Answers
To solve this system of linear equations using the elimination method, first, add both equations:
[tex]\begin{gathered} 8x+5y=38\Rightarrow\text{ Equation 1} \\ -8x+2y=4\Rightarrow\text{ Equation 2} \end{gathered}[/tex][tex]\begin{gathered} 8x+5y=38 \\ -8x+2y=4\text{ +} \\ --------- \\ 0x+7y=42 \\ 7y=42 \end{gathered}[/tex]Now solve for y dividing by 7 on both sides of the equation:
[tex]\begin{gathered} \frac{7y}{7}=\frac{42}{7} \\ y=6 \end{gathered}[/tex]Finally, replace the value of y in any of the initial equations, for example in equation 1
[tex]\begin{gathered} 8x+5y=38 \\ 8x+5(6)=38 \\ 8x+30=38 \\ \text{ Subtract 30 from both sides of the equation} \\ 8x+30-30=38-30 \\ 8x=8 \\ \text{ Divide by 8 from both sides of the equation} \\ \frac{8x}{8}=\frac{8}{8} \\ x=1 \end{gathered}[/tex]Therefore, the solution of the system of equations is
[tex]\begin{cases}x=1 \\ y=6\end{cases}[/tex]Related Questions
Zacaria's kayaks store annual rent and fixed cost are $ 15,600. The variable cost each kayak old is $315 and the price of each kayak is $425.e. What is the number of kayaks that must be sold to obtain $ 50,000 in the profits?
Answers
The profit function can be gotten using the formula below:
[tex]P(x)=R(x)-C(x)[/tex]where R(x) is the revenue function and C(x) is the cost function.
As previously calculated, the revenue and cost functions are given to be:
[tex]\begin{gathered} R(x)=425x \\ C(x)=315x+15600 \end{gathered}[/tex]Therefore, the profit function is:
[tex]\begin{gathered} P(x)=425x-(315x+15600) \\ P(x)=425x-315x-15600 \\ P(x)=110x-15600 \end{gathered}[/tex]The profit to be made is $50,000. Equating the profit function to this amount, we can get the number of kayaks required. This is shown below:
[tex]\begin{gathered} 50000=110x-15600 \\ 110x=50000+15600 \\ 110x=65600 \\ x=\frac{65600}{110} \\ x=596.4 \end{gathered}[/tex]Therefore, the number of kayaks that must be sold is approximately 597 kayaks to make $50,000 in profits.
Write a system of equations that could be used to determine the number of commercials and the number of movies on which Alexa songs were played Define the variables that you use to write the system.
Answers
We make a system of equations from the statement
Alexa will earn $20 every time one of her songs is played in a commercial and she will $110 every time one of her songs is played in a movie.
[tex]T=20c+110m[/tex]
where T is the total earned, c the number of commercials and m the number of movies
Alexa earned a total of $340 in 8 commercials and movies
we replace the total (340) on the first equation and make and equation for the total of commercials and movies
[tex]\begin{gathered} 340=20c+110m \\ c+m=8 \end{gathered}[/tex]it is our system
which equation , together with y=-1.5x+3 , makes a system with just on solution.y = -1.5x+6y = -1.5x2y = -3x+62y + 3x = 6y = -2x + 3
Answers
EXPLANATION
Given the equation y= -1.5x + 3
In order to get a system with just one solution, the viable options are those that allow both lines to intersect in just one point.
Those equations are:
y= -1.5x
y=-2x + 3
The system of equations y=-1.5x+3 and y=-1.5x+6 has no solution because subtracting both expressions give us the result 3=0
The system y=-1.5x+3 and 2y = -3x+6, or in the same way the system y=-1.5x+3 and 2y + 3x = 6 has no solution because they have the same expression.
which point is located at (0,8)
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The point (0, 8) simply means the x axis is 0 while the y axis is 8. The answer is C.
