Mr. Clayton is contemplating which chauffeured car service to take to the airport. The first costs $5 up front and $4 per kilometer. The second costs $15 plus $3 per kilometer. For a certain driving distance, the two companies charge the same total fare. What is the distance? Write a system of equations, graph them, and type the solution.______ kilometers
Answers
Given in the question:
a.) The first costs $5 upfront and $4 per kilometer.
b.) The second costs $15 plus $3 per kilometer.
Let's generate the equation of each of the car service charges,
Let,
y = total cost of service
x = distance traveled
a.) The first costs $5 upfront and $4 per kilometer.
[tex]\text{ y = 5 + 4x}[/tex]b.) The second costs $15 plus $3 per kilometer.
[tex]\text{ y = 15 + 3x}[/tex]Let's determine the driving distance when the two companies charge the same.
We get,
[tex]y_{1st\text{ Company}}=y_{2nd\text{ Company}}_{}[/tex][tex]\text{ 5 + 4x = 15 + 3x}[/tex][tex]\text{ 4x - 3x = 15 - 5}[/tex][tex]\text{ x = 10}[/tex]Therefore, the two companies charge the same at a driving distance of 10 kilometers.
Summary:
1. The system of equations.
y = 5 + 4x
y = 15 + 3x
2. The solution.
x = 10
3. Graphing the system of equations.
Related Questions
A planner at Barnes and Noble originally cost $10. During the weekend, the planner went on sale for $9. What is the price markdown (percent of change)?
Answers
new cost = $9
original cost = $10
Substitute the value into the formula;
[tex]\text{percentage change =}\frac{10-9}{10}\times100^{}[/tex]
= 1/10 x 100%
= 10%
hello I need on this hw question please thank you
Answers
Given:
The given equation is,
[tex]3x-19+(?)x=-5x-19[/tex]Required:
To find the missing value.
Answer:
The given equation is,
[tex]\begin{gathered} 3x-19+(?)x=-5x-19 \\ \end{gathered}[/tex]By putting (-8) in place of (?) in the given equation, we get,
[tex]\begin{gathered} 3x-19+(-8)x=-5x-19 \\ \Rightarrow3x-19-8x=-5x-19 \\ \Rightarrow-5x-19=-5x-19 \\ \Rightarrow-19=-19 \end{gathered}[/tex]This shows that the given equation has infinitely many solutions.
Final Answer:
The missing value is -8.
Determine whether the point (2,0) is a solution to the system of equations.
Answers
From the given graph of the system of equations
[tex]\begin{gathered} f(x)=|x-1|+1 \\ g(x)=3x+2 \end{gathered}[/tex]It is the point (2,0) is not on any of the graphs of f(x) and g(x). Also,
[tex]\begin{gathered} f(2)=|2-1|+1 \\ =2 \\ \ne0 \\ g(2)=8 \\ \ne0 \end{gathered}[/tex]Since (2,0) doesn't satisfy given equations, therefore, (2,0) is not a solution of the given system.
It can be noted that the solution of the system is (0,2) as it lies on the intersection of f(x) and g(x)
Lisa started a busines 8 years ago with an intial investment of $250,000. It is now worth 6 times that amout. How much is the company worth now?
Answers
Answer:
1,500,000 is the answer
Answer:
Step-by-step explanation:
1,500,000 million, enjoy
3. Is there another method to determine this value besides a calculator? What are the pros and cons to using the nCr function on yourgraphing calculator in comparison to the other method(s) you mentioned?
