Find the area of the region bounded by the line y=3x−6 and line y=−2x+8. a) the x-axis.
Answers
Answer:
[tex]\displaystyle A = \frac{12}{5}[/tex]
General Formulas and Concepts:
Math
Number LinePre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightEquality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityAlgebra I
Terms/CoefficientsFactoringCoordinates (x, y)Solving systems of equations using substitution/eliminationSolving systems of equations by graphingFunction NotationInterval NotationCalculus
Integration
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Splitting Integral]: [tex]\displaystyle \int\limits^c_a {f(x)} \, dx = \int\limits^b_a {f(x)} \, dx + \int\limits^c_b {f(x)} \, dx[/tex]
Integration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Area of a Region Formula: [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]
f(x) is always top functiong(x) is always bottom function"Top minus Bottom"Step-by-step explanation:
Step 1: Define
Identify bounded region. See attached graph.
y = 3x - 6
y = -2x + 8
Bounded by x-axis and between those 2 lines (already pre-determined; taking an integral always takes it to the x-axis).
Step 2: Analyze Graph
See attached graph.
Looking at our systems of equations on the graph, we see that our limits of integration is from x = 2 to x = 4.
We don't have a continuous top function through the interval [2, 4] (it switches from y = 3x - 6 to y = -2x + 8), so we need to split it into 2 integrals to find the total area.
We can either use the graph and identify the intersection point, which is x = 2.8, or we can solve it algebraically (systems of equations - substitution method):
Substitute in y: 3x - 6 = -2x + 8[Addition Property of Equality] Add 2x on both sides: 5x - 6 = 8[Addition Property of Equality] Add 6 on both sides: 5x = 14[Division Property of Equality] Divide 5 on both sides: x = 14/5Our 2 intervals would be [2, 14/5] and [14/5, 4] for their respective integrals.
Step 3: Find Area
Our top functions are the linear lines y = 3x - 6 and y = -2x + 8 and our continuous bottom function is the x-axis (x = 0).
We can redefine the linear lines as f₁(x) = 3x - 6, f₂(x) = -2x + 8, and g(x) = 0.
Integration
[Area of a Region Formula] Rewrite/Redefine [Int Prop SI]: [tex]\displaystyle A = \int\limits^b_a {[f_1(x) - g(x)]} \, dx + \int\limits^c_b {[f_2(x) - g(x)]} \, dx[/tex][Area of a Region Formula] Substitute in variables: [tex]\displaystyle A = \int\limits^{\frac{14}{5}}_2 {[(3x - 6) - 0]} \, dx + \int\limits^4_{\frac{14}{5}} {[(-2x + 8) - 0]} \, dx[/tex][Integrals] Simplify Integrands: [tex]\displaystyle A = \int\limits^{\frac{14}{5}}_2 {[3x - 6]} \, dx + \int\limits^4_{\frac{14}{5}} {[-2x + 8]} \, dx[/tex][Integrals - Algebra] Factor: [tex]\displaystyle A = \int\limits^{\frac{14}{5}}_2 {[3(x - 2)]} \, dx + \int\limits^4_{\frac{14}{5}} {[-2(x - 4)]} \, dx[/tex][Integrals] Simplify [Int Prop MC]: [tex]\displaystyle A = 3 \int\limits^{\frac{14}{5}}_2 {[x - 2]} \, dx - 2 \int\limits^4_{\frac{14}{5}} {[x - 4]} \, dx[/tex][Integrals] Integrate [Int Rule RPR]: [tex]\displaystyle A = 3(\frac{x^2}{2} - 2x) \bigg| \limits^{\frac{14}{5}}_2 - 2(\frac{x^2}{2} - 4x) \bigg| \limits^4_{\frac{14}{5}}[/tex][Integrals] Evaluate [Int Rule FTC 1]: [tex]\displaystyle A = 3(\frac{8}{25}) - 2(\frac{-18}{25})[/tex][Expression] Multiply: [tex]\displaystyle A = \frac{24}{25} + \frac{36}{25}[/tex][Expression] Add: [tex]\displaystyle A = \frac{12}{5}[/tex]We have found the area bounded by the x-axis and linear lines y = 3x - 6 and y = -2x + 8.
