If b and t are real numbers such that 0<|t|<|b|, which of the following infinite series has sum 1b2 t2

The 2-point midpoint formula is a method for finding the equation of a line that passes through the midpoint of two given points.

The formula for the 2-point midpoint is:

Where (x1, y1) and (x2, y2) are the two given points, and m is the slope of the line.

The slope of line is calculated by (y2-y1)/(x2-x1)

By using the midpoint of two given points, the 2-point midpoint formula eliminates the need for calculating the y-intercept of the line, which can save time and effort. It is particularly useful when working with geometric figures or real-world applications that involve moving objects or changing data. It also helps in predicting the values of future point when we know the past point.

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The y intercepts of the quadratic equation y = x² - 5x + 6 is given by (0 , 6)

and the x intercepts are ( 3 , 0 ) and ( 2, 0 )

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

y = x² - 5x + 6   be equation (1)

On simplifying the equation , we get

y = x² - 2x - 3x + 6

Taking the common factors of the equation , we get

y = x ( x - 2 ) - 3 ( x - 2 )

On factorizing the equation , we get

y = ( x - 3 ) ( x - 2 )

To find the y intercepts , substitute the value of x = 0 , we get

y = ( 0 - 3 ) ( 0 - 2 )

y = ( -3 ) ( -2 )

So , y = 6

Hence , the y intercepts of the equation is  ( 0 , 6 )

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Answer:  A

Step-by-step explanation:  They both go up but they have diffrent patterns

hopes this helps any

Answer:

A.

Step-by-step explanation:

the 'x' slot is going up two and the 'y' slot is going up one every change.

The solution is 40°

The measure of the angle ∠ABE = 40°

Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. The angles that are created when any two parallel lines are intersected by a line (referred to as the transversal) have a relationship. Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles are some of the several pairs of angles that are created at this intersection.

Corresponding angles

When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position

Alternate Interior Angles

Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.

Alternate Exterior Angles

The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.

Consecutive Interior Angles

When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles.

Given data ,

Let the angle be represented as ∠ABE

Now , let the line be EBC and the total angle of a straight line = 180°

And , the measure of ∠CBD = 40°

Since , ∠ABE and ∠CBD are vertically opposite angles ,

The measure of ∠ABE = measure of ∠CBD

Therefore , the value of ∠ABE = 40°

Hence , the measure of vertically opposite angle ∠ABE = 40°

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The discriminant of  quadratic equation 3x^2 + 2x + 1 =0 is -8

We know that the standard form of quadratic equation is ax^2 + bx + c = 0, with a ≠ 0

The discriminant of quadratic equation ax^2 + bx + c = 0 is:

D = b^2 - 4ac

Comparing given quadratic equation 3x^2 + 2x + 1 =0 with ax^2 +bx + c = 0 we get,

a = 3, b = 2 and c = 1

So, the discriminant of given equation would be,

D = b^2 - 4ac

D = 2^2 - 4(3)(1)

D = 4 - 12

D = -8

Therefore, the discriminant is D = -8

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By simple algebra, The number of counters in each box is 2.

Algebra is the study of mathematical symbols and the methods for incorporating them into formulas.

Since algebra is the first math subject most students take where they must deal with variables, complex concepts, and problem-solving abilities, many find it scary.

Given,

counter in Box A = 6y+2

counter in Box b=4y+6

Since there are the same amount of counters in both boxes.

hence

6y+2=4y+6

6y-4y=6-2

2y=4

y=2

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The process of solving the 3 variable with 2 equation is explained below.

The term equation is defined as a relationship between two terms on either side of an equal sign.

Here we have the following steps to solve the 3 variable for two equation is solved accordingly.

First of all we have to take any two equations and solve it for one variable.

And then again we have to take another two pair of equations and solve for the same variable.

Now, we have a system of two equations with two unknown variables.

Then we have to solve the equation by using the appropriate arithmetic operations.

and then substitute it accordingly until all the value of the variable are solved.

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The simplified ratio that compares 5 meters to 100 centimeters is 5: 1 .Option A

Ratio is simply described as the non equal comparison of two numbers, variables, or events.

It shows how many times a number or variable contains another.

The comparison is also based on size.

