The sum of the first 3 terms of a geometric series is 171 and the common ratio is 2/3. What is the first term of this series

Answer:

0.00578034682

Step-by-step explanation:

9/1557

keep on adding .0 to the end of your number.

You will eventually get the answer.

Answer:

173.

Step-by-step explanation:

Answer:

$1560.60

Step-by-step explanation:

PV (1+V)^n

= 1500 (1+2%)² = 1560.6

Answer:146,600,000

1.496*10^8

Step-by-step explanation:

The number of pie each got-

For the given question;

Let the number of pie eaten by Alex be 'a'.

Let the number of pie eaten by Bob be 'b'.

Let the number of pie eaten by Chuck be 'c'.

Then, for the given condition.

If you add Alex’s and bobs pie total together, they ate 22 pies,

a + b = 22 .....eq 1.

Bobs and chucks pies sum to 24.

b + c = 24   .......eq 2

Alex and chucks pie together be 16.

a + c = 16      .......eq 3

Solving equation 1 and 3 by elimination.

Subtract eq 3 from 1.

c = b - 6 .....eq 4

Solving equation 4 and 2.

b = 15

Put in eq 4

c = 9

Put the values of b and c in eq 1.

a = 7

Thus, the number of pie shared by Alex, Bob and Chuck are 7, 15 and 9 respectively.

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The ratios 9:6 and 12:8 does not form a proportion, since the products of the two are not equal.

Given we have two ratios:

9:6 and 12:8

An equation in mathematics that shows that two ratios expressed in fraction form are equivalent is known as a proportion. The rule that says a/b= c/d if and only if ad=bc allows us to assess whether two ratios, a: b and c: d, constitute a proportion.

To determine if 9:6 and 12:8 form a proportion, we use the rule of proportion.

That is, 9/12 = 8/6

If only if 9×6=12×8

Therefore,  9×6=54

and 12×8=96

since these two products are not equal, we have that 9:12 and 8:6 do not form a proportion.

Hence the ratios 9:6 and 12:8 are not in proportion.

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Answer:

I believe cubic function

Step-by-step explanation:

the x^3 represents a cubic function

Inequality - Trevor needs to tutor more than 6 hours in order to make at least $180.

What is inequality?

inequality, A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to. Either questions or theorems can be used to express inequality problems, and both can be solved using methods similar to those used to solve equations. The triangle inequality, for instance, states that the length of the remaining side of a triangle is greater than or equal to the sum of the lengths of any two of its sides. Many of these inequalities, including the Cauchy-Schwarz inequality, are used by mathematical analysis to prove some of its most significant theorems.

Total number of hours = 15

Let the hours spent tutoring French is x

Therefor, hours spent in scooping ice cream = (15-x)

Tutoring French is $15 an hour, total for x hours = 15x

Scooping ice cream is $10 an hour, 10×(15-x)= 150-10x

To make more than $180,

= 15x+ (150-10x)> 180

= 15x+150-10x>180

=15x-10x>180-150

=5x>30

=x>6

So, Trevor needs to tutor more than 6 hours.

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Answer: 4b+6a+3c

Step-by-step explanation:

Answer: $3.55

Step-by-step explanation:

5 oranges * $2.84/4 oranges =

5 oranges * $0.71/1 orange=

5 oranges/1 orange * $0.71=

5/1 * 0.71=

5*0.71=$3.55

[tex]\displaystyle\\Answer:\ (0,-\frac{29}{13} )[/tex]

Step-by-step explanation:

[tex]\displaystyle\\A(-3,-5)\ \ \ \ \ B(10,7) \ \ \ \ \ \lambda=3/10=0.3\ \ \ \ \ C(x_C,y_C)=?\\\\\boxed {x_C=\frac{x_A+\lambda x_B}{1+\lambda} }\ \ \ \ \ \ \ \ \ \ \boxed {y_C=\frac{y_A+\lambda y_B}{1+\lambda} }\\\\x_C=\frac{-3+0.3(10)}{1+0.3} \\\\x_C=\frac{-3+3}{1.3} \\\\x_C=\frac{0}{1.3}\\\\x_C=0\\[/tex]

[tex]\displaystyle\\y_C=\frac{-5+0.3(7)}{1+0.3} \\\\y_C=\frac{-5+2.1}{1.3} \\\\y_C=\frac{-2.9}{1.3} \\\\y_C=-\frac{2.9(10)}{1.3(10)} \\\\y_C=-\frac{29}{13}[/tex]

[tex]\displaystyle\\Thus,\ C(0,-\frac{29}{13} )[/tex]

Using the sine rule we estimate the value of b to be approximately 4.6 units.

The sine law, often referred to as the sine formula, sine rule, or law of sines, is a trigonometrical equation that connects the lengths of any triangle's sides to its sines.

The sine rule states that [tex]\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}[/tex] , where A ,B and C are the three vertices of the triangle and a, b and c are the three side lengths.

