How many term of the A. P. 16,14,12,. Are needed to give the um 60? explain why do we get two anwer

Answers

Answer 1

The sum of first five or twelve term in the A.P given the value 60.

The term AP refers a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value.

Here we have given that  A. P. 16,14,12,.

And we need to find the number of term to get the value of 60.

While we looking into the given question we have identified that the  common difference d of the A.P. is − 2

Here we also know that the terms of the A.P. are in descending order.

Now, we have to take n = 5  then then first 5 terms are 16,14,12,10,8.

Here we have identified that the sum is 60.

Similarly, here by taking n = 12 , then the last 7 terms ( 12 − 5 ) (12-5) are 6 , 4 , 2 , 0 , − 2 , − 4 , − 5 6,4,2,0,-2,-4,-5

Here we have identified that the sum of these seven terms is 0.

Therefore, sum of first 12 terms is also 60.

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Related Questions

What is an example of f x G X?

Answers

The example of composition function f(g(x)) is given by f(x) = 2x + 1   and g(x) = 3x then f(g(x)) = 6x + 1.

As given in the question,

Composition function is written as :

(fog)(x) = f(g(x))

Here substitute the value x in the function f(x) as function g(x) :

Example of the composition function is:

f(x) = 2x + 1

g(x) = 3x

(fog)(x)

= f(g(x))

=f(3x)

= 2(3x) + 1

= 6x + 1

Therefore, the example of the composition function f(g(x)) is given by :

f(x) = 2x + 1   and g(x) = 3x then f(g(x)) = 6x + 1.

The above question is incomplete, the complete question is:

What is an example of the function f (g(x))?

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Is area and volume inversely proportional?

Answers

Yes, the area and the volume are inversely proportional to each other.

Here we have to verify that the area and volume inversely proportional.

As we all know that in math, the term area is used for the 2 dimensional shapes where as the volume refers the 3 dimensional shapes.

Let us consider the example of square.

We all know that the area of square is a x a whereas the volume of square is a x a x a.

Here we have identified that the volume is one step ahead of the area and each of them are inversely proportional to each other.

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The Cruisers scored a total of 105 points in a basketball game against the Strikers. The Cruisers had a total of 43 baskets, some of which were two-point shots and some of which were three-point shots. How many two-point and three-point shots did the Cruisers score?

Answers

The number of two-points and three points shot the cruisers scored are 24 and 19 respectively.

How to find the number of two and three points made?

The Cruisers scored a total of 105 points in a basketball game against the Strikers. The Cruisers had a total of 43 baskets, some of which were two-point shots and some of which were three-point shots.

Therefore, the number of two-points and three-points the cruiser scored is as follows:

let

x = number of two-points

y = number of three-points

Hence, using equation

x + y = 43

2x + 3y = 105

Multiply equation(i) by 2

2x + 2y = 86

2x + 3y = 105

subtract equation(i) from equation(ii)

y = 19

Let's find x as follows:

x = 43 - 19

x = 24

Therefore,

number of two points = 24

number of three points = 19

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The point (5,5) is on a line with slope 1/3. How much is is the bonus/penalty in this equation?

Answers

The equation is y = 1/3 x + 10/3. The y-intercept is 10/3.

What is an equation of the line?

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given that the point (5,5) is on a line with slope 1/3. The y-intercept will be calculated as,

y = mx + c

5 = (5/3)) + c

c = ( 15 - 5 ) / 3

c = 10 / 3'

y = 1/3x + 10/3

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у +4=3x
2y-6x=-8
Help

Answers

Answer:

x=0, y=-4

Step-by-step explanation:

y=3x-4

2(3x-4)-6x=-8

6x-8-6x=-8

An Olympic-sized pool, which holds 660,000 gallons of water,
is only 63% full. The pool maintenance company adds more
water, filling the pool to 90% full. How many gallons of water
did they add?
P
7.AR 3.1
a
244 200
178 200
B) 594 000
415.800
134

Answers

Answer:

  178,200

Step-by-step explanation:

You want to know the number of gallons added to a 660,000 gallon pool to raise it from 63% full to 90% full.

Increase

The increase from 63% to 90% is an increase of ...

  0.90 -0.63 = 0.27

of the capacity of the pool. That fraction of the capacity is ...

  0.27 × 660,000 gallons = 178,200 gallons

The maintenance company added 178,200 gallons.