Topic: Calculus BC
Unit: Area between 2 Curves, Volume, Arc Length, Surface Area
Chapter 7 (College Textbook - Calculus 10e)
Hope this helped!
Answer:
A = 12/5 units
Step-by-step explanation:
USING ALGEBRA:
We can find the intersection point between these two lines;
y = 3x - 6y = -2x + 8Set these two equations equal to each other.
3x - 6 = -2x + 8Add 2x to both sides of the equation.
5x - 6 = 8Add 6 to both sides of the equation.
5x = 14Divide both sides of the equation by 5.
x = 14/5Find the y-value where these points intersect by plugging this x-value back into either equation.
y = 3(14/5) - 6Multiply and simplify.
y = 42/5 - 6Multiply 6 by (5/5) to get common denominators.
y = 42/5 - 30/5Subtract and simplify.
y = 12/5These two lines intersect at the point 12/5. This is the height of the triangle formed by these two lines and the x-axis.
Now let's find the roots of these equations (where they touch the x-axis) so we can determine the base of the triangle.
Set both equations equal to 0.
(I) 0 = 3x - 6Add 6 both sides of the equation.
6 = 3xDivide both sides of the equation by 3.
x = 2Set the second equation equal to 0.
(II) 0 = -2x + 8Add 2x to both sides of the equation.
2x = 8Divide both sides of the equation by 2.
x = 4The base of the triangle is from (2,0) to (4,0), making it a length of 2 units.
The height of the triangle is 12/5 units.
Formula for the Area of a Triangle:
A = 1/2bhSubstitute 2 for b and 14/5 for h.
A = (1/2) · (2) · (12/5)Multiply and simplify.
A = 12/5The area of the region bounded by the lines y = 3x - 6 and y = -2x + 8 between the x-axis is 12/5 units.
Related Questions
3y + 2/5 = -1/5 what is y?
Answers
Answer:
3.6
Step-by-step explanation:
3y+2/5=-1/5
3y=-1/5-2/5
3y=-0.6
0.6/3=y
-3.6=y
y=-3.6
1 1/2 as a fraction
Answers
Answer:
1.5
Step-by-step explanation:
divide 1/2 and add 1
Can anyone help me with a math paper via direct message
Answers
the table shows transactions in a checking account
A) Find the total of the transactions for each month
B) Find the mean total for the four months
Answers
Answer:
i) number of transactions for the month of January = 4
number of transactions for the month of February = 4
number of transactions for the month of March = 4
number of transactions for the month of April = 4
ii) Mean of four months = -495.7 /4 = -123.93
Step-by-step explanation:
i) number of transactions for the month of January = 4
number of transactions for the month of February = 4
number of transactions for the month of March = 4
number of transactions for the month of April = 4
ii) January February March April
-38.50 250.00 -14.00 -86.80
126.30 -135.20 99.00 -570.00
429.40 35.50 -82.70 100.00
-265.00 -62.30 -1.50 -280.10
Total 252.20 88.20 0.80 -836.9
Total of four months = 252.2 + 88.20 + 0.80 - 836.9 = -495.7
Mean of four months = -495.7 /4 = -123.93
Answer:
1) number of transactions for the month of January = 252.20
number of transactions for the month of February = 88.00
number of transactions for the month of March = 1.70
number of transactions for the month of April = -836.90
2. mean total of the four months -123.93
Step-by-step explanation:
Step-by-step explanation:
Forty-seven percent of fish in a river are catfish. Imagine scooping out a simple random sample of 25 fish from the river and observing the sample proportion of catfish. What is the standard deviation of the sampling distribution? Determine whether the 10% condition is met.
The standard deviation is 0.0998. The 10% condition is met because it is very likely there are more than 250 catfish in the river.
The standard deviation is 0.0998. The 10% condition is not met because there are less than 250 catfish in the river.
The standard deviation is 0.9002. The 10% condition is met because it is very likely there are more than 250 catfish in the river.
The standard deviation is 0.9002. The 10% condition is not met because there are less than 250 catfish in the river.
We are unable to determine the standard deviation because we do not know the sample mean. The 10% condition is met because it is very likely there are more than 250 catfish in the river.
