Kelly started running around a track two laps before Anne. They are running at the same speed. Write an equation to find the number of laps, y Kelly

has run given the number of laps, X Anne has run.



1. X= 2y

2. Y= 2x

3. X= y+2

4. Y= x+2

To prove the inverse :

You assemble the functions (that is, insert x into one function, plug that function into the suggested inverse function, then simplify) and check that you end up with simply "x" to establish (or refute) that two functions are the inverses of one another. The functions are inverses if you get x; otherwise, they are not.

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On solving the provided question we cans ay that - the value of the following exponent is

Exponentiation, often known as "b raised to the nth power," is a mathematical operation denoted by the symbol bn that involves two numbers: a base number, b, and an exponent, or power, n. Exponents show how many times a number has been multiplied by itself. As an illustration, 2-3 (written as 23) denotes: 2 x 2 x 2 = 8. 23 is not equivalent to 2 + 3 = 6. Recall that an integer raised to the power of one equals itself. A approach to express huge numbers as powers is through the use of exponents. Exponent, then, is the quantity that indicates how many times a number has been multiplied by itself. As an illustration, 6 is multiplied by 4 to provide 6 x 6 x 6 x 6. It may be expressed as 64. 4 is where

here,

= [tex]10^2 X 10^-3[/tex] X 32

= 100 X 1/1000 X 32

=1/10 X 32

=3.2

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Answer:

Answer:

Foci: (±5, 0)

Vertex: ( ±4 , 0)

Eccentricity: e = 5/4

Step-by-step explanation:

Hyperbola:

Write the equation of hyperbola in the form,

\boxed{\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1}

a

2

x

2

−

b

2

y

2

=1

9x² - 16y² = 144

Divide the entire equation by 144,

\begin{gathered}\sf \dfrac{9x^2}{144}-\dfrac{16y^2}{144}=\dfrac{144}{144}\\\\\\ \dfrac{x^2}{16}-\dfrac{y^2}{9}=1\\\\\\\dfrac{x^2}{4^2}-\dfrac{y^2}{3^2}=1\end{gathered}

144

9x

2

−

144

16y

2

=

144

144

16

x

2

−

9

y

2

=1

4

2

x

2

−

3

2

y

2

=1

a = 4 and b =3

Eccentricity: e

\boxed{e=\sqrt{1+\dfrac{b^2}{a^2}}}

e=

1+

a

2

b

2

\begin{gathered}\sf = \sqrt{1+\dfrac{9}{16}}\\\\=\sqrt{\dfrac{16}{16}+\dfrac{9}{16}}\\\\=\sqrt{\dfrac{25}{16}}=\sqrt{\dfrac{5*5}{4*4}}\\\\\\=\dfrac{5}{4}\end{gathered}

=

1+

16

9

=

16

16

+

16

9

=

16

25

=

4∗4

5∗5

=

4

5

Foci:

(ae, 0) & (-ae , 0)

\begin{gathered}\sf \left(4*\dfrac{5}{4},0 \right) \ ; \ \left( -4*\dfrac{5}{4},0 \right)\\\\\\(5, 0) \ ; \ (-5,0)\end{gathered}

(4∗

4

5

,0) ; (−4∗

4

5

,0)

(5,0) ; (−5,0)

Vertex of hyperbola:

The vertex of the hyperbola is a point where the hyperbola cuts the axis. (-a , 0) ; (a , 0)

Vertex : (-4 , 0) ; (4 , 0)

What the height would need  for this curve to be a density curve is; One-half

The criteria for a curve to be a density curve is as follows;

1. The curve must always be non-negative. This tells us that the y-value of the curve must be greater than or equal to 0 at every given point.

2. The area under the curve must always be equal to 1.

Now, we are told that the curve starts at (-2, 0) and then goes to (5, question mark), and then goes down to (6, 0),.

This means that the area under the curve will be a trapezoid that has a height of question mark and then bases of length 3 (from -2 to 5) and length 1 (from 5 to 6).

