Mathematics High School

a(1)=20​​
a(n)=a(n−1)−17​​
Find the 3rd term in the sequence

Answers

Answer 1
Answer: The third term is -14

----------------------------------------------

Explanation:

First term = A(1) = 20, which is given

Second term
A(n) = A(n-1) - 17
A(2) = A(2-1) - 17
A(2) = A(1) - 17 .... note: second term = (first term) - 17
A(2) = 20 - 17
A(2) = 3

Third term
A(n) = A(n-1) - 17
A(3) = A(3-1) - 17
A(3) = A(2) - 17 ... note: third term = (second term) - 17
A(3) = 3 - 17
A(3) = -14
Answer 2

Answer:

-14

Step-by-step explanation:

khan academy

Related Questions

Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located. x2 + 4x + 3 = 0

Answers

x= -1/2 so exact should be x

How do I do this someone please explain I need help

Answers

so.. she washes cars and charges 15 bucks per car...ok... Revenue( sales income), in this case is how much she gets in total income from the car washing.. .well, if she washes, say "a" automobiles, then she makes 15*a, or 15a in income, or Revenue.

now, she pays in advertising 145 bucks... and for cleaning products, she spends 3 bucks for each washed car... ok.. .so if she washes say "a" automobiles, then she spends 3*a or 3a, ok.... so, her costs for the washing cars business is 145 for ads plus 3a, or 145 + 3a is her Cost.

now, Profit is the surplus amount after you remove the cost expenses, and can only happen if the Revenue is higher or greater than the Cost.

Revenue > Cost
  15a      > 145 + 3a

when will she turn a profit?

[tex]\bf 15a \ \textgreater \ 145 + 3a\implies 15a - 3a\ \textgreater \ 145\implies 12a \ \textgreater \ 145 \\\\\\ a\ \textgreater \ \cfrac{145}{12}\implies a\ \textgreater \ 12\frac{1}{12}[/tex]

she will turn a profit after washing 12 cars and 1/12 of a car, maybe just the windshield =).... anyhow..... namely, the revenue then is greater than the cost after that, or one can say, after the 13th car washed. 

What is the slope of the line below

Answers

Answer: m = 2
The formula for slope can be found by finding the difference in y between two values divided by the difference in x between the same two values. In this case, you would subtract 4 from 8 and 2 from 4, to get 4/2, or 2. The slope is represented by the variable m, so m = 2.

Simplify.

Square root of 121m^8n^4

A. 11mn

B. 11m^2n^2

C. 11m^4n^2

Answers

[tex] \sqrt{121m^8n^4}= \sqrt{121} \sqrt{(m^4)^2} \sqrt{(n^2)^2}=11 m^4n^2 [/tex]

Answer:

B

Step-by-step explanation:

no

In a survey, the planning value for the population proportion is p*=.35. how large a sample should be taken to provide a 95% confidence interval with a margin of error of .05 (to the nearest whole number)?

Answers

Given:
p* = 0.35, the populatin proportion.
Sp = 0.05, the margin of error

Let n =  the size of the sample.

Because the standard error is 0.05, therefore
[tex] \sqrt{ \frac{p(1-p)}{n} } =0.05[/tex]
[tex] \sqrt{ \frac{0.35(1-0.35)}{n} } =0.05[/tex]
[tex] \frac{0.2275}{n} =0.05^{2} =0.0025[/tex]
n = 0.2275/0.0025 = 91

Answer: The sample size is 91.

In 1980, the United States' national debt exceeded $9 billion dollars. Express the exact dollar amount in scientific notation.

Answers

9 billion = 9,000,000,000 = 9.0 x 10^9

Sandy can assemble a particular type of light fixture in 3/8 hour. it takes her 2/3 hour to hang the fixture and another 1/6 hour to wire the fixture once it is hung. how many fixtures could sandy install in 29 hours?

Answers

Final answer:

Sandy can install a maximum of 24 fixtures in 29 hours.