Answers
Answer:
Therefore the correct option is a.) The standard deviation is 0.0998. The 10% condition is met because it is very likely there are more than 250 catfish in the river.
Step-by-step explanation:
i) Let p = 0.47
ii) therefore q = 1 - 0.47 = 0.53
iii) sample size, n =25
iii) standard deviation = [tex]\sqrt{\frac{p \times q}{n} } = \sqrt{\frac{0.47 \times 0.53}{25} } = 0.0998[/tex]
Therefore the correct option is
a.) The standard deviation is 0.0998. The 10% condition is met because it
is very likely there are more than 250 catfish in the river.
The standard deviation of the sampling distribution of the sample proportion is 0.0998. To determine whether the 10% condition is met, the total population of catfish should be at least 10 times the sample size.
Explanation:The question asks about determining the standard deviation of the sampling distribution of the proportion of catfish in a river and if the 10% condition is met for the sampling distribution to be approximately normal. First, to calculate the standard deviation of the sampling distribution of the sample proportion (p-hat), we use the formula √[(p(1-p))/n], where p is the population proportion and n is the sample size. In this case, p = 0.47, so 1 - p = 0.53, and n = 25. The standard deviation is then √[(0.47*0.53)/25], which is approximately 0.0998.
Next, the 10% condition checks whether we can consider the population large enough that the sample size doesn't affect the population proportion notably when taking without replacement. This condition states that the sample size, n, should be no more than 10% of the population. If there are indeed more than 250 fish in the river (10 times the sample size), we can be confident that the 10% condition is met. If not, the condition is not met.
Therefore, the correct response would state the standard deviation and appropriately evaluate whether the 10% condition is met based on the estimated number of catfish in the river.
Ron decided to use blocking to deal with extraneous factors in his
experiment. If 4 treatments are applied to one of his groups, how many
treatments should be applied to each of his other groups?
A. 3
B. 6
C. 5
D. 4
Answers
Is 1/4 greater than 1/3? Why?
Answers
Step-by-step explanation: Notice that the fractions that we're comparing in this problem have different denominators.
When fractions have different denominators, they're called unlike fractions. To compare unlike fractions, we must first get a common denominator.
The common denominator of 4 and 3 will be the least common multiple of 4 and 3 or 12. To get a 12 in the denominator of 1/4, we multiply the numerator and the denominator by 3 which gives us 3/12. To get a 12 in the denominator of 1/3, we multiply the numerator and the denominator by 4 which gives us 4/12.
Now we have the fractions 3/12 and 4/12.
The fraction with the greater denominator is larger so 4/12 is bigger which means that 1/3 is bigger.
1/4 is not greater than 1/3. In fact it is less than 1/3.
We have two fractions, 1/4 and 1/3.
We know that,
For a fraction, when the value of the denominator increases, the value of the fraction decreases.
So here the denominator of 4 is greater than 3.
So 1/4 is less than 1/3.
In other words, 1/4 can be defined as a part when 1 is divided in to 4 parts.
1/3 is one part when 1 is divided in to 3 parts.
So clearly, 1/4 < 1/3.
Hence 1/4 is less than 1/3.
Learn more about Fractions here :
https://brainly.com/question/10354322
#SPJ6
7x5 answer plz i need help
Answers
7x5=35
Answer:
35
Step-by-step explanation:
7 x 7 = 35
You are sitting in row 23 and notice there are 65 seats in your row. The row in front of you
has 63 seats and the row behind you has 67 seats. There are 42 rows in the auditorium.
How many seats does the auditorium contain? (Hint: Find the number of seats in the first
and last rows)
A. 2,604
B. 2,163
C. 2,422
D. 2,803
Answers
Answer: A. 2,604
Step-by-step explanation:
According to the given information the number of sets in rows following arithmetic progression (in short form AP).
Where , 23rd term is 65.
Common difference = 65-63=2
nth term in AP: [tex]a_n=a+(n-1)d[/tex]
For n= 23 , we have [tex]a_{23}=65[/tex] , d= 2
[tex]23=a+(23-1)2\\\\ 23= a+(22)2\\\\ 23=a+44\\\\ a=44-23=21[/tex]
Formula for the sum of first n terms in AP= [tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]
Since, There are 42 rows in the auditorium.
