the following sequence is an arithmetic sequence.you are now shown very many terms of this sequence,but you are shown enough to fill in the missing number.what number goes in the blank? 14, _,56 ...?

Answers

Answer 1

because it is arithmetic not geometric 14,x,56 An = An-1 + d x = 14 +d --> d = x-14 56 = x +d --> d = 56-x By substitution x-14 = 56-x 2x = 70 x = 35 the sequence is 14,35,56

Related Questions

What fraction of an hour is 46 minutes??

Answers

60mins per hour
46/60=23/30

Fiona has to choose a bouquet for her wedding. The probability that she uses red roses is 98%, the probability that she uses orchids is 87%, and the probability that she uses Gerber daisies is 94%. Given the probability that she has both roses and orchids is 0.87 and the probability that she has both Gerber daisies and roses is 0.97 what is the probability that her bouquet contains roses or Gerber daisies?

Answers

the answer would be b.) .84

solve for x enter your answer in interval notation using grouping symbols x²+2x<8

Answers

x^2 + 2x < 8 x^2 + 2x - 8 < 0 (x + 4)(x - 2) < 0 ,, {x + 4 < 0 and x - 2 > 0} or {x + 4 > 0 ,,and x - 2 < 0} ,, {x < -4 and x > 2} or {x > -4 and x < 2},, Discard x < -4 and x > 2 because it has no solutions, leaving just x > -4 and x < 2 ,, -4 < x < 2

If you save two pennies on January 1, four pennies on January 2, six pennies on January 3, and continue this pattern for one year (not a leap year), what will be the value of your entire savings, in dollars, at the end of that one year? Express your answer as a decimal without commas.

...?

Answers

the answer is
1J, 2J, 3J, ...............29D, 30D, 31D = 365 days
2 4 6 ........................................
let be S the value of entire savings
S= Sum 2K= 2 Sum K = 2 [365(365+1) / 2],
1<K<365 1<K<365
because Sum K = n(n+1) /2
1<K<n

finally S= 133590 pennies

Answer:

1335.90

Step-by-step explanation:

Choose two axioms that allow 6 + (x + 5) to be written x + 11.
A) commutative - addition
B) distributive
C) associative - multiplication
D) symmetric
E) commutative - multiplication
F) associative - addition
G) identity - addition

Answers

associative means that you can move the parenthesis around the problem and still get the same answer. like (4+2)+3=4+(2+3)
first & sixth are the true

Basic number properties:

The Distributive Property: [tex]a\cdot (b+c)=a\cdot b+a\cdot c;[/tex]The Associative Property for addition: [tex]a+(b+c)=(a+b)+c;[/tex]The Associative Property for multiplication: [tex]a\cdot (b\cdot c)=(a\cdot b)\cdot c;[/tex]The Commutative Property for addition: [tex]a+b=b+a;[/tex]The Commutative Property for multiplication: [tex]a\cdot b=b\cdot a;[/tex]Identity Property : Any number add to the zero the answer is the number itself;The symmetric property states that if one number is equal to a second number, then the second number is equal to the first number.

For the expression 6 + (x + 5):

use The Commutative Property for addition - 6+(x+5)=(x+5)+6;use The Associative Property for addition - (x+5)+6=x+(5+6)=x+11.

Explain the correlation between the graph of a line, direction of the line and the positive or negative slope of the line.

Answers

Well if the slope is positive the graph of the line will go up. If the slope if negative the graph of the line will go down. Also, depending on the y-intercept the graph will start on a negative integer or a positive integer

Proof that x^y + y^x > 1 for all x,y > 0 ...?

Answers

To prove this inequality we need to consider three cases. We need to see that the equation is symmetric and that switching the variables x and y does not change the equation.