From the information given, we have;

5 meter to 100 centimeters

It is important to note that;

100 centimeters = 1 meters

Also, 1 meter= 100 centimeters

5 meters = x centimeters

cross multiply

x = 100(5)

Multiply the values

x = 500 centimeters

Then,

5 meters = 1 meter

Hence, the ratio is 5:1

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Answer:

62$

Step-by-step explanation:

Board in square meters = 2×1 = 2 m²

Cost per square meter = $31.00

Total cost = 31×2 = $62.00

Answer:

The cost of the chalkboard  is $27.74

Step-by-step explanation:

right!!

The solution is Option C and Option D.

The exponential function is given by f ( x ) = 2 ( 3 )ˣ

The exponential function is given by f ( x ) = 800 / 4ˣ

What are the laws of exponents?

When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.

The different Laws of exponents are:

mᵃ×mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

( mᵃ )ᵇ = mᵃᵇ

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

m⁻ᵃ = ( 1 / mᵃ )

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

Let the x values be x = { 0 , 1 , 2 , 3 }

Let the y values be y = { 7 , 19 , 31 , 43 }

The equation of line is y = 12x + 7

This is a linear equation

b)

Let the x values be x = { 0 , 1 , 2 , 3 }

Let the y values be y = { 5 , 10 , 15 , 30 }

The equation is a quadratic equation

c)

Let the x values be x = { 0 , 1 , 2 , 3 }

Let the y values be y = { 2 , 6 , 18 , 54 }

The equation is y = 2 ( 3 )ˣ

This is an exponential function

d)

Let the x values be x = { 0 , 1 , 2 , 3 }

Let the y values be y = { 800 , 200 , 50 , 12.5 }

The equation is f ( x ) = ( 800 / 4ˣ )

This is an exponential function

Hence , the exponential equations are solved

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The measure of length of FG is 105 units.

What is bisection?

To determine the roots of a polynomial problem, utilise the bisection method. It splits and separates the interval in which the equation's root is located. The continuous functions intermediate theorem serves as the method's guiding premise.

From the given diagram, since Line DF bisects angle EDG, then -

EF = FG

Given the following parameters -

EF = 9n - 3

FG = 8n + 9

Equating both expressions -

9n - 3 = 8n + 9

9n - 8n = 9 + 3

n = 12

Get the measure of FG -

FG = 8n + 9

FG = 8(12) + 9

FG = 96 + 9

FG = 105

Hence, the line FG measures as 105 units.

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The probability that the other side of the card is red is [tex]\frac{4}{5}[/tex].

The possibility of an event or outcome happening contingent on the occurrence of a prior event or outcome is known as conditional probability. The probability of the prior event is multiplied by the current likelihood conditional, occurrence to determine the conditional probability.

Suppose you choose a red/black card:

The probability of choosing a red and black card is [tex]\frac{1}{6}[/tex].

Now, since this card has one side as red the probability of seeing a red side in this card is [tex]\frac{1}{2}[/tex].

Suppose you choose a red/red card:

The probability of choosing red and red card is 2/6.

Now, since the card has two red sides the probability of seeing red side in this card is [tex]\frac{2}{2}[/tex] .

Considering we see a single side of the card we have the following probability:

[tex]\frac{2}{6} * \frac{2}{2} = \frac{1}{3}[/tex]

The total probability of seeing a red side is [tex]\frac{1}{12} + \frac{1}{3} = \frac{5}{12}[/tex].

The probability that you pick red-red card and see a red side is [tex]\frac{1}{3}[/tex].

So, the conditional probability of both red sides is given as:

[tex]\frac{\frac{1}{3} }{\frac{5}{12} } = \frac{4}{5}[/tex]

Hence, the probability that the other side of the card is red is [tex]\frac{4}{5}[/tex].

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For the expression to be negative (m + p) < 2.

An expression is a group of terms and mathematical symbols which can be evaluated to a given value.

Since we have the expression -2 + (m + p), we need to determine the value of (m + p) for which the value of the expression is negative.

This implies that the value of the expression is less than zero.

So, we proceed as follows.

Since the expression is -2 + (m + p), for it to be negative, it must be less than zero.

So, -2 + (m + p) < 0

⇒ -2 < -(m + p)

Dividing both sides by -1, we have that

-2/-1 < -(m + p)/-1

2 > (m + p)

(m + p) < 2

So, for the expression to be negative (m + p) < 2.