Answers
Given:
The expression is:
[tex]_{12}C_5[/tex]Find-:
The value of the expression
Explanation-:
The formula of:
[tex]_nC_r[/tex]Combination formula:
[tex]_nC_r=\frac{n!}{(n-r)!r!}[/tex]The given expression is:
[tex]\begin{gathered} n=12 \\ \\ r=5 \end{gathered}[/tex]So, the value is:
[tex]\begin{gathered} _{12}C_5=\frac{12!}{(12-5)!5!} \\ \\ =\frac{12\times11\times10\times9\times8\times7!}{7!\times5!} \\ \\ =\frac{12\times11\times10\times9\times8}{5!} \\ \\ =\frac{12\times11\times10\times9\times8}{5\times4\times3\times2\times1} \\ \\ =792 \end{gathered}[/tex]The value is 792.
find the following and trophs velties. Foeliconicagate axis enda ontsuchsympotes 28-12-22graph item 1
Answers
vertices: (3, 2) and (-1, 2)
foci: (1+√13, 2) and (1-√13, 2)
conjugate axis endpoints: (1, 5) and (1, -1)
asymptotes: y = 2 + 3/2(x - 1) and y = 2 - 3/2(x - 1)
Simplity 24 ÷ (-2)(3) + 7
Answers
Nashia, this is the solution:
24 ÷ (-2)(3) + 7
• We use ,PEMDAS, for the order of operations, as follows:
Step 1: Solve the parenthesis
24 ÷ -6 + 7
Step 2: We solve the division
-4 + 7
Step 3: We solve the addition
3
The result is 3
Find the length of the leg of a triangle with a hypotenuse of 16 and a side of 12
Answers
c= 4√7
1) Given that we have a leg of 12 and a hypotenuse of 16 units. Let's use the Pythagorean Theorem to find the missing leg.
2) a² =b²+c²
hypotenuse² = leg² +leg²
16² =12² +c²
256= 144 + c²
256 -144 = c²
112=c²
√c²=√112
c=4√7 (approximately 10.58 units)
3) Hence, we can state that the missing leg has the size of 4√7 units
What is x?
-2 + 3x = 5x - 8
Answers
Answer:
x = 3
Step-by-step explanation:
-2 + 3x = 5x - 8
add 8 to both sides:
-2 + 3x + 8 = 5x - 8 + 8
6 + 3x = 5x
subtract 3x from both sides:
6 + 3x - 3x = 5x - 3x
6 = 2x
divide both sides by 2:
6/2 = 2x/2
x = 3
check: when x = 3
-2 + 3(3) = 5(3) - 8
-2 + 9 = 15 - 8
7 = 7
Answer:
X = 3
Step-by-step explanation:
-2 + 3x = 5x - 8
+8 Because -8 is lower then -2 we start by doing the opposite and +8 to -2
6 + 3x = 5x
-3x Because now we have to do the opposite on the variable too.
6 = 2x
/2 Because you have to divide the integer by the variable
x = 3
|5а + 10| = |6a - 8|
i don’t understand how to do this pls help
Answers
Answer:
Step-by-step explanation:
|5a+10|=|6a-8|
5a+10=±(6a-8)
5a+10=6a-8
10+8=6a-5a
a=18
or
5a+10=-(6a-8)
5a+10=-6a+8
5a+6a=8-10
11a=-2
a=-2/11
If D = t +9t2 and C = t - t - 8, find an expression that equals D - 3C in standard form?
Answers
we have
[tex]\begin{gathered} D-3C=t+9t^2-3(t-t-8)=t+9t^2-3(-8) \\ =t+9t^2+24 \end{gathered}[/tex]in standard form
[tex]9t^2+t+24[/tex]calculate the cost of manufacturing a standard cereal box if cardboard costs $0.05 per square inchsurface area 290inches^2 volume is 264in^2cost would be?
Answers
We will have that the cost of manufacturing would be:
[tex]C=(0.05)(290)\Rightarrow C=14.5[/tex]So, the cost per box is $14.5.
Find the angle between the following pair of vectors: Around your answers to nearest tenths.p = < -8 , 1 > r = < -4 , 0 >
Answers
Angle = 7.1°
Zak jogs from his house to a lake. He then jogs 5 laps around the lake at a constant speed. The table shows thetotal amount of time, in minutes, Zak has been jogging after completing x laps.Which equation represents the time, m, in minutes, Zak has been jogging after completing x laps?A m = 12x + 5B m = 5x + 12C m = 24x + 5D m = 5x + 24
Answers
We are given Zak's laps jogged along with the minutes elapsed.