Then,
[tex]S_{42}=\dfrac{42}{2}[2(21)+(42-1)2]\\\\=21(42+82)\\\\=21(124)=2604[/tex]
Hence, the the auditorium contains 2,604 seats.
Thus , the correct answer is A. 2,604
We want to find the total number of seats in the auditorium, knowing that the number of seats is given by an arithmetic sequence.
The correct option is A: there are 2,604 seats in total.
We know that in the row before you (the number 22) there are 63 seats, in your row (number 23) there are 65 seats, and in the next row there are 67 seats, then we can write the 3 terms of a sequence:
[tex]a_{22}= 63\\a_{23} = 65\\a_{24} = 67[/tex]
Is simple to see that this is an arithmetic sequence, such that the difference between consecutive terms is 2, then the number of seats in the n-th row is given by:
[tex]a_n = a_{n-1} + 2[/tex]
or:
[tex]a_n = a_1 + (n - 1)*2[/tex]
Using this second equation, we can find the value of the first term of the sequence:
[tex]a_{23} = 65 = a_1 + 2*(23 - 1)\\\\65 - 44 = a_1 = 21\\[/tex]
Now, if we define d as the difference between consecutive terms in an arithmetic sequence, the sum of the first N terms is given by:
[tex]S(N) = N*(2*a_1 + (N - 1)*d)/2[/tex]
Here we have a total of 42 rows, so we use N = 42.
d =2
a₁ = 21
Then the total number of seats is:
[tex]S(N) = 42*(2*21 + (42 - 1)*2)/2 = 2,604[/tex]
This means that the correct option is A: there are 2,604 seats in total.
If you want to learn more, you can read:
https://brainly.com/question/18109692
what is 6(5−8v)+12=−54
Answers
Answer: v = 2
Step-by-step explanation:
30-48v+12 = -54
-48v = -54-30-12
[tex]\frac{-48v}{-48}[/tex] = [tex]\frac{-96}{-48}[/tex]
v = 2
Answer:
2
Step-by-step explanation:
6(5−8v)+12=−54
Divide through by 6, we have
5 — 8v + 2 = — 9
Collect like terms
— 8v = —9 — 2 — 5
—8v = — 16
Divide both side by the coefficient of v i.e —8
v = — 16/ —8
v = 2
If the simple interest on $6 comma 000 for 2 years is $480, then what is the interest rate?
Answers
Answer:
4%
Step-by-step explanation:
To solve this problem we can use a modified version of the simple interest formula which is shown below:
[tex]r=\frac{I}{Pt}[/tex]
I = interest amount
P = principal amount
t = time (years)
Lets plug in the values:
[tex]r=\frac{480}{(6,000)(2)}[/tex]
[tex]r=0.04[/tex]
The last step is to convert 0.04 into a percent:
0.04(100) = 4
The interest rate is 4%.
Helene spends 12% of her budget on transport expenses. Write this percent as a fraction and as a decimal
Answers
Answer:
3/25 is the fraction .12 is the decimal
Step-by-step explanation:
What do I have to do with this question? r=?, d=5m, C=15.70m
Answers
you add them then divide ur answer by 2
find the area of the regular polygon, 6 sides, 12 in, rounded to the nearest tenth
Answers
Answer:
Step-by-step explanation:
6 ×12=72 rounded to the nearest tenth 5 or more add one more 4 or less let it rest
72 it would be 70 because 2 is not more than 5
_
Topic/Objective: Function Applications pp. 228-252
• Write the equation of a linear function and determine the rate of change of the function using a point on the line and the slope of the line.
Write the equation of a linear function and determine the rate of change of the function using two points on the line.
• Determine whether a function is linear or nonlinear using a graph.
• Determine whether a function is linear or nonlinear using a table.
• Determine whether a function is linear or nonlinear using an equation.
• Compare the properties of two linear functions that are represented differently.
Name
Class/Time
Date
Essential Question: How can we model relationships between quantities?
Questions/Voc. Terms/Properties
Define the vocabulary terms below:
Linear function
Nonlinear function
Increasing function
Decreasing function
Constant
How can linear models be interpreted?