Case 1: x >= 1, y >= 1

It is obvious that

x^y >= 1, y^x >= 1
x^y + y^x >= 2 > 1
x^y + y^x > 1

Case 2: x >= 1, 0 < y < 1

Considering the following sub-cases:

- x = 1, x^y = 1
- x > 1,

Let x = 1 + n, where n > 0

x^y = (1 + n)^y = f_n(y)

By Taylor Expansion of f_e(y) around y = 0,

x^y = f_n(0) + f_n'(0)/1!*y + f_n''(0)/2!*y^2 + ...
= 1 + ln(1 + n)/1!*y + ln(1 + n)^2/2!*y^2 + ...

Since ln(1 + n) > 0,

x^y > 1

Thus, we can say that x^y >= 1, and since y^x > 0.

x^y + y^x > 1

By symmetry, 0 < x < 1, y >= 1, also yields the same.

Case 3: 0 < x, y < 1

We can prove this case by fixing one variable at a time and by invoking symmetry to prove the relation.

Fixing the variable y, we can set the expression as a function,

f(x) = x^y + y^x
f'(x) = y*x^(y-1) + y^x*ln y
For all x > 0 and y > 0, it is obvious that
f'(x) > 0.

Hence, the function f(x) is increasing and hence the function f(x) would be at its minimum when x -> 0+ (this means close to zero but always greater than zero).

lim x->0+ f(x) = 0^y + y^0 = 0 + 1 = 1

Thus, this tells us that

f(x) > 1.

Fixing variable y, by symmetry also yields the same result: f(x) > 1.

Hence, when x and y are varying, f(x) > 1 must also hold true.
Thus, x^y + y^x > 1.

We have exhausted all the possible cases and shown that the relation holds true for all cases. Therefore,

x^y + y^x > 1

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

I have to give credit to my colleague, Mikhael Glen Lataza for the wonderful solution.

I hope it has come to your help.

In 2010, the United States national debt was estimated to be nearly 13,000,000,000,000 dollars. Which of the following represents the national debt in scientific notation?

a. 1.3 x 10^11

b. 1.3 x 10^12

c. 1.3 x 10^13

d. 1.3 x 10^14 ...?

Answers

Answer:

option C

Step-by-step explanation:

In United States national debt in 2010 was estimated to be nearly $13,000,000,000,000.

Now we have to convert this debt in scientific notation.

In scientific notation we have to convert this number in to 10ˣ.

13000000000000 = 1.3 × 10¹³

Therefore option C is the answer.

Expand and simplify 2 (x+7)+3(x+1)

Answers

I hope this helps you

(2x+14)+(3x+3)= (2x+3x)+(14+3)= 5x+17

When f is defined by
f(x) = sqrt(x) ,
find a so f'(a) is two times the value of f'(4).

Answers

After all calculations you will get this [tex] \frac{1}{2 \sqrt{vectora}} = \frac{1}{2} [/tex]. Then find a. a is the key and it's equals to 1. This is your answer.

The dimensions of a smaller rectangle are 3 ft. by 9 ft. The dimensions of a larger rectangle are 5 ft. by 11 ft. Find the ratio of the perimeter of the larger rectangle to the perimeter of the smaller rectangle. Options are 11:9, 3:4, 4:3, and 5:3 ...?

Answers

perimeter of smaller rect = 2L + 2B = 2*3ft + 2*9ft = 2(3 + 9) ft perimeter of bigger rect = 2L + 2B = 2*5ft + 2*11ft = 2(5 + 11) ft perimeter of larger rect 2(3 + 9) ft 12 3 --------------------- = ----------- = ------ = ----- perimeter of smaller rect 2(5 + 11) ft 16 4 so their ratio is 3:4

Answer:

Option 3rd is correct

4: 3

Step-by-step explanation:

Perimeter(P) of rectangle is given by:

[tex]P =2(l+w)[/tex]

where, l is the length and w is the width of the rectangle respectively.

Given that:

The dimensions of a smaller rectangle are 3 ft. by 9 ft.

Perimeter of smaller rectangle= 2(3+9) =2(12) = 24 ft.

It is also given that: The dimensions of a larger rectangle are 5 ft. by 11 ft.