38. Light house is a tower which is designed to exit light from a system of lamps and to
serve as a navigational aid for maritime pilots at sea. Two boats approaching a light
house in mid sea from opposite direction as shown in figure. The angle of elevation
of light house from both boats are also given.
45°
B(Boat)
(i) Find the height of the light house.
(ii) Find the distance BP.
(iii) Find the distance AB.

Answers

Answer:

  (i) height: 36.6 m

  (ii) BP = 36.6 m

  (iii) AB = 51.8 m

  (iv) AC = 73.2 m

Step-by-step explanation:

Given angles of elevation of 45° and 30° to the same point A from locations 100 m apart, you want to know the height of A, and distances BP, AB, and AC in the diagram.

Special triangles

The figure is divided into two special triangles. The one on the left is an isosceles right triangle with side lengths in the ratio 1:1:√2. The one on the right is a 30°-60°-90° triangle with side lengths in the ratio 1:√3:2. The common side AP corresponds to one ratio unit in each of these ratios.

(i) and (ii)

BP = AP = 1 ratio unit means BP : PC = 1 : √3, and ...

  BP/BC = 1/(1+√3)

  BP = BC/(1+√3) ≈ (100 m)/2.73205

  BP ≈ 33.6 m

  AP = 33.6 m . . . . . . same as BP

(iii)

AB is √2 times AP, so is ...

  AB = √2 · 36.6 m

  AB ≈ 51.8 m

AC

AC is 2 times AP, so is ...

  AC = 2·(36.6 m)

  AC = 73.2 m

For questions 7 - 10, determine whether the angle of rotation is 90,180'or 270'. Each rotation is clockwise from the pre-image to the new image.

Answers

Answer:

7/ 180 degree

8/ 90 degree

9/ 270 degree

10/ 180 degree

Step-by-step explanation:

7/ Each square box is 90 degrees, and we see that the square rotated over 2 boxes, so it is 180 degrees clockwise.

8/ We see that the triangle rotated 90 degrees clockwise.

9/ We see that the triangles rotate over three boxes, which is 270 degrees clockwise.

10/ We see that the triangles rotate over 2 boxes, which is 180 degrees clockwise.

Answer:

7) 180°

8) 90°

9) 270°

10) 180°

Step-by-step explanation:

7)

The notation for rotating 180 degrees clockwise about the origin is (the degrees symbol was omitted): [tex]R_{-180, O} (x,y) - > (-x,-y)[/tex]

This means that when you rotate 180 degrees clockwise about the origin, the coordinates of the figure become their opposite.

C(2,-1) -> C'(-2,1)

N(4,-2) -> N'(-4,2)

W(3,-4) -> W'(-3,4)

Y(1,-3) -> (-1,3)

..............fun fact: rotating 180 degrees clockwise is the same as rotating 180 degrees counterclockwise

8)

The notation for rotating 90 degrees clockwise about the origin is (the degrees symbol was omitted): [tex]R_{-90, O} (x,y) - > (y,-x)[/tex]

This means that when you rotate 90 degrees clockwise about the origin, the x and y coordinates flip, and the x coordinate becomes its opposite.

B(-4,-2) -> B'(-2,4)

E(-1,-5) -> E'(-5,1)

I(0,-1) -> I'(-1,0)

..............fun fact: rotating 90 degrees clockwise is the same as rotating 270 degrees counterclockwise

9) The notation for rotating 270 degrees clockwise about the origin is (the degrees symbol was omitted): [tex]R_{-270, O} (x,y) - > (-y,x)[/tex]

This means that when you rotate 270 degrees clockwise about the origin, the x and y coordinates flip, and the y coordinate becomes its opposite.

G(-4,2) -> G'(-2,-4)

Z(-1,5) -> Z'(-5,-1)

T(0,2) -> T'(-2,0)

..............fun fact: rotating 270 degrees clockwise is the same as rotating 90 degrees counterclockwise

10) The notation for rotating 180 degrees clockwise about the origin is (the degrees symbol was omitted): [tex]R_{180,O} (x,y) - > (-x,-y)[/tex]

This means that when you rotation 180 degrees clockwise about the origin, the coordinates of the figure become their opposite.