How are independent and dependent variables represented on a coordinate plane?
What is the slope and y-intercept of the helicopter altitude from the graph?
What does 35 and 1.2 in the equation represent in the equation?
Describe the situation each equation represents for the water level in other tanks.
How can we represent the water level in a tank that’s empty at first but rises at a rate of 2.1 /s?
What is the process for solving problems involving constant rates?
What is the total cost for movie rental for 1 month? 5 months? 7 months? 1 year?
Is this a linear model? Explain.
What describes the relationship between the independent and dependent variables of the function?
What determines whether a function is linear or nonlinear?
How can we determine if a function is increasing or decreasing?
How can we determine whether a graph is increasing or decreasing?
How can functions be compared?
How can functions be represented?
How can we determine which line has a greater rate of change?
When interpreting a function graph, what key features can we look for?
How can we draw conclusions about an object’s speed?
Example Problems & Steps/Vocabulary Definitions/Property Descriptions
Write/type definitions beside each term below:
p. 228 Copy yellow box
p. 228 Copy purple box
pp. 228-229 Study graph and copy solutions below:
Example 1
A.
B.
pp. 229-230 Copy solution below:
Example 2
A.
p. 230 Copy solution below:
B.
p. 230 Copy solution below:
C.
pp. 231-231 Study table and graph and copy steps below:
Example 1
pp. 232-233 Study table and copy solution below:
Example 2
A.
Study rate of change between values and copy solution below:
B.
p. 234 See yellow box
pp. 234-235 Study tables & graph and copy solutions below:
Example 1
A. y = 2x - 1
B.
pp. 236 See pink box
pp. 236-237 Study graphs and write solutions below:
Example 2
A.
B.
C.
D.
p. 240 See yellow box
p. 240 See paragraph
Study functions pp. 240-244
p. 244 see graph and pink box
p. 246
p. 247 see pink box
Study pp. 247-252
Summary: Connections, Reflections, Analysis about what you learned (3 or more sentences, or you may use the following prompts - be specific):
Today my notes say…
I can use my notes to…
My notes mean…
Answers
Answer:
Are the following linear or nonlinear? Circle the correct response.
Step-by-step explanation:
The numder are hard to explain but
You can tell if a table is linear by looking at how X and Y change. If, as X increases by 1, Y increases by a constant rate, then a table is linear. You can find the constant rate by finding the first difference.
Answer:Your answer i
Step-by-step explanation:You can tell if a table is linear by looking at how X and Y change.
fine the equation of m= -5 (-1,3)
Answers
Answer:
The required equation to the given slope m=-5 and a point (-1,3) is 5x+y+2=0
Step-by-step explanation:
Given that the slope m=-5 and a point (-1,3)
Now we have to find an equation with the given slope and point :
Let [tex](x_1,y_1)[/tex] be the given point (-1,3)
The slope point formula is [tex]y-y_1=m(x-x_1)[/tex]
y-3=-5(x-(-1))
y-3=-5(x+1)
y-3=-5(x)-5(1) ( by using the distributive property a(x+y)=ax+ay here a=-5,x=x and y=1 )
y-3=-5x-5
y-3-(-5x-5)=-5x-5-(-5x-5) ( by using the distributive property a(x+y)=ax+ay here a=-1,x=-5x and y=-5)
y-3+5x+5=-5x-5+5x+5
y+2+5x=0
5x+y+2=0 which is the required equation
The polynomial 4x^3 - 6x^2 + 8x – 12 can be grouped in different ways to factor by
grouping.
Try it both ways:
(4x3 – 6x>) + (8x – 12)
(4x3 + 8x) + (- 6x2 – 12)?
Answers
Answer:
(4x3-6x) + (8x-12)= 2x
(4x3+8x) + (-6x2-12)= 2(2x-3) (x^2+2)
Step-by-step explanation:
All you have to do is simplify.
Answer:
A,B,E
Step-by-step explanation:
Did on edgen
Sara bought a car for $15700 with interest rate of 5 3/7% and the contract is for 7 years.
How much interest will Sara owe? How much will the payments be with a seven year agreement?