Perimeter of Larger rectangle = 2(5+11) =2(16) = 32 ft.

We have to find the ratio of the perimeter of the larger rectangle to the perimeter of the smaller rectangle.

[tex]\frac{\text{Perimeter of the larger rectangle}}{\text{Perimeter of the Smaller rectangle}}[/tex]

Substitute the given values we have;'

[tex]\frac{32}{24}=\frac{4}{3}[/tex]

Therefore, the ratio of the perimeter of the larger rectangle to the perimeter of the smaller rectangle is, 4 : 3

How many solutions does this linear system have?

y = x+ 2

6x – 4y = –10

one solution: (–0.6, –1.6)
one solution: (–0.6, 1.6)
no solution
infinite number of solutions

Answers

i hope this helps you

6x-4 (x+2)= -10x

6x-4x-8= -10

2x= 2

x= 1

y=1+2=3

The solution of a linear system of an equations is (-1, 1).

The given linear system of equations are y = x+ 2 and 6x – 4y = –10.

What is a linear system of equations?

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

The system of linear equations can be solved as follows

x-y=-2 --------(1)

6x – 4y = –10 --------(2)

Multiply equation (1) by 4

That is, 4x - 4y= -8 --------(3)

Subtract equation (3) from the equation (2)

So, 6x-4y-(4x-4y)=-10-(-8)

2x=-2

⇒ x=-1

Put x=-1 in x-y=-2

Now, y=1

So, solution is (-1, 1)

Therefore, the solution of a linear system of an equations is (-1, 1).

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convert 5/8 to percent notation

Answers

Hi , the answer is 62.5 percent , because 5 divided by 8 equals to 0.625 , then we move the decimal two spaces to the right .

We can multiply 5/8 directly by 100 and then simplify the fraction into a decimal or first convert the fraction to a decimal and then multiply by 100.
5/8 = 0.625
0.625 x 100 = 62.5%

One's intelligence quotient, or IQ, varies directly as a person's mental age and inversely as that person's chronological age. A person with the mental age of 25 and a chronological age of 20 has an IQ of 125. What is the chronological age of a person with a mental age of 40 and an IQ of 80?

Answers

Final answer:

The chronological age of a person with a mental age of 40 and an IQ of 80 is calculated to be 50 years by using the direct and inverse proportionality of the IQ, Mental Age, and Chronological Age.

Explanation:

The subject of your question is related to a mathematical concept known as Direct and Inverse Proportion. In this scenario, the IQ is directly proportional to the Mental Age and inversely proportional to the Chronological Age. Therefore, the formula is given as: IQ = (Mental Age / Chronological Age) * 100.

From the first example that indicates a person with the mental age of 25 and a chronological age of 20 has an IQ of 125, we can determine the proportionality constant as follows: 125 = (25 / 20 ) * 100.

Now, to find out the chronological age of a person with a mental age of 40 and an IQ of 80, we use the same proportionality and solve the equation for chronological age: 80 = (40 / Chronological Age) * 100. Solving the equation, the Chronological Age equates to 50 years.

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Final answer:

To find the chronological age of a person with a mental age of 40 and an IQ of 80, we can use the fact that IQ varies directly with mental age and inversely with chronological age. The specific chronological age depends on the value of the constant of variation, k.

Explanation:

To find the chronological age of a person with a mental age of 40 and an IQ of 80, we can use the fact that IQ varies directly with mental age and inversely with chronological age. Let's denote the chronological age as x. We can set up the equation as follows:

IQ = (k * mental age) / chronological age

where k is the constant of variation.

Given that the mental age is 40 and the IQ is 80, we can plug in these values into the equation:

80 = (k * 40) / x

To solve for x, we can cross-multiply and then divide both sides by 80:

80x = k * 40

x = (k * 40) / 80

Since we don't have the value of k, we can't determine the specific value of x. However, we can determine the relationship between x and the mental age:

x = 40 / k

Therefore, the chronological age of a person with a mental age of 40 and an IQ of 80 depends on the value of the constant of variation, k.

