation:

8 (sin θ / cos θ) / cos θ = 3

Simplifying further, we get:

8 sin θ / cos^2 θ = 3

Now, multiplying both sides of the equation by cos^2 θ, we have:

8 sin θ = 3 cos^2 θ

Using the identity cos^2 θ = 1 - sin^2 θ, we can substitute it into the equation:

8 sin θ = 3(1 - sin^2 θ)

Expanding the equation, we get:

8 sin θ = 3 - 3 sin^2 θ

Rearranging the terms, we have:

3 sin^2 θ + 8 sin θ - 3 = 0

Therefore, we have successfully shown that the equation can be rewritten in the form 3 sin^2 θ + 8 sin θ - 3 = 0.

b) Now, let's solve the equation 3 sin^2 θ + 8 sin θ - 3 = 0.

To solve the quadratic equation, we can use factoring, quadratic formula, or other appropriate methods.

In this case, the equation factors as:

(3 sin θ - 1)(sin θ + 3) = 0

Setting each factor equal to zero, we have two equations:

3 sin θ - 1 = 0    or    sin θ + 3 = 0

For the first equation, solving for sin θ, we get:

3 sin θ = 1

sin θ = 1/3

Taking the inverse sine (sin^-1) of both sides, we find:

θ = sin^-1(1/3) ≈ 19.47 degrees (to 2 decimal places)

For the second equation, solving for sin θ, we have:

sin θ = -3

Since the range of sine is between -1 and 1, there are no solutions for this equation in the given range (0 ≤ θ ≤ 90 degrees).

Therefore, the only solution for the equation 8 tan^2 θ = 3 cos^2 θ in the given range is θ ≈ 19.47 degrees.

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Answer:

7

Step-by-step explanation:

you do 11-4 to get 7, which is how you solve for missing expontentials

Step-by-step explanation:

\( \frac{ {5}^{11} }{ {5}^{x} } = {5}^{4} \\ {5}^{x} = \frac{ {5}^{11} }{ {5}^{4} } \\ {5}^{x} = {5}^{(11 - 4)} = {5}^{7} \\ \boxed{x = 7}\)

Answer:

Step-by-step explanation:

Answer:

1. what I the square root of negative 4

2. one is minusing the square root of 4

Answer:

The height is 1.25m.

Step-by-step explanation:

Volume = 1/3 πr²h

Given:

V = 13.4 m³

r = 3.2 m

Asked: height (h)

Substitute the formula with the given values then solve

13.4m³ = 1/3π(3.2m)²h

13.4(3) = 10.24πh

40.2 = 10.24πh

h = 40.2/10.24π

h = 1.25m

The height of the cone is 1.25 meters.

We know that the volume of the cone is given by

V = (1 / 3) * π * r ^2 * h................equation 1

where,

V is the volume of the cone.

r is the radius of the cone's base

h is the height

The volume and radius of the cone are given,

V = 13.4 m

r = 3.2m

substituting these values in equation 1 we get,

13.4 = (1 / 3) * 3.14 * 3.2 ^ 2 * h

on simplifying further

13.4 = 10.717  * h

h = 1.25m

The height of the cone is 1.25 meters.

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Steps to solve:

b + 4.22 = 7.08

~Subtract 4.22 to both sides

b = 2.86

Best of Luck!

Answer:

exact form : 2√3

decimal form : 3.46410161… or 3.46

hope this helps you!

Answer:

The value of the function is \(\sqrt{12}\). Rounded to the nearest hundredth, the answer is 3.46

Step-by-step explanation:

We are given the value of x, so we simply have to evaluate the function:

\(f(x)=\sqrt{x+4}\)

Substitute 8

\(f(8)=\sqrt{8+4}\)

Add in the radical

\(\sqrt{12}\)

The value of the function is sqrt(12).