B(-3,-5) -> B'(3,5)

G(-4,0) -> G'(4,0)

C(-5,-4) -> C'(5,4)

..............fun fact: rotation 180 degrees clockwise is the same as rotation 180 degrees counterclockwise

Help me with this geometry pls

Answers

Answer:

Cos A = adjacent/hypotenuse

Cos A = 15/17

Cos A = 2.143

tan A = opposite/adjacent

tan A = 8/15

tan A = 0.533

sin A = opposite/hypotenuse

sin A = 8/17

sin A = 0.471

Step-by-step explanation:

heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ  -{ elyna s }-

How to get Universal Credit Loophole $1,500?

Answers

You can get Universal Credit Loophole for $1,500 through Advance Payment.

While you wait for the first distribution of Universal Credit, advance payments up to the full amount of the first anticipated payment are available if you need money to pay bills and other household needs. In your online account or by contacting your Job-Centre Plus job coach, you can submit an application for an advance payment.

You will require:

Describe why you require an advance.the identity of the person (you do this when you apply online or on the phone with a work coach)supply the advance's bank account information (talk to your work coach if you cannot open an account)

The money must be repaid within a year by taking deductions from your Universal Credit installments.

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For what value of k are the roots of the quadratic equation 3x 2 2kx 27 0?

Answers

The values of k are 9, – 9 for which roots of the quadratic equation are real and equal.

What is a quadratic equation?

An equation containing one term in which the unknown is squared and no term in which it is raised to a power higher than 2.

Given: 3x² + 2kx + 27 = 0

Comparing with standard quadratic equation ax² + bx + c = 0

a = 3 b = 2k c = 27

Given that the roots of the equation are real and equal

Thus, D = 0

Discriminant D = b² – 4ac = 0

(2k)² – 4.3.27 = 0

4k² – 324 = 0

4k² = 324

k² = 81 taking square root on both sides

k = 9 or k = – 9

Hence, The values of k are 9, – 9 for which roots of the quadratic equation are real and equal.

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What is the area of a triangle with a base of 7 1/2 feet and a height of 8 feet

Answers

Answer:

[tex]30ft^{2}[/tex]

Step-by-step explanation:

What is the percent of decrease from 63.2 to 35?

Answers

Answer:

The percentage of decrease from 63.2 to 35 is 44.5%.

Step-by-step explanation:

To calculate the percent of decrease from 63.2 to 35, we can use the following formula:

percent of decrease = (original value - new value) / original value * 100%

Plugging in the values given in the question, we get:

percent of decrease = (63.2 - 35) / 63.2 * 100%

Solving for the percent of decrease, we get:

percent of decrease = 44.5%

Therefore, the percentage of decrease from 63.2 to 35 is 44.5%.

Answer:

44.6202532 % decrease

Step-by-step explanation:

To find the percent decrease, take the original amount, subtract the new amount and then divide by the original amount

(63.2 - 35) /63.2

28.2/63.2

.446202532

Change to percent form

44.6202532 %

if the percentage increase is 79%, what is the growth factor?

PLS HELP TYSMMM

Answers

With an increase of 79% the growth factor is 1.79.

What is growth factor?

The rate at which a quantity multiplies itself over time is known as its growth factor.

A quantity's growth rate is the factor by which it grows (or shrinks) over time.

An increase of 79% is the same result as multiplying with 1.79.

We call 1.79 a growth factor.

In other words:

With an increase of 79%,

you will get 100+ 79 = 179%.

The growth factor that corresponds with 179% = 179 : 100 = 1.79.

Written as a formula, it looks like this:

With an increase of p % the growth factor is

g = (100 + p) / 100

Simplifying,

g = 1 + p /100

g = 1 + 79/100

g = 1 + 0.79

g = 1.79.

Therefore, the growth factor is 1.79.

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How do you find the standard deviation of the sum of 4 random variables?

Answers

Standard deviation:

Step 1: Find the mean.
Step 2: For each data point, find the square of its distance to the mean.
Step 3: Sum the values from Step 2.
Step 4: Divide by the number of data points.
Step 5: Take the square root.

In the figure, Angle A =120° . Find the remaining angles.​

Answers

This is a cyclic quadrilateral so the opposing angles have to add up to 180 degrees.

Since Angle A = 120 degrees
Angle C = 180 degrees - 120 degrees
Angle C = 60 degrees

Hope this helps :D

The remaining angles  ∠B ,∠C and ∠D is 90°,60°,90°.

Given : Angle A = 120°

To find: ∠B ,∠C , ∠D

Solution: In figure, an inscribed angle is the angle formed in the innards of a circle when two heartstrings cross on the circle. It can also be outlined as the angle subtended at a point on the circle by two presented junctures on the circle. Inversely, an incised angle is defined by two heartstrings of the circle sharing an endpoint .