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What value(s) of x make the equation x2 - 18x + 81 = 0 true?

Answers

We can factorise this to get (x-9)(x-9). To find the value, each bracket needs to equal 0, so the value would be x=9

Answer:

Step-by-step explanation:

Write a function rule for the area A of a triangle whose base, b, is 2 cm less than seven times the height, h. What is the area of the triangle when the height hits 16 cm.
A. 4h^2-5h;944cm^2
B. 4h-5/2; 29.5***********
C. 4h^3-5h/2; 427
D. 4h-5; 59cm

I think it is B

Answers

i hope this helps you

4 x plus= equals what

Answers

32 + 42 = 52, 52 + 122 = 132, and 82 + 152 = 172= F=dAF=dA
dF=0dF=0
d⋆F=⋆J
Fab=2∇[aAb]Fab=2∇[aAb]
∇[aFbc]=0∇[aFbc]=0
∇aFab=
∇⋅B⃗=0∇⋅B→=0
∇⋅E⃗=4πρ∇⋅E→=4πρ
∂B⃗∂t=−∇×B⃗∂B→∂t=−∇×B→
∂E⃗∂t=+∇×B⃗−4πJ⃗.
∇⋅v⃗=∂vi∂xi∇⋅v→=∂vi∂xi
and the curl is defined as
(∇×v⃗)i=ϵijk∂vk∂xj.
∇⋅v⃗=∂vx∂x+∂vy∂y+∂vz∂z∇⋅v→=∂vx∂x+∂vy∂y+∂vz∂z
and curl is defined as
(∇×v⃗)z=∂vy∂x−∂vx∂y
= meaning of life 42

betty has a cow.the cow produces 5 liters of milk in a day. if the cows diet is improved the cow will produce 200% more milk.how much milk would the cow make in a day.

Answers

10 liters, google 5 liters times 200%...

10 liters. I hope this really helps!

Whut is 2 pus 2 i dount no

Answers

the answer to this is 4

80 POINTS!!!

A line segment has endpoints at (4, –6) and (0, 2). What is the slope of the given line segment? What is the midpoint of the given line segment? What is the slope of the perpendicular bisector of the given line segment? What is the equation, in slope-intercept form, of the perpendicular bisector?

Answers

Answer:

1). Slope = (-2)

2). Midpoint = (2, -2)

3). Slope of the perpendicular bisector = (1/2)

4). Equation of perpendicular bisector will be x - 2y = 6

Step-by-step explanation:

A line segment has the endpoints at (4, -6) and (0, 2).

1). Then the slope of the given line segment will be = (y - y')/(x - x') = (2 + 6)/(0 - 4) = 8/(-4) = (-2)

2). Mid point of the line segment is given by [tex](\frac{x_{1}+x_{2}}{2}) , (\frac{y_{1}+y_{2}}{2})[/tex]

Therefore midpoints of the line segment will be [tex]\frac{4+0}{2},\frac{-6+2}{2}[/tex] = (2, -2)

3). Slope of the perpendicular bisector is represented by [tex]m_{1}.m_{2}=(-1)[/tex]

⇒ (-2)×m2 = (-1)

⇒ [tex]m_{2}=\frac{1}{2}[/tex]

4). Now we have to find the equation of perpendicular bisector passing through (2, -2) and slope (1/2).

Since standard equation of the line will be given as y = mx + c

[tex]y=\frac{1}{2}x+c[/tex] passes through (2, -2).

[tex](-2) = \frac{1}{2}(2) + c[/tex]

c = (-1) - 2 = -3

Finally the equation of perpendicular bisector will be

[tex]y=\frac{1}{2}x+(-3)[/tex]

⇒ 2y = x - 6

⇒ 2y - x = -6

⇒ x - 2y = 6

Answer: the answers are in the explanation, they are also in order

Step-by-step explanation:

-2

(2,-2)

1/2

y=(1/2)x - 3

Austin takes 1 minute and 45 seconds to run three-quarters of a circular track. His rate of motion is π/ radians per second.

