An arithmetic sequence has this recursive formula:
A1=6
An=an-1-3
What is the explicit formula for this sequence?

Answer:

equation: y=-150m+2250

Height after:

6 Minutes: 1350 ft

8 Minutes: 1050 ft

10 Minutes: 750 ft

Step-by-step explanation:

We know that the hot air balloon has an initial height of 2250 ft, so that is our y-intercept (in the equation, y =mx+b, the y-intercept is b). Next you know that after every minute, the balloon goes down 150 ft. So that means -150 ft per minute. Now put it together, the equation is written as "y = 150m+2250" (since m is the required variable, that's what is written in the equation instead of x).

Next, to make a table, you need to determine what value goes in the left side, the x values (the independent variables) and what goes in the right side, the y values (the dependent variables). The two variables here are Height and Time. Time is not dependent on the height of the balloon-- the height depends on how much time has passed. So Time on the left and height on the right. Next just plug in the values 6, 8, and 10 into your equation. Your answer will be the output, aka the height of the hot air balloon after x minutes.

Your table should look something like this:

m       y

6       1350

8       1050

10       750

Hope this helps :)

Answer:

A = 1024π units², A ≈ 3216.99 units²

Step-by-step explanation:

The equation of the area of a circle is A = πr², where A = area and r = radius.

Given that, we can plug in r as 32 units: A = π(32 un.)²

Simplifying that gives us A = 1024π units², or A ≈ 3216.99 units²

Answer:

Ali-13

Ben-26

Joe-34

Step-by-step explanation:

Ali-x

Ben-2x

Joe-2x+8

x+2x+2x+8=73

3x+2x+8=73

5x+8=73

5x=73-8

5x=65

x=65/5

=13

Ali sells 13 tickets

Ben sells 13×2

=26 tickets

Joe sells (13×2)+8

=34 tickets

Ali sells 13 tickets. Ben sells 26 tickets. Joe sells 34ctickets

Let

Ali = x

Ben = 2x

Joe = 2x+8

⇒ x+2x+2x+8=73

⇒ 3x+2x+8=73

⇒ 5x+8=73

⇒ 5x=73-8

⇒ x=65/5

⇒ 13

Ali sells 13 tickets.

Ben sells 13×2

= 26 tickets.

Joe sells (13×2)+8

= 34 tickets.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

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Answer:

Option A) f(2)=0 and g(-2)=0

Step-by-step explanation:

we know that

The vertex of f(x) is equal to (2,0)

The vertex of g(x) is equal to (-2,0)

step 1

Find the value of f(x) and g(x) for x=2

Observing the graph

For x=2

f(2)=0 ----> the y-coordinate of the vertex

g(2) > 12

step 2

Find the value of f(x) and g(x) for x=-2

Observing the graph

For x=-2

f(-2)> 12

g(-2)=0 ----> the y-coordinate of the vertex

therefore

The statement that is true regarding the graphed functions is

f(2)=0 and g(-2)=0

Answer:

2

Step-by-step explanation:

The average rate of change from x=1 to x=2 is the same as finding the slope of a line at x=1 and x=2.

So we are going to need to corresponding y coordinates.

What y corresponds to x=1? y=3

What y corresponds to x=2? y=5

So we have the ordered pairs (1,3) and (2,5).

Line the points up vertically and subtract vertically then put 2nd difference over 1st difference.

(2 , 5)

-(1  , 3)

-----------

1      2

The average rate of change is 2/1 or just 2.

Now since we were asked to find the average rate of change given the function was a line, it really didn't matter what two points you used on that line.

Answer: Fourth option

[tex]m=2[/tex]

Step-by-step explanation:

If we call m the average change rate of a function between [tex]x_1[/tex] and [tex]x_2[/tex], then, by definition:

[tex]m=\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]

In this case the function is the line shown in the graph. Then we look for the values of [tex]y = f (x)[/tex] for [tex]x = 1[/tex] and [tex]x = 2[/tex]

When [tex]x=1[/tex] then [tex]f(x)=3[/tex]

When [tex]x=2[/tex] then [tex]f(x)=5[/tex]

Therefore

[tex]m=\frac{5-3}{2-1}[/tex]

[tex]m=\frac{2}{1}[/tex]