Explanation:

To calculate the number of fixtures Sandy can install in 29 hours, we need to determine the amount of time it takes for Sandy to complete one installation process (excluding assembly time).

Sandy takes 2/3 hour to hang the fixture and another 1/6 hour to wire it, totaling

2/3 + 1/6 = 7/6 hour.

Therefore, Sandy takes 7/6 hour per fixture.

Next, we can calculate the number of fixtures by dividing the total time available (29 hours) by the time it takes for one installation process.

Number of fixtures = Total time available / Time per fixture

Number of fixtures = 29 / (7/6) = 29 * (6/7) = 174/7 = 24.86

Since we can't have a fraction of a fixture, Sandy can install a maximum of 24 fixtures in 29 hours.

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1. Given f(x)=3x+8f(x)=3x+8 and g(x)=6x+6g(x)=6x+6 then what is (f+g)(−1))(f+g)(−1)) ?
2. Given f(x)=6x+4f(x)=6x+4 and g(x)=3x+7g(x)=3x+7 then what is (f−g)(1)) ?

Answers

f(x)=3x+8 and g(x)=6x+6 (f+g)(x) = f(x) + g(x) = (3x+8) + (6x+6) = 9x + 14 Then (f+g)(−1) = 9(-1) + 14 = 5 f(x)=6x+4 and g(x)=3x+7 (f+g)(x) = f(x) + g(x) = (6x+4) + (3x+7) = 9x + 11 Then (f−g)(1) = 9(1) + 11 = 20

How much dirt is there in a hole 3 feet deep, 6 ft long and 4 ft wide?

Answers

the volume of the hole would be  3 * 6 * 4 =72 cubic feet.

 However, since it is a hole, there would be no dirt in it.

1. What is 3/8x < -6 or 5x>2 solved and graphed?
2. What is 2<10 -4d< 6 solved and graphed?
I appreciate your help!

Answers

The first one is a disjunction, an "or", meaning that the solution set shares no numbers on the number line.  That's how you graph these...on a number line.  Solving the first one, multiply both sides by 8 to get
[tex]3x\ \textless \ -48[/tex] and divide to get x<-16.  Now the second one, just divide both sides by 5 to get
[tex]x\ \textgreater \ \frac{2}{5} [/tex]
On a single number line, make 0 your center, put -16 where it belongs in reference to the 0 and put 2/5 where it belongs in reference to the 0. The numbers to the left of -16 are those that are less than -16, and the circle above the -16 is an open one, not including the -16.  The numbers to the right of 2/5 are those numbers that are greater than 2/5, so put an open circle above the 2/5 and go to the right with that line.  And you can see that you have a big open space between the -16 and the 2/5 where the solution set is not the same at all.  For b, solve this one simultaneously.  It is a conjunction, an "and", where there will be a solution set that is shared by both values for x.  Solve it like this...start by subtracting 10 from both sides:
-8< -4d < -4   Now, when you divide by the negative 4, you have to change the signs to greater than: 2 > d > 1.  That means, in words, that "d is less than 2 and greater than 1".  On a single number line you will have open circles above the 1 and the 2 and the numbers in between 1 and 2 are shared solutions.

Directions: Describe the transformation. (x,y) -> (5x,5y)

Answers

Final answer:

The transformation (x, y) -> (5x, 5y) is a scaling transformation that dilates a point by a factor of 5 in both the x and y directions, making the entire figure five times larger while preserving its shape.

Explanation:

The transformation described by (x, y) -> (5x, 5y) is a scaling transformation or dilation in both the x and y directions by a factor of 5. What this means is that any point on the plane, when subjected to this transformation, will move five times further away from the origin along both axes. For example, if you begin with the point (1, 1), applying this transformation will result in the point (5, 5). This dilation affects all points equally, meaning that the relative distances between points are preserved, but the entire figure is made larger by a factor of 5. Therefore, if you have a figure with dimensions of length and width, after the transformation, both dimensions will be increased by five times their original measure.