Answers

Length of circular track is:

L = 2*r*pi

He run 3/4 of it so length is:
L' = 3*2/4*r*pi = 3/2*r*pi

To calculate speed of his movement we use formula:
v = s/t where s = L' and t = 1 minute 45 seconds = 105 seconds

v = L'/t = [tex] \frac{3*r*pi}{2*105} [/tex]

v = r* pi/70

If we take that r = 1 answer is [tex] \pi /70[/tex]

Lamar bought 20 pounds of dog food for $4.99 for his dog, Buster. The next day, the shop down the street offered 50 pounds of the same brand of dog food for $12.50. Did Lamar get a better deal? ...?

Answers

To calculate what is better deal we need to calculate how much 1 pound of dog food costs at both shops.

First shop:
4.99/20 = 0.2495$/pound

Second shop:
12.50/50 = 0.25$/pound

This means that first shop had slightly better deal since at that place pound was a bit less expensive.

A school soccer team has just purchased new uniforms. The team now has 2 different colors of shorts (white and red) and 3 different colors of shirts (white, red, and gold).

How many different uniform combinations are there? ...?

Answers

Basic combinations are calculated with
number of shorts * number of shirts = 2 * 3
so the answer will be 6.

let f=cos^2x and g=sin^2x which of the following lie in the space spanned by f and g
a)cos2x
b)3+x^2
c)1
d)sinx
e)0 ...?

Answers

I'm pretty sure that these are lying in the space spanned by f and g: a)cos2x, e)0. Use common formulas to check it.

What is the prime factorization of 19??

Answers

19 is already a prime number......so ur answer would be 19 or 19 x 1

The prime factorization of 19 is 19, as it is a prime number and can only be divided by 1 and itself.

To determine the prime factorization of a number, we identify all the prime numbers that multiply together to give the original number. In the case of 19, we need to check if it can be divided by any primes (like 2, 3, 5, 7, 11, 13, 17).

After testing, we find that 19 is only divisible by 1 and itself, making it a prime number. Therefore, the prime factorization of 19 is simply 19.

Convert 0.84 into a simplified fraction

Answers

100÷84
Or
84 upon 100
Maybe the answer is correct

how many times does 28 go into 126

Answers

In order to know that, you need to divide 28 from 126
It would be:126/28 = 4.5

So, your final answer is 4.5

Hope this helps!

if the tank is half full, approximately how many miles has troy driven since last filling up his tank

BTW troy truck has a 30 gallon gas tank and gets an average of 21 miles per gallon

ASAP plz I really need help

Answers

Answer: 315 Miles.

30 Gallon Tank on Half: 30 / 2 = 15.
21 miles per gallon: 21 x 15 = 315 Miles.

I hope this helps!

Answer:

Toy truck will drive 315 miles since last the tank was filled.

Step-by-step explanation:

BTW troy truck has tank of capacity = 30 gallons

Since the toy truck is half filled so gas in the tank = [tex]\frac{30}{2}[/tex]

= 15 gallons of gas

Average of the toy truck is given as = 21 miles per gallon

That means in 1 gallon truck travels = 21 miles

Therefore in 15 gallons of gas truck will travel = 21 × 15

= 315 miles

Toy truck will drive 315 miles since last the tank was filled.

In triangle abc, sin a = 2425. which other expression has a value of 2425?

Answers

cos b, I think this should help...

A basketball court is in the shape of a rectangle. It has a length of (x − 7) meters and a width of (x + 3) meters. The expression below represents the area of the court in square meters.

(x − 7)(x + 3)

Which of the following simplified expressions represents the area of the basketball court in square meters?

− 6x + 3

x2 − 21

x2 − 4x − 21

x2 − 7x + 3 ...?

