At a hockey game, a vendor sold a combine of 125 sodas and hotdogs. The number of Sotos sold was 37 more than a number of hotdogs sold. find the number of sodas sold and the number of hotdogs sold.

The solution and extraneous solution of the equation as given are; x=7 and x=-2 respectively.

It follows that the equation given is;

(3/(x²+5x+6)) + ((x-1)/(x+2)) = 7/(x+3)

Hence, by multiplying both sides by (x²+5x+6); we have;

3 + x² +2x -3 = 7x + 14.

x²-5x -14 = 0

On this note, the solutions of the quadratic equation are; x =7 and x=-2.

It therefore follows that x= 7 is a solution while x=-2 is an extraneous solution because it renders (x-1)/(x+2) undefined.

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Answer:

x=7  

x=-2

Step-by-step explanation:

Answer:

53.7

Step-by-step explanation:

The area of the rectangular base is 7(2.3)=16.1.

So, the total volume is (1/3)(16.1)(10), which is about 53.7

Answer:

D. {-2, -3, 12, 8, 4, −5}

Step-by-step explanation:

The domain is the set of x coordinates, so the answer is {-2, -3, 12, 8, 4, −5}.

Using an exponential equation, supposing a rate of 5%, it is found that it will take about 2.9 years for Emma's balance to reach $450.

An increasing exponential function is modeled by:

[tex]A(t) = A(0)(1+r)^t[/tex]

In which:

A(0) is the initial value.

r is the growth rate, as a decimal.

In this problem:

Her initial balance is of $300, hence . A(0)=300

The growth rate is of 15%, hence R =0.15

Then,

[tex]A(t) = A(0)(1+r)^t[/tex]

[tex]A(t) = 300(1+0.15)^t\\A(t) = 300(1.5)^t\\[/tex]

It will reach $450 after t years, for which A(t) = 450, hence:

[tex]A(t) =300(1.15)^t\\450= 300(1.15)^t\\1.15^t=\frac{450}{300}\\\\1.15^t =1.5\\log(1.15)^t=log1.5\\t log 1.15 = log 1.5\\t = \frac{log1.5}{log1.15}\\\\ t =2.9[/tex]

It will take about 2.9 years for Emma's balance to reach $450

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Answer:

2nd, 3rd, and 6th option are correct

Step-by-step explanation:

using a²+b²=c² those are the obly that meet the criteria (im pretty sure)

In the given triangle equations AC² = AB² + BC², AB² = AD² + BD² and BC² = CD² + BD² are true.

A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or any angle is a right angle.

Given that,

ABC is a right angle triangle.

And BD is perpendicular to AC.

To show the equations which are true,

Use Pythagorean theorem,

(Hypotenuse)² = (base)² + (height)²

In triangle ABC,

AC² = AB² + BC²

In triangle ABD,

(AB)² = AD² + BD²

And in triangle BCD,

BC² = CD² + BD²

Therefore, option (2), (3) and (6) are correct.

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The rational function represented in the given graph is; f(x) = 1/(x - 4)

From the given graph , the vertical asymptote is at x = 4

Let's find out the vertical asymptote of each function

To find out vertical asymptote we set the denominator = 0

A) x + 4 = 0

x = -4

This is not correct

B) 4x = 0

x = 0

Not correct

C) Denominator does not have a variable and so is also incorrect

D) x - 4 = 0

x = 4

Thus, this is correct

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The biotic factors of an ecosystem are arranged in feeding levels known as trophic levels.

The trophic level of an organism is the position it occupies in a food web. The trophic level of an organism is the number of steps it is from the start of the chain.

Below are the list of the trophic levels:

The biotic factors of an ecosystem are arranged in feeding levels known as trophic levels.

