The sum of the first three terms of a G.p is half its sum to infinity.find the positive common ratio

The quadratic equation 8x² + 16x + 3 = 0 can be solved by using the quadratic formula.

The given quadratic equation is : 8x² + 16x + 3 = 0

Comparing this equation with  ax² + bx + c = 0 we get :

a = 8 , b = 16 and c = 3

Now we will use the quadratic formula:

[tex]{\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}}[/tex]

Now we will substitute the values in this formula to find the values of x that satisfy the quadratic equation.

[tex]{\displaystyle x={\frac {-16\pm {\sqrt {16^{2}-4\times8\times3}}}{2\times8}}}\\\\{\displaystyle x={\frac {-16\pm {\sqrt {160}}}{16}}}\\\\[/tex]

The values for x that satisfy the equation are the roots or zeros of both expressions on the left-hand side of the equation. In a quadratic problem, there can only be two possible solutions.

A problem is said to have a double root if there is only one solution. One real double root, two complex solutions that appear to be complex conjugates of one another, two real solutions, or two real solutions if all the coefficients have real values are the only options.

Hence the values of x are : [tex]-\frac{4-\sqrt{10}}{4}[/tex] and [tex]-\frac{4+\sqrt{10}}{4}[/tex].

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Answer: -8

Step-by-step explanation:

Assuming that [tex]x[/tex] is the wind speed and [tex]y[/tex] is the wind chill, we can set [tex]x=58[/tex].

[tex]y=-0.36(58)+12.6 \approx -8[/tex]

The equation that models the balance y after x​ months is: y = -130x + 1200.

Month    Balance

0             1200

6            420

8             160

Hence,

m = (y2 - y1)/(x2 - x1)

First coordinate:

m = (420 - 1200)/(6 - 0)

m = -780 /6

m = -130

Second coordinate;

m = (160 - 420)/(8 - 6)

m = -260/2

m = -130

The formula for equation in slope intercept is

y = mx + c

where;

m = slope

c = y-intercept

So, equation is;

y = -130x + 1200

Therefore the equation is y = -130x + 1200.

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Answer:

A. 5/3

Step-by-step explanation:

The line is in a positive trend we can see it because when we read it from left to write we can see it go up. The point where we start is 5 levels down from the second point  3 units to the left.

We can model this using  rise/run

Rise = 5

Run = 3

5/3

Michael will be spending the cost of $ 15.652 on the Furry Fabric.

Given, that Michael is dressing up as Maggie,

He is making his costume and he needs 8.6 yards of furry fabric

The fabric costs $1.82 per yard.

So, as he needs 8.6 yards of fabric and each yard of that fabric costs him $1.82.

1 yard of Furry Fabric = $1.82

8.6 yards of Furry Fabric = $1.82 × 8.6

8.6 yards of Furry Fabric = $ 15.652

Hence, Michael will be spending the cost of $ 15.652 on the fabric.

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Answer:

[tex]p+p+2=20[/tex]

Step-by-step explanation:

This is what my math teacher told us, so I don't know try this.

Step-by-step explanation:

p + j = 20

j = 2p + 2 --> -2p + j = 2

[tex] \binom{1 \: 1}{ - 2 \: 1} \: \binom{20}{2} = \binom{p}{j} [/tex]

The expression that represents "10 subtracted from the quotient of 3 and a number" is D. 3 over n - 10.

An expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

Let the number be n

The expression will be:

= 3/n - 10

Therefore, the correct option is D.

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The total 18 numbers such  that n<150 exist, if the sum of the numbers of factors of N and N^2 is 34

Let me give you an example. 12. Both 2- 2 times and 3- 1 times are factors of 12.

Factors in total (2+1)*(1+1)=6

It will have 2- 4 times and 3-2 times for 122.

15 total factors of 5*3

Situation 1: N = xy

attempting a reverse strategy for N*N Factors in 35=5*7 are x-4 times and y-6 times.

Regarding N-x-2 and Y-3 timings.

There are a total of (2+1)*(3+1)=12 factors.

Situation 2

Since N2 has 34 factors if N2 is raised to the power of 34, there are 17 factors for N.

Consequently, 17+1 = 18 factors in total.

