![Solve The Following Trigonometric Equation On The Interval [0, 2]12sin2x3=0](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/ol22tGGJmYzVwsVopA9sNwzVMtmi5iWP.png)
Answers
Given the expression:
[tex]12sin^2(x)-3=0[/tex]To solve the expression, follow the steps below:
Step 01: Add 3 to both sides.
[tex]\begin{gathered} 12sin^2(x)-3+3=0+3 \\ 12sin^2(x)=3 \end{gathered}[/tex]Step 02: Divide both sides by 12.
[tex]\begin{gathered} \frac{12sin^2(x)}{12}=\frac{3}{12} \\ sin^2(x)=\frac{1}{4} \end{gathered}[/tex]Step 03: Take the square root of both sides.
[tex]\begin{gathered} \sqrt{sin^2(x)}=\pm\sqrt{\frac{1}{4}} \\ sin(x)=\pm\frac{1}{2} \end{gathered}[/tex]Step 04: Evaluate the results.
First, let's evaluate sin(x) = 1/2.
Sin(x) is positive in the first and in the second quadrant. Then,
[tex]\begin{gathered} sin^{-1}(\frac{1}{2})=x \\ x=\frac{\pi}{6},x=\frac{5}{6}\pi \end{gathered}[/tex]Second, let's evaluate sin(x) = -1/2.
Sin(x) is negative in the third and in fourth quadrant. Then,
[tex]\begin{gathered} sin^{-1}(-\frac{1}{2})=x \\ x=\frac{7}{6}\pi,x=\frac{11}{6}\pi \end{gathered}[/tex]Answer:
[tex]x=\frac{\pi}{6},x=\frac{5}{6}\pi,x=\frac{7}{6}\pi,x=\frac{11}{6}\pi[/tex]Related Questions
what is the slope of the line with the equation x+1=-y?
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The slope intercept form of a line is given by:
[tex]\begin{gathered} y=mx+b \\ \text{where:} \\ m=\text{slope} \\ b=y-\text{intercept} \end{gathered}[/tex]rewrite the equation in its slope intercept form:
[tex]\begin{gathered} x+1=-y \\ \text{ Multiply both sides by -1:} \\ -1(x+1)=-1(-y) \\ y=-x-1 \\ m=-1 \\ b=-1 \end{gathered}[/tex]Therefore, the slope is -1
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using the above procedure:
[tex]\begin{gathered} 9x=6+6y \\ \text{subtract 6 from both sides:} \\ 9x-6=6+6y-6 \\ 9x-6=6y \\ \text{divide both sides by 6:} \\ \frac{6y}{6}=\frac{9x-6}{6} \\ y=\frac{3}{2}x-1 \\ m=\frac{3}{2} \\ b=-1 \end{gathered}[/tex]A sandwich shop was willing to pay $2 to each person interviewed about the likes and dislikes of types of sandwich breads. Of the people interviewed 40 liked white bread, 75 liked wheat bread, 35 liked both, and 15 liked neither type. A. Construct a Venn diagram that illustrates the interview results.B. What is the total number of people that were interviewed. What was the total amount that the sandwich shop paid for the interviews?C. What percent of the people interviewed liked either white or wheat bread.
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ANSWER and EXPLANATION
A. First, we have to find the number of people that liked white bread only and wheat bread only.
To find the number of people that liked white bread only, subtract the number of people that liked both from the number of people that liked white bread:
[tex]\begin{gathered} n(white\text{ }bread\text{ }only)=40-35 \\ n(white\text{ }bread\text{ }only)=5 \end{gathered}[/tex]To find the number of people that liked wheat bread only, subtract the number of people that liked both from the number of people that liked wheat bread:
[tex]\begin{gathered} n(wheat\text{ }bread\text{ }only)=75-35 \\ n(wheat\text{ }bread\text{ }only)=40 \end{gathered}[/tex]Now, we can draw the Venn diagram:
B. The total number of people interviewed is the sum of all the numbers on the Venn diagram.
Therefore, the total number of people interviewed is:
[tex]\begin{gathered} n(total)=5+35+40+15 \\ n(total)=95 \end{gathered}[/tex]That is the total number of people that were interviewed.