[tex]m=2[/tex]

Answer:

105

Step-by-step explanation:

Evaluate 4 a^3 - 2 b^2 + 5 where a = 3 and b = -2:

4 a^3 - 2 b^2 + 5 = 4×3^3 - 2×(-2)^2 + 5

3^3 = 3×3^2:

4×3×3^2 - 2×(-2)^2 + 5

3^2 = 9:

4×3×9 - 2×(-2)^2 + 5

3×9 = 27:

4×27 - 2×(-2)^2 + 5

(-2)^2 = 4:

4×27 - 24 + 5

4×27 = 108:

108 - 2×4 + 5

-2×4 = -8:

108 + -8 + 5

| | 1 |  

| 1 | 0 | 8

+ | | | 5

| 1 | 1 | 3:

113 - 8

| | 0 | 13

| 1 | 1 | 3

- | | | 8

| 1 | 0 | 5:

Answer:  105

Answer:

105

Step-by-step explanation:

4a^3 -2b^2 +5

Let a=3 and b= -2

4 (3)^3 -2 (-2)^2 +5

4 *27 -2 (4) +5

108 -8+5

105

Answer:

The first term (2x) represents Jillian's earnings at the end of the week. Where the 2 represents the amount of money she earns per pag, and the 'x' is the number of bags sold.

Let us explain this with an example: if Jillian sells 36 bags, then she will earn 2×36 = $72

Answer:

option C is true.

Step-by-step explanation:

We are given that Jack and Jillian sell apples at a produce stand .

We are given that an expression which shows Jack's earning=2x-8

We have to find that first term what represent in the given expression

Jillian earns for each bag  of apples she sells=$2

Let Jillian sold number of bags of apples =x

Then ,Jillian earn total at the end of the week =[tex]2\timesx=$2x[/tex]

Jack has earned $ 8 less than Jillian earn

Therefore, total earning of jack=[tex]2x-8[/tex]

In the given expression the first term 2x represent the earning of Jillian.

Hence, option C is true.

Answer: C: JIllian's earning at the end of the week

The perimeter of a rectangle, is all of the sides added up.

In a rectangle, there are two widths (right and left), and two lengths (up and down)

So:

Perimeter = 2 × width + 2 × length.

To get the equation we just substitute in the values that we are given:

length = (x)

width = (x - 4)

perimeter = 87

So just put these values into:  perimeter = 2 × width + 2 × length:

87  =  2(x) + 2(x - 4)

_____________________________

Answer:

The equation is:       87 = 2(x) + 2(x - 4)

(note: this can be simplified down like so:

87 = 2x + 2x - 8

87 = 4x - 8

95 = 4x

23.75 = x    

)

[tex]\bf 8~~,~~\stackrel{8\cdot \frac{1}{2}}{4}~~,~~\stackrel{4\cdot \frac{1}{2}}{2}~~,~~\stackrel{2\cdot \frac{1}{2}}{1}~~,~~\stackrel{1\cdot \frac{1}{2}}{\cfrac{1}{2}} \\\\\\ a_n=\cfrac{1}{2}\cdot a_{n-1}\qquad \begin{cases} a_1=\textit{previous term}\\ a_n=\textit{current term}\\ a_1=\textit{first term}\\ \qquad 8 \end{cases}[/tex]

Answer:

[tex]\cos(\theta)=\pm \frac{24}{25}[/tex]

Step-by-step explanation:

I don't know where [tex]\theta[/tex] is so there is going to be two possibilities for cosine value, one being positive while the other is negative.

A Pythagorean Identity is [tex]\cos^2(\theta)+\sin^2(\theta)=1[/tex].

We are given [tex]\sin(\theta)=\frac{7}{25}[/tex].