The area of this trapezoid will be equal to the sum of the bases times the height divided by 2, or:

Area = ((3 + 1) × question mark)/2

Since the area under the curve must be equal to 1, we can set up the equation:

1 = ((3 + 1)  ×  question mark) / 2

Solving for question mark, we will:

The question mark = 2/4

The question mark = 1/2

Therefore, we can conclude that the height of the curve is  1/2

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Answer:

15

Step-by-step explanation:

to determine the number of plants per row, take the square root of 225

sqrt(225) = 15

There should be 15 plants per row

Answer:

Step-by-step explanation:

Since the formation of the strawberry plants should represent a square, it implies that the dimensions of the formation (i.e length and breadth) must be equal.

To achieve this, we have to calculate its square root as the formula for the area of any square is given as (side)^2.

Now, [tex]\sqrt{225}[/tex] = 15

implies that each as well as each column will contain 15 strawberry plants  

Answer:

0

Step-by-step explanation:

625 / 25 = 25

55g + 25 = 25

55g = 25 - 25

55g = 0

g = 0/55

g = 0

Answer:

[tex] \sf \: g = 0[/tex]

Step-by-step explanation:

Given equation,

→ 55g + 25 = 625 ÷ 25

Now the value of g will be,

→ 55g + 25 = 625 ÷ 25

→ 55g + 25 = 25

→ 55g = 25 - 25

→ g = 0 ÷ 55

→ [ g = 0 ]

Hence, the value of g is 0.

Function: This means that 2.7 x 10^3 is about 201.593 times smaller than 5.481 x 10^5. This can also be expressed as 0.049 or 4.9%.

A function is a mathematical relation between two sets of values, usually between an input and an output. It can be thought of as a machine that takes a certain input and produces a certain output.

2.7 x 10^3 is about 0.049 times smaller than 5.481 x 10^5.
To determine this, we can divide the two numbers. 5.481 x 10^5 divided by 2.7 x 10^3 equals about 201.593.
This means that 2.7 x 10^3 is about 201.593 times smaller than 5.481 x 10^5. This can also be expressed as 0.049 or 4.9%.

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Answer:

  1/2log₂(a-1) -log₂(9)

Step-by-step explanation:

You want the expanded form of log₂(√(a-1)/9).

The relevant rules of logarithms are ...

  log(a^b) = b·log(a)

  log(a/b) = log(a) -log(b)

The rules are applicable for any base.

  [tex]\log_2{\dfrac{\sqrt{a-1}}{9}}=\log_2{(\sqrt{a-1})}-\log_2{(9)}=\boxed{\dfrac{1}{2}\log_2{(a-1)}-\log_2{(9)}}[/tex]

Answer:

1. 30 − 6q

3. −7d − 14 OR -7d + -14

4. = −4x + 24y

5. a) −3b − 15           b)−12x + 24

6. For the first answer to this question: 3x + 3y OR 3x = t

For the second answer to this question: 3x = t and it costs 15 dollars in total with x = 5.

Answer:

26 - 11√5

Step-by-step explanation:

(4√5-3)(√5-2)

= 4√5 (√5-2) -3 (√5-2)

= 4√5 √5 + 4√5 ⋅ -2 -3 (√5-2)

= 4√5 √5 + 4√5 ⋅ -2 -3√5 -3 ⋅ -2

= 26 - 11√5

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The mean number of rooms = 6

We know that the formula for the mean.

mean = sum of all observations / total number of observations

First we find thr total number of rooms, from given frequency table.

Number of Rooms        Frequency          Total number of rooms

           4                             4                              16

           5                             7                              35

           6                             10                            60

           7                             12                             84

           8                             5                              40

           9                             2                               18

So, the total number of rooms of 40 houses in a town would be,

16 + 35 + 60 + 84 + 40 + 18 = 253

And the total number of houses = 40

Using above formula of mean,  the mean number of rooms would be,

x = 253/40

x = 6.325

Therefore, on an average there are 6 rooms in each house.