Final answer:

The transformation (x, y) -> (5x, 5y) represents a dilation, enlarging a figure by a factor of 5 along both the x-axis and y-axis, which alters size but not shape.

Explanation:

The transformation described by the rule (x, y) -> (5x, 5y) is a geometric transformation known as a dilation or scaling. This type of transformation alters the size of a figure without changing its shape. Specifically, the coordinates of each point in the figure are multiplied by 5, which means that the figure is enlarged by a factor of 5 in both the x-axis (east-west direction) and the y-axis (north-south direction). If, for example, we apply this transformation to a point (1, 2), the resulting coordinates will be (5, 10), and similarly, applying it to (3, 7) would yield (15, 35). This illustrates the dependence of y on x as each x-coordinate and y-coordinate are scaled by the same factor, maintaining the shape but increasing the size.

How can you tell whether a rational expression is in simplest form? Include an example with your explanation.

Answers

a rational in its most simple an be written as a fraction a/b where a and b are co-prime. Which means that there are no common factors in a and b 

for example 4/6  is not simplest form because  2 is a factor of 4 and 6
In its simplest form 4/6  is 2/3.

Rational numbers are numbers that are written as a ratio of two integers.

Let a and b be integers, hence a rational expression can be expressed as a/b

In order to tell whether a rational expression is in its simplest form, we need to ensure no integer can go in both the numerator and the denominator.

For instance, given the rational number 10/15, the simplest form of the rational number will be expressed as (5*2)/(5*3) = 2/3

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What is the inverse of f(x)=70x^3/4 ?

Answers

y/70=x^3/4
x=(y/70)^(4/3)
Final answer:

The inverse of the function [tex]f(x) = 70x^{(3/4)[/tex] is [tex]f^{(-1)}(x) = (x/70)^{(4/3)[/tex].

Explanation:

The inverse of the function [tex]f(x) = 70x^{(3/4)}[/tex] can be found by interchanging the roles of x and y and solving for y. The goal is to isolate y on one side of the equation.

Step 1: Replace f(x) with y: [tex]y = 70x^{(3/4)}[/tex]

Step 2: Swap x and y: [tex]x = 70y^{(3/4)}[/tex]

Step 3: Solve for y: Divide both sides of the equation by 70 and raise both sides to the power of 4/3 to undo the exponent: [tex]y = (x/70)^{(4/3)}[/tex]

Therefore, the inverse of [tex]f(x) = 70x^{(3/4)}[/tex] is [tex]f^{(-1)}(x) = (x/70)^{(4/3)}[/tex].

Helpppppppppp me!!!!!!!!!

Answers

A) w/9=6

w=9*6

w=54

B) 5q=15

q=15/5

q=3

C)2s-3s=20

-1s=20

s=20/-1 = -20

s=-20

D)4-a=-12

a= 4+12 = 16

a=16


HELP might fail class

Answers

By not using the digit 0, John has 9 digits left to choose from.  By not using the letter m, John has 25 letters left to choose from.

The password pattern is <letter><letter><digit><digit><digit><digit>.  Use the Multiplication Principle:

25 x 25 x 9 x 9 x 9 x 9 = 4,100,625

Two trucks leave a warehouse at the same time. one travels due north at an average speed of 4747 miles per hour, and the other travels due south at an average speed of 5050 miles per hour. after how many hours will the two trucks be 388388 miles apart?

Answers

the combined speed are 47 + 50 = 97 mph

required number of hours = 388/97 =  4 hours

in how many ways can a judge award first, second, and third place in a contest with 10 entries

Answers

Since order is important, this is a problem solved by:

n!/(n-k)!, where n=total choices available, k=number of choices made.

10!/(10-3)!

10!/7!