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The length of HI will be;

⇒ 6 units.

The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.

Given that;

HIJK is a square.

The length of KI = 6√2

Now,

Since, HIJK is a square.

Hence, There are all sides are equal.

Let the side of square = x

So, By Pythagoras theorem, we get;

⇒ KI² = HI² + HK²

Substitute the given values, we get;

⇒ (6√2)² = x² + x²

⇒ 72 = 2x²

⇒ x² = 36

⇒ x = √ 36

⇒ x = 6

Thus, The length of HI = 6 units

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The area of the scale drawing is 108 square inches.

I know this because I divided 36 by 13 to get 3. Then I took 27/3 and got 9. So I knew that the scale drawing was 9 by 12 and so then I just multiplied 9 by 12 and got 108

The three steps which Patel could use to solve the quadratic equation include the following:

A. 8(x² + 2x + (2/2)²) = -3 + 8.

B. x = -1 ±√5/8

E. 8(x² + 2x) = -3.

In order to solve the given quadratic equation, we would use the completing the square method as follows;

Separating the variables in the quadratic equation from constant, we have the following;

8x² + 16x + 3 = 0

8x² + 16x = -3

By factorizing the common variables in the quadratic equation from constant, we have the following;

8(x² + 2x) = -3 (step 1).

By completing the squares in the brackets and then balancing the expression on the right-hand side, we have the following;

8(x² + 2x + (2/2)²) = -3 + 8 (step 2).

8(x² + 2x + 1) = -3 + 8

8(x + 1)² = 5

Dividing both sides of the quadratic equation by 8, we have the following;

(x + 1)² = 5

Taking the square root of both sides of the quadratic equation, we have the following;

(x + 1) = ±√5/8

x = -1 ±√5/8 (step 3).

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To graph the equation y = 1x / 2 + (-5), you will need to plot several points that satisfy the equation and then connect them with a line.

To do this, you can pick a few values of x, substitute them into the equation to find the corresponding values of y, and then plot these points on the coordinate plane.

For example, if you choose x = -2, the corresponding value of y is (-2) * (1 / 2) + (-5) = -5.5. If you choose x = 0, the corresponding value of y is (0) * (1 / 2) + (-5) = -5. And if you choose x = 2, the corresponding value of y is (2) * (1 / 2) + (-5) = -4.

You can then plot these points on the coordinate plane and connect them with a line to graph the equation.

Im really sorry that I was unable to provide a picture.  I hope this helped!

Answer:

Graph the line using the slope and y-intercept, or two points.

Slope:

1/2

y-intercept: (0,−5)

x   y

0 −5

2 −4

Step-by-step explanation:

Answer:

Step-by-step explanation:

-2y-10=x-10x

-2(-14) - 10= x - 10x

28 - 10 = x - 10x

18= x-10x

18= -9x

/-9    /-9

-2=x

Each side when you plug in (-2) for x and (-14) for y you get 18.

If, when you plug in the number, you get different numbers for each side, then that means there's a mistake and the answer is wrong.

Hope this helps!

The cheapest way of buying exactly 7 litres with no extra is buying 500 ml bottle for £1.40

The amount of buying 7 litres of orange juice at the cheapest buy is £2.52

500 ml bottle for £1.40

Convert ml to liters:

500 ml = 0.5 liters

Unit rate = 0.5/1.40

= £0.36 per liter

2 litre carton for £2.50

Unit rate = 2/2.50

= £0.8 per liter

2 cartons for £4.50

Unit rate = 2/4.50

= $0.44 per carton

3 litre carton for £3.50

Unit rate = 3 / 3.50

= £0.86 per liter

The cheapest buy per liter of the orange juice is buying 500 ml bottle for £1.40.

Therefore, the cost of 7 liters at the cheapest buy

= £0.36 per liter × 7

= £2.52

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The syntax for using BASE in Excel is "=LN(number,base)" where "number" is the number for which you want to calculate the logarithm and "base" is the base to which the logarithm should be calculated.

For example, if you want to calculate the logarithm of 10 to the base 2, you would use the formula "=LN(10,2)".

The idea is to express the given integer (20) in terms of either the base or the values given (3 and 5).

Next, since we have the multiplication sign, we use the addition law:

The power of the number becomes the product of the log, so we have:

When you have the same base and number, the result is always 1.