∠A+∠C=180

 ∠C=180-120

 ∠C= 60;

 In triangle ABC :  ∠BAC + ∠ACB+∠ABC=180°

                               60° + 30° + ∠ABC = 180°

                                ∠ABC = 180°-90°

                                ∠ABC = 90° (so B is 90°)

Therefore, ∠B+∠D=180°

                   ∠D=180°-90°

                    ∠D=90°

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Is 31 is a prime number or not?

Answers

There are only two factors of the number 31 which are 1 and 31. Then the integer number 31 will be a prime number.

What is a prime number?

A prime number is a positive integer having exactly two factors which are 1 and the number itself. Any number that does not follow this is termed a composite number.

The prime numbers from 1 to 100 are given below.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

The factor of the 31 will be given as,

31 = 1 x 31

There are only two factors of the number 31 which are 1 and 31.

Thus, the integer number 31 will be a prime number.

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What is the value of the expression 1 2 3 4 5?

Answers

The value of the given and completed expression in this problem is

-1

What are combined operations?

Combined operations are defined as a set of operations applied to the same problem, for example addition, subtraction, multiplication, are frequently used in arithmetic polynomials.

In this case we have an arithmetic polynomial.

We complete the expression as follows:

1 + 2 - 3 + 4 - 5

We group the positive terms on one side and negative terms on the other:

(1 + 2 + 4) - (3 + 5)7 - (8)-1

The value of the expression (1 + 2 - 3 + 4 - 5) is -1

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[tex](9b+3)^{2}[/tex]

Answers

Answer:

81b^2 + 54b + 9

Step-by-step explanation:

(9b+3)^2=

(9b+3)(9b+3)=

9b(9b+3) + 3(9b+3) =

(9b*9b + 3*9b) + (3*9b + 3*3)=

9*9*b*b + 27b + 27b + 9 = 81b^2 + 54b + 9

For this question, you should use the formula (x+y)^2 = x^2+2xy+y^2, which in this case, x=9b and y=3. Feel free to clarify if you don’t understand!

What is edge computing and how does it work Mcq?

Answers

The edge works by myaming sure the mcq gets lined up with the edge and goes straight across the line that is parallel

What is the standard deviation of 7?

Answers

Standard Deviation of 7 is  2.983.

How to interpret  standard deviation?

The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean.

                    Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.

Describe standard deviation using an example.

Think about the following data: 2, 1, 3, 2, 4. The average and the sum of squares representing the observations' variances from the mean will be 2.4 and 5.2, respectively. This means that (5.2/5) = 1.01 will be the standard deviation.

     

       Mean = 7,

Standard Deviation of 7 =   2.983.

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T/F if an > 0 and lim n→[infinity] an + 1 an < 1, then lim n→[infinity] an = 0.

Answers

The expression  aₙ > 0 and lim n → [∞] aₙ + 1 is true.

The term expression in math is defined as a sentence with a minimum of two numbers or variables and at least one math operation.

Here we have given that if an > 0 and lim n→[infinity] an + 1 an < 1, then lim n→[infinity] an = 0.

And we need to check whether the given statement is true or not.

While we looking into the given question, we have identified the following expression,

=> lim n → [∞] aₙ + 1

Here we have also know that the value of aₙ > 0.

When we equate the given expression with zero, we have get the following expression,

=> lim n → [∞] aₙ + 1 = 0

=>  lim n → [∞] aₙ = -1

Here we have given the condition that,  aₙ >0, so

=> lim n → [∞] aₙ = 0

Therefore, the expression is zero.

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Is quadratic equation class 11?

Answers

In class 11 we learn more than the basics of solving quadratic equations.

What is a quadratic equaton?

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

A quadratic equation is of the form ax² + bx + c = 0.

Quadratic equations can be solved using one of three main strategies, factoring, the quadratic formula, or completing the square.

Generally, quadratic equation starts from mid school where we learn all the basics and then we learn to solve word problems using quadratic equations and in high school, we learn quadratic equations of complex numbers.

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What is the standard deviation of 5 5 9 9?

Answers

We calculated the standard deviation for the given data set is 2.

What is standard deviation?

In the statistics, standard deviation is an estimation that implies how far each available data apart from the mean value.

What is the formula for determining standard deviation?

we have data, 5 5 9 9. Let, X is the list of data and X² is the square of data set.