To find the total amount that the sandwich shop paid, multiply the total number of people interviewed by $2:
[tex]\begin{gathered} Total\text{ }amount\text{ }paid=2*95 \\ Total\text{ }amount\text{ }paid=\$190 \end{gathered}[/tex]That is the total amount that the sandwich shop paid for the interviews.
C. To find the percentage of people that liked either white bread or wheat bread, find the sum of people that liked white bread only, wheat bread only, and both types of bread, divide it by the total number of people interviewed and multiply by 100:
[tex]\begin{gathered} \Rightarrow\frac{5+35+40}{95}*100 \\ \\ \Rightarrow\frac{80}{95}*100 \\ \\ \Rightarrow84.2\% \end{gathered}[/tex]That is the percent of people that like either white or wheat bread.
Graph eat equation rewrite i.n slope-intercept form first if necessary.Y=2x-1
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Given:
[tex]y=2x-1[/tex]Find-:
Graph of equation
Explanation-:
The equation is:
[tex]y=2x-1[/tex]The general form of a straight line is:
[tex]y=mx+c[/tex]Where,
[tex]\begin{gathered} m\text{ = slope} \\ \\ c=\text{ y-intercept} \end{gathered}[/tex]At x = 0 value of y is:
[tex]\begin{gathered} y=2x-1 \\ \\ y=2(0)-1 \\ \\ y=-1 \end{gathered}[/tex]At y = 0 value of x is:
[tex]\begin{gathered} y=2x-1 \\ \\ 0=2x-1 \\ \\ x=\frac{1}{2} \end{gathered}[/tex]So the line passes the point (0,-1) and (1/2, 0).
The graph of the line is:
The class president collected data on 150 randomly selected 17-year-olds at his school. He surveyed students on if they had a job and driver's license. The results are shown. 93 of the students had a job128 of the students had a driver's license76 of the students had both a job and a driver's licensePart A: Construct a two-way frequency table summarizing the dataPart B: What percent of the students who have a job, do not have a driver's license?pls help!
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Total: 150
Job: 93
Driver's license: 128
Both: 76
We construct the table:
Now, using the fact that the total is 150, from the last row:
[tex]\begin{gathered} 128+17+y=150 \\ y=5 \end{gathered}[/tex]And from the last column:
[tex]\begin{gathered} 93+52+y=150 \\ y=5 \end{gathered}[/tex]Finally, the complete table is:
The coordinates of the image of P(3,-4)under a reflection in the x-axis are:
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Given:
The point is (3, -4).
To find:
The coordinates of the image of the point under a reflection on the x-axis.
Explanation:
The reflection over the x-axis rule is,
[tex](x,y)\rightarrow(x,-y)[/tex]Applying the rule, we get
[tex](3,-4)\rightarrow(3,4)[/tex]Therefore, the coordinates of the image of the given point are (3, 4).
Final answer:
The coordinates of the image of the given point are (3, 4).
In-district students at a college pay $427 for 7 credit hours (units) of classes and $549 for 9 credit hours of classes. Find the average rate of change of the total cost of classes with respect to the number of credit hours of classes.The rate of change is: $___ per credit hour
Answers
$427 for 7 credit hours of classes
$549 for 9 credit hours of classes
Unit rate: cost: credit hours
So, we have to divide the cost by the number of hours:
427/7 = 61
549/9 = 61
The rate of change is: $61 per credit hour
The lowest point in a particular country is - 596 feet at a particular lake in a particular place. If you are standing at a point 745 feet above the lake. What is your evevatipn?
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ANSWER:
149 feet
STEP-BY-STEP EXPLANATION:
We can determine the elevation by subtracting the depth of the lake from the highest point, like this:
[tex]745-596=149[/tex]The correct answer then is 149 feet
I am assuming the answer is A b/c the square root of 8 is irrational but I 'm not sure
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simplify: which value is an irrational number.
Explanation:(a) the perimeter of the square whose side length is
[tex]\sqrt{8}[/tex]the perimeter of the square is
[tex]\begin{gathered} 4a \\ =4\sqrt{8} \\ =4\sqrt{4*2} \\ 4*2\sqrt{2} \\ 8\sqrt{2} \end{gathered}[/tex]we know that
[tex]\sqrt{2}[/tex]is an irrational number hence the perimeter of the square will also irrational .