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The ratios are not equivalent.

Answer:

25

Step-by-step explanation:

so molly and liza are exercising right?.so 10 push-ups at the same time wich means they do 10 push-ups together and liza push-ups 15 and molly does 40 pushups so. its addition so 10+15=25 so thats the answer.

The statements that are true, based on the multiples of 3 and 6 are:

When a number is a multiple of a smaller number, then all the multiples of that larger number, will be the multiples of the smaller number.

This means that all the multiples of 6 ( including b ) will be multiples of 3 as well because 6 is a multiple of 3.

It is also interesting to note that the difference between the multiples of 3 are also multiples of 3. This means that a - b will result in a number that is a multiple of 3.

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Answer:

Step-by-step explanation: Because all three angles of the triangle must equal to 180 degrees, the two smaller angles of the right triangle must be 45 degrees. This is because a right angle always is 90 degrees and because you know that the other two angles are the same, and it must all equal to 180, the angles must be 45 degrees, 45 degrees, and 90 degrees.

Angle 1: (right angle) 90 degrees

Angle 2: 45 degrees

Angle 3: 45 degrees

For the given Augmented Matrix ,the correct option is :

A) The solution set has exactly one element.

The exact solution is x = -25 , y = 2 and z = 2.

Augmented Matrix:

An augmented matrix is ​​a means of solving simple linear equations. Coefficients and constant values ​​of linear equations are represented as matrices called augmented matrices. Simply put, an augmented matrix is ​​a combination of two simple matrices along columns. If the first matrix has m columns and the second matrix has n columns, then the augmented matrix has m + n columns.

Now, as given the Augmented matrix:

[1 7 3 -5]

[0 0 0 3]

[0 0 1 2]

[0 1 -1 4]

From this system we get:

y - z = 4       --------------------------- (1)

    z = 2

and, z = 3

and, x + 7y + 3z =-5   ---------------- (2)

Now, Solving the equation with z = 2,

    y - 2 = 4

⇒ y = 6

and, putting y = 6 and z = 2

   x + 7× 6 + 3×2 = -5

⇒ x + 42 + 6 = -5

⇒ x +48 = -5

⇒ x = -53

Therefore, x = -53, y=6 and z =2

Now, for z = 3 in equation (1)

   y - 3= 4

⇒ y = 7

Putting y =7  and z =3, we get:

   x + 7 × 7 + 3×3 = -5

⇒ x + 49 + 9 =-5

⇒ x + 58 = -5

⇒ x = -63

Therefore, x = -63, y =7 and z =3

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The number of times which the two computers back up at the same time in twenty four hours as required is; 144.

It follows from the task content that the first computer backs up after every five minutes and the second computer backs up every two minutes.

On this note, the least common multiple of both backup times represents when the two computers back up at the same time.

Hence, since the LCM of 5 and 2 is; 10.

It follows that the two computers back up at the same time after every ten minutes.

Ultimately, the number of times for which they backup at the same time in 24 hours; since 60 minutes = 1 hour is;

= ( 24 × 60 ) / 10

= 24 × 6

= 144 times.

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The value of x is 15 units and the value of y is 12 units from the given figure.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

From the figure, AB is parallel to CD.

∠AOB=∠COD (Vertically opposite angles)

∠OAB=∠ODC (Alternate angles)

By AA similarity ΔAOB similar to ΔCOD

Now, 9/x =y/20 =3/5

9/x=3/5

x=15 units

y/20=3/5

y/4=3/1

y=12 units

Therefore, the value of x is 15 units and the value of y is 12 units from the given figure.

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She will make a total profit of $220. Profits are amounts of money paid to a person with the right of immediate occupation for using the land when no permission has been granted for that use.

Profit is the term used to describe the monetary gain experienced when the revenue from a commercial activity outpaces the costs, costs, and taxes incurred to support the activity in question. There are three primary ways to measure profit. These include operating profit, net profit, and gross profit. Gross profit and operating profit are indicators of how efficiently your company uses its resources to produce its goods and run day-to-day operations.

number of bracelets sold for $12 each=9

number of bracelets sold for $8 each=14

Total profit=9x12+8*14=$220

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In linear equation, Ben is 9 years old currently.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                    Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

Ben's mom = 22 years

Ben is 9 years old currently.

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