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The algebraic expression for: the sum of a number and 5 decreased by twice the number is (n + 5) - 2n

let

sum of a number and 5

= n + 5

decreased by twice the number

= -2(n)

= - 2n

sum of a number and 5 decreased by twice the number

= (n + 5) - 2n

= n + 5 - 2n

= 5 - n

Therefore, the algebraic expression which can be used to represent; the sum of a number and 5 decreased by twice the number is (n + 5) - 2n

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The expression that shows the amount of money in dollars that Maggie has d - 3

An equation is an expression that shows the relationship between two or more numbers and variables.

Let d represent the amount of money Ron has on Tuesday. Hence:

Money Maggie has = d - 9 + 6 = d - 3

The expression that shows the amount of money in dollars that Maggie has d - 3

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The expression that is not a rational expression is:

[tex]\frac{(x + 3)(2x - 1)}{x + 3}[/tex]

A rational expression is an expression that has a variable in the denominator.

For expression [tex]\frac{(x + 3)(2x - 1)}{x + 3}[/tex], x + 3 is a common term to the numerator and denominator, hence it is simplified to 2x - 1 and is not a rational expression.

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The option that is not a rational expression is [tex]\frac{3x + 4\sqrt{x} -7}{2x+2}[/tex]

Rational expression are fraction whose numerator and denominator are polynomials.

In other words, rational expression is the ratio of two polynomials.

Therefore, an example of a ration expression is as follows:

[tex]\frac{x^{2}+9 }{x + 1}[/tex]

Therefore, the option that is not a rational expression is as follows;

[tex]\frac{3x + 4\sqrt{x} -7}{2x+2}[/tex]

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The second bus is traveling at a speed of 33.3 miles per hour.

Given that the speed of first bus is 60 miles per hour , distance between both the buses is 700 miles after 8 hour.

We are required to find the speed of second car which is heading towards south.

If first car is travelling at a speed of 60 miles per hour then the distance of first car after 8 hours is 60*8=480 miles.

We have been given that the distance between both the cars after 8 hours is 700 miles,So,

Distance of second car after 8 hours=700-480=220 miles.

We know that the speed is equal to distance divided by time.

We know that we have calculated distance after 8 hours so the speed of second car will be =20/6

=33.3 miles per hour

Hence the speed of second car which is heading towards south is 33.3 miles per hour.

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Answer:

C

Step-by-step explanation:

There are 6 outcomes and you are seeking 2 of them.  

2/6 or 1/3 1:3

Using the Fundamental Counting Theorem, the sample size of these outcomes is of 12.

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

Considering the number of options for Entree, Side and Drink, the parameters are:

n1 = 3, n2 = 2, n3 = 2.

Hence the sample size of outcomes is:

N = 3 x 2 x 2 = 12.

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Step-by-step explanation:

Find lower quartile first: 1/4 (61)th term which equals to 15.25th term. Use your graph to estimate where 15.25 is and draw a line till it meets tne curve. As soon as it touch the curve, continue the line downward and you'll get LQ in kg. Secondly, find upper quartile: 3/4(61)th term which equals to 45.75th term. Proceed the same thing I mentioned above for lower quartile. Then the formula for interquartile range is upper quartile minus lower quartile and you'll get the answer in kg.

The equation that runs through the location (4,-6) has the slope-intercept form,  [tex]y=-\frac{3}{4}x-3[/tex] .

A line's equation written in the slope-intercept form:

y=mx+b

where m= slope & b= y-intercept

The slope of two parallel lines is equal.

Currently, we know the line's equation:

[tex]y=-\frac{3}{4} x-5[/tex]

here, slope, m= [tex]-\frac{3}{4}[/tex]

A line equation is created by adding the slope's value and the point's coordinates (4, -6):

[tex]-6=-\frac{3}{4}(4)+b[/tex]

⇒ -6=-3 +b [adding 3 to both sides]

⇒-3=b

⇒b= -3

Hence the solution is  [tex]y=-\frac{3}{4}x-3[/tex] .

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The angle formed by the line of sight and the horizontal line can best be described as an angle of elevation.