720


720. just multiply 10 9 and 8 because  first, second, and third, that is means three and that's how many numbers you multiply from 10,so it equals 720.


hope this helps

cheers! 

One side of triangle is half the longest side. the third side is 7 feet less than the longest side. the perimeter is 43. find all three sides.

Answers

If x is the longest side, and y is half that length, you would have the equation

2y = x

If z is 7 less than x then that equation would look like

X = z +7

The perimeter is the sum of all the sides

P = x + y + z = 43

Now by using all three equations, we can find the value of each variable by plugging into the equations.
First, let's start by changing the first two equations to compare the values of z and y to x.

Y = x/2
Z = x - 7

Now we can use these new equations to plug into the perimeter equation and find the value of x.

43 = x + y + z Plug in your variables
43 = x + x/2 + x-7 Add 7 to both sides
50 = x + x/2 + x Multiply both sides by 2 to get rid of the fraction
100 = 2x + x + 2x Add all your x's together
100 = 5x Divide both sides by 5

X = 20

No we can use the value of x to find the values of y and z by plugging into the two equations before.

2y = 20
Y = 10

Z = 20 - 7
Z = 13

Therefore, the lengths of the sides are 20, 10, and 13

In which of the following quadrilaterals are consecutive angles always congruent? Check all that apply.

Answers

rectangle and square.
Consecutive angles are next to each other. squares and rectangles are the only to that has angles with the same values that are next to each other

Answer:

Rectangle and Square.  

Step-by-step explanation:

To know if the angles of a quadrilateral is congruent you must overlap these angles one over the other, if all elements of the angles coincide, the angles are congruent; if the elements do not match, the angles are not congruent. In quadrilateral rectangle and square consecutive angles are always congruent.

In other words, two or more angles are said congruent if and only if they have the same measurement.

What is another name for angle 2?

Answers

The rays MR and MP intersects at the point M, this means the point M is the vertex of the ∠2.

Another name for ∠2 is ∠PMR.
Final answer:

Angle 2 could refer to different things, such as an angular velocity, a direction angle, or a contact angle, depending on its context within a mathematical or physical scenario.

Explanation:

In mathematical terms, angle 2 refers to a particular position or orientation, typically specified in degrees. For instance, if points 1 and 2 rotate through the same angle (AO), angle 2 might move through a greater arc length because it is farther from the center of rotation. This concept is related to the mathematical definition of angular velocity, defined as radians per unit time.

Alternatively, angle 2 could also refer to the direction angle, which is the angle measured counterclockwise from the positive direction on the x-axis to a vector. This term is often used when calculating vector components. In this context, a positive angle indicates a counterclockwise rotation, whereas a negative angle implies a clockwise rotation.

Finally, angle 2 might specify the contact angle, which is the angle between the tangent to the liquid surface and the surface itself. To figure out the precise name for angle 2 in your particular context, I would need further information about the specific scenario or diagram you're referring to.

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WILL GIVE A BRAINLIEST PLEASE HELP!!!

Use the formula below to find the 6th term in the geometric sequence.

a(n)=(5)x(3/2)n-1

A.
5
B.
15/2
C.
1,215/32
D.
3,645/64

Answers

a(n) = a₁.(r)ⁿ⁻¹, where a₁ = 1st term, r= common ratio and n, the rank

In the formula given a₁ = 5, r = 3/2 and n = 6 (we have to find the 6th term value).

a₆ = 5.(3/2)⁶⁻¹ = 5.(3/2)⁵ = 1215/32 (answer C)

AB and BC are tangent to circle D. Find x if AB = 2x + 9 and BC = 3x + 6. Find x.

Answers

it woulds be x+15 because if you take 2x and subtracted from the 3x then you get x and then you add the 9 and 6 witch you get 15 

Answer:

the value of X comes out to be equal to 3

Step-by-step explanation:

since AB and BC are tangent to the circle D

then the length of the tangent will be same

AB will be equal to BC

where,

AB = 2 x + 9

and

BC = 3 x + 6

2 x + 9 = 3 x + 6

3 x - 2 x = 9 - 6

    x = 3

hence, the value of X comes out to be equal to 3

Explain how you would use trig ratios to find the height of the tree if you know you are standing 30 feet from the base of the tree when you measure the 37-degree angle.