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Answer:

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

Step-by-step explanation:

[tex]\frac{2}{3}[/tex][tex](t-2)\\[/tex]
=> [tex](\frac{2}{3} * t ) + (\frac{2}{3} * -2)[/tex]
=> [tex]\frac{2t}{3} + (-\frac{4}{3})[/tex]
=> [tex]\frac{2t-4}{3}[/tex]

Hope you understood!!

Answer:

2.7n + 6.6 or 6.6 + 2.7n

Step-by-step explanation:

Algebraic Expressions are just like Numerical Expressions but instead of numbers, alphabets are used, these alphabets can also be used as variables. (BODMAS rule applies to Algebraic Expressions as well.)

Eg. 45x + 31x(2) = 45x + 62x = 107x

Given from the question:

[tex]0.3(9n + 22) \\ = 2.7n + 6.6 \: or \: 6.6 + 2.7n[/tex]

Answer: The odds against an event occurring are the ratio of the probability that the event will not occur to the probability that the event will occur. To find the odds against an event, you can use the formula:

Odds against = (1 - probability of event occurring) / probability of event occurring

In this case, the event is that exactly 5 cars will pass over the bridge in a 4-minute period. The probability that this event will occur is 0.16. Therefore, the odds against this event occurring are:

Odds against = (1 - 0.16) / 0.16

= 0.84 / 0.16

= 5.25

So, the odds against exactly 5 cars passing over the bridge in a 4-minute period are 5.25 to 1.

It means that there are 5.25 times more likely that it will not happen compare to happen.

Step-by-step explanation:

The coefficient of [tex]x^{2}[/tex] in [tex](2x^{2}-3x-4)-(5x^{2}+6x-7)[/tex] is -3.

A coefficient is a multiplicative factor in a polynomial, series, or expression in mathematics. It is typically a number, although it can also be any expression (including variables such as a, b and c). They may also be referred to as parameters if the coefficients are variables in and of themselves. The coefficient in an expression that is not related to any variables is called the constant coefficient (also known as constant term or free coefficient).

Given equation,

[tex](2x^{2}-3x-4)-(5x^{2}+6x-7)[/tex]

= [tex]2x^{2}-3x-4-5x^{2}-6x+7[/tex]

= [tex]-3x^{2}-9x+3[/tex]

Hence, coefficient of [tex]x^{2}[/tex] is -3.

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20 dodgeballs have been pumped up by Ttaloc.

Ttaloc has 36 additional pumped-up balls.

The complete ball's original number is 14.

The relationship between two or more numbers is expressed by the ratio. It displays the frequency of how often one value is encapsulated by another value (s).

The number of dodgeballs Ttaloc pumped up = (5/14) x 56 = 20

The number of other balls Ttaloc pumped up = (9/14) x 56 = 36.

A ratio in mathematics demonstrates how many times one number is present in another.

A ratio can have any number of quantities, such as counts of people or things or measurements of length, weight, time, etc. Both numbers must be positive in most situations.

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The correct answer is   A.  {(-8,-14), (-7,-12), (-6,-10), (-5,-8)} which  sets of ordered pairs represents a function.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

Here, we have,

sets of ordered pairs represents a function are,

{(-8,-14), (-7,-12), (-6,-10), (-5,-8)}

{(-4,-14), (-9,-12), (-6,-10), (-9,-8)}

{(8,-2), (9,-1), (10,2), (8,-10)}

{(-8,-6), (-5,-3), (-2,0), (-2,3)}

Now, we know that,

A function has no repeated values of the independent variable.

So, we have now,

Only choice A meets that requirement.

And,

B: (-9, 12) and (-9, 8) both have -9 as a first value; not a function.

C: (8, -2) and (8, -10) both have 8 as a first value; not a function.

D: (-2, 0) and (-2, 3) both have -2 as a first value; not a function.

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The solution of the fraction 3/4 is 0.75

The term fraction is defined as represent the parts of a whole or collection of objects

Here we have given the fraction 3/4.

Now, we have to do the following steps in order to find the decimal equivalent for the fraction.