If the equation of a line is:
m = kx + b
Where m is the number of minutes.
k is the slope of the line
x is the Laps
b is the y-intercept (or where the line crosses the y-axis)
In order to get the equation of the relationship between Laps (x) and Minutes (m),
we need to calculate the slope k and intercept b.
The formulas for doing these are given below:
[tex]\begin{gathered} m=\frac{\sum(x_i-X)(y_i-Y)}{(x_i-X)^2} \\ \text{where,} \\ x_i=\text{data points of Laps x} \\ X=\text{ Average of the Laps x} \\ y_i=\text{data points of Minutes m} \\ Y=\text{Average of Minutes m} \end{gathered}[/tex]The formula for intercept (b) is;
[tex]b=Y-kX[/tex]where Y and X are the averages of m and x values from the table.
[tex]\begin{gathered} Y=\frac{\sum m}{n}\text{ (n is the number of data values of Y)} \\ Y=\frac{17+41+65}{3} \\ \\ Y=41 \\ \\ X=\frac{\sum x}{n}\text{ (n is the number of data values of X)} \\ X=\frac{1+3+5}{3} \\ \\ X=3 \end{gathered}[/tex]In order to be tidy and quick, a table is used to solve.
This table is shown in the image below:
Therefore, we can now calculate slope (m):
[tex]\begin{gathered} m=\frac{\sum(x_i-X)(y_i-Y)}{(x_i-X)^2} \\ \\ m=\frac{\mleft(-24\mright)\mleft(-2\mright)+0\mleft(0\mright)+\mleft(24\mright)\mleft(2\mright)}{4+0+4} \\ m=\frac{96}{8} \\ \\ m=12 \end{gathered}[/tex]Now that we have slope (k) = 12, we can get the intercept b
[tex]\begin{gathered} b=Y-kX \\ Y=41-12(3) \\ Y=41-36 \\ Y=5 \end{gathered}[/tex]Therefore, the equation is:
m = 12x + 5
√45 + √20 = 5√5
———————————————
Answers
Answer:
and the fact that she got to the shoe store and bought it for her if she was a kid she would have a lot of gumball toys
Step-by-step explanation:
perpendicular
A store purchased an item for $90 and planned to sell it for $162.00 so that their profitwould be 40% of their cost. If they were unable to sell it for this amount, what minimumselling price would allow them to break even?$
Answers
Given that a store purchased an item for $90.
They want a profit of 40% of their costs.
So, 40% of their costs = 40% of $90
= 40/100 * 90
= $36
Let y be the minimum selling price
So, from the question we c an say thst:
y = $(90 + 36)
y = $126
Therefore the minimum selling price of $126 would give the profit of 40% of their cost.
Select all points from the list below that lie in the solution set of the system of inequalities graphed below?
Question 3 options:
(7, 0)
(3, 0)
(0, 7)
(-3, -5)
(9, -3)
(0, -1)
Answers
The points that lie in the solution set of the system of inequalities graphed are: (7, 0), (3, 0), (9, -3)
In this question, we have been given a graph system of inequalities.
We need to select all points from the given list that lie in the solution set of the system of inequalities.
The solution set for given inequalities is the set of all points which satisfy inequalities.
The solution set is represented by the common region shaded between two inequalities.
From graph, we can see that the points (7, 0), (3, 0), (9, -3) lie in the solution set of the system of inequalities graphed.