Answers
1. How much interest will Sara owe?
She will owe 5,966 dollars
2. How much will the payments be with a seven year agreement?
Sara will pay 21,666 dollars
Explanation:The simple interest formula is as follows:
[tex]A=P(1+rt) \\ \\ \\ Where: \\ \\ A: \ is \ the \ Final \ Investment \Value \\ \\ P: \ is \ the \ Principal \ amount \ of \ money \ to \ be \ invested \\ \\ r: \ is \ the \ rate \ of \ interest \\ \\ t: \ is \ \ Number \ of \ Time \ Periods[/tex]
First, converting r percent to r a decimal
[tex]r = (5 \frac{3}{7})\%=(5+\frac{3}{7}))\%=\frac{38}{7}\% \\ \\ r=\frac{38/7}{100}=\frac{19}{350} \ per \ year[/tex]
Solving our equation:
[tex]A=15700 (1+\frac{19}{350}\times 7) \\ \\ A=15700(\frac{69}{50}) \\ \\ \boxed{A=\$21,666}[/tex]
So Sara will owe in interest the following amount of money:
[tex]I:Interest \\ \\ \\ I=21,666-15,700 \\ \\ \boxed{I=\$5,966}[/tex]
Finally, answering the questions:
1. How much interest will Sara owe?
She will owe 5,966 dollars
2. How much will the payments be with a seven year agreement?
Sara will pay 21,666 dollars
Learn more:Simple interest: https://brainly.com/question/11911443
#LearnWithBrainly
Factor this: a^n+a^n+1
Answers
Answer:
1 + 2 a^n
Step-by-step explanation:
Which statements are true about the multiplication and division properties of rational expressions? Check all that apply.
Answers
Answer: A, B, E
Step-by-step explanation:
Answer:
A, B, E.
Step-by-step explanation:
The closure property of multiplication states that the product of two rational expressions is a rational expression.
The commutative property only holds true for the multiplication of rational expressions.
The properties of rational expression multiplication and division are parallel to the properties of rational number multiplication and division.
whats the root and vertex for y= 2x squared -5x-604
Answers
Vertex is calculated by -b/2a
So we have -(-5)/2(2)=5/4
The root is determined through the quadratic formula:
x=(-b+sqrt(b^2-4ac))/2a
x=(-(-5)+sqrt(-5^2-4(2)(-604)))/2(2)
x=(5+sqrt(25-4832))/4
x=(5+sqrt(-4807))/4
So the root is some imaginary number
Hope this helped!
Solve 5x + 7 > 17.
{x | x < 2}
{x | x > 2}
{x | x < -2}
{x | x > -2}
Answers
Answer:
5x + 7 < 17
5x < 10
x < 2
answer is a
Ingrid has $27 to buy oil paints for her painting class. Each tube of paint
costs $4. How many tubes can she buy? Do not include units in your answer.
Answers
Answer:
6
Step-by-step explanation:
27/4= 6 3/4
That doesn't work because we need whole numbers.
24/4=6
That is the solution. For $24 we buy 6 tubes for $4 each and we have $3 left over.
Answer:
6
Step-by-step explanation:
each tube of paint(one) = $ 4
(x) tube of paint = $ 27
Therefore,
x= (27/4)
= 6.75 tubes ; which is equivalent to 6 whole tube of paint
A circular playground has an area of about 1500 square feet. If the committee decides to double the radius, what is the approximate area of the new playground?
Answers
If the committee decides to double the radius, the approximate area of the new playground is; A_new = 6000 sq.ft
How to find the area of a Circle?We are given the area of a circular playground as;
A = 1500 ft²
Formula for area of Circle is;
A = πr²
Thus;
πr² = 1500
r = √(1500/π)
Now, they want to double the radius. Thus approximate area of the new playground is;
A_new = π * [2√(1500/π)]²
A_new = π * [4(1500/π)]
A_new = 6000 sq.ft
Read more about Area of Circle at; https://brainly.com/question/15673093
#SPJ1
Answer:
c
Step-by-step explanation:
time 4 learning and it was right people :)
tickets for admission to a high school football game cost $3 for students and $5 for adults. During one game, $2995 was collected from the sale of 729 tickets. Write and solve a system of linear equations to find the number of tickets sold to students and the number of tickets sold to adults.