Find the equation of the exponential function represented by the table below: C y 03 1 6 2 12 3 24 Submit Answer Answer: y =
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Solution
Step 1:
Create a table
Step 2:
Write an exponential function with constant a and b
[tex]y\text{ = a\lparen b\rparen}^x[/tex]Step 3:
Find a and b by substituting x = 0, y = 3 and x = 1 , y = 6
[tex]\begin{gathered} y\text{ = a\lparen b\rparen}^x \\ 3\text{ = a }\times\text{ b}^0 \\ a\text{ = 3} \\ 6\text{ = a }\times\text{ b}^1 \\ 6\text{ = ab} \\ 6\text{ = 3b} \\ b\text{ = }\frac{6}{3}\text{ = 2} \end{gathered}[/tex]a = 3 , b = 2
Step 3
[tex]\text{y = 3}\times\text{ 2}^x[/tex]Final answer
[tex]\text{y = 3 }\times\text{ 2}^x[/tex]5/12 - ? + 5/4 = 2/3
Answers
Solve;
[tex]\begin{gathered} \frac{5}{12}-x+\frac{5}{4}=\frac{2}{3} \\ Collect\text{ all like terms and you'll have,} \\ \frac{5}{12}+\frac{5}{4}-\frac{2}{3}=x \\ \text{Take the LCM of the fractions and you'll have} \\ \frac{5}{12}+\frac{15}{12}-\frac{8}{12}=x \\ \frac{5+15-8}{12}=x \\ \frac{12}{12}=x \\ x=1 \end{gathered}[/tex]The missing value represented by the question mark is 1
Complete the square to rewrite y = x2 + 8x + 7 in vertex form, and then identifythe minimum yvalue of the function.A. The minimum value is -2.B. The minimum value is -9.C. The minimum value is -23.D. The minimum value is -4.
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Given
[tex]y=x^2+8x+7[/tex]Now,
[tex]\begin{gathered} x^2+8x+7=x^2+8x+16-9 \\ =(x+4)^2-9 \end{gathered}[/tex]solve for theta. Enter answer only round to the whole number
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You have a right triangle and know the length of the hypotenuse and opposite leg (opposite to angle theta)
Then, you use the trigonometric function of sine of the angle as follow:
[tex]\begin{gathered} \sin i\theta=\frac{oppoite}{hypotenuse} \\ \\ \sin \theta=\frac{8in}{16in} \\ \\ \theta=\sin ^{-1}(\frac{8}{16}) \\ \\ \theta=30 \end{gathered}[/tex]how do I solve the equation 3/4x=4+1/3x?
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3/4x=4+1/3x. Solving
Raina will rent a car for the weekend. She can choose one of two plans. The first pñan has an initial few od $49 and costs an additional $0.11 per mile driven. The second plan has an initial fee of $42 and costs an additional $0.13 per mile driven.For what amount of driving do the two plans cost the same?mileswhat is the cost when the two plans cost the same? $=
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Given : Raina will rent a car for the weekend.
The cost of the first plan : $49 and costs an additional $0.11 per mile driven.
The cost of the second plan: $42 and costs an additional $0.13 per mile driven.
Let the number of the miles driven = m
So, the cost of the first plan = 0.11 m + 49
The cost of the second plan = 0.13 m + 42
For what amount of driving do the two plans cost the same?
So, equating the two costs:
[tex]\begin{gathered} 0.13m+42=0.11m+49 \\ 0.13m-0.11m=49-42 \\ 0.02m=7 \\ \\ m=\frac{7}{0.02}=350 \end{gathered}[/tex]So, the number of miles = 350 miles
what is the cost when the two plans cost the same?
