a) The simplified expression is \frac{(x-4)}{2(x+2)}. b) The solution to the equation is x = -7.
a) To simplify the expression \frac{7}{x^2\ -\ 4}\div\frac{14}{x^2\ -6x\ +8}, we need to multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by flipping the numerator and denominator. So, the reciprocal of \frac{14}{x^2\ -6x\ +8} is \frac{x^2\ -6x\ +8}{14}.
Now, we can multiply the two fractions: \frac{7}{x^2\ -\ 4} \times \frac{x^2\ -6x\ +8}{14} = \frac{7(x^2\ -6x\ +8)}{14(x^2\ -\ 4)}
Next, we can simplify the expression by canceling out any common factors. In this case, both the numerator and denominator have a factor of 7, so we can cancel them out:
\frac{7(x^2\ -6x\ +8)}{14(x^2\ -\ 4)} = \frac{x^2\ -6x\ +8}{2(x^2\ -\ 4)}
Finally, we can factor the numerator and denominator to see if there are any other common factors that can be canceled out:
\frac{x^2\ -6x\ +8}{2(x^2\ -\ 4)} = \frac{(x-4)(x-2)}{2(x+2)(x-2)}
Since both the numerator and denominator have a factor of (x-2), we can cancel them out:
\frac{(x-4)(x-2)}{2(x+2)(x-2)} = \frac{(x-4)}{2(x+2)}
So, the simplified expression is \frac{(x-4)}{2(x+2)}.
b) For the second part of the question, we need to solve the equation \frac{6}{x\ +1}\ =\ \frac{3}{x\ +\ 4}. To do this, we can cross-multiply and then simplify:
6(x+4) = 3(x+1)
6x + 24 = 3x + 3
3x = -21
x = -7
So, the solution to the equation is x = -7.
Note: The question is incomplete. The complete question probably is: a) Simplify the expression \frac{7}{x^2\ -\ 4}\div\frac{14}{x^2\ -6x\ +8} . b) Solve the equation \frac{6}{x\ +1}\ =\ \frac{3}{x\ +\ 4}.
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Factor the following polynomial with a negative coefficient. -5x^(6)+15x^(4)+20x^(3)
The factored form of the polynomial is (5x^(3))(-x^(3)+3x+4).
To factor the polynomial with a negative coefficient, -5x^(6)+15x^(4)+20x^(3), we can use the content loaded factor method. This method involves factoring out the greatest common factor (GCF) of all the terms in the polynomial.
The GCF of -5x^(6), 15x^(4), and 20x^(3) is 5x^(3). So, we can factor out 5x^(3) from each term:
-5x^(6) = -(5x^(3))(x^(3))
15x^(4) = (5x^(3))(3x)
20x^(3) = (5x^(3))(4)
Now, we can rewrite the polynomial as:
-5x^(6)+15x^(4)+20x^(3) = (5x^(3))(-x^(3)+3x+4)
So, the factored form of the polynomial is (5x^(3))(-x^(3)+3x+4).
In summary, the polynomial -5x^(6)+15x^(4)+20x^(3) can be factored as (5x^(3))(-x^(3)+3x+4) using the content loaded factor method.
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The figure shown is a rhombus. Find the length of ST.
The length of ST is 57 unit.
What is Perimeter?A perimeter is a closed path that covers, surrounds, or outlines a two-dimensional shape or length. The circumference of a circle or an ellipse is its perimeter.
As, we know that the four sides of Rhombus are equal.
So, TR = QR
-x+ 68 = 5x + 2
-x - 5x = 2 - 68
-6x = - 66
x= -66/ (-6)
x= 11
So, the length of ST = 5x+ 2 = -x+ 68 = 57 unit
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In the same year, at the Avondale golf club, there are 12 women and 56 men members. Write the ratio of women: men, in its simplest form.
Answer:
3:14
for every 3 women, there is 14 men
Step-by-step explanation:
Alex spent One Hour Twenty Minutes less than Lane Reading Last Week Lane spent Fifty Minutes less than Pete pete spent Three Hours Reading How Long did Alex spend Reading
Using unitary method, we can find out that Alex spent 50 minutes reading.
Unitary Method: What is it?By using the unitary technique, we can determine both the value of many units from the value of a single unit as well as the value of multiple units from the value of a single unit.