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Step-by-step explanation:

that simply means we use one equation to express one variable by the other, and then we use that identity in the second equation (substituting one variable by the expression of the other variable. and then we solve for that remaining variable.

finally we use one of the original equations to solve for the second variable.

4x + y = 19

so, that gives us

y = 19 - 4x

we use that now in the second equation :

6x + 7(19 - 4x) = 1

6x + 133 - 28x = 1

-22x + 133 = 1

-22x = -132

22x = 132

x = 6

now, let's use e.g.

4x + y = 19

4×6 + y = 19

24 + y = 19

y = -5

Answer: $4

Step-by-step explanation: we know he spent 28 dollars in total and 16 of those was on a pair of pants so we can subtract 16 from 28 to get 12

we also know he bought 3 shirts in total and because 12/3=4 each shirt must have cost 4 dollars.

We can check the answer by combining the price of the shirts (12)

with the price of the pants (16) because 12+16=28 we know the cost of each shirt has to be $4.

Answer:

Each shirt was 4 dollars.

Step-by-step explanation:

28 - 16 = 12. 12 divided by 3 = 4.

Yes this question can be proven by mathematical induction

What do you mean by induction in mathematics?

For each and every natural number n, a statement, theorem, or formula can be proved using the mathematical induction technique. By generalizing this into the "Principle of Mathematical Induction," which we would utilize to demonstrate any mathematical assertion.

Here, n ≥ 1

1/1.2 + 1/2.3 + 1/3.4 + .............. + 1/n(n +1)

We employ the idea of Sigma here.

S/1/r(r + 1) { r = 1 to n }

Sigma [1/(r + 1) - 1/(1/r)] { r = 1 to n }

put r = 1 \s1/1 - 1/(1 + 1) = 1 - 1/2

put r = 2 \s1/2 - 1/(2 +1) = 1/2 - 1/3

put r = 3 \s1/3 - 1/(3 +1) = 1/3 - 1/4

........................................................... put r = n 1/n - 1/(n + 1)

after adding

Sigma = [1/(r+1) - 1/(1/r)] {r = 1 to n } = 1 -1/2 + 1/2 -1/3 + 1/3 - 1/4 + ............1/n - 1/(n +1)

= 1 - 1/( n +1) = n/( n +1)

Consequently, 1/1.2 + 1/2.3 + 1/3.4 +... 1/n(n + 1) = n/(n + 1).

so it proved

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Answer:

5 hours

Step-by-step explanation:

$65 - $15 = $50

$50/$10 = 5

The price of the share 3 years later, given the increase in value, can be found to be $43.29

The value of the Southside stock sold was $ 37 at the current age. Three years later, this value had increased by 17 %.

This means that the price of the share 3 years later would be:

= Share price currently x ( 1 + increase in value)

= 37 x ( 1 + 17 % )

= 37 x 1. 17

= $ 43. 29

The price is  $43.29

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aₙ=a+(n-1)d is the formula can be used to find the nth term of the sequence.

Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

Given sequence is 5,9,13,17,21

Five comma nine comma thirteen comma seventeen comma twenty one.

We need to find the nth term of the sequence.

Firstly we need to find the sequence is AP or GP.

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same.

so 9-5=4,

13-9=4

Hence the sequence is a Aritmetic sequence.

In arithmetic sequence the nth term can be find by using the formula

aₙ=a+(n-1)d

where a is first term and d is common difference.

Hence aₙ=a+(n-1)d is the formula can be used to find the nth term of the sequence.

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The commission that thereal estate agency gets is $16885.

The commission that the agent gets is $76750

The selling price for a house = $ 307,000

The commission rate for real estate agency = 5.5 %

The commission rate for the agent = 25 %

So, the commission which real estate agency gets:

= 5.5 % of $307,000

= 0.055 × $ 307,000

= $16885

The commission which agent get:

= 25% of $ 382,000

= 0.25 × $ 307,000

= $76750

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According to the solving the area of the square is 68.0625.

As is common knowledge, a square is a four-sided, two-dimensional figure. It is also referred to as a quadrilateral. The total quantity of unit squares forming a square is referred to as the square's area. In other words, it is described as the area that the square takes up.

