the three consecutive term of geometric series be increased by their middle term, then prove that the resulting term will be in Harmonic series.

​

Answer:

the lenght of the rectangle is five more than the width

Answer:

72

Step-by-step explanation:

48÷2= 24

48+24= 72

Hope this helps! :)

Answer:

its 72.00

Step-by-step explanation:

48.00 increased by 50% is 72.00

The increase is 24.00

Answer:

I believe that the answer is C.

Step-by-step explanation:

Because 6 is probably the closest then farthest than 0

We shall use graphical method

Both the graphs of the inequalities have been attached

Answer:

When graphing inequalities:

< or > : draw a dashed line

≤ or ≥ : draw a solid line

< or ≤ : shade under the line

> or ≥ : shade above the line

Question 14

Given inequalities:

\(y \geq x - 3\)

\(y > -4x + 2\)

Treat the inequalities as equations (swap the inequality sign for an equals sign) to find two points on the line to help draw the lines.

\(y \geq x - 3\)

\(x=0 \implies y=-3\)

\(x=3 \implies y=0\)

Plot the points (0, -3) and (3, 0).

Draw a solid straight line through the points.

\(y > -4x + 2\)

\(x=0 \implies y=2\)

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

Plot the points (0, 2) and (1, -2)

Draw a dashed straight line through the points.

Shade the intersecting area above the two lines.

Question 15

Given inequalities:

\(y \geq -3x - 3\)

\(y \geq -\dfrac{1}{2}x + 2\)

Treat the inequalities as equations (swap the inequality sign for an equals sign) to find two points on the line to help draw the lines.

\(y \geq -3x - 3\)

\(x=0 \implies y=-3\)

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

Plot the points (0, -3) and (-2, 3).

Draw a solid straight line through the points.

\(y \geq -\dfrac{1}{2}x + 2\)

\(x=0 \implies y=2\)

\(x=2 \implies y=1\)

 Plot the points (0, 2) and (2, 1)

Draw a solid straight line through the points.

Shade the intersecting area above the two lines.

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Answer:

He was given 26 crayons

Step-by-step explanation:

If he gave 12 and had 14 crayons left, then add 14 + 12 to get your answer

Answer:

x-12=14

he got 26 crayons as a gift.

Step-by-step explanation:

you can find how many he got by taking x (amount he was gifted)

subtract the amount he gave away (12)

then he was left with 14 so

12+14=x

since that isnt an option it is x-12=14 if that makes sense

Answer:

2292.03

Step-by-step explanation:

Start with the formula for continuously compounded interest.

Then substitute all given values in the formula.

Finally, solve for the only variable remaining.

\( A = Pe^{rt} \)

A = future value = $5000

P = principal (deposited amount) = unknown

r = 6.5% = 0.065

t = time = 12 years

\( 5000 = Pe^{0.065 \times 12} \)

\( 5000 = Pe^{0.78} \)

\(5000 = P \times 2.18147\)

\( P = \dfrac{5000}{2.18147} \)

\( P = 2292.03 \)

Answer: $2292.03

Answer:

P = $2366.91

(maybe try answering without a comma)

Step-by-step explanation:

The formula for continuous compounding is:

A = Pe^(rt)

Where:

A = final amount

P = principal amount (initial deposit)

e = Euler's number (approximately 2.71828)

r = annual interest rate (as a decimal)

t = time (in years)

We are given:

r = 6.5% = 0.065 (annual interest rate)

t = 12 years

A = $5000 (final amount)

So we can rearrange the formula to solve for P:

P = A / e^(rt)

Substituting the values:

P = 5000 / e^(0.065*12)

P = $2366.91 (rounded to the nearest cent)

Therefore, you would need to deposit $2366.91 in an account with a 6.5% interest rate, compounded continuously, to have $5000 in your account 12 years later.