Rounded to the nearest hundredth: \(3.46\)

Answer:

x = 3

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Answer:

1.67square foot/hr

Step-by-step explanation:

If a fertilizer covers 5/6 square foot in 1/2 hour, then;

5/6 square foot  = 1/2 hour

To determine the unit rate, we will say;

x square foot = 1 hr

Divide both expressions

5/6x = 1/2

5 * 2 = 6x

10 = 6x

x = 10/6

x = 1.67square foot/hr

Hence the unit rate is 1.67square foot/hr

Answer:

hfcfkyhgctyirkgt,ckcikkccy

Step-by-step explanation:

Answer:

Length = 5

Width = 21

Step-by-step explanation:

(x)(x + 16) = 105

x^2 + 16x = 105

x^2 + 16x - 105 = 0

(x - 5) x ( x + 21) = 0

x - 10 = 0

x = 5

x + 21 = 0

x = -21

Now that we have the zeroes.

We have to find the most viable one to put in.

Using -21 would not make sense, so we will use 5.

Plug it in:

x = 5

(5) (5 + 16) = 105

5 ( 21) = 105

Answer:

5

Step-by-step explanation:

1/2÷1/10=

1/2x10/1=

10/2=5

Answer:

the answer is 5

Step-by-step explanation:

keep change flip

1/2 x 10 =5

Answer:

4 coins

Step-by-step explanation:

First, let's find out how much she gave the teller:

2($20)=$40

Now, let's find out how much change the teller owes her:

$40.00-$39.63=$0.37 or 37 cents

The largest coin (under 37 cents), is a quarter which is worth 25 cents...

37-25=12 cents

The largest coin (under 12 cents), is a dime which is worth 10 cents...

12-10=2

The largest coin (under 2 cents), is a penny which is worth 1 cent...

2-1=1

And one more penny...

1-1=0

Therefore the fewest amount of coins she can get in change are a quarter, a dime, and two pennies, which is 4 coins.

Answer:

x = 99°

Step-by-step explanation:

first: find the supplement to 123°:

180 - 123 = 57°

second: since all triangle interior angles total a80°:

180 - 42 - 57 = 81°

third: x = the supplement to 81°, so, x = 180 - 81 = 99°

The value of the discriminant for the quadratic equation –3 = –x2 + 2x is  16

The quadratic equation is given as:

–3 = –x^2 + 2x

Rewrite the equation as:

x^2 - 2x - 3 = 0

A quadratic equation is represented as;

ax^2 + bx + c = 0

So, we have

a = 1

b = -2

c = -3

The discriminant is

d = b^2 - 4ac

So, we have

d = (-2)^2 - 4 * 1 * -3

Evaluate

d = 16

Hence, the value of the discriminant for the quadratic equation –3 = –x2 + 2x is  16

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Answer:

16

Step-by-step explanation:

If needed, delete the comma and/or the dollar sign.

=========================================================

Work Shown:

mu = 27989 = population mean

sigma = 3250 = population standard deviation

z = (x-mu)/sigma

z*sigma = x-mu

x = z*sigma + mu

x = 0.34*3250 + 27989

x = 29,094

The salary of $29,094 corresponds to the z score of 0.34.

This indicates the salary $29,094 is exactly 0.34 standard deviation units above the mean.

Answer:

w≥31.25

Step-by-step explanation:

175+8w≥425

-175        -175

8w≥250

/8       /8

w≥31.25

Answer:

X is greater than or equal to 125/4

Step-by-step explanation:

Subtract 175 from both sides which will turn 425 into 250

Divide 8 from 8x to the other side to turn 250 into 125/4

In the end, you get X is greater or equal to 125/4

Answer:

2x8=16-6=10

Step-by-step explanation:

10 is the answer

Answer:

The answer is c

Step-by-step explanation:

Beacuse when u the shape is transfrromed that what u get

Answer:

x= -4

Step-by-step explanation:

−2(4x+4)−3x−2=34

(−2)(4x)+(−2)(4)+−3x+−2=34(Distribute)

−8x+−8+−3x+−2=34

(−8x+−3x)+(−8+−2)=34(Combine Like Terms)

−11x+−10=34

−11x−10=34

−11x−10+10=34+10

−11x=44

−11x /−11  =  44 /−11

x=−4

Step-by-step explanation:

The ONE  solution to this system of two lines is the point where the two lines cross   at   (1,4)

Answer:

I'm not exactly sure yet but i believe the 3rd choice is best!