The worth of many things is supplied in the unitary technique, and we must either determine the value of more or fewer items. To do that, we must first determine the value of a single item by division and then determine the value of further or other items by multiplication.
Given in the question,
Alex spent 1 hour 20 minutes less than Lane.
Lane spent 50 minutes less than Pete.
Pete spent 3 hours reading.
Since, Pete spent 3 hours.
So, Lane spent:
= 3 hours or (180 minutes) - 50 minutes
= 2 hours 10 minutes.
Now, Alex spent:
= 2 hrs 10 minutes - 1 hour 20 minutes
= 50 minutes
Therefore, Alex spent 50 minutes reading.
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Choose all the due process rights that are found in the 6th Amendment.
A)
the right to be assisted by counsel
B)
the right to a speedy and public trial
C)
the right to confront and cross-examine witnesses
D)
the right to not be 'deprived of life, liberty or property without due process
of law
E
the right of the people to be secure in their persons, houses, papers, and
effects, against unreasonable searches and seizures
The due process rights found in the 6th Amendment are: the right to be assisted by counsel, the right to a speedy and public trial, and the right to confront and cross-examine witnesses. Option A, B, C are correct.
The right to assistance of counsel - this means that a defendant has the right to be represented by an attorney, who can help them prepare their defense, cross-examine witnesses, and navigate the complexities of the criminal justice system.
The right to a speedy and public trial - this means that a defendant has the right to a trial that is conducted promptly and is open to the public, so that justice can be done fairly and transparently.
The right to confront witnesses - this means that a defendant has the right to cross-examine witnesses who testify against them in court, in order to test their credibility and the accuracy of their testimony.
Option D is a due process right found in the 5th Amendment, while option E is a right found in the 4th Amendment.
Hence, A. B. C. the right to be assisted by counsel, right to a speedy and public trial, right to confront and cross-examine witnesses is the correct option.
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Find the point (x, y) on the unit circle that corresponds to the real number t. ON THE BLANK WRITE DOWN sqrt(2) for √2 or sqrt(3) for √3. t = 5????/6 the corresponding (x,y) is
The point (x, y) on the unit circle that corresponds to the real number t = 5π/6 is (-√3/2, 1/2).
The point (x, y) on the unit circle that corresponds to the real number t can be found using the following equations:
x = cos(t)
y = sin(t)
Since t = 5π/6, we can plug this value into the equations to find x and y:
x = cos(5π/6) = -√3/2
y = sin(5π/6) = 1/2
Therefore, the point (x, y) on the unit circle that corresponds to the real number t = 5π/6 is (-√3/2, 1/2).
Note: The unit circle is a circle with a radius of 1 that is centered at the origin (0, 0) of the coordinate plane. The x-coordinate of a point on the unit circle corresponds to the cosine of the angle formed by the positive x-axis and the radius connecting the origin to the point, while the y-coordinate corresponds to the sine of this angle.
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can some one please help me with this
We can rewrite the inequality as:
95 ≤ u ≤ 155
How to solve the inequality?Here we have the absolute value inequality:
|125 - u| ≤ 30
Where the variable is u.
The absolute value can be decomposed into two inequalities:
(125 - u) ≤ 30
(125 - u) ≥ -30
Solving these two we will get:
125 - 30 ≤ u
125 + 30 ≥ u
Then the compound inequality is:
95 ≤ u ≤ 155
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What is the highest number of degrees (as a whole number) an image can rotate without returning to it's exact original position?
please answer in __°!
Answer:
359°
Step-by-step explanation:
When an image is rotated by a multiple of 360 degrees, it returns to its original position because it has completed one full revolution. However, if the image is rotated by any angle less than 360 degrees, it will not return to its exact original position.
For example, if an image is rotated by 45 degrees, it will not return to its exact original position, but will instead be in a new and unique position. If the image is then rotated by another 45 degrees, it will again be in a new and unique position, and so on.
Therefore, the highest number of degrees an image can rotate without returning to its exact original position is 359 degrees.
Answer: 359 degrees
Step-by-step explanation:
If you rotate any object exactly 360 degrees, it returns to it's original position. Remember that phrase "360 no-scope?" It involves spinning until you're back where you started; try doing it right now. You'll be back where you were. But this question wants to know how far you can rotate an object without it being back where it was. I would usually say 359.999999999, but it's a whole number answer, so we'll stick with 359. Hope this helps!