The results of the product of 12 and 4 decreased by 15 is 33

Product refers to another term which means multiplication of numbers.

product of 12 and 4

= (12 × 4)

decreased by 15 means 15 is subtracted from the expression

= (12 × 4) - 15

Following the rules of PEMDAS

P = parenthesis

E = exponents

M = multiplication

D = Division

A = addition

S =subtraction

So,

(12 × 4) - 15

= 48 - 15

= 33

Hence, 33 is the product of 12 and 4 decreased by 15

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The value of the product of 12 and 4 decreased by 15 is 33

From the question, we have the following parameters that can be used in our computation:

The product of 12 and 4 decreased by 15

The product of 12 and 4 is expressed as

12 * 4

Evaluate

12 * 4 = 48

When decreased by 15, we subtract 15 from both sides of the equation

using the above as a guide, we have the following:

12 * 4 - 15 = 48 - 15

Evaluate

12 * 4 - 15 = 33

Hence, the product of 12 and 4 decreased by 15 is 33

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The three statements that are true include the following:

A. The radius of the circle is 3 units.

B. The center of the circle lies on the x-axis.

D. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

In Mathematics, the standard form of the equation of a circle is represented by this mathematical expression;

(x - h)² + (y - k)² = r²   .......equation 1.

Where:

h and k represents the coordinates at the center of a circle.

r represents the radius of a circle.

Based on the information provided, we have the following equation of a circle:

x² + y² – 2x – 8 = 0      ......equation 2.

In order to determine the true statements, we would rewrite the equation in standard form and then factorize by using completing the square method:

x² – 2x + y² = 8 = 0

x² – 2x + (2/2)² + y² = 8 + (2/2)²

x² – 2x + 1 + y² = 8 + 1

(x – 1)² + (y - 0)² = 9         .......equation 3.

By comparing equation 1 and equation 3, we have the following:

Center (h, k) = (1, 0)

Radius (r) = 3

Additionally, this line and the center of the given circle lies on the x-axis (x-coordinate) because the y-value is equal to zero (0).

(x - 0)² + (y - 0)² = 3²

x² + y² = 9.

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Answer:

• This student received Met because the student stated that the 2 in Danny’s number is ten times greater than the 2 in Delilah’s number.  The student stated that the 4 in Delilah’s number is one tenth the value of the 4 in Danny’s number.  The student stated that the 7 in Delilah’s number is 100 times the 7 in Danny’s number.

This student received Progressing because the student correctly stated that Danny’s number was ten times bigger.  The student also stated that the 4 in Delilah’s number is ten times smaller.  The student stated the value of the digit 7 without referring to how the values compared.

Step-by-step explanation:

hope this helps :) (:

angle 2 and angle 6 are corresponding angles.

Since the lines crossed by the trnasversal are parallel, corresponding angles are congruent. (equal)

angle 6 = 106°

Answer:

the price of one gallon of milk has increased by 25%.

Step-by-step explanation:

The price of one gallon of milk has increased from $3.24 to $4.05, which is an increase of $4.05 - $3.24 = $0.81. To find the percentage increase, we can divide the amount of the increase by the original price and multiply by 100%. This gives us:

(0.81 / 3.24) * 100% = 25%

Therefore, the price of one gallon of milk has increased by 25%.

The solution is 25 %

The percentage increase in the price of one gallon of milk is given by the equation P = 25 %

What is Percentage Error?

The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.

Percentage error is the difference between the measured value and the true value , as a percentage of the true value

Percentage Error = [ ( | Measured Value - True Value | ) / True Value ]x 100

Given data ,

Let the original price of the milk be A = $ 3.24

Let the increased price of the milk be B = $ 4.05

Let the percentage increase in the price be = P

Now , the equation will be

Percentage Error = [ ( | Measured Value - True Value | ) / True Value ]x 100

Substituting the values in the equation , we get

Percentage increase P = [ ( 4.05 - 3.24 ) / 3.24 ] x 100

On simplifying the equation , we get

Percentage increase P = ( 0.81 / 3.24 ) x 100

Percentage increase P = 0.25 x 100

Percentage increase P = 25 %

Therefore , the value of P is 25 %

Hence , the percentage increase is 25 %

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Answer:

The answer is B. -10 and E. 1

Answer:None

Step-by-step explanation:

The greatest distance that can be filmed by the drone is 6374.5 km. Rounded to the nearest kilometer, 6375 km.