Comment!

(Soon i will give reasoning and answer or change it unless i am right)

Tell me stuff in comments i'll see what i can do.

Step-by-step explanation:

Hope i helped!

Thanks,

Your helper :)

Friend me!

Answer: D

Step-by-step explanation:

You just have to test pi/6

\(\dfrac{30}{cos(6*\dfrac{Pi}{6})} =\dfrac{30}{cos(\Pi)} =-30\)

The expression (p⁶ +q) + 8 is equivalent to the given expression. which is the correct answer would be an option (C).

The commutative property is associated with mathematical operations such as addition and multiplication. It indicates that switching the order or location of two integers while adding or multiplying them has no effect on the outcome. For example, 4 + 5 gives 9, and 5 + 4 also gives 9.

The expression is given in the question below as

p⁶ + (q + 8)

We have to determine the expression equivalent to the given expression.

As per the given question, we have

⇒ p⁶ + (q + 8)

Using the commutative property of addition, we get

⇒ (p⁶ +q) + 8

Thus, the expression (p⁶ +q) + 8 is equivalent to the given expression.

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Answer:

Each month he will save $ 50

Each month he will spend $1,250

Raking will have $600 in his checking account at the end of the year.

Step-by-step explanation:

1300 - 500 - 750 = $50

$50 x 12 month = $600

The required amount Rakim saves and sped each month is $50 and $1250.

Given that,
Rakim's goal is to have at least $500 in his checking account at the end of the year. The table shows his activity for the month of January. Will Rakim make his goal.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
According to the question,
Total money he has = 1300
Total money spend = 750 + 500 = 1250
Money he save = 1300 - 1250 = 50
For the condition of at end of the year he must have at least $500
So,
Yearly saving = 50 × 12 = $600, which greater than $500.

The required amount Rakim saves and sped each month is $50 and $1250.

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Answer:

If x is the length of the square tomato patch, then the width of the tomato patch is also x, since it is a square.

According to the problem, the length of the rectangular vegetable garden must exceed three times the length of the tomato patch by 2 feet, so the length of the garden is:

3x + 2

The width of the rectangular vegetable garden must exceed the width of the tomato patch by 5 feet, so the width of the garden is:

x + 5

To find the area of the garden, we multiply its length by its width:

Area of garden = length x width

Area of garden = (3x + 2)(x + 5)

To find the area of the tomato patch, we note that it is a square with side length x, so its area is:

Area of tomato patch = x²

Therefore, the area of the vegetable garden that is not taken up by the tomato patch is:

(3x + 2)(x + 5) - x²

And the total area of the vegetable garden, including the tomato patch, is:

x² + (3x + 2)(x + 5)

Simplifying:

x² + (3x² + 17x + 10)

4x² + 17x + 10

So the total area of the garden is 4x² + 17x + 10 square feet.

According to the described situation, we have that:

The decision rule is:

The value of the test statistic is of z = -0.866.

The claim is:

"Forty percent or more of those persons who retired from an industrial job before the age of 60 would return to work if a suitable job were available"

At the null hypothesis, we consider that the claim is false, that is, the proportion is of less than 40%, hence:

\(H_0: p < 0.4\)

We have a right-tailed test, as we are testing if a proportion is less/greater than a value. Since we are working with a proportion, the z-distribution is used.

Using a z-distribution calculator, the critical value for a right-tailed test with a significance level of 0.01 is of z = 2.327, hence, the decision rule is:

The test statistic is given by:

\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)

In which:

In this problem, the parameters are:

\(p = 0.4, n = 200, \overline{p} = \frac{74}{200} = 0.37\)

Hence:

\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)

\(z = \frac{0.37 - 0.4}{\sqrt{\frac{0.4(0.6)}{200}}}\)

\(z = -0.866\)

The value of the test statistic is of z = -0.866.

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