Meena’s father’s present age is six times Meena’s age. Five years from now she will be one-third of her father’s present age. What are their present ages?

Hello,

[tex] \frac{32 {x}^{8} }{8x {}^{32} } = \frac{4 \times 8 \times x {}^{8} }{8x {}^{32} } = \frac{4x {}^{8} }{x {}^{32} } = 4x { }^{8 - 32} = 4x {}^{ - 24} [/tex]

Answer:

[tex] \red{4 {x}^{ - 24} }[/tex]

Step-by-step explanation:

We know that,

[tex] {a}^{m} \times {a}^{m} = {a}^{m + n} \\ \\ \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} \: \: \: \: \: \: \: \: \: \: \: \\ \\ ({a}^{m})^{n} = {a}^{mn} \: \: \: \: \: \: \: \: \: \: [/tex]

Now using the above knowledge let us solve the sum.

[tex] \frac{32 {x}^{8} }{8 {x}^{32} } \\ ( \frac{32}{8} ) \times ( \frac{ {x}^{8} }{ {x}^{32} } ) \\ 4 \times {x}^{8 - 32} \\ 4 \times {x}^{ - 24} \\ = 4 {x}^{ - 24} [/tex]

Answer:

Step-by-step explanation:

rounded to the nearest cent his answer would be $212.24

The unit conversion for the given values are explained below.

Unit conversion is the process of changing a quantity's measurement between different units, frequently using multiplicative conversion factors.

The following measurements: length, weight, capacity, temperature, and speed are all measured in units.

Some basic unit conversions are-

There are two methods to convert the units

The unit conversion for the following factors are-

i) 1 mm = _ m

Here, conversion is from smaller to larger. So, divide by conversion factor.

  1 mm = (1/100)m

ii) _ mm = 1 m

Here, conversion is from larger to smaller. So, multiply with conversion factor.

  1000 mm = 1 m

iii) 1 cm = _ m

Here, conversion is from smaller to larger. So, divide by conversion factor.

   1 cm = (1/100)m

iv) _ cm = 1 m

Here, conversion is from larger to smaller. So, multiply with conversion factor.

  100 cm = 1 m

v) 1 km = _m

Here, conversion is from larger to smaller. So, multiply with conversion factor.

  1 km = 1000 m.

vi) _ km = 1 m

Here, conversion is from smaller to larger. So, divide by conversion factor.

(1/1000) km = 1 m.

vii) 1 cm = _mm

Here, conversion is from larger to smaller. So, multiply with conversion factor.

   1 cm = 10 mm

viii) _cm = 1 mm

Here, conversion is from smaller to larger. So, divide by conversion factor.

   (1/10) cm = 1 mm.

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The polynomial which can be used to support the idea that the set of polynomials is closed under multiplication is: A. (5x - 1)(3x² + 4x).

A polynomial can be defined as a mathematical expression which comprises intermediates (variables), constants, and whole number exponents with different numerical value, that are typically combined by using mathematical operations such as:

In Mathematics, a set is considered as closed under a multiplication operation, if the multiplication performed on two (2) elements of the set produces an element of the same set.

Note: The exponents of the variables are added when multiplying polynomials in accordance to the rules of exponents.

For option A, we have:

P = (5x - 1)(3x² + 4x)

P = 15x³ - 3x² + 20x² - 4x

P = 15x³ - 23x² - 4x.

For option B, we have:

P = (9x⁻³ - 5)(3x - 17)

P = 27x⁻² - 15x - 153x⁻³ + 85.

In conclusion, we can infer and logically deduce that the polynomial (5x - 1)(3x² + 4x) can be used to support the idea that the set of polynomials is closed under multiplication.

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Answer:

51

Step-by-step explanation:

Translate the problem into an equation and solve the equation.

(x - 9)/6 = 7

x - 9 = 42

x = 51

Answer: 51

Answer:

51

Step-by-step explanation:

Create an equation.

[tex]\frac{(x-9)}{6} = 7[/tex]

Multiply 6 to both sides.

x-9 = 42

Add 9 to both sides.

x=51

To check if this is correct follow the steps given in the question.

51-9=42

42÷6=7

It is correct.

Hope this helps!

Answer:

No solution

Step-by-step explanation:

The equations:

2x – 3y = 10 → equ(1)

–4x + 6y = 20 → equ(2)

Using elimination method, and solving with y, we have:

3( –4x + 6y = 20) → equ(3)

6( 2x – 3y = 10) → equ(4)

Opening the bracket, we have:

–12x + 18y = 60

+12x – 18y = 60

From the above, we can see that both x and y are now eliminated, thereby giving us: 0 = 120 which makes no sense to me as it looks incorrect.

Therefore, there is no solution to the given equation.