The box formed after cutting the square from each corner will have the dimensions as,

length = 104 - 2x, width = 39 - 2x, height = x.

∴ volume of the box = length × width × height

∴ v = (104 - 2x)(39 - 2x)(x) -----(i)

∴ v = (104 - 2x) (39x - 2[tex]x^{2}[/tex])

∴ v = 104(39x - 2[tex]x^{2}[/tex]) -2x(39x - 2[tex]x^{2}[/tex])

∴ v = 4056x - 208[tex]x^{2}[/tex] - 78[tex]x^{2}[/tex] + 4[tex]x^{3}[/tex]

∴ v = 4[tex]x^{3}[/tex] - 286[tex]x^{2}[/tex]  + 4056x

let f(x) =  4[tex]x^{3}[/tex] - 286[tex]x^{2}[/tex]  + 4056x  -----(ii)

To, find x for which f(x) is maximum,

⇒we should apply second derivative test ,

According to this test, first we should find critical points at which f'(x) = 0.

then if f''(x) < 0 for that critical point then f(x) is maximum at that critical point.

∴ let us consider, f'(x) = 0.

now, f(x) =  4[tex]x^{3}[/tex] - 286[tex]x^{2}[/tex]  + 4056x

⇒ f'(x) = 12[tex]x^{2}[/tex] - 572x + 4056.  -----(iii)

⇒ f'(x) = 4(3[tex]x^{2}[/tex] - 143x + 1014)

⇒ f'(x) = 0.

⇒  f'(x) = 4(3[tex]x^{2}[/tex] - 143x + 1014) = 0

⇒ x = (-b ± [tex]\sqrt{b^{2} - 4ac }[/tex])/2a    ; where a = 3, b = -143, c = 1014.

∴ x = (-(-143) ± [tex]\sqrt{(-143)^{2} -4(3)(1014)}[/tex])/2×3

∴ x = (143 ± [tex]\sqrt{8281}[/tex])/6.

∴ x = [tex]\frac{143 + 91}{6}[/tex]  , x = [tex]\frac{143 - 91}{6}[/tex]

⇒ x = 39, 8.25

the square of length 8.25 inch should be cut from each side to det contained with the maximum volume.

Area of the square is = [tex]x^{2}[/tex] = [tex]8.25^{2}[/tex]

∴ Area = 68.0625

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Answer:

11/36 = 0,305556 = 30,5556%

Step-by-step explanation:

5/6 * 5/6 = 25/36

36/36 - 25/36 = 11/36

Answer:

A right-angled triangle

The information about the graph of the relationship that is given is: E. y-intercept and a point that is not an intercept.

In Mathematics, the y-intercept of any graph such as a linear, quadratic, trigonometric function, generally occurs at the point where the value of "x" is equal to zero (x = 0).

Mathematically, the slope-intercept form of a straight line is generally modeled or represented by this mathematical expression;

y = mx + c

Where:

In this context, we can reasonably infer and logically deduce that the total number of pages (y-intercept) which is equal to 180 is an information that was provided, as well as the number of hours (666 hours), which represents a data point on the x-coordinate of the graph.

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The equation for the nth term of the arithmetic sequence 4, 7, 10, 13 is aₙ = 3n + 1

Arithmetic sequence can be represented with the formula as follows:

aₙ = a + (n - 1)d

where

Therefore, let's write the equation for the nth term of the arithmetic sequence 4, 7, 10, 13..

a = 4

d = 7 - 4 = 3

Therefore,

aₙ = 4 + (n - 1)3

aₙ = 4 + 3n - 3

aₙ = 3n + 4 - 3

aₙ = 3n + 1

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Answer: final answer = 3/8

Step-by-step explanation:
it says 1/8 + 1/4. before you can add them you have to make sure that both fractions have the same denominator first you have to make both of the bottom denominators the same so its 1/8+2/8.
1/8+2/8=3/8

If repetition is allowed then the required passwords generated are 17576.

If repetition is not allowed then the required passwords generated are 15600.

Given that;

We need to get 3 letter passwords using a through z by two case;

(a) If repetition is allowed

(b) If repetition is not allowed

Case (a): If repetition is allowed.