Now, For the greatest distance that can be filmed by a drone with a maximum altitude of 0.12 km, we can use the Pythagorean theorem.

Let's a right triangle with one leg being the radius of the Earth 6378 km and the other leg being the maximum altitude of the drone 0.12 km.

Hence, The hypotenuse of this triangle represents the line of sight from the drone's camera to the horizon.

Hence, By Using the Pythagorean theorem, we can solve for the length of the hypotenuse:

h² = 6378² + 0.12²

h = √40684000.145

h = 6374.5 km

Therefore, The greatest distance that can be filmed by the drone is 6374.5 km. Rounded to the nearest kilometer, 6375 km.

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Answer:

SAS and not similar

Step-by-step explanation:

For the first one, the two triangles are similar (SAS) because the ratio of the two sides is the same (3:5) and the angle in between them is the same.

For the second one, the two triangles are not similar because if we look at the lengths of the sides which is the only information we have of them, we can see that their ratios are not the same.

The required simplification of given function is \(\frac{(x-1)^{2}}{x-2}\) and restriction on domain are x  ≠ 1, 2.

The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0. We can also define special functions whose domains are more limited.

We have,

\(\frac{(x+3)(x-1)}{x-2}\) ÷ \(\frac{x+3}{x-1}\)

\(\frac{(x+3)(x-1)}{x-2}\) × \(\frac{x-1}{x+3}\)

\(\frac{(x-1)^{2}}{x-2}\)

For domain, Function should have solution should not be not defined.

For this, denominator must not equal to zero

Then, x -2 ≠ 0, x - 1  ≠ 0

x  ≠ 2, x  ≠ 1

Thus, option(3) \(\frac{(x-1)^{2}}{x-2}\) x  ≠ 1,2 is correct.

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Answer:

  (b)  (x -1)²/(x -2), x ≠ -3, 1, 2

Step-by-step explanation:

You want to know the domain restrictions and the simplified form of ...

  \(\dfrac{(x+3)(x-1)}{(x-2)}\div\dfrac{x+3}{x-1}\)

We can "invert and multiply", then cancel the common factor from numerator and denominator.

  \(\dfrac{(x+3)(x-1)}{x-2}\div\dfrac{x+3}{x-1}=\dfrac{(x+3)(x-1)}{x-2}\times\dfrac{x-1}{x+3}=\dfrac{(x+3)(x-1)^2}{(x+3)(x-2)}\\\\=\dfrac{(x-1)^2}{x-2}\qquad x\ne -3\)

The values of x that must be excluded from the domain are those values for which any part of this expression is undefined. The expression is undefined when any denominator is zero: at x = 2 (left "factor"), at x = 1 (right "factor"), and at x = -3.

The factor (x +3) doesn't show up in the simplified form, but it is a "hole" in the graph of the original expression—a value of x where the function is not defined.

Here is a summary of what you get at the restricted values:

The simplified form with restrictions is ...

  \(\boxed{\dfrac{(x-1)^2}{x-2},\ x \ne -3,1,2}\)

Step-by-step explanation:

D) The volume of the pyramid is 3 times larger than the prism.

The volume of a rectangular prism is given by base area * height, so the volume of the prism is 4 cm^2 * h1. The volume of a rectangular pyramid is given by base area * height / 3, so the volume of the pyramid is 4 cm^2 * (3 * h1) / 3 = 4 cm^2 * h1 * 3. Hence, the volume of the pyramid is 3 times larger than the prism.

Answer:

Your answer is: D) The volume of the pyramid is 3 times larger than the prism

Step-by-step explanation:

Answer:

it's the second to last one on the right side

Answer: (Not if I'm involved!)