Answers
Answer:
404 tickets to adults have been sold .
325 tickets to students have been sold .
Step-by-step explanation:
A system of linear equations is a set of two or more first degree equations, in which two or more variables are related.
In this case, a system of two linear equations with two unknowns is solved.
To assemble the system of equations you must first define the variables, which in this case will be:
x: tickets for admission to a high school football game for students.y: tickets for admission to a high school football game for adults.On the one hand, you know that 729 tickets were sold, that is to say that tickets sold for students and adults must add 729. Expressed in an equation this is: x+y=729 equation (A)
On the other hand, you know that during a game, $ 2995 was raised for the sale of those 729 tickets. And you also know that tickets for a high school football game cost $ 3 for students and $ 5 for adults.
Then the proceeds from the sale of tickets for students is 3*x and for adults it is 5*y. And your sum must be $ 2995. Expressed in an equation this is:
3*x + 5*y=2995 Equation (B)
So the system of equations is:
[tex]\left \{ {{x+y=729} \atop {3*x+5*y=2995}} \right.[/tex]
There are several methods of solving a system of equations. In that case, the substitution method will be used, which consists of isolating an unknown element in one of the equations, which will be a function of the other unknown. In the other equation that has not been used, the same unknown is replaced by the expression previously obtained. In this case, the value of variable x in equation (A) will be isolated:
x+y=729 ⇒ x=729-y Equation (C)
Replacing this expression in equation (B) you get:
3*(729-y)+5*y=2995
Solving this equation:
3*729-3*y+5*y=2995
2187+2*y=2995
2*y=2995-2187
2*y=808
y=808÷2
y=404
Remembering that "y" is tickets for admission to a high school football game for adults. this indicates that 404 tickets to adults have been sold .
Replacing this value in equation (C), which is the previously isolated equation, you get:
x=729-y
x=729-404
x=325
Remembering that "x" is tickets for admission to a high school football game for students. this indicates that 325 tickets to students have been sold .
By setting up a system of linear equations, it's found that 325 student and 404 adult tickets were sold.
Explanation:The subject of this question is a linear system, specifically related to the ticket sales at a high school football game. Let's denote 's' as the number of student tickets sold, and 'a' as the number of adult tickets sold. We'll use the following two equations to reflect the given information:
s + a = 729 (This equation represents the total number of tickets sold.) 3s + 5a = 2995 (This equation represents the total cost of tickets sold.)
To solve the system of equations, one method is substitution or elimination. Using the elimination method, you could multiply the first equation by 3, getting 3s + 3a = 2187. Then, subtracting this from the second equation gives 2a = 808. Dividing by 2, we find that a = 404. Plugging this value into the first equation gives s = 729 - 404 = 325. Therefore, 325 student tickets and 404 adult tickets were sold.
Learn more about Systems of Linear Equations here:https://brainly.com/question/27063359
#SPJ3
What is 4 tens and 6 tenths as a decimal
Answers
Answer 4.6
Step-by-step explanation:
Is this no solution or infinite solutions?
2x+y=2
y=-2x-1
Answers
Answer:
infinite solutions
Step-by-step explanation:
Length 30.25
Volume7193.45
Width 14.5
What is the width?
Answers
Answer:
Height = 16.4 inches
Step-by-step explanation:
V = Length*Width*Height, so solving for the Height by dividing the Volume with the product of the Length and Width gives:
Height = Volume/Length*Width = 7193.45/(30.25*14.5) = 16.4 inches
Complete the table for the given Rule:y=x-3
Answers
Answer:
1 = 2 - 3. is this what you mean?
Plzzzzzzzz help will give brainliest!!!!!!!!
Answers
[tex]A = 100\pi cm^{2}[/tex]
Step-by-step explanation:
Given that an engineer is planning to install a new water pipe.
The diameter of the circular pipe is
d = 20 cm
Let us find the radius (r)
radius = diameter / 2
r = 20 / 2 = 10 cm
The area of circle (A) is given as:
[tex]A = \pi r^{2}[/tex]
[tex]A = \pi 10^{2}[/tex]
[tex]A = 100\pi cm^{2}[/tex]