First of all we just need to divide the numerator by the denominator.

Then we get the fraction is 3/4 which means we need to divide: 3 ÷ 4.

The division process is illustrated on the following image.

Then the decimal equivalent to the fraction written as 3/4 is expressed as 0.75 in the decimal form.

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The volume of the prism in the attached figure is calculated to be

672 m³

In the given problem, the formula used for volume of prism is

= area of base * height

Assuming a triangular base

area of triangular base = 1/2 * base * height

where

base = 12 m

height = 14 m

area of triangular base = 1/2 * 12 * 14

area of triangular base = 84 m²

The volume of the prism with a triangular base

volume of the prism = area of triangular base * height

where

area of triangular base = 84 m²

height = 8 m

volume of the prism = 84 * 8

volume of the prism = 672 m³

The volume of the prism is solved to be 672 m³

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To find the third angle of a triangle if you know the measures of the other two angles, you can use the fact that the sum of the measures of the angles in any triangle is always 180 degrees.

For example, let's say you know that angle A measures x degrees and angle B measures y degrees. To find the measure of angle C (the third angle), you can use the following equation:

x + y + C = 180°

To solve for C, you can subtract x and y from both sides of the equation:

C = 180 - x - y

So, the measure of angle C is equal to 180 degrees minus the measure of angle A and angle B.

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The dimensions length is 10 feet, width is 10 feet and height is 5 feet and the smallest possible surface area is 300 square feet.

Volume=lbh

lbh=500 cubic feet

h=500/lb

Surface area S=lb+2bh+2lh...(1) {rectangular tank has no top}

S=lb+2b(500/lb)+2l(500/lb) {substituting the value of h in 1}

S=lb+1000/l+1000/b { partially differentiating S with respect to l and b}

for S to be minimum dS/dl=0 and dS/db=0

dS/dl= b-1000/l^2

dS/dl=0

b=1000/l^2...(2)

dS/db= l-1000/b^2

dS/db=0

l=1000/b^2

l=1000/(1000/l^2)^2 {substituting the value of b from 2}

l=(1000 x l^4)/(1000000)

1000000/1000=l^4/l

1000=l^3

l=10  feet

b=1000/l^2

b=1000/100=10  feet

lbh=500

h=500/(10x10(

h=5  feet

S=10x10+2x5x10+2x10x5

S=300 square  feet

Length is 10 feet, width is 10 feet and height is 5 feet and the smallest possible surface area is 300 square feet of the  rectangular tank.

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The angles that would make triangle ABC congruent to triangle PDF by AAS are ∠ ACB and ∠ PFD i.e. ∠ ACB = ∠ PFD.

Three straight lines coming together create a triangle. There are three sides and three corners on every triangle (angles). A triangle's vertex is the intersection of two of its sides. Any one of a triangle's three sides can serve as its base, however typically the bottom side is used.

Given:

The triangle ABC and PDF are concurrent by AAS,

The AAS concurrency required two angles and one side to be equal,

Here,

AB = PD,

∠ ABC = ∠ PDF

Now one more angle is required to be equal,

∠ ACB = ∠ PFD  

Thus, the missing angle is ∠ ACB and ∠ PFD.

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Parallelogram M'N'P'Q' is larger than parallelogram MNPQ because MN and M'N' have lengths of 2 and 5 respectively, and parallelogram MNPQ is dilated by a factor of 5/2 to give parallelogram M'N'P'Q'.

A parallelogram is a straightforward quadrilateral in Euclidean geometry that has two sets of parallel sides. In a particular kind of quadrilateral known as a parallelogram, both sets of opposite sides are parallel and equal. There are four different kinds of parallelograms, including three unique kinds. Parallelograms, squares, rectangles, and rhombuses are the four different shapes. Having two sets of parallel sides makes a quadrilateral a parallelogram. In a parallelogram, the opposing sides and angles are both the same length. On the same side of the horizontal line, the interior angles are additional angles as well. 360 degrees is the total number of interior angles.