The cost will be = 0.11 * 350 + 49 = $87.5
Teachers* Salaries The average annual salary for all teachers is $47,750. Assume that the distribution is normal and the standard deviation is $5680.Find the probabilities. P (42.000 ≤ X ≤ 58.500)
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Remember that
z =(x - μ)/σ
In this problem
μ=47,750
σ=5,680
so
For x=42,000
z=(42,000-47,750)/5,680 --------------> z=-1.0123
For x=58,500
z=(58,500-47,750)/5,680 -----------> z=1.8926
using a z-scores table
we have that
P (42,000 ≤ X ≤ 58,500)=0.8151what makes 3 plus 7 plus 2 = plus 2 true
Answers
We have the following:
[tex]3+7+2=x+2[/tex]Now, for this to be true we must look for a number that makes the sum of both sides equal, as follows
[tex]\begin{gathered} 3+7+2=x+2 \\ x=3+7 \\ x=10 \\ \text{then} \\ 3+7+2=10+2 \\ 12=12 \end{gathered}[/tex]Therefore, the number that makes the equality true is 10
Answer:
10
Step-by-step explanation:
3 plus 7 equals 10
A bag contains red marbles and blue marbles. The ratio of red marbles to blue marbles is 3 to 4. If there are a total of 49 marbles in the bag, how many marbles are red?
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Answer:
21 red marbles
Explanation:
The ratio of red marbles to blue marbles = 3 : 4.
The proportion of red marbles in the bag
[tex]\begin{gathered} =\frac{3}{3+4} \\ =\frac{3}{7} \end{gathered}[/tex]If the total number of marbles in the bag = 49
Then, the number of marbles which are red
[tex]\begin{gathered} =\text{Proportion of red marbles x Total number of marbles} \\ =\frac{3}{7}\times49 \\ =3\times7 \\ =21 \end{gathered}[/tex]There are 21 red marbles in the bag.
3. Draw a mapping diagram for the graph. Then describethe pattern of inputs and outputs.
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For this case the mapping diagram would be:
We have the following points given:
(1,8), (3,6) and (5,4)
Since we have a line pattern we can find the equation with this formula:
[tex]y=mx+b[/tex]Where m is the slope and b the intercept:
[tex]m=\frac{8-6}{1-3}=-2[/tex]And for the intercept we got:
[tex]8=-2(1)+b[/tex]And solving for b we got:
[tex]b=10[/tex]And the equation would be given by:
[tex]y=-2x+10[/tex]You spin the spinner. Are the possible outcomes 1,2, and 3 equally likely show probabilities for each circle yes or no
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EXPLANATION
The probability for 1 , 2 and 3 are not equally likely because the fill different dimensions on the spinner.
The equation for the probability is as follows:
[tex]P(x)=\frac{Number\text{ of favourable outcomes}}{\text{Total numbers of possible outcomes}}[/tex]We need to divide the spinner in same divided parts:
#1 Parts: 3
#2 Parts: 5
#3 Parts: 4
Number of total parts = 12
The possible outcome for number 1 is:
[tex]P(1)=\frac{3}{12}=\frac{1}{4}[/tex]The possible outcome for #2 is as follows:
[tex]P(2)=\frac{5}{12}[/tex]The possible outcome for #3 is as shown as follows:
[tex]P(3)=\frac{4}{12}=\frac{1}{3}[/tex]Hello, I need some assistance with this precalculus question, please?HW Q6
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The augmented matrix of an equation contains only its numerical coefficients.
Let's list down the numerical coefficients of each equation.
Equation 1: 1, -1. 1, and 20
Equation 2: 6, 6, 0, and 4. (We have zero because there is no coefficient for variable z.)
Equation 3: 1, 1, 5, and 5
Let's fill in the blanks in the augmented matrix using the numerical coefficients above.
The augmented matrix of the given system of equations is:
I'm using system of equations and I have to use either substitution or elimination. My two equations are 2x - 6y = 138x - 24y = 8
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Therefore, the system doesn't have solution
A spinner numbered from 1 to 5 is spun 10 times. The number 5 appeared four times. What is the probability of getting 5? A) 7/10 B) 6/10 C) 5/10 D) 4/10
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The experimental probability of an event occurring is the number of times that it occurred when the experiment was conducted as a fraction of the total number of times the experiment was conducted.
Since we repeated the spinning 10 times, and we got 5 four times, this means that our probability is the ratio between 4 and 10.