I hope this helps

Answer:

One

Step-by-step explanation:

Answer: 5

Step-by-step explanation:

We have the equation of the line is of the form [tex]y=-\frac{1}{6}x+b[/tex].

Substituting in the coordinates (12,3), we get that:

[tex]3=-\frac{1}{6}(12)+b\\\\3=-2+b\\\\b=5[/tex]

Considering the definition of an inequality, the maximum number of tickets that they can buy is 10.

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

An inequality contains one or more unknown values ​​called unknowns, in addition to certain known data.

Solving an inequality consists of finding all the values ​​of the unknown for which the inequality relation holds.

In this case, you know that

So, they want to spend on the purchase of tickets for the merry-go-round a value less than or equal to $36 - $15= $21.

Being "x" the maximum number of tickets that they can buy, the inequality that expresses the previous relationship is

2x≤ 21

Solving:

x≤ 21÷2

x≤ 10.5

Then, the maximum number of tickets that they can buy is 10.

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The length of ED is half the length of AB.

Reasons:

The given parameters are;

In ΔABC, point E is the midpoint of AC

The midpoint of BC is the point D

Segment ED = s

Segment CE = p

Segment EA = r

Segment CD = q

Segment DB = t

Segment ED = s

Segment AB = u

Required:

The expression that represents the value of [tex]s[/tex].

Solution:

CE = 0.5 × AC Definition of midpoint

CD = 0.5 × CB Definition of midpoint

Therefore, we have;

[tex]\frac{CE}{AC} =\frac{CD}{CB} =0.5[/tex]

Therefore, given that ∠C ≅ ∠C, by the reflexive property, we have;

ΔABC is similar to ΔCDE by Side-Angle-Side similarity

Which gives;

[tex]\frac{CE}{AC} = \frac{CD}{CB} = \frac{ED}{AB} =0.5=\frac{1}{2}[/tex]

ED = s and AB = u which gives;

[tex]\frac{ED}{AB}=\frac{s}{u} =0.5=\frac{1}{2}[/tex]

[tex]\frac{s}{u} =\frac{1}{2}[/tex]

Which gives:

[tex]s=\frac{1}{2} *u[/tex]

The expression that represents the value of s is; s = one-half u

Therefore, the length of ED is half the length of AB.

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The question you are looking for is here:

If point E is the midpoint of segment AC and point D is the midpoint of segment BC, which expression represents the value of s? triangle CAB, point E is on segment AC between points A and C and point D is on segment BC between points B and C, creating segment ED, CE equals p, EA equals r, CD equals q, DB equals t, ED equals s, and AB equals u s equals p over q s = one half s equals q over p s = 2u

The missing step in the proof is: D. Statement: XW/UT = XV/UV, Reason: Corresponding sides of similar triangles are proportional.

When two triangles are proven to be similar to each other, their corresponding angles would be congruent while their corresponding sides will be proportional to each other.

In the proof given, both triangles are proven to be similar by the AA similarity theorem, therefore their corresponding sides will be proportional. This implies that: XW/UT = XV/UV.

The answer is D.

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The age of twenty other members is 48 years.

Given that the average age of the members of a country club is 54 years old and if there are ten 36-year-olds, fifty 60-year-olds, and twenty other members all of the same age.

The average is defined as the sum of a set of values divided by n, where n is the total set of values. A mean is another name for an average.

The average age is given by=(Sum of ages)/(Number of members (n))

Let x be the age of other twenty members.

Given A=54  years and n=10+50+20=80

So, now, we will substitute the values in the formula, we get

[tex]\begin{aligned}54&=\frac{10\times 36+50\times 60+20\times x}{10+50+20}\\ 54&=\frac{360+3000+20x}{80}\\ 4320&=3360+20x\end[/tex]

Further, subtract 3360 from both sides, we get

4320-3360=3360+20x-3360

960=20x

Furthermore, we will divide both sides with 20, we get

960/20=20x/20

48=x

Hence, the age of the twenty other members when average age of the members of a country club is 54 years old is 48 years.

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Answer:

[tex]BC=5\sqrt{2}[/tex], [tex]AC=5\sqrt{4}[/tex]

Step-by-step explanation:

In a 45-45-90 relation triangle the two shortest sides will have equal length, meaning:

[tex]BC=5\sqrt{2}[/tex]

To find the hypotenuse we must multiply the shortest side by [tex]\sqrt{2}[/tex], both sides are equal so it doesn't matter which we multiply.

[tex]AC=5\sqrt{2} \sqrt{2} \\AC=5\sqrt{4}[/tex]

Answer:

98.5 degrees

Explanation:

According to the 'angles inside the circle theorem,' do

(101+96)/2 = 98.5

Have a blessed day!