Perform (3x3 – 2x2 + 3x – 4) ÷ (x – 3) to find the value of the remainder.Question 3 options:A) 98B) 88C) 68D) 78
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The remainder of the division can be found below
The answer is definitely C.
Find 5x3 + 2y2 - 9, where x = 4 and y = 2
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The equation can be solved when we substitute the value of x and y accordingly .
[tex]\begin{gathered} 5(4)^3+2(2)^2\text{ - 9} \\ 5\text{ }\times\text{ 64 + 2 }\times\text{ 4 - 9} \\ 320\text{ + 8 - 9} \\ =319 \end{gathered}[/tex]What is an equation of the line that passes through the point (1,-3) and is perpendicular to the line x+3y=21
The answer I need begins with y =
Please do not answer if your solution doesn't end that way, thank you.
Answers
The linear equation that is perpendicular to the line x+3y=21 is:
y = 3*x - 6
How to find the equation of the line?A general line in the slope-intercept form is written as:
y = m*x + b
Where m is the slope and b is the y-intercept.
Two linear equations are perpendicular if the product between the two slopes is equal to -1.
Rewriting the given line we can get:
x +3y = 21
3y = 21 - x
y = 21/3 - x/3
y = (-1/3)*x + 21/3
Then the slope is (-1/3), if our line is perpendicular to this one, then:
m*(-1/3) = -1
m = 3
our line is:
y = 3*x + b
To find the value of b, we use the fact that our line passes through (1, - 3)
-3 = 3*1 + b
-3 - 3 = b
-6 = b
The line is y = 3*x - 6
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If anyone to solve this problem it will be greatly appreciated and I will be sure to give the best possible rating
Answers
Step 1
Graph the points from the table and make a plot that can help determine the possible line of best fit.
Hence, the equation of the line of best fit with values to the nearest hundredths will be;
[tex]y=0.06x+2.57[/tex]6. 5.6% of 283 is what number?7. 55% sign of 104 is what number?
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To solve the exercise you can use a rule of three:
[tex]\begin{gathered} 283\rightarrow100\text{\%} \\ x\rightarrow5.6\text{\%} \end{gathered}[/tex][tex]\begin{gathered} x=\frac{5.6\text{\%}\cdot283}{100\text{\%}} \\ x=\frac{5.6\cdot283}{100} \\ x=\frac{1584.8}{100} \\ x=15.848 \end{gathered}[/tex]Therefore, 5.6% of 283 is 15.848.
1/2(x+6) = 2x and 5-2x =7x-h
Answers
Expression given:
[tex]\frac{1}{2}(x+6)=2x[/tex][tex]5-2\cdot(\frac{4}{5})=7\cdot(\frac{4}{5})-h[/tex]Procedure:
0. Solving for ,x: ,multiplying both sides by 2
[tex]2\cdot\frac{1}{2}(x+6)=2x\cdot2[/tex][tex]x+6=4x[/tex]Substracting both sides by x
A store is having a 20% off sale on all merchandise if my buys one item and see if $13 what was the original price of a purchase
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Since all merchandise has 20% off, so the original price is multiplied by 0.8 (80%).
Let's use the variable x to represent the original price. So we can write the following equation and solve it for x:
[tex]\begin{gathered} 0.8\cdot x=13 \\ x=\frac{13}{0.8} \\ x=16.25 \end{gathered}[/tex]Therefore the original price is $16.25.
An airplane pilot over the Pacific sights an atoll at the angle of depressionof 5º. At this time, the horizontal distance from the airplane to the atoll is4,535 meters. What is the height of the plane to the nearest meter?
Answers
Answer:
397 meters
Explanation:
Let us draw a diagram to understand the situation better.
Where H is the height of the plane.