[tex]\frac{4}{10}[/tex]i am stuck on a question and i don’t understand it, if i could get some help that would be great
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In order to find the equation, let's use the slope-intercept form:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
Parallel lines have the same slope, so if the slope of the given line is 2/3, the slope of the wanted parallel line is m = 2/3.
Now, to find the value of b, let's use the point (-9, 3) in the equation:
[tex]\begin{gathered} y=\frac{2}{3}x+b\\ \\ 3=\frac{2}{3}\cdot(-9)+b\\ \\ 3=-6+b\\ \\ b=3+6\\ \\ b=9 \end{gathered}[/tex]So the wanted equation is:
[tex]y=\frac{2}{3}x+9[/tex]Question 8 using radians, find the amplitudeand period of each function and graph it
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The function is given as
[tex]y=3cos\frac{\theta}{3}[/tex]RequiredTo determine the amplitude and period.
ExplanationThe general trigonometric equation is
[tex]y=Acos(Bx-C)+D[/tex]where A is the amplitude.
Compare with the given equaiton.
A =3.
Then the amplitude is 3.
Now , find the period.
[tex]P=\frac{2\pi}{B}[/tex]Substitute the value of B in the expression.
[tex]P=\frac{2\pi}{(\frac{1}{3})}=6\pi[/tex]AnswerHence the amplitude is 3 and period is
[tex]6\pi[/tex]The graph of the equation is determined as
A train leaves the station at time x=0. Traveling at a constant speed, the train travels 334 km in 3.4 h. Round to the nearest 10 km and the nearest whole hour. Then represent the distance, y, the train travels in x hours using a table, an equation, and a graph.
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First, let's round the distance to the nearest 10 km.
The distance is 334 km, so the nearest 10 km is 330 km.
Then, let's round the time to the nearest whole hour.
The time is 3.4 h, so rounding to the nearest whole hour we have 3 hours.
Now, let's represent the distance y and time x using an equation
To do so, let's use the following equation for distance:
[tex]\begin{gathered} \text{distance}=\text{speed}\cdot\text{time} \\ \text{speed}=\frac{\text{ distance}}{\text{time}}=\frac{330}{3}=110\text{ km/h} \\ \\ y=110\cdot x \end{gathered}[/tex]Now, to create a table, let's choose some values of x and then calculate the corresponding values of y:
Graphing these ordered pairs (x, y) into the cartesian plane, we have:
One-third of a number w is 16.
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One-third of a number w is 16. The equation for this statement is:
[tex]\frac{w}{3}=16.[/tex]We find the value of w multiplying both sides of the equation by 3:
[tex]\begin{gathered} 3\cdot\frac{w}{3}=3\cdot16, \\ w=48. \end{gathered}[/tex]Answer
The number is w = 48.
Answer:
w = 48
Step-by-step explanation:
[tex]\frac{1}{3}[/tex] w = 16 ( multiply both sides by 3 to clear the fraction )
w = 3 × 16 = 48
I just got a tutor to help me with this but realize I have a question now!Should both denominators be simplified further? For example, shouldn't 6^2 be 36 and 8^2 should be 64??
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Answer:
The standard form of a hyperbola is given below as
[tex]\begin{gathered} \frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1 \\ around\text{ the origin,we will have the equation to be} \\ \frac{x^2}{a^2}-\frac{y^2}{b^2}=1 \end{gathered}[/tex]Given that the equation of the hyperbola is given below as
[tex]\frac{y^2}{6^2}-\frac{x^2}{8^2}=1[/tex]Therefore,
The standard form of a hyperbola should be left like that
Except if asked otherwise in an objective question with options
1 You are running a fuel economy study. One of the cars you find is blue. It can travel 31 miles on 2 1 3 4 17 gallons of gasoline. Another car is red. It can travel 25 miles on gallon of gasoline. What is 5 5 the unit rate for miles per gallon for each car? Which car could travel the greater distance on 1 gallon of gasoline? The unit rate for the blue car is mile(s) per gallon,
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You are running a fuel economy study. One of the cars you find is blue. It can travel 31 1/2 miles on 1 1/4 gallons of gasoline. Another car is red. It can travel 25 3/5 miles on a 4/5 gallon of gasoline. What is the unit rate for miles per gallon for each car? Which car could travel the greater distance on 1 gallon of gasoline? The unit rate for the blue car is a mile(s) per gallon
____________________________________________
Milles per gallon
Blue 31 1/2miles on 1 1/4 gallons of gasoline
31 1/2 ÷ 1 1/4 = (31*2 +1)/2 ÷ (1*4 +1)/ 4 = 63/2 ÷ 5/4 = 63/2 * 4/5 = 63*4/ (2*5) = 126/ 5
= 25.2 milles / gallon
The unit rate for the blue car is a mile(s) per gallon = 25.2
____________________
Red 25 3/2 miles on a gallon of gasoline
25 3/5 ÷ 4/5 = (25*5 +3) /5 x 5/4 = 128 *5/(5*4)= 128/4
= 32 milles / gallon
The unit rate for the red car is a mile(s) per gallon = 32
__________________
Which car could travel the greater distance on 1 gallon of gasoline?