Move the dot to the fourth tick mark to the right of zero.

Step-by-step explanation:

Each of the tick marks represent two, & 8 is the fourth positive multiple of 2. So move the dot to the fourth tick mark to the right of zero, which will represent 8.

Answer:

30 minutes to 40 minutes.

Step-by-step explanation:

From the graph attached,

Distance of Sabrina from her home has been given on y-axis and time taken is on x-axis.

Sabrina's walked 2 miles to reach the library in the duration = 30 - 0

= 30 minutes

She stayed at the library from 30 minutes to 40 minutes (Represented by the straight horizontal line).

Then the third segment represents the journey of Sabrina from library to home.

Therefore, Sabrina was at the library between 30 minutes to 40 minutes.

7/12 of the people who visited the West branch of the store indicated that they had not purchased the product.

Out of the 168 people who visited the West branch of the store,

98 indicated that they had not purchased the product.

Therefore, the fraction of people who visited the West branch and had not purchased the product is:

98/168

Simplifying this fraction by dividing the numerator and denominator by 14, we get:

7/12

Hence, 7/12 of the people who visited the West branch of the store indicated that they had not purchased the product.

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The minimum length of the box to hold the smaller mirror is 10 inches for largest mirror fits in a box that is 18 inches wide by 20 inches long her smaller mirror.

What is proportion ?

In mathematics, proportion refers to the equality of two ratios. Two ratios are said to be proportional if they have the same relative size, meaning they represent the same relationship between quantities.

For example, if we have two ratios, such as 2/3 and 4/6, they are proportional because they represent the same relationship between two quantities. We can say that 2 is to 3 as 4 is to 6, and we can simplify both ratios by dividing the numerator and denominator of each by their greatest common factor, which in this case is 2.

Since the smaller mirror is similar in proportion to the larger mirror, the ratio of their corresponding sides is the same. Therefore, the width of the smaller box is half of the width of the larger box (9 inches is half of 18 inches).

To find the minimum length of the smaller box, we need to use the same ratio of sides. The length of the larger box is 20 inches, so the length of the smaller box should be half of 20 inches, which is 10 inches.

Therefore, the minimum length of the box to hold the smaller mirror is 10 inches.

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The image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin is (-3,4).

In the given question,

We have to find the image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin.

Since we have to find the image after a dilation.

So we learn about it now,

Any scale factor will dilate the image of any coordinate. A specific scale factor can be used to scale the coordinate up or down. To determine the answer, consider the scale factor in the equation and multiply or divide the coordinates of dilation by the appropriate scale factor.

So the given point is (-9,12).

Scale factor is 1/3.

So the image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin is define as

=(-9×1/3,12×1/3)

Simplifying

=(-3,4)

Hence, the image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin is (-3,4).

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The expression is:

So:

It means that the expression is equal to:

The simplified expression is 4/9

The expressions x - 5 and x - 5 gives the equal value for the different values of x, therefore expressions are equivalent.

An algebraic expression is consists of variables, numbers with various mathematical operations,

The given expressions are,

x - 5 and x - 5

To determine the expressions are equivalent,

Since, in the both, the expression x is a variable, and 5 is an integer,

Therefore, for the values of x the value of expression should be equal.

Substitute x = 0,

x - 5 = 0 - 5 = - 5

And

x - 5 = 0 - 5 = - 5

Substitute x = 1

x - 5 = 1 - 5 = - 4

and

x - 5 = 1 - 5 = - 4

Since, for the different values of x the values of expressions are equal.

Hence, expression x - 5 and x - 5 are equivalent.

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I think it might be six, sorry if its wrong, but I hope its right!!

Hope this helps!!!!

love: Deku <3

Answer:

D.

Step-by-step explanation:

4/5 ÷ 3 = 4/5 * 1/3

This is 1/3 of 4/5.

Answer:

red +blue marbles :- 15 +13=28 marbles.

yellow marbles:- 50+28=22 marbles.

probability of yellow marble :- 22/50 i.e 11/25