Now the tan ratio for 5° gives
[tex]\tan 5^o=\frac{opposite}{\text{adjacent}}[/tex]Since opposite = H and adjacent = 4535 meters, the above gives
[tex]\tan (5^o)=\frac{H}{4535}[/tex]Multiplying both sides by 4535 gives
[tex]\tan (5^o)\times4535=H[/tex]Since tan(5°) =0.0875.., ( just used a calculator to find out) the above becomes
[tex]0.0875\times4535=H[/tex][tex]H=396.8125[/tex]rounding to the nearest meter gives
[tex]\boxed{H=397.}[/tex]i need help simplifying 1/3(3n+9)
Answers
Answer:
n+3
Explanation:
Given the expression:
[tex]\frac{1}{3}(3n+9)[/tex]To simplify, we first open the bracket.
[tex]=\frac{1}{3}(3n)+\frac{1}{3}(9)[/tex]We can then divide common factors:
[tex]\begin{gathered} =\frac{3n}{3}+\frac{9}{3} \\ =n+3 \end{gathered}[/tex]The simplified form is: n+3
(2x³-7x² + 7x-2) ÷ (x-2)
Answers
Answer:
Please look at the attachment below, thanks! :D
Step-by-step explanation:
what is the slope - intercept form of a line that passes through points(2,12) and (4,17) ?
Answers
A line pass through points (2, 11) and (4, 17);
The slope-intercept form of a line is given as;
[tex]\begin{gathered} y=mx+c \\ \text{Where m = slope} \\ c=\text{ y-intercept} \\ \\ \text{But slope m=}\frac{y_2-y_1}{x_2-x_1} \\ \text{Where x}_1=2 \\ x_2=4 \\ y_1=11 \\ y_2=17 \\ m=\frac{17-11}{4-2}=\frac{6}{2} \\ m=3 \end{gathered}[/tex]Also, for the y-intercept c;
[tex]\begin{gathered} \text{But when x=2, y=11} \\ \text{let's use this point to get the c} \\ 11=3(2)+c \\ c=11-6 \\ c=5 \\ \end{gathered}[/tex]Thus, the slope intercept equation of the line is;
y = 3x + 5
6 - 2x = 5x - 9x + 20
Answers
Answer:
x = 7
Step-by-step explanation:
6 - 2x = 5x - 9x + 20
−2x + 6 = −4x + 20
2x + 6 = 20
2x = 14
x = 14 : 2
x = 7
There are 1300 people over the age over the age of 12 in the small town. If the same rate of cell phone usage continues , how many yrs will it takes for 1300 people have a cell phone.
Answers
We have to find how many years it will take for the 1300 people to have a cellphone.
This means we have to find x for f(x) = 1300, that is "the number of people using cellphones at time x is 1300".
Then, we can write:
[tex]\begin{gathered} f(x)=1300 \\ 880(1.03)^x=1300 \\ 1.03^x=\frac{1300}{880} \\ 1.03^x\approx1.477 \\ x\cdot\ln (1.03)=\ln (1.477) \\ x=\frac{\ln (1.477)}{\ln (1.03)} \\ x\approx\frac{0.39}{0.03} \\ x\approx13.2 \end{gathered}[/tex]Answer: it will take 13.2 years for the 1300 people to have a cellphone.
Solve the inequality AND graph the solution set. 7(4y - 8) < -5(y-2)
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A solution to the given inequality is y < 2, which is represented by the graph shown in the image attached below.
What is a graph?In Mathematics, a graph simply refers a type of chart that is typically used for the graphical representation of data on both the horizontal and vertical lines of a cartesian coordinate or a number line.
Next, we would solve the given inequality by simplifying it as follows:
7(4y - 8) < -5(y - 2)
Opening the bracket, we have the following:
28y - 56 < -5y + 10
Rearranging the inequality by collecting like terms, we have the following:
28y + 5y < 10 + 56
33y < 66
Dividing both sides of the inequality by 33, we have the following:
y < 66/33
y < 2
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Under her cell phone plan, Ella pays a flat cost of $58.50 per month and $3 per gigabyte, or part of a gigabyte. (For example, if she used 2.3 gigabytes, she would have to pay for 3 whole gigabytes.) She wants to keep her bill under $65 per month. What is the maximum whole number of gigabytes of data she can use while staying within her budget?