The angle of elevation is an angle that is formed between the horizontal line and the line of sight.

The angle of elevation is says to be the angle made between a horizontal plane and a straight line to a given object that is elevated off the ground.

Therefore, the angle formed by the line of sight and the horizontal line can best be described as an angle of elevation.

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Step-by-step explanation:

Pythagoras :

c² = a² + b²

the only problem : we don't know which one of the 3 expressions is the longest side (= c = Hypotenuse).

let's try with 8x -21

(8x - 21)² = (3x - 7)² + (6x)²

64x² - 336x + 441 = 9x² - 42x + 49 + 36x²

19x² - 294x + 392 = 0

the general solution to such a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 19

b = -294

c = 392

x = (294 ± sqrt(86436 - 4×19×392))/(2×19) =

= (294 ± sqrt(56644))/38 =

= (294 ± 238)/38

x1 = (294 + 238)/38 = 532/38 = 14

x2 = (294 - 238)/38 = 56/38 = 28/19 = 1.473684211...

I assume, we are looking for a whole number solution.

so, x = 14 is the solution.

The joint relative frequency is 21%.

Joint relative frequency can be described as the ratio of the frequency of data in a certain category to the total number of data points in that category.

The joint relative frequency for teachers who teach math and not English = number of teachers who teach maths and not English / total number of teachers

(22 / 104) x 100 = 21%

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The system of equations that can be used to find the lengths of the legs of the sun shade is given as follows:

y = 0.5x², y = 64.

The system of equations is obtained considering the equation for the area of a right triangle, which is given by half the multiplication of the legs.

In this problem, we have an isosceles right triangle, meaning that both legs have the same measure.

The area of the right triangle is of 64 feet, hence the area is calculated as follows:

0.5x² = 64.

Thus the equations that compose the system are:

Meaning that the second option is correct.

The options are given by the image shown at the end of the answer.

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There is a total of 10 games played.

There are 5 players, If we select a given player, then that player will play one game with each of the other 4 players.

So we have 4 games at the moment.

Now we select one of the other 4 players, (we don't count the one we choose before). The one that we choose now will play one game wich each one of the remaining 3, so we add 3 more games.

Now we do the same with the remaining 3, this time we add 2 more games.

Now we do that with the remaining 2, now we add 1 more game.

Adding all the games we have:

4 + 3 + 2 + 1 = 10

There is a total of 10 games played.

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The terms that explains the value of Sin(pi/3) on the unit circle would be Sin(pi/3) = Opposite side of angle.

According to the statement

we have to give the terms which explain the sin (pi/3) perfectly.

And we have choose these terms from the these below written conditions like From Right Triangle, Hypotenuse, and unit circle.

And Now we explain all terms below

So,

"Right Triangle is a triangle whose one of the angle measures 90° "

And "The hypotenuse is a longest side of the right triangle.

And"Unit Circle is a circle with radius 1."

For given question,

We have been  given a unit circle.

So, We need to find the sin (pi/3)

We know, in a right triangle for any angle , θ

Sinθ = Opposite side of angle / Hypotenuse

So, for , Sin(pi/3) = Opposite side of angle / 1

Sin(pi/3) = Opposite side of angle

Therefore, The terms that explains the value of Sin(pi/3) on the unit circle would be Sin(pi/3) = Opposite side of angle.

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If Aaron is designing a party game in which he needs exactly 24 possible outcomes, then he can use the following sets of actions to have a statistically fair game from the Statistics point  of view,

Toss a coin twice, and then then roll a 6-sided number cube.

How can he play a statistically fair game to get exactly 24 outcomes?

The game has 24 alternative outcomes, as far as we know. The next step is to identify a series of activities that produces 24 distinct outcomes with equal probabilities.

The first of the alternatives is the only one with a sample space of 24 elements.

Flip two coins, then roll a D6.

The results of each coin toss are 2:  (tails and heads).