The greatest distance on 1 gallon of gasoline is 32 miles / gallon
Danielle construct a scale model of a building with a rectangular base her model is 2 inches in length and 1 inch in width the scale of the model is 1 in equals 47 ft what is the actual area in square feet of the base of the building The possible answers are:1412822,2094,418
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Given:
a.) The scale of the model is 1 in equals 47 ft.
b.) Danielle constructs a scale model of a building with a rectangular base her model is 2 inches in length and 1 inch in width.
To be able to determine the actual area of the base, let's first identify the actual dimensions of the base.
We get,
[tex]\text{Length: 2 (inches) x }\frac{47\text{ ft.}}{1\text{ (inch)}}\text{ = 2 x }\frac{47\text{ ft.}}{1}\text{ = 94 ft.}[/tex][tex]\text{Width: 1 (inch) x }\frac{47\text{ ft.}}{1\text{ (inch)}}\text{ = 1 x }\frac{47\text{ ft.}}{1}\text{ = 47 ft.}[/tex]Let's now solve for the area of the base, since it is a rectangle, we will be using the formula below:
[tex]\text{ Area = L x W ; where L = Length and W = Width}[/tex]We get,
[tex]\text{ Area = L x W}[/tex][tex]\text{ = 94 ft. x 47 ft.}[/tex][tex]\text{ Area = 4,418 ft.}^2[/tex]Therefore, the actual area of the base is 4,418 ft.².
The school that Felipe goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 10 senior citizen tickets and 14 student tickets for a total of $200. The school took in $152 on the second day by selling 9 senior citizen tickets and 7 student tickets. Find the price of a senior citizen ticket and the price of a student ticket.
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We are looking at the price of the senior citizen ticket and the price of the student ticket. Knowing the total sales from the first day and second day, we can solve this problem by using a system of equations.
We let x be the price of the senior citizen ticket while y be the price of the student ticket. On the first day, the school sold 10 senior citizen tickets and 14 student tickets. The total sales are $200. We can represent this in equation form as
[tex]10x+14y=200[/tex]For the second day, the school sold 9 senior tickets and 7 student tickets, with a total sales of $152. This can be represented in a mathematical expression as
[tex]9x+7y=152[/tex]Hence, we now have our system of equations written as
[tex]\begin{gathered} 10x+14y=200 \\ 9x+7y=152_{} \end{gathered}[/tex]Let's solve for the values of x and y using the elimination method. I will multiply -2 on the second equation so that y can be eliminated. We now have
[tex]\begin{gathered} 10x+14y=200 \\ -2(9x+7y=152) \\ \\ 10x+14y=200 \\ -18x-14y=-304 \\ \\ \frac{-8x}{-8}=\frac{-104}{-8} \\ \\ x=13 \end{gathered}[/tex]We can use this value of x and substitute it on either of the equation present in the system of equations. In this case, I will be using the first equation. We have
[tex]\begin{gathered} 10(13)+14y=200 \\ 130+14y=200 \\ 14y=200-130 \\ \frac{14y}{14}=\frac{70}{14} \\ y=5 \end{gathered}[/tex]Hence, the price for the senior citizen ticket is $13 while the price for the student ticket is $5.
Answer:
Senior citizen ticket price = $13
Student ticket price = $5