Therefore, the points that lie in the solution set of the system of inequalities graphed are: (7, 0), (3, 0), (9, -3)
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Factors of 12: 1. 2. 3. 4. 6. 12 Factors of 20: 1, 2, 4, 5, 10, 20 • Which numbers are common factors of 12 and 20? Choose ALL that apply. 1 2 3 6 10 12 20
Answers
The common factors are; 1,2,4
700 tickets were sold for a game for a total of $900.00 If adult tickets sold for $2.00 and children's tickets sold for $1.00 how many of each kind of ticket were sold?
Answers
Let x be the number of adult tickets and let y be the number of children.
We know that in total there were sold 700 tickets, that means:
[tex]x+y=700[/tex]Now we know that each adult ticket was $2 and the children's tickets was $1, and that the total was $900, this means that:
[tex]2x+y=900[/tex]Then we have the following system of equations:
[tex]\begin{gathered} x+y=700 \\ 2x+y=900 \end{gathered}[/tex]To solve it we substract the second equation from the first one, then we have:
[tex]\begin{gathered} x+y-2x-y=700-900 \\ -x=-200 \\ x=200 \end{gathered}[/tex]Now that we have the value of x we plug it in the first equation to find y:
[tex]\begin{gathered} 200+y=700 \\ y=700-200 \\ y=500 \end{gathered}[/tex]Therefore, there were 200 adult's tickets and 500 children's tickets sold.
What is the equation for a line transforming from y= x with a slope 5/6?
Answers
The equation of the transformed function is y' = 5/6x
How to determine the equation of the transformed function?From the question, we have the following equation that can be used in our computation:
y = x
Also, we have the slope of the linear function to be
Slope = 5/6
This can be rewritten as:
m = 5/6
When the function is transformed, we have the following representation:
y' = m * y
Substitute the known values in the above equation
y' = 5/6 * x
Evaluate
y' = 5/6x
Hence, the equation is y' = 5/6x
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Our school district is sending two teachers to a 3-day training session on innovative teaching
strategies. Expenses per person: registration, $275; supplies, $40; breakfast, $8; lunch $15;
and dinner $20. Total transportation cost for the two people is $120. If our district has
budgeted $1,500 for the 2 to attend the training session, what is the most they can each pay
for their hotel per person per night?
Answers
Answer: Approximately $117.33
Step-by-step explanation:
1. Add all the Expenses per person to get $338
2. Multiply these expenses by 2 for each person to get $676
3. Add $120 for Transportation to get $796
4. Multiply the people going by the amount of days they are staying to get 6
5. Subtract the total expenses by the budget to get $704
7. Divide the answer of step 4 by the remaking budget to get the final answer of approximately $117.33
write the equations of all the circles in the design from smallest to biggest .( please help me )
Answers
The equation of a circle is given by the formula;
(x-h)² + (y-k)² = r²
r is the radius of the circle
(h,k) is the center of the circle
Smallest circle (Red circle)
r = 1
(h,k)= (0, 7)
substitute the values into the formular
(x - 0)² + (y-7)² = 1²
x²+ (y-7)² =1
Bigger circle (Blue circle)
r= 3 h=0 K=3
substitute the values into the formula
(x -0)² + (y-3)²= 3²
x² + (y-3)² = 9
Biggest circle ( Orange Circle)
r=5 h=0 K=-5
substitute the values into the formula and evaluate
(x-0)² + (y+5)² = 5²
x² +(y+5)² = 25
The cost per student of a ski trip varies inversely as the number of students who attend. It will cost each student $250 if 24 students attend. How many students would have to attend to get the cost down to $200?
Answers
ANSWER
30 students
EXPLANATION
The cost per student varies inversely as the number of students.
Inverse proportion is written as:
[tex]\begin{gathered} y\propto\frac{1}{x} \\ y=\frac{k}{x} \\ \text{where k = constant of proportionality} \end{gathered}[/tex]Let the cost per student be y.
Let the number of students be x.
It will cost each student $250 if 24 students attend. This means that:
[tex]\begin{gathered} 250=\frac{k}{24} \\ \Rightarrow k=250\cdot24 \\ k=6000 \end{gathered}[/tex]If the cost is down to $200, it means that y is now $200.