So we are going to input [tex]\frac{7}{25}[/tex] for the [tex]sin(\theta)[/tex]:

[tex]\cos^2(\theta)+(\frac{7}{25})^2=1[/tex]

[tex]\cos^2(\theta)+\frac{49}{625}=1[/tex]

Subtract 49/625 on both sides:

[tex]\cos^2(\theta)=1-\frac{49}{625}[/tex]

Find a common denominator:

[tex]\cos^2(\theta)=\frac{625-49}{625}[/tex]

[tex]\cos^2(\theta)=\frac{576}{625}[/tex]

Square root both sides:

[tex]\cos(\theta)=\pm \sqrt{\frac{576}{625}}[/tex]

[tex]\cos(\theta)=\pm \frac{\sqrt{576}}{\sqrt{625}}[/tex]

[tex]\cos(\theta)=\pm \frac{24}{25}[/tex]

Answer:

Prime Numbers

Step-by-step explanation:

Two sets are being considered in the given statement:

A universal set is defined as such a set from which all the other subsets are taken for a given case. Or in other words, a universal set is such a set to which all the subsets belong and this universal set contains all the elements being studied/considered.

For the given case, set of Even Numbers is the subset which is being taken from the set of prime numbers. The set of prime numbers contains all the elements which we are considering for this very scenario.

Therefore, the set of prime numbers is the universal set.

Answer:

c

Step-by-step explanation:

Answer:

c. $280

Step-by-step explanation:

first you times the total profits by the percent that the girls get then the percent the boys get to find out how much of the profit the girls and boys basketball teams each get, then you subtract the profits the boys get by the profits the girls get to find out how much more the boys get than the girls.

7,115.03 x .07 = 498.0521

7,115.03 x .11 = 782.6533

782.6533 - 498.0521 = 284.6012

the boys receive 284.6012 more in profits than the girls

so c. $280 would be the best estimate of how much more the boys team will receive

Answer:

There is a multiplication error

Step-by-step explanation:

Long division method is used to divide greater  number by a smaller number.

Here, greater number is known as the dividend and smaller number is known as divisor.

As per division algorithm,

Dividend = Divisor [tex]\times[/tex] quotient + remainder

Here, dividend = [tex]8x^3-36x^2+54x-27[/tex]

Divisor = [tex]2x-3[/tex]

Here, we need to find the error in the long division .

In step:

[tex]18x+27[/tex] , it should be 18x-27 as [tex]-3\times 9=-27[/tex] not +27

So, there is a multiplication error .

The correct option is c) she makes a multiplication error.

Step-by-step explanation:

Given :

Dividend = [tex]8x^3-36x^2+54x-27[/tex]

Divisor = [tex]2x-3[/tex]

Solution :

In step [tex]18x +27[/tex] there is mistake. It should be [tex]18x - 27[/tex] because [tex]-3 \times 9= -27[/tex] not +27.

Therefore the correct option is c) she makes a multiplication error.

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Answer:

20.

Step-by-step explanation:

P(5,3)  = 5! / 3!

= (5*4*3*2*1) / (3*2*1)

= 20.

Answer:

9 geese

11 cows

Step-by-step explanation:

Say x is cows, and y is geese.

x + y = 20 animals

x * 4 + y * 2 = 62

x = 20 - y

(20 - y) * 4 + y * 2 = 62

80 - 4y + 2y = 62

- 2y = -18

y = 9 geese

x = 20 - 9 = 11 cows

Lisa has 11 cows and 9 geese.

To solve the problem involving Lisa's barn with 20 animals having 62 legs in total, and knowing she only has cows and geese, we can use a system of linear equations. We can denote the number of cows as c and the number of geese as g. Cows have 4 legs and geese have 2 legs.

We can then set up the following equations based on the information given:

Cows and geese equation: c + g = 20 (since there are 20 animals in total)

Legs equation: 4c + 2g = 62 (because cows have 4 legs and geese have 2 legs)

Now, let's solve the system of equations:

Multiply the first equation by 2 to match the number of geese legs in the second equation: 2c + 2g = 40

Subtract the modified first equation from the legs equation: (4c + 2g) - (2c + 2g) = 62 - 40, which simplifies to 2c = 22, and then c = 11. Lisa has 11 cows.

Substitute the number of cows back into the first equation to find the number of geese: 11 + g = 20, which leads to g = 9. Lisa has 9 geese.

Therefore, Lisa has 11 cows and 9 geese.

The mathematical expression is 6 + 8x

The sum of 6 and the product of 8 and x  can be written  mathematically by first  getting the product of  8 and x  which equals 8x

Sum means addition( +)

So the sum of 6 is written as 6 +

We  thus have  the mathematical expression Translated as  6 + 8x

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The mathematical expression for 'the sum of 6 and the product of 8 and x' is 6 + 8x.