Answers

The answer is x² - 4x - 21.

The area (A) of the rectangle is:
A = l * w (l - length, w - width)

We have:
l = x - 7
w = x + 3
Therefore:
A = (x - 7)(x + 3)

Now, multiply each factor with another:
A = (x - 7)(x + 3) = x * x + x * 3 - 7 * x - 7 * 3 = x² + 3x - 7x - 21 = x² - 4x - 21

The expression x²- 4x - 21 represents the area of the basketball court in square meters.

What is Area ?

The area can be defined as the space occupied by a flat shape or the surface of an object.

The area of a figure is the number of unit squares that cover the surface of a closed figure.

It is given that the area of a rectangle is (x − 7)(x + 3)

when It has a length of (x − 7) meters and a width of (x + 3) meters.

The simplified expression of the area is equal to

(x-7)(x-3)

This can also be written as

x *(x+3) - 7*(x+3)

x²+3x-7x-21

x²- 4x - 21

Therefore x²- 4x - 21 represents the area of the basketball court in square meters .

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Read the excerpt from "The Yellow Wallpaper." He said that after the wall-paper was changed it would be the heavy bedstead, and then the barred windows, and then that gate at the head of the stairs, and so on. You know the place is doing you good, he said, and really, dear, I dont care to renovate the house just for a three months rental. Based on this excerpt, which statement best describes Johns viewpoint of the wallpaper?A. He believes that the wallpaper should be replaced. B. He believes that the wallpaper is unattractive. C. He believes that his wife is overreacting to the wallpaper. D. He believes that his wife likes the wallpaper. Determine the nature of this statement. the author makes the reader feel the discomfort of the dirty, drab, noisy steel mill where the story takes place. fact opinion If a is an integer, when is a/b always equal to an integer (I'm terrible at math btw) Which statement about an elements average atomic mass is correct? a. It is determined by counting the number of isotopes in a sample of the element. b. It is equal to one-twelfth the mass of the most common isotope. c. It is a weighted average, so common isotopes have a greater effect than uncommon ones. d. It is based on an isotopes charge, so negatively charged isotopes have a greater effect than positive ones. 1.Name the two factors that give federal courts jurisdiction over a case. Give an example of each.2.Why do presidents prefer federal judges who tend to agree with their views?3. How is a case usually heard and decided when it reaches the supreme court. Consider the functions f(x) = x2 13 and g(x) = x + 5. What is the value of (f g)(4)? ...? Define divine intervention and provide examples from the book illustrating ways that Athena assisted the main characters in their plights by divinely intervening. A popular extreme sport is artificial wall climbing. A climber is resting at a height of 42 feet while on a climbing tower. If this is 60% of the tower's total height, find the height of the tower. Is black coffee an element compound or mixture In paragraph 3 which rhetorical technique is being used to add emphasis the sum of two numbers is 85. twice one number plus four times the other is 218. find the numbers Any ordered pair that makes all equations in a system of equations true is a(n) ...? How does distance affect force when the amount of work remains the same?A) As distance increases the amount of force needed increases. B) As distance decreased the amount of force needed decreases. C) As the distance increases the amount of force needed decreases. D) As the distance increases the amount of force is not affected. What is the approximate difference in the amount of wax needed to make a candle from each of these molds? (Use = 3.14.)a) 4.19 cubic inches b) 10.4 cubic inches c) 12.56 cubic inches d) 20.93 cubic inches HELP! According to the author, is the law of the jungle strong on its own? If not, what makes it strong? Give one example from the poem or story to support your ideas Anyone pleas I will help you after!! Physical aggression is one of the _______ misbehaviors because it can lead to physical harm Which of the three states of matter has the highest density? A:solid B:liquid C:gas The preparatory test for the sat is called the _____. Double Suicide of Romeo and Juliet.A) Falling ActionB) ClimaxC) DenouementD) ResolutionA? A compound composed of electrically chargerd atoms is called? Steam Workshop Downloader