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She can consume up to 2 gigabytes of data at a time without exceeding her monthly budget.
Given that Ella pays a one-time fee of $58.50 and has to pay $3 per gigabyte used. She must pay $3xg if she utilizes g gigabytes.
We now need to determine how many gigabytes of data she can utilize in total while staying within her budget.
She is spending less than $65.
For this, we can construct an inequality statement as shown below.
58.50+3g< 65
3g<65-58.50
3g<6.5
g<6.5/3
g<2.163.
Therefore, she should only use a total of 2 gigabytes to keep the cost within her budget.
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Harold cut 18 1/2 inches off a rope that was 60 inches long. How is the length of the remaining rope written in decimals?
Answers
Substract 18 1/2 from 60 to determine the length of remaining rope.
[tex]\begin{gathered} 60-18\frac{1}{2}=60-\frac{37}{2} \\ =\frac{120-37}{2} \\ =\frac{83}{2} \\ =41.5 \end{gathered}[/tex]So length of remaining rope is 41.5 inches.
Bella works at a popular clothing store. Last winter, her manager asked her to track thestore's sweater sales. This box plot shows the results.Price of sweaters sold ($)304050607080What fraction of the sweaters cost $50 or less?
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From the given graph, it appears that the price of the sweaters sold ranges in 3 bars - from $45 up $60.
Sweaters costing $50 or less covers 1 out of the 3 bars in the graph. In its equivalent fraction, we get:
[tex]undefined[/tex]=O GRAPHINGFinding the next terms of an arithmetic sequence with integersThe first three terms of an arithmetic sequence are as follows.-5, -8, -11Find the next two terms of this sequence.5.-8.-11.008 OBx 6
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Solution:
Given the first three terms of an arithmetic sequence as;
[tex]-5,-8,-11[/tex]An arithmetic sequence is a sequence with a common difference d, The common difference is the difference between two consecutive terms. Where;
[tex]\begin{gathered} d=a_2-a_1 \\ \text{Where;} \\ a_2=\text{ second term;} \\ a_1=\text{first term} \end{gathered}[/tex]Thus;
[tex]\begin{gathered} d=-8-(-5) \\ d=-8+5 \\ d=-3 \end{gathered}[/tex]Also, the next term of the sequence can be known by adding the common difference to the previous term.
Hence, the next two terms are;
[tex]\begin{gathered} =-11+(-3) \\ =-11-3 \\ =-14 \\ \text{and } \\ =-14+(-3) \\ =-14-3 \\ =-17 \end{gathered}[/tex]FINAL ANSWER:
[tex]-14,-17[/tex]Sketch the graphs of each of the following functions showing all steps on the same set of axe
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Part D
we have the function
[tex]\begin{gathered} y=\frac{4}{-(x+1)}+3=\frac{4-3(x+1)}{-(x+1)}=\frac{4-3x-3}{-(x+1)}=\frac{1-3x}{-(x+1)}=\frac{3x-1}{x+1} \\ \\ y=\frac{3x-1}{x+1} \end{gathered}[/tex]In this rational function
Remember that
The denominator cannot be equal to zero
so
The value of x cannot be equal to x=-1
At x=-1 there is a vertical asymptote
Find out a horizontal asymptote
Degree on Top is Equal to the Bottom
so
the horizontal asymptote is at y=3/1=3
Find out the intercepts
y-intercept (value of y when the value of x=0)
For x=0
[tex]y=\frac{3(0)-1}{0+1}=-1[/tex]The y-intercept is (0,-1)
Find out the x-intercept (value of x when the value of y=0)
For y=0
[tex]\begin{gathered} 0=\frac{3x-1}{x+1} \\ \\ 3x-1=0 \\ 3x=1 \\ x=\frac{1}{3} \end{gathered}[/tex]The x-intercept is (0.33,0)
With the given information
Graph the function
using a graphing tool
see the figure below
Simplify: (3x-8)+(4x-17)
Answers
Answer:
7x-25
Explanation:
Given the expression:
[tex]\mleft(3x-8\mright)+\mleft(4x-17\mright)[/tex]First, we open the brackets
[tex]=3x-8+4x-17[/tex]Next, we rearrange bringing like terms together.