Answers

check the picture below.

make sure your calculator is in Degree mode.

From use of trigonometric ratios, it is seen that the height of the tree is; 22.61 feet

How to work with trigonometric ratios?

We are told that you are standing 30 ft from the base of a tree.

Now, the distance from where you are standing to the top of the tree will be the hypotenuse of the triangle formed by you and the tree.

Thus, if the height of the tree is h and the angle the hypotenuse makes with the 30 ft base is 37°, then we have;

h/30 = tan 37

h = = 30 * tan 37

h = 22.61 ft

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Factor the expression.

4r^2 – 64

1)(4r + 5)(r – 16)
2)4(r – 4)(r – 4)
3)(4r – 5)(r + 16)
4)4(r + 4)(r – 4)

Answers

4r^2-64
4(r^2-16)
4(r+4)(r-4)
First factor out the gcf. Because (r^2-16) has perfect squares, you can factor it out one more time.
Final answer: D
Hey!

First, let's write the problem,
[tex]4r^2-64[/tex]
Factor out the common term, which is 4,
[tex]=4\left(r^2-16\right)[/tex]
Then, let's factor this part: [tex]r^2-16[/tex]
We are going to factor it using the difference of squares rule.
[tex]=\left(r+4\right)\left(r-4\right)[/tex]
Our final factored answer would be,
[tex]=4\left(r+4\right)\left(r-4\right)[/tex]

Thanks!
-TetraFish

the sum of 3 numbers is 26. the second number is twice the first and the third number is 6 more than the second. find the number

Answers

Answer:

  the numbers are 4, 8, 14

Step-by-step explanation:

If we subtract 6 from the third number and from the total, we find that we now have 5 times the first number for a total of 20.

The first number is 4.

The second number is 2×4 = 8.

The third number is 8 + 6 = 14.

List all your possibility of outcomes (there are 36 outcomes) if you roll a dice containing numbers 1-6 two times. Determine the probability of each outcome.

Answers

Check the table attached. 

The first coordinates of each pair represent the 1.roll, and the second coordinates the 2nd, roll.

All the possible outcomes are {(1, 1), (1, 2).... (6, 5), (6, 6)}, a total of 36, as can be seen in the table.

Each outcome has a chance of 1 out 36 total possible outcomes of occurring.

So the probability is 1/36=0.02778



Need help with math problem


Multiply

(3x – 7)(3x – 5)

A.
9x 2 + 6x + 35

B.
9x 2 + 36x + 35

C.
9x 2 – 36x – 35

D.
9x 2 – 36x + 35

Answers

(3x – 7)(3x – 5) term by term
1 step: 3x term 
3x*3x - 3x*5  the minus comes as you multiply by -2
2 step: -7 term
-7*3x + 7*5 the second plus comes from -*-=+

add these together
3x*3x-3x*5-7*3x+7*5 and do the multiplications: 
9x^2 -15x-21x+35=9x^2-36x+35

Find the take home percent of the gross pay: net pay $298.76, gross pay $402.38. round to the nearest percent.

Answers

298.76 / 402.38 = 0.742 = 74%

What is i^16 simplified

Answers

[tex]\bf i^{16}\implies i^{4+4+4+4}\implies i^4\cdot i^4\cdot i^4\cdot i^4\implies 1\cdot 1\cdot 1\cdot 1[/tex]

and fairly sure you know how much that is.

Harry Hoodeen made $24,567.00 net pay last year. His monthly expenses averaged $1,980.00. How much was left over for savings for the year?

Answers

24,567 - 12(1980)
24,567 - 23760
807

His left over savings was $807.

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