To make parallelogram M'N'P'Q, parallelogram MNPQ was enlarged.

Points include M(2, 2), N(4, 2), P(3, 3), and Q. (1,-3)

M'(5, 5), N'(10, 5), P'(8, 7), and Q' (3,-7)

A) First, determine Minnesota's length:

|MN| = 2

|M'N'| = 4

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The value of the polynomial "5x - 4x^2 + 3" at x =- 1 is -6.

The polynomial is 5x - 4x^2 + 3, and it is required to find its value at x = -1,

Now solve the polynomial by putting the value of x equal to -1:

5(-1) - 4(-1)^2 + 3        ,  x =  - 1

-5 - 4 ( 1 ) + 3             , squaring -1 gives + 1

minus 5 minus 4 plus 3

( - 9 + 3)

( - 6 )

Hence, is shown that the value - 6 is obtained when the given polynomial "5x - 4x^2 + 3" is solved for x = -1.

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An undecidable problem is one for which it has been demonstrated that it is impossible to develop an algorithm that always leads to the correct yes-or-no answer. Two examples are:

The halting problem is the problem of determining whether a computer programme will finish running or continue to run indefinitely based on a description of the programme and an input. Alan Turing demonstrated in 1936 that a general algorithm for solving the halting problem for all possible program-input pairs does not exist.

A "pathological" programme g, when called with some input, can pass its own source and input to f and then specifically do the opposite of what f predicts g will do. This case cannot be handled by any f. A key part of the proof is a mathematical definition of a computer and programme, known as a Turing machine; the halting problem is intractable over Turing machines.

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The lengths of the sides of the kite LM is 13√2.

According to the Pythagorean theorem, the hypotenuse of a right-angled triangle's other two sides add up to a square whose length equals the hypotenuse's.

The hypotenuse (longest side) of a right-angled triangle's square is equal to the sum of its other two sides, according to the Pythagoras theorem (base and perpendicular). Hypotenuse2 = Base2 + Perpendicular2 is how this is expressed. A2 + B2 = C2 is the formula for the hypotenuse.

According to question:-

LM = 13√2

Hypotenuse = Base 2 + Perpendicular 2.

So,

LM = √7² + 17²

LM = √49 + 289

LM = √338

LM = 13√2.

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Answer:

9 loaves of bread

Step-by-step explanation:

We know

8 days = 6 loaves of bread

1 day = 0.75 loaves of bread

12 days = 0.75 x 12 = 9 loaves of bread

So, she should pack 9 loaves of bread for a 12-day hiking trip.

Answer: Kendra will need to back 9 loaves of bread for a 12 day hiking trip.

Step-by-step explanation:

Alright, the first step to solve any math problem is to take a look at the information we have. We know that Kendra has eaten through 6 loaves over the course of 8 days. We want to know how much bread she needs if she takes a 12 day hiking trip.

Because she's eating the same amount of bread each day, we need to find out how much of a loaf she eats daily. In order to find that number, we have to divide. In this case, it would be 6/8. (Amount of bread she has/Time taken to eat that bread).

This gives us 0.75. This means that Kendra eats 0.75 of a loaf of bread daily. In order to find out how much bread she needs for a 12 day hiking trip, all we have to do is multiply by 12.

0.75 * 12 = 9.

Kendra will need to back 9 loaves of bread for a 12 day hiking trip.

P.S. You could also do this with fractions by simplifying 6/8 to 3/4 (divide the numerator and denominator by 2, as they're both divisible by 2), and then multiply like 12 in the same way. They both yield the same answer, so it's a matter of preference. I used decimals as I found them easier to work with!

The two posters will cover 776 square inches of Melody's bedroom wall.

To find this, you add the area of the two posters together. Poster A has an area of 450 square inches, and poster B has an area of 326 square inches. By adding these two values together, we get 450 + 326 = 776 square inches. This is the total area that the two posters will cover on Melody's bedroom wall. It is important to note that this is assuming that the posters do not overlap each other and that they are placed next to each other, covering an equal area of the wall.

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