Kayak rental company A charges an initial fee of $12 plus $3.25 for every hour spent kayaking. Kayak rental company B charges $9.25 for every hour spent kayaking. A customer finds that after h hours, the kayak rental companies will cost the same. Which equation represents this situation? Responses 3.25h+12=9.25h , 3.25 h plus 12 equals 9.25 h, 9.25h+3.25h=12 , 9.25 h plus 3.25 h equals 12, 9.25h=12−3.75h , 9.25 h equals 12 minus 3.75 h, 3.25h=12+9.25h
Answer: 3.25h + 12= 9.25
Step-by-step explanation:
12 is the initial fee which we will just add to our answer
3.25 is the rate per hour, it is being multiplied by the number of hours.
the number of hour it took to reach the same cost is not told so we will just put a variable.
please help and hurry i really need help and i also need to know where to drag the bar to it will only let me move it past 10 not before 10
The answer of the given question based on statistical measures the answer is, Min: 2,Max: 15,Med: 8,Q1: 4,Q3: 13.
What is Statistics?Statistics is branch of mathematics that deals with collection, analysis, interpretation, presentation, and organization of the data. It provides way to summarize and describe numerical information in meaningful way, and it enables us to make the informed decisions based on that information. Statistics is used in many things , including business, finance, health, engineering, social sciences, and more.
To create the box and whisker plot:
Draw a number line that includes all the data points.
Mark the minimum and maximum values with a horizontal line.
Locate the median and draw a vertical line through it.
Draw a box from the first quartile (Q1) to the third quartile (Q3).
Draw whiskers from the box to the minimum and maximum values.
Here is the completed box and whisker plot:
O
1
2 3 4 5 6 7 8
|--------|
9
10 11 12 13 14 15 16 17 18
|--------------|
X
The box represents the middle 50% of the data, with the bottom of the box at Q1 and the top of the box at Q3. The median is marked by a vertical line inside the box. The whiskers extend from the box to the minimum and maximum values, with any data points outside the whiskers shown as individual points (outliers).
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What is this answer to this
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{-16})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{-12}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-12}-\stackrel{y1}{(-16)}}}{\underset{\textit{\large run}} {\underset{x_2}{8}-\underset{x_1}{4}}} \implies \cfrac{-12 +16}{4} \implies \cfrac{ 4 }{ 4 } \implies 1[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-16)}=\stackrel{m}{ 1}(x-\stackrel{x_1}{4}) \implies y +16 = 1 ( x -4) \\\\\\ y+16=x-4\implies y=x-20\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
The ratio of roses to carnations in a floral shop is 1:4. If there are 240 carnations, how many roses are there?
Using the ratio, there are 60 roses in the floral shop.
To find the number of roses in the floral shop, we can use the ratio given in the question. The ratio of roses to carnations is 1:4, which means that for every 1 rose, there are 4 carnations.
If there are 240 carnations, we can use cross multiplication to find the number of roses.
1/4 = x/240
Cross multiplying gives us:
4x = 240
Solving for x, we get:
x = 240/4
x = 60
In conclusion, if the ratio of roses to carnations in a floral shop is 1:4 and there are 240 carnations, there are 60 roses.
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50 points pls help it’s math
The inequalities seen on Cartesian plane are - 2 · x + y > 1 and - (1 / 2) · x + y ≤ 2, respectively.
How to determine the inequalities representing a graph
In this problem we find two graphs by inequalities on Cartesian plane, whose definitions are listed below:
Case 19:
f(x) > y
Case 20:
f(x) ≤ y
Each inequality has a function of the form:
y = m · x + b
Where:
x - Independent variable.y - Dependent variable.m - Slopeb - InterceptAnd the slope can be determined by secant line formula:
m = Δy / Δx
Now we proceed to determine each inequality:
Case 1:
Slope
m = 4 / 2
m = 2
Intercept
b = 1
Inequality
y > 2 · x + 1
- 2 · x + y > 1
Case 2:
Slope
m = 1 / 2
Intercept
b = 2
Inequality
y ≤ (1 / 2) · x + 2
- (1 / 2) · x + y ≤ 2
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The delgados obtained an instrument loan of $12,000 from the credit union to pay for their son's tuitions. They obtained the loan at an apr of 10 percent and agreed to repay the loan in 12 mounths what is the finance charge the
The Finance Charge for the Delgados obtained for an instrument is $1200 to repay the loan in 12 months.
The given data is as follows:
Instrument loan = $12,000
Loan at APR = 10%
Number of months = 12 Months
The finance charge is calculated by using the formula,
Finance charge = Loan amount x APR x No' of months to repayment / No' of months in a year
Finance charge = ($12,000 x 10% x 12) / 12
Finance charge = 14400 / 12
Finance charge = $ 1200
Therefore we can conclude that the Finance charge for the Delgados obtained for an instrument is $1200.
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\[ \begin{array}{l} f(x)=2 x^{2}+5 \\ f-1(x)= \end{array} \] fx domain \( f x \) range \[ \begin{array}{l} f(x)=\frac{1}{2} x+4 \\ g(x)-6 x-2 \\ f \circ g(x)= \\ g \circ f(x)= \\ f(x)=\frac{1}{x-9} \\
The f(g(x)) is equal to 72x^2+48x+9 and g(f(x)) is equal to 3x+22.
To provide an accurate answer, it's important to first understand what the question is asking for. From the given information, it appears that there are several different parts to this question, so I will address each one individually.
1. Finding f-1(x)
To find the inverse of f(x), we can switch the x and y values and solve for y.
\begin{align*}
f(x) &= 2x^2+5 \\
y &= 2x^2+5 \\
x &= 2y^2+5 \\
2y^2 &= x-5 \\
y &= \sqrt{\frac{x-5}{2}} \\
f^{-1}(x) &= \sqrt{\frac{x-5}{2}}
\end{align*}
Therefore, f-1(x) is equal to √((x-5)/2).
2. Determining fx domain and range
The domain of f(x) is all real numbers since there are no restrictions on the input value x. However, the range of f(x) is limited by the fact that 2x^2+5 is always greater than or equal to 5. Therefore, the range of f(x) is [5,∞).
3. Finding f(g(x)) and g(f(x))
To find f(g(x)), we first need to substitute g(x) into f(x) wherever x appears:
\begin{align*}
f(g(x)) &= 2(g(x))^2+5 \\
&= 2(6x+2)^2+5 \\
&= 72x^2+48x+9
\end{align*}
To find g(f(x)), we first need to substitute f(x) into g(x) wherever x appears:
\begin{align*}
g(f(x)) &= 6f(x)-2 \\
&= 6\left(\frac{1}{2}x+4\right)-2 \\
&= 3x+22
\end{align*}
Therefore, f(g(x)) is equal to 72x^2+48x+9 and g(f(x)) is equal to 3x+22.
4. Explaining f(x)=1/(x-9)
The function f(x)=1/(x-9) is a rational function with a vertical asymptote at x=9. This means that as x approaches 9 from either direction, the function values become increasingly large (either positive or negative infinity).
The domain of f(x) is all real numbers except for x=9 (since dividing by zero is undefined). The range of f(x) is all real numbers except for zero (since 1/0 is undefined).I hope this helps! Let me know if you have any further questions.
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A group of 8 friends went to lunch and spent a total of $76, which included the food bill and a tip of $16. They decided to split the bill and tip evenly among themselves. Which equations and solutions describe the situation? Select two options. The equation StartFraction 1 over 8 EndFraction (x + 16) = StartFraction 76 over 8 EndFraction represents the situation, where x is the food bill. The equation StartFraction 1 over 8 EndFraction (x + 16) = 76 represents the situation, where x is the food bill. The solution x = 60 represents the total food bill. The solution x = 60 represents each friend’s share of the food bill and tip. The equation 8 (x + 16) = 76 represents the situation, where x is the food bill.
We can state this by responding to the provided question Each friend's equation portion of the tab and the tip is represented by the equation x = 60.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
The circumstance, where x is the cost of the groceries, is represented by the equation StartFraction 1 over 8 EndFraction (x + 16) = StartFraction 76 over 8 EndFraction. As the lunch cost and the gratuity were shared equally among the eight companions, this equation accurately depicts the total sum that each of them paid.
The scenario is represented by the equation 8 (x + 16) = 76, where x is the cost of the groceries. This calculation is incorrect since it includes the tip and includes the total amount paid by all 8 friends rather than just the cost of the meal.
Each friend's portion of the tab and the tip is represented by the equation x = 60.
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Use the pair of functions to find f(g(x)) and g(f(x)). Simplify your answers.
f(x) = x2 + 3, g(x) = x + 4 f(g(x)) = g(f(x)) =
f(g(x))=x² + 8x +19 ; g(f(x))=x² + 7 are the value of the asked functions
explanation:-
the given functions are: f(x) = x² + 3 and g(x) = x + 4
f(g(x)) = f(x + 4) = (x + 4)² + 3 = x² + 16 + 8x +3 = x² + 8x +19
g(f(x)) = g(x² + 3) = x ²+ 3 + 4 = x² + 7
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5) A decade of inflation
a) Suppose the annual inflation rate was 3% for 10 years in a row. What was the inflation rate for that decade?
b) Find the inflation rate for the decade from 1960 to 1970. If the inflation rate had been the same for each year in that decade, what would that annual rate have been? The answer to part a) will help you with this problem. This might be difficult depending on your math background, but try to be creative.
The inflation rate for that decade will be 34.39%. If the inflation rate had been the same for each year in that decade, the annual rate would have been 2.79%.
a) If the annual inflation rate was 3% for 10 years in a row, the inflation rate for that decade would be 34.39%. This is calculated by using the formula (1 + annual inflation rate)^number of years - 1. So in this case, it would be (1 + 0.03)^10 - 1 = 0.3439 or 34.39%.
b) To find the inflation rate for the decade from 1960 to 1970, we need to know the Consumer Price Index (CPI) for both years. The CPI for 1960 was 29.6 and the CPI for 1970 was 38.8.
We can use the formula (CPI in later year/CPI in earlier year)^(1/number of years) - 1 to find the annual inflation rate.
So in this case, it would be (38.8/29.6)^(1/10) - 1 = 0.0279 or 2.79%. Therefore, if the inflation rate had been the same for each year in that decade, the annual rate would have been 2.79%.
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what is 8 3/4 + 1 1/2 - 1/4
Answer:
10
Step-by-step explanation:
Answer:
good morning i hope your day is going well so far
Step-by-step explanation:
the answer to your question is 10
i hope this helps!!!
Use the associative property to
write an equivalent expression.
9 x (2 x 5) =
Answer: 90
Step-by-step explanation:
Answer:
90
Step-by-step explanation:
HELP!!
One cubic foot of water is equivalent to 7.48 gallons. If the capacity of the fish tank is 100 gallons, find the maximum possible height for the fish tank. Round your answer to the nearest thousandth of an inch.
Show your work.
The height of the fish tank should be approximately 1.981 feet which is also equivalent to 23.772 inches.
What is the maximum possible height for the fish tank?As desired capacity of the fish tank is 100 gallons, and 7.48 gallons of water are equivalent to 1 cubic foot, the desired volume of the fish tank is (100 / 7.48) cubic feet, or approximately 13.369 cubic feet.
The desired volume is stated as a number of cubic feet so the known dimensions of the fish tank must be converted from inches to feet.
length = 54 inches = 4.5 feet
width = 18 inches = 1.5 feet
The formula for the volume V of a rectangular prism with length l, width w, and height h is V = lwh. We will substitute the known dimensions into the formula and solve for h.
V = ℓwh
13.369 ≈ 4.5 × 1.5 × h
13.369 ≈ 6.75h
h ≈ 13.369 / 6.75
h ≈ 1.981
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Use Pascal’s Triangle to determine the fifth term of the expansion of (x − 5)6
The fifth term of the expansion of (x − 5)⁶ is found as: 937x².
Explain about the Pascal’s Triangle?The Pascal triangle has a lengthy history. It may be traced back to India's Pingala people in the second century BC, who also knew various other binomial formulas at the same time.
Using the binomial series:
(n C r) = n! / (r1(n - r)!
Given equation: (x − 5)⁶
On comparing:
a = x, b = -5 and n = 6
x⁶ + (6C1).x⁶.(-5)¹ + (6C2).x⁴.(-5)² + (6C3)x⁴(-5)³ + (6C4).x²(-5)⁴ + (6C5).x¹.(-5)⁵ + (-5)
Using binomial calculator to solve the expression as;
x⁶ - 30x⁵ + 375x⁴ - 2500x³ + 937x² - 1870x + 15625
Thus, the fifth term of the expansion of (x − 5)⁶ is found as: 937x².
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A charity organization had to sell a few tickets to their fundraiser just to cover necessary production costs. After selling. 10 tickets, they were still at a net loss of
$800 (due to the production costs). They sold each ticket for
$70
Let y represent the net profit (in dollars) when they have sold. X tickets. Complete the equation for the relationship between the net profit and number of tickets sold. Y=
The equation for the relationship between the net profit and the number of tickets sold is Y= 70x - 1500.
We are aware that the group charges $70 for each ticket and that after selling 10 tickets, there was a net loss of $800. Thus, the sum of the proceeds from the sale of the ten tickets was:
10 tickets sold for $70 each will bring in a total of $700.
The total production expenses must have been: Given that the net loss was $800:
Costs of production in total are $700 + $800 = $1500.
Let x be the number of purchased tickets. The sum of the sales of x tickets is:
Selling x tickets will bring in a total of $70.
The sum of the revenue less the sum of the production costs is the net profit:
All revenue minus all costs of production equals net profit.
[tex]Y = x × $70 - $1500[/tex]
Thus, the following equation represents the connection between the net profit and the number of tickets sold:
Y = 70x - 1500
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The cost for an 8th grade party isv$450 for a room rental, entertainment, and decorations, plus $20 per person for food. Tickets for the party are sold $25. What is the break-even point?
The break-even point is 45 tickets.
Describe Algebraic Expression?Algebraic expressions can include one or more variables, which are typically represented by letters, such as x, y, or z. These variables can be used to represent unknown quantities or to express relationships between different quantities in a problem.
Algebraic expressions can also include constants, which are fixed numbers, and coefficients, which are the numbers that multiply the variables in the expression. For example, in the algebraic expression 3x + 2y, the constants are 3 and 2, and the coefficients are 3 and 2, respectively.
To find the break-even point, we need to determine the number of tickets that need to be sold in order to cover the costs of the party.
Let's start by setting up an equation to represent the total cost of the party as a function of the number of tickets sold:
Total Cost = Room Rental + Entertainment + Decorations + Food Cost - Ticket Sales Revenue
Total Cost = 450 + 20n - 25n
where n is the number of tickets sold.
Simplifying this equation, we get:
Total Cost = 450 - 5n + 20n
Total Cost = 15n + 450
Now, we need to set the total cost equal to the revenue from ticket sales:
15n + 450 = 25n
Subtracting 15n from both sides, we get:
450 = 10n
Dividing both sides by 10, we get:
n = 45
Therefore, the break-even point is 45 tickets. If the organizers sell 45 tickets, the revenue from ticket sales will cover the total cost of the party, including the room rental, entertainment, decorations, and food cost.
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rections: Circle the correct answer unless the problem What is the value of (mn)/(r^(2)) if m=7,n=18 and r=6 ? A. 3.5
The correct answer is A. 3.5.
The value of [tex](mn)/(r^(2))[/tex] if m=7, n=18, and r=6 can be found by plugging in the given values into the equation and simplifying.
Step 1: Plug in the given values:
[tex](mn)/(r^(2)) = (7*18)/(6^(2))[/tex]
Step 2: Simplify the equation:
[tex](7*18)/(6^(2)) = (126)/(36)[/tex]
Step 3: Simplify further:
(126)/(36) = 3.5
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Given a line and a point, not on the line, there is one and only _____ line which passes through the given point and______ is to the given line.
A. one, parallel
B. one, perpendicular
C. two, parallel
D. two, perpendicular
Given a line and a point, not on the line, there is one and only one line which passes through the given point and is perpendicular to the given line. The correct answer is B.
A line and a point not on the line are given. We are asked to find the one and only line that passes through the given point and is perpendicular to the given line. The line that passes through the given point and is perpendicular to the given line is known as the perpendicular bisector.
The perpendicular bisector passes through the midpoint of the line segment formed by the two endpoints of the given line. Therefore, the answer is B. There is one and only one line that passes through the given point and is perpendicular to the given line. Therefore the correct answer of this question is option B
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Solve for x. If there is more than one solution, separate the solutions (1)/(x-6)+(x)/(x)=(-9x+3)/(2)
The value of x for this solution is x = -2, 3, -3.
To solve for x, we need to combine like terms and then isolate x on one side of the equation. Here are the steps:
1. Multiply both sides of the equation by the common denominator of (x)(x-6)(2) to eliminate the fractions:
(1)(x)(2) + (x)(x-6)(2) = (-9x+3)(x)(x-6)
2x + 2x^2 - 12x = -9x^3 + 3x^2 - 54x + 18
2. Combine like terms:
2x^2 - 10x = -9x^3 + 3x^2 - 54x + 18
3. Move all terms to one side of the equation:
9x^3 - x^2 + 44x - 18 = 0
4. Use the Rational Root Theorem to find possible solutions:
The possible rational roots are ±1, ±2, ±3, ±6, ±9, ±18
5. Use synthetic division to test the possible roots and find the actual solutions:
When we divide by -2, we get a remainder of 0, so -2 is a solution.
When we divide by 3, we get a remainder of 0, so 3 is a solution.
When we divide by -3, we get a remainder of 0, so -3 is a solution.
6. The solutions are x = -2, x = 3, and x = -3.
So the final answer is:
x = -2, 3, -3
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8:02 PM Wed Feb 22 L Allie Stevenson's practice S.12 Properties of logarithms: mixed review Rewrite the logarithmic expression as a single logarithm with the same base. Assume all expressions exist and are well-defined. Simplify any fractions. 2log_(w)x+4log_(w)2x
The simplified expression is log_(w)(16x^6)
To rewrite the logarithmic expression as a single logarithm with the same base, we need to use the properties of logarithms. The properties we will use are:
1) log_b(x)+log_b(y) = log_b(xy)
2) a*log_b(x) = log_b(x^a)
Using the first property, we can combine the two terms with the same base:
2log_(w)x+4log_(w)2x = log_(w)x^2+log_(w)(2x)^4
Using the second property, we can simplify the exponents:
log_(w)x^2+log_(w)(2x)^4 = log_(w)x^2+log_(w)16x^4
Using the first property again, we can combine the two terms with the same base:
log_(w)x^2+log_(w)16x^4 = log_(w)(x^2*16x^4)
Simplifying the expression inside the logarithm:
log_(w)(x^2*16x^4) = log_(w)(16x^6)
Therefore, the final expression is:
2log_(w)x+4log_(w)2x = log_(w)(16x^6)
Answer: log_(w)(16x^6)
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Eric bought a truck in 2015 for $43,500. By 2020, the truck was worth $36,500.
Part A. What function type could model the given situation?
Part B. What is the rate of change in the truck's worth per year?
Part C. Which model describes this situation?
A function type that could model the given situation is a linear function.
The rate of change in the truck's worth per year is -1400.
A model that describes this situation is y = -1400x + 43500
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Substituting the given data points into the slope formula, we have the following;
Slope (m) = (36,500 - 43,500)/(2020 - 2015)
Slope (m) = -7,000/5
Slope (m) = 1,400.
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The state capitals of Santa Fe, Oklahoma City, and Austin are shown in the map below. Abbreviating the cities by their first letter, write a mathematical statement using the Triangle Inequality Theorem to prove the distance from Santa Fe to Austin to Oklahoma City is greater than the distance from Santa Fe to Oklahoma City. (PLEASE HELPPPPP!!)
Using the Triangle Inequality Theorem the correct option is [tex]$SA + AO > SO$[/tex].
What is triangle inequality theorem?
The Triangle Inequality Theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side. In mathematical notation, for a triangle with sides of lengths a, b, and c, this can be written as:
a + b > c
b + c > a
a + c > b
The correct mathematical statement using the Triangle Inequality Theorem to prove the distance from Santa Fe to Austin to Oklahoma City is greater than the distance from Santa Fe to Oklahoma City is:
[tex]$SA + AO > SO$[/tex]
where:
SA is the distance from Santa Fe to Austin
AO is the distance from Austin to Oklahoma City
SO is the distance from Santa Fe to Oklahoma City
This inequality states that the sum of the distances from Santa Fe to Austin and from Austin to Oklahoma City is greater than the distance from Santa Fe to Oklahoma City.
Therefore the correct option is [tex]$SA + AO > SO$[/tex].
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