       The total number of letters from a through z are 26

   ⇒ The total number of 3 letter passwords made are;

        = 26³

        = 26 * 26 * 26

        = 17576

If repetition is allowed then the required passwords generated are 17576.

Case (b): If repetition is not allowed.

      ⇒ The total number of 3 letter passwords made are;

         = 26 * 25 * 24

         = 15600

If repetition is not allowed then the required passwords generated are 15600.

Therefore,

If repetition is allowed then the required passwords generated are 17576.

If repetition is not allowed then the required passwords generated are 15600.

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Answer: 264.5

Step-by-step explanation:

(-81.7) + 346.2

346.2 - 81.7 = 264.5

The factored form of the given algebraic expression by factoring out the Greatest Common Factor is 6y^2 (3y^2 + 4y + 1). Option A is correct.

We are given an algebraic expression:

18y^4 + 24y^3 + 6y^2

We need to factorize by factoring out the Greatest Common Factor.

In the given algebraic expression, we can see that;

6 is the Greatest Common Factor of 18, 24, and 6.

y^2 is the Greatest Common Factor of y^4, y^3 and y^2.

So, we will take the common 6y^2 from the given expression;

18y^4 + 24y^3 + 6y^2

= 6y^2 (3y^2 + 4y + 1)

So, option A is correct.

Thus, the factored form of the given algebraic expression by factoring out the Greatest Common Factor is 6y^2 (3y^2 + 4y + 1). Option A is correct.

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The street was 900m long when the speed is 15m/s and, the time is 60 seconds.

To calculate speed, divide the distance traveled by the time it took to complete the voyage, so speed = distance divided by time. To determine the distance, multiply the speed by the passage of time. These equations can be reduced as s=d/t, where s represents speed, d represents distance, and t represents time.

Distance divided by time equals speed. Distance = time * speed

To solve for speed or rate, utilize the speed formula, s = d/t, which implies speed equals distance divided by time. To solve for time, utilize the time formula, t = d/s, which implies time equals distance divided by speed.

Given,

Speed of the biker who travels down the street=15m/s

Time taken=60seconds

Distance=?

We know that,

Distance=Speed× Time

Distance=15×60

Distance=900m

Therefore, the street was 900m long

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The price of a pack of balloons is 4. 39

The price of a pack of party favors is 0. 36

We have that;

Let the cost of balloons be x

Let the cost of party favors by y

From the information given, we have that;

3x + 4y = 14. 63   (1)

2x + 4y = 16. 03  (2)

Now, let's make 'x' the subject from equation (1)

x = 14. 63 - 4y/ 3  (3)

Substitute in equation (2)

3( 14. 63 - 4y/ 3) = 16. 03

expand the bracket

43. 69 - 12y /3 = 16. 03

cross multiply

43. 69 - 12y = 48. 09

collect like terms

- 12y =  - 4. 4

make 'y' the subject

y = 0. 36

substitute in equation (3)

x = 14. 63 - 4(0. 36)/ 3

x = 13. 1/ 3

x = 4. 39

Hence, the prices are 4. 39 and 0. 36 respectively.

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Answer:

The second option.

Step-by-step explanation:

We can figure this out by going down each option and checking if it works and is arranged from least to greatest.

The first option provides the numbers -3.5, -1/4, 2, 1/3 in that order.

This does not work because 1/3 is less than 1 which is less than 2. 1/3 should come before 2.

The second option provides the numbers -3.5, -1/4, 1/3, 2.

This option does work, because -3.5 is less than -1/4, -1/4 is less than 1/3 because it is negative, and 1/3 is less than 2.

If we look at this on a number line, the numbers that are smaller will appear farther to the left on the number line.

The equation that passes (6,0) and (3,4) is -3y=4(x-6)

What are the different forms of straight lines ?

The following information about the straight line is required if we wish to obtain the equation for it.

1. The y-intercept and slope

2. Two-point and slope

3. Two things.

4. the intersection of the x- and y-axes

the straight line that passes through (6,0) and (3,4).

The equation can be expressed in a point-slope form which is ,

y/x-6=4/-3

∵ -3y=4(x-6)

Hence,

The equation that passes (6,0) and (3,4) is -3y=4(x-6)

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