That is:
[tex]\begin{gathered} 200=\frac{6000}{x} \\ \Rightarrow x=\frac{6000}{200} \\ x=30\text{ students} \end{gathered}[/tex]Therefore, 30 students could attend.
John's bank account was overdrawn. The status of his account was − $162. He did not realize the problem and wrote another check for $78. The bank charged him a $24 fee for being overdrawn.What was the new status of John's account at this point?
Answers
The initial status of John's bank account was -$162.
After he wrote a check for $78 and being charged in $24 for being overdrawn, the new status is - 162 - 78 - 24 = -$264
someone help me thanks! it's on pythagoras theorem btw
Answers
Answer:
y = 3
Step-by-step explanation:
Pythag theorem : ( only applies to RIGHT triangles)
Hypotenuse ^2 = leg1 ^2 + leg 2^2
(7y-1)^2 = (5y-3)^2 + (5y+1)^2
49 y^2 - 14y +1 = 25y^2 -30 y + 9 + 25y^2 + 10y + 1
-y^2 + 6y -9 = 0
or y^2 -6y + 9 = 0 solve by factoring or using Quadratic Formula
( y -3)(y-3) = 0 shows y = 3
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Which equation represents a line that passes through (–9, –3) and has a slope of –6?
Explain How You got the answer
y – 9 = –6(x – 3)
y + 9 = –6(x + 3)
y – 3 = –6(x – 9)
y + 3 = –6(x + 9)
Answers
Answer:
y – 9 = –6(x – 3)
y – 3 = –6(x – 9)
i think im not quit sure if this is correct but i hope this helps :)
URGENT PLEASE HELL SOLVE FOR X . idc if you don’t show work
Answers
For a right triangle ABC, you are told that cos A=X and sun A=y. Which option gives an expression that is equivalent to tan A? X/ x2+y2. X/y. Y/X. Y/x2+y2
Answers
For a right triangle ABC, the expression that is equivalent to tan A is y/x.
What is defined as the trigonometric functions?Trigonometric functions, also recognized as circular functions, are simply functions of a triangle's angle. These trig functions define the relationship between both the angles as well as sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions. The sine, cosine, as well as tangent angles are the primary categorization of trigonometric functions. The primary functions can be used to derive the three functions cotangent, secant, and cosecant.For the given question,
In a right triangle ABC.
The cosine and sin functions are defined as;
cos A=X and sin A=y.
Then, we know that tan A function can be written in the form in the form of cos A and sin A as,
tan A = sin A/ cos A
Put the values,
tan A = y/x
Thus, the expression that is equivalent to tan A is y/x.
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Find the square of each number. (Do not add extra spaces in your response.)
1.) 7 =
2.) 21 =
3.) -3 =
4.) 45 =
5.) 2.7 =
6.) −14=
7.) -5.7 =
8.) 25=
Answers
2.) 21 = 441
3.) -3 = -9
4.) 45 = 2,025
5.) 2.7 = 7.29
6.) -14 = -196
7.) -5.7 = -32.49
8.) 25 = 625
Use the information to find and compare ∆y and dy (Round your answers to three decimal places.)
y=4x^3 x=2 ∆x=dx=0.1
Answers
The values of derivatives Δy and dy are given as 0.48 and 4.8
The values of Δy and dy will be calculated using the formula Δy = f(x + Δx) - f(x) and dy = f'(x)dx. For calculating the values, we put the values which are given in the question that is
Δy = f(x + Δx) - f(x)
Δy = f(2 + 0.1) - f(2)
Δy = f(2.01) - f(2)
Δy = 4(2.01)³ - 4(2)³
Δy = 32.48 - 32
Δy = 0.48
Now, we have f(x) = 4x³, so we have f'(x) = 12x²
Now, dy = f'(x)dx
dy = 12x²dx
dy = 12(2)²(0.1)
dy = 4.8
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