Answer:

Step-by-step explanation:

Formula

<x = 1/2 (arc 1 + arc2)

This is the basic angle formula for the way two chords intersect.

Givens

arc1 = 96

arc2 = 101

Solution

<x = 1/2 (arc1 + arc2)                 Substitute values

<x = 1/2(96 + 101)

<x = 1/2(197)

<x = 98.5

Answer

x = 98.5

Answer:

Option A

Step-by-step explanation:

  In a arithmetic sequence, difference between any two consecutive term is constant.

  a₁ = 9  & d = 7

         t₁ = 9

         t₂ = a₁ + d

             = 9 + 7

             = 16

         t₃ = t₂ + d = 16+ 7

            = 23

        t₄ = t₃ + d

            = 23 + 7

            = 30

        t₅ = t₄ + d

           = 30 + 7

           = 37

9,16,23,30,37,.......

Answer:

Domain: (-∞, ∞)

Range: (-∞, ∞)

Step-by-step explanation:

The domain are the x-values included in the function (the horizontal axis).

The range are the y-values included in the function (the vertical axis).

The two arrows on the ends of the line (pointing upwards and downwards respectively) indicate that the function goes in those direction for infinity. Therefore, if there are an infinite amount of y-values, the range is (-∞, ∞).

While the slope is quite steep, there is still a slope and slowly "expands" the line on the horizontal axis. Because there is no limit to the y-values, the domain will also expand infinitely. Therefore, the domain is also (-∞, ∞).

Answer:

Domain: All real numbers (interval notation: [tex](-[/tex]∞, ∞[tex])[/tex]

Range: All real numbers (interval notation: [tex](-[/tex]∞, ∞[tex])[/tex].

Step-by-step explanation: The domain of a graph is all the x-values where the line touches or will eventually touch.

The range of a graph is like the domain, but it is all the y-values where the line touches or will touch.

In a linear function in the form y = mx + b or ax + by = c, the domain and range will always be "all real numbers" and the interval will always be (-∞,  ∞). This makes sense since a line always goes on forever (unless it's piecewise or an inequality.) So the line will eventually meet every single x and y value on the xy graph.

Answer: 2

Step-by-step explanation:

[tex]\frac{-2-14}{2-10}=\frac{-16}{-8}=\boxed{2}[/tex]

The exponential form of ⁵√13³ is [tex]13^{3/5}[/tex].

Hence, option D) is the correct answer.

This question is incomplete, the complete question is:

Which of the following is equivalent to 5 sqrt 13³ ?.

A) 13^2.

B)13^15.

C)13^(5/3).

D)13^(3/5)

Given the expression; 5 sqrt 13³

This can be represented as; ⁵√13³

To convert from radical form to exponential form, we use apply the radical rule;

[tex]\sqrt[n]{a^m} = a^{m/n}[/tex]

Hence,

[tex]\sqrt[5]{13^3} = 13^{3/5}[/tex]

The exponential form of ⁵√13³ is [tex]13^{3/5}[/tex].

Hence, option D) is the correct answer.

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Answer 1: A and C

Step-by-step explanation:

Use distribution law to see which answer match the equation at the top.

Answer 2: 16q + 4

10q and 6q are like terms

10q + 6q = 16q

+

5 - 1

Answer:

Hello,

Step-by-step explanation:

page 1:

60-36j=12(5-3j) answer C
=6(10-6j) answer A

page 2:

10q+5+6q-1=16q+4=4(4q+1)

page 3:

24j-16=8(3j-2)

page 4:

10h+30+50j=10*(h+3+5j) answer B
=2*(5h+15+25j) answer C

=5(2h+6+10j) not A  nor D

Answer:

blue dot have value of -6 in y inverse axis

Answer:

17,500,000 people

Step-by-step explanation:

70% can be rewritten as 0.7 time 25 million

0.7*25,000,000 = 17,500,000

The amount of material needed for the entire kite is 48 square inches

The given parameters:

KI =6 inches

ET = 8 inches

KT=10 inches

Area of ΔKIT = 17 square inches

Start by calculating the area of the bottom triangle using:

A = 0.5 * Base * Height

This gives

A = 0.5 * 10 * 6

Evaluate

A = 30

The amount of material is

A = 30 + 17

A = 47

Hence, 48 square inches of material is used for the entire kite,  quadrilateral KITE

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The distance between the helicopter and the first home is 369. 87 m

The distance between the helicopter and the first home can be found using sine law,

Therefore,

180 - 72 - 49 = 59 degrees.

Hence,

420 / sin 59 = A / sin 49°

where

A  = distance form the first home to the helicopter.

cross multiply

420 sin 49 = A sin 59°

A = 420 sin 49 / sin 59

A = 316.978023694 / 0.8571673007

A = 369.869339199

A = 369. 87 m

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The equation of constant of proportionality will be y = 2.5x.