Given A = 50° and B = 62 ° and a = 4 .

Now we use the given values to :

[tex]\frac{4}{sin50} =\frac{b}{sin62}[/tex]

or, b = 4.6104...

or , b ≈ 4.6

Hence the length of b is 4.6

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Answer:

I think the answer is d..

As a result of this definition, vertices are intersection of two lines that create an angle as well as the corners of polygons and polyhedra.[tex]f(x)=x^2-2x-10[/tex]  general form to vertex form is y=[[tex](x-1)^{2}[/tex]-9]

The intersection of two or more curves, lines, or edges is known as a vertex in geometry (plural: vertices or vertexes), which is frequently represented by the letters S, P, Q, or R. As a result of this definition, vertices are intersection of two lines that create an angle as well as the corners of polygons and polyhedra.

The point where two rays start or meet, where two line segments join or meet, where two lines intersect (cross), or any other suitable arrangement of rays, segments, and lines that results in two straight "sides" coming together at one location is the vertex of an angle.

[tex]f(x)=x^2-2x-10[/tex]

      = [[tex](x-1)^{2}[/tex]-9]

Use the form, [tex]ax^{2} + bx+c[/tex]

a=1

b=2

c=-10

Consider a vertex form of parabola,

[tex]a(x+d)^{2} + e[/tex]

find the value of d, using the formula d=[tex]\frac{b}{2a}[/tex]

d=[tex]\frac{2}{2*(-1)}[/tex]

simplify the right side,

d= -1

find the value of e, using e= [tex]c-\frac{b^{2} }{4a}[/tex]

e= [tex]-10\frac{2^{2} }{4*(-1)}[/tex]

simplify the right side,

e= -9

substitute the value of a, d and e into vertex form.

y=  [[tex](x-1)^{2}[/tex]-9]

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y = x + 6 and 3x - 3y = -18 will have no solution (parallel lines)

y = −4x + 11 and −6x + y = 11 will have unique solution (intersecting lines)

y = -2x + 5 and 2x + y = -7 will have no solutions (parallel lines)

taking first set of equations,

y = x + 6 and 3x - 3y = -18

rearranging it in the ax+by=c form we get,

x - y = 6

3x - 3y = -18

a1=1, b1= -1, c1= 6

a2=3, b2= -3, c2= -18

now comparing,

1/3 = 1/3 ≠ 6/(-18) 0r -1/3

thus, we get a1/a2=b1/b2≠c1/c2, which satisfies the condition for parallel lines, thus there will be no solution.

taking second set of equations,

y = −4x + 11 and −6x + y = 11

rearranging it in the ax+by=c form we get,

4x+y=11

-6x+y=11

a1=4, b1= 1, c1= 11

a2=-6, b2= 1, c2= 11

4/6 or 2/3≠1/1

thus, we get a1/a2≠b1/b2, which satisfies the condition for intersecting lines, so there will be a unique solution.

taking third set of equations,

y = -2x + 5 and 2x + y = -7

rearranging it in the ax+by=c form we get,

2x+y=5

2x+y=-7

a1=2, b1= 1, c1= 5

a2=2, b2= 1, c2= -7

2/2 or 1/1 =1/1≠ -5/7

thus, we get a1/a2=b1/b2≠c1/c2, which satisfies the condition for parallel lines, thus there will be no solution.

What are intersecting and parallel lines?

Parallel lines never cross, always have distinct ends, and are always spaced at the same distance from one another. Lines that intersect are lines that have a common point and do cross.

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The cost of one ounce of cereal is $0.23

Given:

Amount of cereals a box contain = 24 ounces

Cost of one box = $5.52

Cost of cereal per ounce = Cost of cereal / Amount of cereals in  a box

Cost of cereal per ounce =  $5.52 / 24

Cost of cereal per ounce =  $0.23

An ounce is any of various units of mass, weight or volume derived almost invariably from the ancient Roman unit of measure, the ounce. an avoirdupois ounce is 1⁄16 avoirdupois pound; it is the US and British imperial ounce. 1 ounce is equal to 437.5 grains or 28.349 grams, A US customary fluid ounce is 1⁄16 of a US liquid pint and 1⁄128 of a US liquid gallon or exactly 29.5735295625 mL.

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Answer:

Step-by-step explanation:

The correct answer is option C that is on step 4 - 5 the right side should have been ± i.

A quadratic polynomial function is the one which can be written in the form ax² + bx + c = y where a, b and c are coefficients and x, and y are independent and dependent variables respectively. The quadratic polynomial function is solved using Completing the square method. In this method the quadratic polynomial is converted into the form (x + a)² in order to find the roots of the quadratic polynomial. Here, the steps 1, 2 and 3 are correct but in step 4 after taking square root on both the sides the value of √-1 is not taken as ± i and further it is solved. This becomes an error as we know that the value of √-1 = ± i and if not taken properly errors occur.