A mathematical expression is a combination of numbers, variables, and mathematical operators (e.g., +, -, *, /) that represents a calculation or relationship. Expressions can be simple, like 2x + 3, or complex, serving various purposes in mathematical modeling, calculations, and problem-solving.

To translate the phrase 'the sum of 6 and the product of 8 and x' into a mathematical expression, we can use the symbols and operations of algebra. The sum of 6 and the product of 8 and x can be written as 6 + 8x. Here, 8x represents the product of 8 and x, and the addition symbol, '+', represents the sum of 6 and 8x.

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Answer:

  3 seconds

Step-by-step explanation:

The given equation describes a parabolic curve with zeros at x=-1 and x=7. The line of symmetry of the curve is halfway between the zeros, at ...

  x = (-1 +7)/2 = 6/2 = 3

The maximum of the curve is on the line of symmetry. The ball will reach its maximum height 3 seconds after being thrown.

_____

Additional comment
The maximum height will be 16 meters.

The ball will reach its maximum height 3 seconds after being thrown.

To find the time when the ball reaches its maximum height, we need to determine the vertex of the quadratic equation representing the ball's height. The equation h(x)=-(x+1)(x-7) can be rewritten in vertex form as h(x)=-x^2+6x-7. The x-coordinate of the vertex can be found using the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic equation.

In this case, a = -1 and b = 6. Plugging these values into the formula, we get x = -6/-2 = 3. Therefore, the ball reaches its maximum height 3 seconds after being thrown.

Answer:

The correct option is A.

Step-by-step explanation:

Domain:

The expression in the denominator is x^2-2x-3

x² - 2x-3 ≠0

-3 = +1 -4

(x²-2x+1)-4 ≠0

(x²-2x+1)=(x-1)²

(x-1)² - (2)² ≠0

∴a²-b² =(a-b)(a+b)

(x-1-2)(x-1+2) ≠0

(x-3)(x+1) ≠0

x≠3 for all x≠ -1

So there is a hole at x=3 and an asymptote at x= -1, so Option B is wrong

Asymptote:

x-3/x^2-2x-3

We know that denominator is equal to (x-3)(x+1)

x-3/(x-3)(x+1)

x-3 will be cancelled out by x-3

1/x+1

We have asymptote at x=-1 and hole at x=3, therefore the correct option is A....

Answer:

Its A. I just passed the final exam with 5 minutes left of the SESSION.

Step-by-step explanation:

Answer:

6√10 ≈ 19.0

Step-by-step explanation:

The length of the diagonal is:

d² = w² + l² + h²

Given d = 36, l = 30, and h = 6:

36² = w² + 30² + 6²

1296 = w² + 900 + 36

w² = 360

w = 6√10

w ≈ 19.0

The box should be approximately 19 inches wide.

Answer:

C. [tex]432\text{ units}^2[/tex]

Step-by-step explanation:

We have been given an image of a right  prism. We are asked to find the surface area of our given prism.

The surface area of our given prism will be sum of area of two base right triangles and area of three rectangles.

[tex]SA=2B+Ph[/tex], where,

SA = Surface area,

B = Area of each base,

P = Perimeter of base,

h = Height of prism.

Let us find area of right base of prism.

[tex]B=\frac{1}{2}\times 6\times 8[/tex]

[tex]B=3\times 8[/tex]

[tex]B=24[/tex]

Perimeter of base will be [tex]6+8+10=24[/tex].

Upon substituting these values in surface area formula, we will get:

[tex]SA=2*24+24*16[/tex]

[tex]SA=24(2+16)[/tex]

[tex]SA=24(18)[/tex]

[tex]SA=432[/tex]

Therefore, the surface area of our given prism is 432 square units and option C is the correct choice.

Answer:

The answer is the last option, D.

Step-by-step explanation:

A function with one solution can be added and have a variable and a constant leftover. The variables in the other three options cancel each other out, so none of them have one solution. The first and third equations have no solutions, and the second has infinitely many solutions. The fourth option has only one variable cancel out and still has a constant on the other side of the equation. The fourth option is correct.