Given A 2-column table with 3 rows. Column 1 has entries 2, 4, 5. Column 2 has entries 5, 10, 12.5.

Equation of two variables look like ax+by=c. It can be a linear equation,quadratic equation,cubic equation.

Equation from two points can be found out by putting the values of points in the formula given below:

[tex](y-y_{1})=(y_{2} -y_{1} /x_{2} -x_{1} )*(x-x_{1} )[/tex] in which [tex](x_{1} ,y_{1} ),(x_{2} ,y_{2} )[/tex] are the end points of the line.

Equation of constant proportionality looks like:

k=y/x

in which k is slope which is to be find out according to the same formula as we find in the equation of line.

Slope from (2,5),(4,10) is (10-5/4-2)

=5/2

=2.5

Put the value of k=2.5 in formula of slope.

2.5=y/x

2.5x=y

y=2.5x.

Hence the equation of constant of proportionality is y=2.5x.

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Answer:

C

Step-by-step explanation:

Sin represents opposite/hypotenuse. Thus, when A is the reference angle, 21 is the measure of the opposite side (CB) and 29 is the measure of the hypotenuse (AB).

Cos represents adjacent/hypotenuse. Therefore, when A is the reference angle, 20 is the measure of the adjacent side (AC) and 29 is the measure of the hypotenuse (AB).

The given system of equations has the solution, x = 0, and y = 2, giving the ordered pair (0, 2). Hence, the first option is the right choice.

In the question, we are asked for the ordered pair, which is the solution to the system of equations:

2x + 3y= 6 ... (i)

–3x + 5y = 10 ... (ii).

To solve for the solution to the system of equations, we use the elimination method.

We multiply (i) by 3, and (ii) by 2, and then add the resultant equations to eliminate x as follows:

 6x + 9y = 18 {(i) * 3}

-6x + 10y = 20 {(ii) * 2}

_____________

19y = 38,

or, y = 38/19 = 2.

Substituting, y = 2, in (i), we get:

2x + 3y = 6,

or, 2x + 3(2) = 6,

or, 2x + 6 = 6,

or, 2x = 6 - 6 = 0,

or, x = 0/2 = 0.

Thus, the given system of equations has the solution, x = 0, and y = 2, giving the ordered pair (0, 2). Hence, the first option is the right choice.

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The complete question is:

"Which ordered pair is a solution to the system of linear equations?

2x + 3y= 6

–3x + 5y = 10

(0,2)

(2,0)

(3,2)

(2,3)"

Answer:

x=4.5

Step-by-step explanation:

We know that if all sides are congruent then all angles must also be congruent, therefore you can solve for x with the following equation:

[tex]20x=90[/tex]

Solve

[tex]x=4.5[/tex]

Answer:

1. y = 0

2. f(x) has a horizontal asymptote at y=3/2

I hope this helps and that you can give a brainliest!

Step-by-step explanation:

There is a horizontal asymptote at y = 0 because the degree of the x value in the denominator is greater than the degree of the numerator (since it doesn't exist in the numerator, it counts as 0).

The second question does not have a slant asymptote.

The degree of both numerator and denominator are equal, so the horizontal asymptote is the quotient of the leading coefficients. So, it's 3 divided by 2.

Option D. The most appropriate comparison for the spread is that the interquartile range for town A, 15 degrees is less than that of B.

The inter quartile is solved as Q3 - Q1

This is seen as

For Town A,

30 - 15 = 15 degrees

For town B

40 - 20 = 20 degrees.

Hence we can see that 15 is less than 20, so town A is less than town B. The answer is option D.

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The ratio of the geometric sequence 40[tex]2^{n-1}[/tex] is 2.

Given that geometric sequence is 40*[tex]2^{n-1}[/tex] and we have to find the common ratio of all the terms.

Geometric sequence is a sequence in which all the terms have a common ratio.

Nth termof a GP is a[tex]r^{n-1}[/tex] in which a is first term and r is common ratio.

Geometric sequence=40*[tex]2^{n-1}[/tex]

We have to first find the first term, second term and third term of a geometric progression.

First term=40*[tex]2^{1-1}[/tex]

=40*[tex]2^{0}[/tex]

=40*1

=40

Second term=40*[tex]2^{2-1}[/tex]

=40*[tex]2^{1}[/tex]

=40*2

=80

Third term=40*[tex]2^{3-1}[/tex]

=40*[tex]2^{2}[/tex]

=40*4

=160

Ratio of first two terms=80/40=2

Ratio of next two terms=160/80=2

Hence the common ratio of geometric sequence is 2.

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