                       X     X²

                       5      25

                        5      25

                        9      81

                        9      81    

sum of X= ∑X = 28

sum of X² = ∑X² =212

Standard deviation = √[∑X²/N - (∑X/N)²]

where N is the number of data and N= 4

Now standard deviation = √[212/4 - (28/4)²]

                                     = 2

hence, standard deviation is 2

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How do you draw an angle ABC?

Answers

Draw a line segment, place the compass point on point A, and draw an arc that intersects the line segment. Next, place the compass point on point B, and draw another arc that intersects the first arc at a point on the line segment. Finally, place the compass on the point where the two arcs intersect without changing the width of the second arc, and draw another arc that intersects the line segment. Finally, connect the point where the second arc intersects the segment to point C.

What is an angle?

When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together.

Why do we measure angles?

Angle measures are helpful not just for academic purposes but also for understanding and using the objects around us. They may aid with spatial knowledge and the link between numbers and measurements.

Follow these steps to draw angle ABC:

The base of the angle should be represented by a section of a line.

With the compass's point on point A, draw an arc that crosses the line segment.

Draw a second arc that crosses the previous arc at a point on the line segment by setting the compass's point on point B.

Place the compass on the intersection of the two arcs and create another arc that intersects the line segment without adjusting the compass's width.

To finish the angle, join point C to the location where the second arc crosses the line segment.

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HELP WHAT IS THIS !! i need help

Answers

Step-by-step explanation:

always remember Pythagoras for right-angled triangles :

c² = a² + b²

c is the Hypotenuse (the side opposite of the 90° angle), a and b are the legs.

this principle must be always fulfilled, otherwise it is not a right-angled triangle.

when your have a triangle problem (particularly for a right-angled triangle) with only side information, there is a high chance that you need to use Pythagoras.

in our case

(2×sqrt(3))² = x² + (sqrt(3))²

4×3 = x² + 3

12 = x² + 3

x² = 9

x = 3

that's all.

FYI : sqrt(x²) has actually 2 solutions : -x and +x, as both are squared equal to x².

but a negative number does not make any sense for general side lengths and similar things. so, the positive solution here is the only valid one.

How do you know if it's AAS or ASA?

Answers

The triangles are congruent if two sets of comparable angles and the side separating them are known to be congruent. Angle-side-angle is the name of this shortened phrase (ASA). Angle-angle-side (AAS), which takes use of the fact that two sets of angles and the excluded side are known to be congruent, is another shortcut.

ASA is another name for angle side angle. According to the criterion, any two angles and the side that is contained between them in one triangle are equivalent to the corresponding angles and the included side of the other triangle if the two triangles are congruent.

According to the Angle Angle Side (AAS) Postulate, two triangles are congruent if two consecutive angles and a non-included side of one triangle are congruent with the equivalent two consecutive angles and a non-included side of another triangle.

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The amount of what used by a washing machine varies directly with the weight of the load being washed. The washing machine uses 28 gallons to wash 7 pounds of clothing. How many gallons of water will the machine use to wash 24.5 pounds of laundry?

Answers

Answer:

140 gallons of water would it use for 10 loads of laundry.

Step-by-step explanation:

w ∝ l

w = kl

k = proportionality constant.

For, w =  28 gallons

l = 2 loads of laundry

Put in the equation;

28 = 2 k

k = 14

Now, when l = 10 loads of laundry, w = ?

w = 14 × 10

w = 140

1) Rewrite f(x)=[x] as a piecewise linear function from 6

Answers

Answer:

[x] is the greatest integer function, which returns the greatest integer less than or equal to x. This can be written as a piecewise linear function as follows:

f(x) =

x-1, if x is not an integer and x>1

x, if x is an integer or x<=1

For example, if x=6, then f(x)=6. If x=6.5, then f(x)=5. If x=0.5, then f(x)=0.

So, the piecewise linear function for f(x)=[x] is:

f(x) =

x-1, if x is not an integer and x>1

x, if x is an integer or x<=1

Solve pls brainliest

Answers

1

y-8=6x+10

y=6x+10+8

y=6x + 18

this follow y = mx+x it means it's a linear

2

y= 5x²+19

it doesn't follow y = mx+x so it's a Non Linear

3

4y = x

it doesn't follow y = mx+x so it's a Non Linear

4

y = 2x + 9

this follow y = mx+x it means it's a linear

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