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Answer:

Step-by-step explanation:

It could be

ax(x - 4)(x - 3)(x + 3)     where a is some constant ( a could be 1 of course)

For a = 1 the polynomial is

x(x - 4)(x - 3)(x + 3)

In expanded form this is

x^4 - 4x^3 - 9x^2 + 36x

Answer:

i'm sure you would have a amount of 1,200 dollars because there are 12 months in a year and you just got to x times 100 x 12=1,200 Booyah

Step-by-step explanation:

Answer:

4 2/3

Step-by-step explanation:

1 3/4 x 2 2/3

We need to change the mixed numbers to improper fractions

1 3/4 = ( 4*1+3) /4 = 7/4

2 2/3 = ( 3*2 +2) /3 = 8/3

7/4 * 8/3

Rewriting

7/3 * 8/4

Simplify

7/3 *2

14/3

Make this a mixed number

4 goes into 14 4 times with 2 left over

4 2/3

Answer:

[tex]4\frac{2}{3}[/tex]

Step-by-step explanation:

[tex]1\frac{3}{4} *2\frac{2}{3}[/tex]

First, make fractions as improper fractions.

[tex]\frac{7}{4} *\frac{8}{3}[/tex]

Now multiply the answers.

[tex]\frac{56}{12}[/tex]

Now make the answer a mixed number.

[tex]4\frac{8}{12}[/tex]

To write the answer in its simplest form, divide the numerator and denominator by 4.

[tex]4\frac{2}{3}[/tex]

Answer:

0.7

Step-by-step explanation:

From the characteristics of the given cylinder, we have that:

a) The equation is h = 15 - 2r.

b) The volume of the cylinder is of V = πr²(15 - 2r).

c) The values of r should be in the range of 0 < r < 7.5.

The volume of a cylinder of radius r and height h is given according to the following equation:

V = πr²h.

The sum of the height and the diameter is of 15 feet, hence:

h + d = 15.

The diameter is twice the radius, hence:

h + 2r = 15.

For item a, the solution of h in terms of r is:

h = 15 - 2r.

Hence, in item b, the equation is:

V = πr²h.

V = πr²(15 - 2r).

For item c, there are two constraints, as follows:

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<B, <ABC, <CBA

based off the image

The expression is multiplied to give 1728x^6

Index forms are simply defined as the power or exponent of a variable, number or element.

It is also seen as an arithmetic method of writing numbers that are too large or too small into simpler forms.

The rules of exponents are;

Given the expression;

2^3x^3.6^3x^3

We have to determine the product of the index forms

First, we have to multiply the numbers, we have;

2^3 = 2 × 2 × 2 = 8

6^3 = 6 × 6 × 6 = 216

Now, substitute the values

8x³ × 216x³

Multiply through

1728x^3 + 3

1728x^6

Thus, the value is 1728x^6

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Answer:

distance: 11

there are 11 points between 12 and 23, they are:

12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22 and 23.

Step-by-step explanation:

The value of x based on the equation given as 3(4x + 6) = 9x + 12 is -2.

It should be noted that an equation shows that relationship between the variables that are given or illustrated in the data.

The value for x based on the equation will be:

3(4x + 6) = 9x + 12

Open bracket

12x + 18 = 9x + 12

Collect like terms

12x - 9x = 12 - 18

3x = -6

Divide

x = -6/3

x = -2

Therefore, x is -2.

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Answer:

4x - 5y = 30

4x - 5(0) = 30

x1 = 7.5 y1 = 0

Find y-intercept

The y-intercept is where the graph crosses the y-axis. To find the y-intercept, we set x2=0 and then solve for y.

4x - 5y = 30

4(0) - 5y = 30

y2 = -6 x2 = 0

(x1,y1) and (x2,y2)

(7.5,0) and (0,-6)

Solve for x

To solve for x, we solve the equation so the variable x is by itself on the left side:

4x - 5y = 30

x = 1.25y + 7.5

Solve for y

To solve for y, we solve the equation so the variable y is by itself on the left side:

4x - 5y = 30

y = 0.8x - 6

Solution of the given equation -3x =2x² -4,using quadratic formula is (-3 ±√41) /4.

As given in the question,

Given equation is:

-3x =2x² -4

Rearrange the terms in proper order:

2x² + 3x -4 =0

Solve it using quadratic formula

x = (-b ±√b²-4ac)/ 2a

Here compare the given equation with general quadratic equation:

a =2 , b=3 , c=-4

Substitute the values in the quadratic formula we get,

x = [ -3± √(3)² -4(2)(-4)]/2(2)

  = (-3 ± √9+32)/4

  = (-3 ±√41) /4

Therefore, Solution of the given equation -3x =2x² -4, using quadratic formula is (-3 ±√41) /4.

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Answer:

f= -g/3

Step-by-step explanation: