Answer:
10 soccer club members are going to the tournament.
Step-by-step explanation:
Let x be the number of soccer club members who are going to the tournament,
Given,
The cost of transportation of x students = $ 192
⇒ The cost of transportation of 1 student = [tex]\frac{192}{x}[/tex]
⇒ The cost of transportation of (x+2) student = [tex]\frac{192}{x-2}[/tex]
According to the question,
[tex]\frac{192}{x}-\frac{192}{x+2}=3.20[/tex]
[tex]192(\frac{1}{x}-\frac{1}{x+2})=3.20[/tex]
[tex]192(\frac{x+2-x}{x(x+2)})=3.20[/tex]
[tex]\frac{384}{x^2+2x}=3.20[/tex]
[tex]3.2x^2+6.4x=384[/tex]
[tex]3.2x^2+6.4x-384=0[/tex]
By the quadratic formula,
[tex]x=\frac{-6.4\pm \sqrt{40.96+4915.2}}{6.4}[/tex]
[tex]\implies x = \frac{-6.4\pm 70.4}{6.4}[/tex]
[tex]\implies x = 10\text{ or } x = -12[/tex]
Since, the number can not be negative,
Hence, 10 soccer club members are going to the tournament.
To find the number of soccer club members going to the tournament, we set up an equation based on the total cost of the van and the drop in cost per person when two additional students join. Solving the quadratic equation reveals that the number of soccer club members is 10.
Explanation:The question asks us to determine the number of soccer club members going to the tournament given that the cost of the van is $192 and that the cost per person drops by $3.20 when 2 additional students join the trip. Let's denote the number of club members as 'x'. Before the 2 students join, the cost per person is $192 / x. After they join, the cost per person becomes $192 / (x + 2), which is $3.20 less than the original cost per person, so:
192 / x - 192 / (x + 2) = $3.20
Multiplying through by x(x + 2) to clear the denominators gives us:
192(x + 2) - 192x = 3.20x(x + 2)
This simplifies to:
192x + 384 - 192x = 3.20x^2 + 6.4x
The term 192x cancels out on both sides, so we have:
384 = 3.20x^2 + 6.4x
To solve for 'x', we divide both sides by 3.20:
120 = x^2 + 2x
Now we solve the quadratic equation x^2 + 2x - 120 = 0. Factoring this equation, we get (x + 12)(x - 10) = 0. Thus, x can be -12 or 10. However, since we can't have a negative number of club members, the number of soccer club members is 10.
Subtract.
(6k+2)−(3k−2)
Enter your answer, in simplified form, in the box.
Please answer!
the speed of an object in space is shown in the graph
what is the slope of the line ?
Answer:
Step-by-step explanation:
The answer is fifteen
Explanation: 6-3/0.4-0.2=3 over 0.2 which is equivalent to 15
Answer B: 15
Step-by-step explanation:
Factories and solve x^2 +x -12=0
Help please!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!11
A bicycle manufacturer is reducing the number of spokes on each bicycle wheel by 4. a wheel on one of the other companies new cross-country bike has 32 spokes. Which equation could be used to determine the number of spokes that a wheel on a cross country bike used to have?
The original number of spokes on the wheel was 36.
The question seeks to determine the original number of spokes on a bicycle wheel, given that the current number is 32 after reducing by 4. To find the original number of spokes, we need to use a simple algebraic equation that adds the removed spokes back to the current number.
Let x represent the original number of spokes. The manufacturer has reduced the number of spokes by 4, so we subtract 4 from the original number to get the current number of spokes. The equation that represents this scenario is:
x - 4 = 32
To find the original number of spokes, we need to solve for x:
x = 32 + 4
x = 36
Therefore, the original number of spokes on the wheel was 36.
Each of the two congruent sides of an isosceles triangle is 8 inches less than twice the base.the perimeter of the triangle is 74 inches ,what is the length of the base
The length of the base of the isosceles triangle is 18 inches.
Explanation:Let the length of the base be 'b' inches. According to the given information, each of the congruent sides of the isosceles triangle is 8 inches less than twice the base. So, the length of each congruent side is (2b - 8) inches.
The perimeter of the triangle is the sum of all three sides, which is given as 74 inches. So, we can write the equation:
(2b - 8) + (2b - 8) + b = 74
Simplifying the equation, we get:
5b - 16 = 74
5b = 90
b = 18
Therefore, the length of the base is 18 inches.
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when the handles are lifted 7.5 centimeters, the load is lifted 3 centimeters. What is the mechanical advantage of this lever?
Answer:
2.5 :)
Step-by-step explanation:
fast help plz.Brennon has a computer game that responds with either "go" or "stop" when a button is pressed. The probability that the response is "stop" is not known to game players. Brennon presses the button repeatedly and records the numbers of "stop" responses.
Number of button presses 10 50 100
Number of "stop" responses 2 18 33
Estimate P(go) using the collected data
G. 67%
O. 18%
L. 50%
D. 33%
plz help i had to write this whole thing
The vertices of triangle ABC are A(2,3), B(–1,2), and C(3,1). If ΔDEF ∼ ΔABC and DE = 4AB, what is the length of EF? √10
Answer:
The length of EF is [tex]4\sqrt{17}[/tex] units.
Step-by-step explanation:
The vertices of triangle ABC are A(2,3), B(–1,2), and C(3,1).
Using distance formula:
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]BC=\sqrt{(3+1)^2+(1-2)^2}=\sqrt{17}[/tex]
It is given that ΔDEF ∼ ΔABC.
If two triangles are similar then the corresponding sides are proportional.
[tex]\frac{AB}{DE}=\frac{BC}{EF}[/tex]
[tex]\frac{AB}{4AB}=\frac{BC}{EF}[/tex] (DE = 4AB)
[tex]\frac{1}{4}=\frac{BC}{EF}[/tex]
[tex]EF=4\times BC[/tex]
[tex]EF=4\times \sqrt{17}[/tex]
[tex]EF=4\sqrt{17}[/tex]
Therefore the length of EF is [tex]4\sqrt{17}[/tex] units.
what is the scale factor of 25ft by 75ft and 1:15
The graph shows how the cost of gasoline
need help with my hw
5. this gate contains a series if congruent quadrilaterals. Are the quadrilaterals also parallelograms? Explain.
The shaded area represents a cement walkway around a pool. State the algebraic expression that represents the difference between the outside perimeter of the walkway and the perimeter of the pool.
The difference between the outside perimeter of the walkway and the perimeter of the pool in algebraic expression is (2x + 14).
How to solve perimeter of rectangle?Pool:
Length = 2x - 1
Width = 12
The perimeter of the pool = 2(length + width)
= 2{(2x - 1) + 12}
= 2(2x - 1 + 12)
= 2(2x + 11)
= 4x + 22
Outside perimeter of the walkway:
Length = (2x - 1) + x
= 3x - 1
Width = 12 + 7
= 19
The perimeter of the walkway = 2(length + width)
= 2{(3x - 1) + 19}
= 2(3x - 1 + 19
= 2(3x + 18)
= 6x + 36
Difference between the outside perimeter of the walkway and the perimeter of the pool = The perimeter of the walkway - The perimeter of the pool
= (6x + 36) - (4x + 22)
= 6x + 36 - 4x - 22
= 2x + 14
Hence, (2x + 14) is the expression which represents the difference between the perimeter of the walkway and the perimeter of the pool.
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Each pair of polygons is similar .Determine the transformation that maps one figure onto the other . Then find the missing side measures number 4 please
Solve the following system of equations by linear combination:
3d – e = 7
d + e = 5
The solution is (3, 2).
The solution is (2, –1).
There is no solution.
There are an infinite number of solutions.
A carpenter makes custom desks. He currently has 7 desks in his showroom. If he can build 3 desks each week, how many weeks will it take him to have a total of 22 desks?
Harrison saved $48.97 from his first paycheck and $67.09 from his second paycheck. How much did he save from the paychecks? A. $18.12 B. $115.96 C. $116.06 D. $116.16
Amy walks 5 miles north. Then, she turns east and walks another 6 miles before she stops to rest.
How far is Amy from her starting point when she stops to rest?
Round your answer to the nearest tenth
Owen plots the numbers 4, ???6, ???8, and ???3 on a horizontal number line. Which list shows the numbers in the order in which they would appear from left to right on the number line?
???8, ???6, ???3, 4
???3, ???6, ???8, 4
???3, 4, ???6, ???8
???8, ???6, 4, ???3
Answer:
The answer is a. the real answer
Step-by-step explanation:
Checking on answer to this
You don't need to explain, just try to write the answer and then PRESS PIC
The annual inflation rate is 3.5% per year. If a movie costs $7.50, determine which of the following graphs best models the change in price, with respect to time, of the movie ticket.
Answer:
Step-by-step explanation:
Let's model the cost by the following exponential function: c (t) = (7.50) * (1.035) ^ t Where, c (t): cost of the movie after t years. 7.50: initial cost of the movie in $ 1,035: annual percentage increase due to inflation. t: time in years. for t = 0 We have: c (t) = (7.50) * (1.035) ^ 0 c (t) = (7.50) * (1) c (t) = 7.50 Answer: The graph that best models the function is: GRAPH 2 (from left to right).
Rewrite the given expression in the form 3^u where u is a constant or an algebraic expression.
(5√3)^x
Rewrite the expression in the form 2^u where u is an algebraic expression
(1/2)^x-3
Rewrite the expression in the form 2 Superscript u where u is an algebraic expression
9/3√3
Rewrite the expression in the form 2 Superscript u where u is an algebraic expression
16/3√2^x
Solution: (1) The expression [tex](5\sqrt{3} )^x[/tex] [tex]\text{ is written as }[/tex] [tex]5^x3^{\frac{x}{2}[/tex].
[tex](5\sqrt{3} )^x=5^x(\sqrt{3} )^x\\(5\sqrt{3} )^x=5^x(3^\frac{1}{2} )^x\\(5\sqrt{3} )^x=5^x3^\frac{x}{2}[/tex]
The value of u is [tex]\frac{x}{2}[/tex].
(2) The expression [tex](\frac{1}{2})^x-3[/tex] is written as [tex]2^{-x}-3[/tex].
[tex](\frac{1}{2})^x-3=(2^{-1})^x-3\\(\frac{1}{2})^x-3=2^{-x}-3[/tex]
The value of u is -x.
(3) The expression [tex]\frac{9}{3\sqrt{3} }[/tex] is written as [tex]\sqrt{3} (2^0)[/tex].
[tex]\frac{9}{3\sqrt{3} }=\frac{9}{3\sqrt{3} }(\frac{\sqrt{3}}{\sqrt{3}} )\\\frac{9}{3\sqrt{3} }=\frac{9(\sqrt{3}) }{3(3) }\\\frac{9}{3\sqrt{3} }=\sqrt{3} \\\frac{9}{3\sqrt{3} }=\sqrt{3}(2^0)[/tex]
THe value of u is 0.
(4)The expression [tex]\frac{16}{3(\sqrt{2^{x}} )}[/tex] is written as [tex]\frac{1}{3}(2^{4-\frac{x}{2}})[/tex].
[tex]\frac{16}{3(\sqrt{2^{x}} )}=\frac{2^4}{3(2^x)^{1/2}}\\\frac{16}{3(\sqrt{2^{x}} )}=\frac{1}{3}(2^{4-\frac{x}{2}})[/tex]
The value of u is [tex]4-\frac{x}{2}[/tex].
Final Answer:
1. [tex]\( (5\sqrt{3})^x \) in the form \( 3^u \): \( 3^{x\log_3(5\sqrt{3})} \)[/tex]
2. [tex]\( (1/2)^{x-3} \) in the form \( 2^u \): \( 2^{-(x-3)} \)[/tex]
3. [tex]\( \frac{9}{3\sqrt{3}} \) in the form \( 2^u \): \( 2^{2/3} \)[/tex]
4. [tex]\( \frac{16}{3\sqrt{2^x}} \) in the form \( 2^u \): \( 2^{(2x-4)/3} \)[/tex]
Explanation:
1. [tex]\( (5\sqrt{3})^x \) in the form \( 3^u \): \( 3^{x\log_3(5\sqrt{3})} \)[/tex]
To express [tex]\( (5\sqrt{3})^x \)[/tex] in the form [tex]\( 3^u \)[/tex], we use the logarithmic property [tex]\( a^{\frac{1}{n}} = n\sqrt[n]{a} \)[/tex]. Applying this, we get [tex]\( 5\sqrt{3} = 3^{\frac{\log_3(5\sqrt{3})}{\log_3(3)}} \)[/tex], and raising it to the power ( x ) yields the desired form.
2. [tex]\( (1/2)^{x-3} \) in the form \( 2^u \): \( 2^{-(x-3)} \)[/tex]
To rewrite [tex]\( (1/2)^{x-3} \)[/tex] in the form [tex]\( 2^u \)[/tex], we use the property [tex]\( a^{-b} = \frac{1}{a^b} \)[/tex]. Applying this, we transform the expression to [tex]\( 2^{-(x-3)} \)[/tex], achieving the desired form.
3. [tex]\( \frac{9}{3\sqrt{3}} \) in the form \( 2^u \): \( 2^{2/3} \)[/tex]
By canceling out the common factor of 3 in the numerator and denominator, we simplify [tex]\( \frac{9}{3\sqrt{3}} \)[/tex]to [tex]\( 2^{2/3} \), as \( \sqrt{3} = 3^{1/2} \)[/tex].
4. [tex]\( \frac{16}{3\sqrt{2^x}} \)[/tex] in the form [tex]\( 2^u \): \( 2^{(2x-4)/3} \)[/tex]
Applying the property[tex]\( a^{-b} = \frac{1}{a^b} \)[/tex] to the denominator, we simplify [tex]\( \frac{16}{3\sqrt{2^x}}[/tex] to [tex]\( 2^{(2x-4)/3} \)[/tex], achieving the desired form.
Help help help help help
Which expression represents the product of Z and 7?
A. Z+7
B. Z-7
C. Z•7
D. Z divided by 7
Identify the corresponding word problem, given the inequality: 16x ≥ 384
A) Clint is going hiking and will need to carry enough water for the duration of the hike. He determines he will need 384 ounces of water. If a bottle holds 16 ounces of water, how many bottles will he need?
B) Clint is going hiking and will need to carry enough water for the duration of the hike. He determines he will need at least 384 ounces of water. If a bottle holds 16 ounces of water, how many bottles will he need?
C) Clint is going hiking and will need to carry enough water for the duration of the hike. He determines he will not need more than 384 ounces of water. If a bottle holds 16 ounces of water, how many bottles will he need?
D) Clint is going hiking and will need to carry enough water for the duration of the hike. He determines he will need at least 24 bottles of water. If a bottle holds 16 ounces of water, what is the total amount of water he will need?
Graph the set of points. Which model is most appropriate for the set? (-2, 10), (-1,1), (0, -2), (1, 1), (2, 10)
Quadratic
Quadratic
Liner
Exponential
Answer:
The model that is most appropriate for the set is:
Quadratic.
Step-by-step explanation:
Clearly after looking at the graph of the function which is made from the given set of points ; we observe that the graph is similar to a graph of the quadratic function whose vertex is at (0,-2) and also the line x=0 is the axis of symmetry of the graph.
Since, the graph is symmetric to this line.
Hence, the model is:
Quadratic.
Determine which of the following expressions simplifies to x - 4y. Select all situations that apply.
-x(-2 + 8y)
-(-2x + 8y)
3(x - 2y) + 2(y - x)
(y - x)(-2) (-2)
Answer:
The above one is partly correct the answer (for odyssey ware) is (-(1)/(2)x+2y)(-2)
-(1)/(2) (-2 x + 8 y)
and 3( x - 2 y) + 2( y - x)
Hope this helps people in the future ☜(ﾟヮﾟ☜)
Step-by-step explanation:
light travels at a rate of 1.86 x 10^5 miles per second. if the distance from a star to a planet and its orbit is 32,000,000 miles, find how long it takes to light of the star to reach the planet in seconds.