[tex]\begin{gathered} =3x+4x-8-17 \\ =7x-25 \end{gathered}[/tex]what is 19,593 in expanded form?
Answers
The extended form of the given number is:
[tex]10000+9000+500+90+3[/tex]A 5000-seat theater has tickets for sale at $25 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $149,000? The number of tickets for sale at $25 should be ____ The number of tickets for sale at $40 should be ____
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Let us call x the number of $25 seats and y $40 seats, then we know that there are in total 5000 seats in a theatre; therefore, we have the equation
[tex]x+y=5000[/tex]Also, after selling this many tickets the total revenue should be $149, 000; therefore, we get the equation
[tex]25x+40y=149,0000[/tex]Hence, we have a system of equations with two equations and two unknowns.
We solve this system by substitution.
First, we solve for x in the first equation to get
[tex]x=5000-y[/tex]we then put this into the second equation to get
[tex]25(5000-y)+40y=149,000[/tex][tex]\rightarrow125,000-25y+40y=149,000[/tex][tex]\rightarrow125,000+15y=149,000[/tex][tex]\rightarrow15y=24,000[/tex][tex]\therefore y=1600.[/tex]Now that we have y, we now solve for x to get:
[tex]x=5000-1600[/tex][tex]x=3400.[/tex]Hence x = 3400 and y = 1600 and the correct statements are as follows.
The number of tickets for sale at $25 should be 3400.
The number of tickets for sale at $40 should be 1600.
2x -10 < 6 solve the inequality[tex]2x - 10 \leqslant 6[/tex]
Answers
The given equation is:
[tex]2x\text{ - 10 }\leq\text{ 6}[/tex]To simply this, just keep the x term on the left side and others at the right side. Therefore,
[tex]2x\text{ }\leq\text{ 6 + 10}[/tex][tex]2x\text{ }\leq\text{ 16}[/tex][tex]x\text{ }\leq\text{ }\frac{16}{2}[/tex]or
[tex]x\text{ }\leq\text{ 8}[/tex]Hence, the solution is x =< 8.
The system of equations(4x-y = 4(x+1) hasly = 6The system of equations 4x-y=4(x+1) , y = 6 has:A. one solutionB. infinitely many solutionsC. no solution
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EXPLANATION
Plugging in y=6 into the first equation:
[tex]4x-6=4(x+1)[/tex]Applying the distributive property:
[tex]4x-6=4x\text{ +4}[/tex]Subtracting -4x to both sides:
[tex]4x-4x-6=4[/tex]Adding +6 to both sides:
[tex]4x-4x=4+6[/tex]Adding like terms:
[tex]0\ne10[/tex]In conclusion, the system of equations has no solutions.
8. An elephant weighs 74,416 ounces. How many tons does it weigh?
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To know how many tons does the elephant weigh, we have to do a convertion:
1 ounce=3.125x10^-5 ton
[tex]74.416ounces\times\frac{3.125\times10^{-5}}{1\text{ ounce}}=2.3255\times10^{-3}[/tex]The elephant weighs 2.3255x10^-3 tons
help me with this question please
Answers
So,
From the graph, we can clearly state that:
In 2 mins, there were 0 calls.
In 3 mins, there was 1 call.
In 4 mins, there were 4 calls.
In 5 mins, there were 6 calls.
In 6 mins, there were 4 calls.
Then, the number of calls that were answered to in 6 mins or less were 0+1+4+6+4 = 15