Answer:

x=pi/3 + 2pi*k

x=2pi/3+2pi*k

Step-by-step explanation:

sin(x)=sqrt(3)/2

This happens twice in the first rotation on our unit circle.

It happens in the first quadrant and in the second quadrant. Third and fourth quadrants are negative for sine.

So we are looking for when the y-coordinate on the unit circle is sqrt(3)/2.

This is at pi/3 and 2pi/3.

So we can get all the solutions by adding +2pi*k to both of those.  This gives us a full rotation about the circle any number of k times. k is an integer.

So the solutions are

x=pi/3 + 2pi*k

x=2pi/3+2pi*k

An equation is formed of two equal expressions. The solution to the equation sin(x)=√3/2 is (π/3 ± 2πn), (2π/3 ± 2πn), where n is any natural number.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The solution of sinx=√3/2 are,

sin(x) = √3/2

x = sin⁻¹ √3/2

x = (π/3 ± 2πn), (2π/3 ± 2πn)

Hence, the solution to the equation sin(x)=√3/2 is (π/3 ± 2πn), (2π/3 ± 2πn), where n is any natural number.

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[tex](x+1)^2=25​\\x+1=5 \vee x+1=-5\\x=4 \vee x=-6[/tex]

Answer:160

Step-by-step explanation:

To solve the problem we must know the concept of the Center angle theorem. The measure of the center angle ∠AOC  is 160°.

According to the central angle theorem, if an arc of a circle makes an angle with any point on the circumference of that circle then the measure of that angle is half the angle made by that arc at the center of the circle.

Given to us

∠ABC = 80°

As we already know the angle made by Arc AC at point B, therefore, the center angle made by ARC AC at the center will be twice of it. Therefore,

∠AOC = 2∠ABC

∠AOC = 2(80°)

∠AOC = 160°

Hence, the measure of the center angle ∠AOC  is 160°.

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Answer:

y = 1

Step-by-step explanation:

Given function is:

[tex]\frac{x^2+8x+3}{x^2+3x+1}[/tex]

In order to find the horizontal asymptote, the coefficients of highest degree variable of numerator and denominator are divided.

In our case,

both the numerator and denominator have 1 as he co-efficient of x^2

So the horizontal asymptote is y = 1/1

Hence, third option y=1 s correct ..

Final answer:

The correct horizontal asymptote for the given rational expression is y = 1, found by comparing the degrees and leading coefficients of the numerator and denominator.

Explanation:

For the expression y = (x² - 8x + 3) / (x² + 3x + 1), the correct horizontal asymptote is determined by looking at the degrees of the polynomials in the numerator and the denominator. When the degrees are the same, the horizontal asymptote is found by dividing the leading coefficients. In this case, both polynomials are of degree 2, and the leading coefficients are both 1. Thus, the horizontal asymptote is y = 1.

Answer:

0.17

Step-by-step explanation:

The numbers are from 1 to 6 on each side.

The total sample space will be 6.

Denoted as:

n(S) = 6

There will be only one outcome as 1

So,

Let A be the event that the number is 1

Then,

n(A) = 1

[tex]P(A) = \frac{n(A)}{n(S)} \\=\frac{1}{6} =0.166[/tex]

Hence the theoretical probability of the number cube showing a 1 is 0.166 ..

Rounding off to the nearest hundred

0.17 ..

Answer: it’s B 0

Step-by-step explanation:

For this case we have that by definition, the area of a circle is given by:

[tex]A = \pi * r ^ 2[/tex]

Where:

r: It is the radius of the circle

As data we have that[tex]r = 6 \ ft[/tex]

Then, replacing we have:

[tex]A = \pi * 6 ^ 2\\A = 36 \pi[/tex]

Taking [tex]\pi = 3.14[/tex]

A = 113.04

So, the pool area is [tex]113.04 \ ft ^ 2[/tex]

Answer:

[tex]113.04 \ ft ^ 2[/tex]

Answer:

9π ft²

Step-by-step explanation:

Answer: z= .6

Step-by-step explanation:

Numerator: When you do 5•.6, you get 3, and then 3-1 equals 2.

Denominator: 8 - 3 = 5.

Therefore you get 2/5 which makes z = .6