There are 6 outcomes for the D6: (1, 2, 3, 4, 5, 6)

The combined outcomes of the two throws and rolling the number are then given by the product between the numbers of outcomes for each individual part, as solved below:

C = 2 × 2 × 6

C = 24

Thus, by tossing a coin twice, and then then rolling a 6-sided number cube, Aron can play a statistically fair game if h needs exactly 24 outcomes.

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Answer:

-3

Step-by-step explanation:

So just like the picture provides, the slope can be defined as: [tex]\frac{\text{change in y}}{\text{change in x}}[/tex]. So this means we can take any two points and find the change in x and y to define the slope, since the slope is constant throughout the entire line, since it's a linear line, meaning it's straight.

So you can use the points (0, 15) and (2, 9). So let's look at the x-values, and you want to make sure, you maintain the order at which you look at the  "change in x", for example I can define the change in x through the two points as 0 to 2, or 2 to 0, one case is 2, and the other is -2, but if I look at the change from 0 to 2, then I looked at the first point first then the second, this means when looking at the y-values I have to find the change from 15 to 9, and not 9 to 15, since I did 0 to 2 in the first case. I could look at the change from 9 to 15, but only if I looked at the changed from 2 to 0.

Anyways let's find the change from 0 to 2, it's 2. Now let's look at the change from 15 to 9, it's -6 (since the value went down). So this gives us equation: -6 / 2 = -3

The slope is -3

Answer:

Step-by-step explanation:

Factors

(b)/(7.8)=-2.15

Multiply each term in the equation by 7.8.

(b)/(7.8)*7.8=-2.15*7.8

Cancel the common factor of (1)/(7.8).

1b=-2.15*7.8

Multiply -2.15 by 7.8 to get -16.77.

1b=-16.77

Divide each term in the equation by 1.

(1b)/(1)=-(16.77)/(1)

Cancel the common factor of 1.

b=-(16.77)/(1)

Divide -16.77 by 1 to get -16.77.

b=-16.77

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⊰___________________ ___________________________________ __⊱

Answer:

Yes, it is a polynomial

Step-by-step explanation:

This polynomial is a trinomial, since it has 3 terms (the prefix tri means three) and its degree is 3 (the degree of a polynomial is the largest exponent in that particular polynomial).

Done !! Hope this made sense to you !!

⊰________________________________________________________⊱

[tex]\small{\pmb{\tt{CALLIGRAPHY}}[/tex]

The possible outcomes are WH, BH, BH, BH, RH, RH, WL, BL, BL, BL, RL, RL

The given parameters are:

Coin = Head (H) and Tail (T)

Marble = W, B, B, B, R, R

See attachment for the tree diagram

From the tree diagram, we have the following possible outcomes

WH, BH, BH, BH, RH, RH, WL, BL, BL, BL, RL, RL

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The value of the given expression (a + b/2)/a - bx² = 219.5/(76 - 287x²).

An expression is the combination of variables, coefficients, and constants that are separated by an arithmetic operator(+, -, ...).

The given expression is

(a + b/2)/a - bx²

It is given that a = 76 and b = 287

On substituting,

(a + b/2)/a - bx² = (76 + 287/2)/76 - 287x²

⇒ (76 + 143.5)/76 - 287x²

⇒ 219.5/(76 - 287x²)

Therefore, the given expression for the values a = 76 and b = 287 is 219.5/(76 - 287x²).

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One accurate statement amount Arab Americans is that b. Arab Americans include both Muslims and Christians.

Arab Muslims are known to include both Muslims and Christians and indeed it is estimated that more Arab Americans are Christians as opposed to Muslims.

They are also quite urbanized and have very high rates of education which has given then access to more income.

Options for this question include:

a. Arab Americans are not urbanized.

b. Arab Americans include both Muslims and Christians.

c. Arab Americans rank relatively low in terms of income and occupation

d. Arab Americans tend to have low levels of education and skills.

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Answer:

((24+13)/28.5

Step-by-step explanation: