Answer:
b
c
Step-by-step explanation:
First question: x - 6 means there is a shift to the right.
Second Question: substitute the given values into the original equation for appropriate transformations.
Answer: 3 |x-4| + 2, because vertical stretch multiplies x, horizontal shifts are subtracted or added to x, and vertical shifts are added or subtracted to the entire function.
The movement of the curve in the graph is shifting of the curve in vertical or the horizontal direction.For the first function the graph horizontal shift of 6 units right and for the second function when it is vertical stretch of 3, a horizontal shift to the right 4 units, and a vertical shift up 2 units the transformation function is,
[tex]g(x)=3|x-4|+2[/tex]
Given-
The equation of the graph given in the problem is,
[tex]f(x)=\sqrt{x} [/tex]
Translation of the graphThe movement of the curve in the graph is shifting of the curve in vertical or the horizontal direction.
a) The equation of the graph when it is transferred is given as,[tex]g(x)=\sqrt{x-6} [/tex]
There is no change with the constant value. Thus the graph will not move in vertical direction. The change in variable of a unit result in the graph shift in horizontal direction.
As it shift -6 thus graph horizontal shift of 6 units right.
b) The given function is,[tex]f(x)=|x|[/tex]
Vertical stretch of 3 means multiply the function with unit 3.
[tex]g(x)=3|x|[/tex]
Horizontal shift to the right 4 units means the difference of 4 units in the variable,
[tex]g(x)=3|x-4|[/tex]
Vertical shifts up with 2 units means the addition of the constant 2.
[tex]g(x)=3|x-4|+2[/tex]
Hence, for the first function the graph horizontal shift of 6 units right and for the second function when it is vertical stretch of 3, a horizontal shift to the right 4 units, and a vertical shift up 2 units the transformation function is,
[tex]g(x)=3|x-4|+2[/tex]
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A quadratic function has its vertex at the point
(
2
,
−
10
)
(
2
,
-
10
)
. The function passes through the point
(
−
6
,
−
5
)
(
-
6
,
-
5
)
. Find the quadratic and linear coefficients and the constant term of the function.
the standard form equation is y=ax²+bx+c where a is the quadratic coefficient, b is the linear coefficient, and c is the constant coefficient.
therefore, for y = 5/16x² - 5x/4 -35/4
Quadratic coefficient = 5/16, linear coefficient = 5/4, constant term = -35/4
What are zeros ?
zeros denotes the factors of the given equation in other words the zeros of the function are the values that make the factors zero. The factors need to multiply out to give the original standard-form equation.
Polynomial roots are the same as polynomial zeros, so they can be found by factoring the quadratic equation into two linear factors, after which they can be equating to zero.
Its easiest to first start out with a vertex form equation because it can then be converted to a standard quadratic equation.
given a vertex at (2,-10) , and point of intersection at (6,-5), the equation can be set up like this in the form of :
y = a(x-h)²+ k
y = a(x-2)^2-10, as we know h and k from the vertex.
We also know y and x from the given point of intersection so a can be solved by substituting the values of x and y to get value of a.
y = a(x-2)²-10
-5 = a(6-2)² - 10
16a = 10-5
a = 5/16
a = 5/16 which is also known as the quadratic coefficient because it is part of a second degree quantity and a Trinomial as a whole(quadratic).
since all the variables are known, you can expand the equation and set it to standard form :
y = 5/16(x-2)²-10
y = 5/16(x-2)² - 10
y = 5/16(x²+4-4x) -10
y = 5/16x² + 5/4 - 5x/4 - 10
y = 5/16x² - 5x/4 -35/4
For reference, the standard form equation is y=ax²+bx+c where a is the quadratic coefficient, b is the linear coefficient, and c is the constant coefficient.
In this instance, 5/16x² - 5x/4 -35/4 = ax²+bx+c
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Determine whether the quadratic function shown below has a minimum or
maximum, then determine the minimum or maximum value of the functio
ƒ(x) = x² + 6x + 7
Answer:
Minimum = (-3, -2)
Step-by-step explanation:
Standard form of a quadratic function:
[tex]f(x)=ax^2+bx+c[/tex]
If a > 0 the parabola opens upwards and the curve has a minimum point.
If a < 0 the parabola opens downwards and curve has a maximum point.
Given function:
[tex]f(x)=x^2+6x+7[/tex]
As a > 0, the parabola opens upwards and so the curve has a minimum point.
The minimum/maximum point of a quadratic function is its vertex.
Vertex form of a quadratic function:
[tex]f(x)=(x-h)^2+k[/tex]
Where (h, k) is the vertex.
To rewrite the given function in vertex form, complete the square.
Add and subtract the square of half the coefficient of the term in x:
[tex]\implies f(x)=x^2+6x+7 +\left(\dfrac{6}{2}\right)^2-\left(\dfrac{6}{2}\right)^2[/tex]
[tex]\implies f(x)=x^2+6x+7 +9-9[/tex]
[tex]\implies f(x)=x^2+6x+9+(7 -9)[/tex]
[tex]\implies f(x)=x^2+6x+9-2[/tex]
Factor the perfect square trinomial formed by x²+6x+9:
[tex]\implies f(x)=(x+3)^2-2[/tex]
Compare with the vertex form:
h = -3k = -2Therefore, the vertex is (-3, -2) and so the minimum value of the given function is (-3, -2).
please help simplify !
Answer:
B
Step-by-step explanation:
using the rule of exponents
[tex]a^{m}[/tex] ÷ [tex]a^{n}[/tex] = [tex]a^{(m-n)}[/tex] , then
[tex]6^{9}[/tex] ÷ 6³ = [tex]6^{(9-3)}[/tex] = [tex]6^{6}[/tex]
The tax on a $30 item is $1.50.
Find the tax on a $50 item.
Answer: $2.50
Step-by-step explanation: To find the tax rate, you need to divide 1.50 by 30
1.5/30 = .05, which is the percent taxed. To find the tax amount for a $50 item, you just need to multiply $50 by the tax rate, which is .05, to get $2.50
Kaleb determined how much money he would spend if he stopped at McDonalds each day after school. His cost can be modeled using c(m)=2.3m+2.50, where m is the number of McGriddle he orders each time. What is the cost that Kaleb would spend at McDonalds if he ordered 3 McGriddles?
Answer:
The cost that Kaleb would spend at McDonalds if he ordered 3 McGriddles would be 11.50.
Step-by-step explanation:
We know this is the answer because, when solving for c(3), we would get c(3)=2.3(3)+2.50=11.50.
i need the scientific notation of 0.0000018(430,000,000) over 0.00008(0.0075)
Answer:
1.29 x [tex]10^{9}[/tex]
Step-by-step explanation:
{(1.8 x 10^-6) x (4.3 x 10^8)} / [(8 x 10^-5) x (7.5 x 10^-3)]
[(1.8 x 4.3)x(10^-6 x 8)] / [(8 x 7.5) x(10^-5 x 10^ -3)]
(.129 x 10^[2-(-8)]
.129 x 10^10
1.29 x 10^-1 x 10^10
1.29 10^9
Which of the following equations represents a linear function?
Question 8 options:
y =[tex]\sqrt4{x}[/tex]
y =6/x
2x – 4y = 6
x3 – y = –2
Answer:
2x – 4y = 6
x3 – y = –2
Step-by-step explanation:
When graphing these two are linear.
Answer:
2x - 4y = –2
x3 – y = –2
Step-by-step explanation:
'cause they both have two unknown digits and this can be worked out with 3 methods;
1. substitution method
2. elimination method
3. grahical method
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The upper arm length of males over 20
years old in the United States is approximately Normal with mean 39.1
centimeters (cm) and standard deviation 5.1
cm. Use the 68−95−99.7
rule to answer the following questions. (Start by making a sketch of the Normal distribution for upper arm lengths for this population.)
A normal plot shows the range of Iowa test scores for 68% of the data, 95% of the data and 99.7% of the data. About 68% of the distribution of scores ranges from 5.29 to 8.39. About 95% of the distribution of scores ranges from 3.74 to 9.94. About 99.7% of the distribution of scores ranges from 2.19 to 11.49. There is an annotation that One standard deviation is 1.55 and another annotation that 2.5% of sores are below 3.74.
What percentage of men over 20
have upper arm lengths greater than 44.2 cm?
Provide your answer to one decimal place.
Using the Empirical Rule, it is found that 16% of men over 20 have upper arm lengths greater than 44.2 cm.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.For the distribution in this problem, we have that:
The mean is of 39.1 cm.The standard deviation is of 5.1 cm.Hence, 44.2 is one standard deviation above the mean, as 44.2 = 39.1 + 1 x 5.1.
The normal distribution is symmetric, meaning that 50% of the measures are above the mean and 50% are below. Of those measures above the mean, 68% are less than 44.2 and 32% are more than 44.2 cm, hence:
0.5 x 32 = 16%.
16% of men over 20 have upper arm lengths greater than 44.2 cm.
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A jar contains 100 marbles. There are 21 blue marbles, 19 green marbles, 37 red marbles, and 23 yellow marbles. What is the probability of randomly selecting a yellow marble? Enter the correct answer
Answer:
23% or 23/100
Step-by-step explanation:
Since there are 23 in 100 is is 23/100 or 23%
Answer:
4.348%
Step-by-step explanation:
blue marbles = 19
yellow marbles = 23
probably of getting yellow = 23/100
= 4.34782608696
then you round then number to three decimal places and there you go
Write the following in terms of sin x and cos x ; then simplify if possible. sec x csc x cot x =
The expression sec x csc x cot x in terms of sin x and cos x is
1/ (sin x)^2.
According to the given question.
We have an expression sec x csc x cot x.
Here, we have to write the above expression in terms of sinx and cosx.
As we know that,
sec x = 1/cos x
csc x = 1/sin x
cot x = cos x/ sin x
Thereofore, the expression sec x csc x cot x in terms of sin x and cos x is given by
sec x csc x cot x
= (1/cos x) (1/sinx) (cosx/ sinx)
= 1/ (sin x)^2
Hence, the expression sec x csc x cot x in terms of sin x and cos x is
1/ (sin x)^2.
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Simplify, if possible.
8ab² +3ab+2a-3b+5
A. The expression is in its simplest form.
B. -10ab² +5
2
C. 8ab² + 2ab +5
D.
8ab²-3ab+5
Please select the best answer from the choices provided
Answer:
A. The expression is in its simplest form.
Step-by-step explanation:
Answer:
i tried this i think the answer is 11a plus 2a subract3b ppus 5
find the value of ...B
Answer:
b=–2
Step-by-step explanation:
we've got:
(3+bx)⁵===> b⁵x⁵+15b⁴x⁴+90b³x³+720b²x²+405bx+243
and we've also got the coefficient of x³ as –720
90b³=–720===> b³=–8===> b=–2
two classes each with 21 students were given a physical fitness test. the result of the number of pull ups performed in 30 seconds were recorded in the table below
Based on the results of the physical fitness test, the reason why we are unable to calculate the mean number of pull-us done by the students in each class is that we don't have the exact number of pull-ups done by each student.
What is needed to calculate mean?To calculate the simple mean of a distribution of numbers, we would need the value of all the numbers to be known. These numbers will then be summed up and divided by the number of the distribution.
In this case of the physical fitness test, the number of pull-ups is not known for all the students as there are some that either did below 5 or above 10 and we don't know the exact number of pull-ups done.
As a result, we are unable to calculate the mean.
Question is:
Explain why we are unable to calculate the mean number of pull-ups done by the students in each class.
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Using company C’s phone plan, the cost of an overseas phone call is a $0.80 connection fee plus 23 cents per minute. If the total cost of the call is 7.93, how long is the phone call?
Answer: 31 Minutes
Step-by-step explanation:
Minus 0.80 from 7.93, and then divide 7.13 by 0.23 and you get 31
12. If √1225 = 35 then √12.25
[tex] \sqrt{12.25 } = 3.5[/tex]
Can y’all help me please??
Answer: 29/21
Quotient: 1
Reminder: 8
Step-by-step explanation:
Add up the amount of 7th graders playing instruments (not including drums) total and put that number under the amount of 8th graders playing a instrument.
Use the 1st digit 2 from dividend 29
21 & 29 squared root
Since 2 is less than 21, use the next digit 9 from dividend 29 and add 0 to the quotient. Find the closest multiple of 21 to 29.
1×21=21 is the nearest. Now subtract 21 from 29 to get reminder 8. Add 1 to quotient.
Since 8 is less than 21, stop the division. The reminder is 8. The topmost line 01 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
1/|2x - 9|≤5
How to solve the inequality
Answer:
5<x<7
Step-by-step explanation:
Hey there !
firstly, in inequality; we must know that we should put the x alone.
so, in order to put the x alone; we should do the following process,
1</2x-9/<5
here,
adding +9 in all sides, we get;
=1+9<2x-9+9<5+9
=10<2x<14
dividing it by 2;we get
=10/2<2x/2<14/2
=5<x<7
This is the following answer. hope it helps!
Thank you!
question is in the photos
Answer:
n(AuB)=15
n(AnB)=8 is the answer!
Wilson hires a financial analyst to analyse costs and profits for his cereal production business. The analyst determines that Wilson’s eventual profit function is given as: , where x is the number of bags of cereal produced. At what point or number of bags of cereal will Wilson’s profit start decreasing
If Wilson produces only one 1 bag, then his profit starts decreasing
How to determine the pointGiven the function;
Let f ( x ) = [tex]2x^4 - 4x^3 + 7[/tex]
Where;
x is the number of bags of cereal produced
[tex]f'x = 2x^4 - 4x^3 + 7[/tex]
[tex]f'(x) = 8x^3 - 12x^2[/tex]
Factorize the expression
[tex]f'(x) = 4x^2(2x - 3)[/tex]
If the value of x is decreasing, we have;
f ′ ( x ) ≤ 0
4x² (2x - 3) ≤ 0
If x² ≥ 0, then;
2x - 3 ≤ 0
x ≤ 3/ 2
With x as the number of bags
x ∈ N
x = 1 is the only possibility
Thus, if Wilson produces only one 1 bag, then his profit starts decreasing
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The complete question:
Wilson hires a financial analyst to analyse costs and profits for his cereal production business. The analyst determines that Wilson’s eventual profit function is given as: pi = 2x ^ 4 - 4x ^ 3 + 7, where x is the number of bags of cereal produced. At what point or number of bags of cereal will Wilson’s profit start decreasing
Which equations have the same value of x as Two-thirds (6 x + 12) = negative 24? Select two options.
4 x + 8 = negative 24 , 9 x + 18 = negative 24 are equations have the same value of x .
What in mathematics is a linear equation?
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.A - 4 x + 8 = negative 24
E - 4 x = negative 32
ARE CORRECT ON EDGE.
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The complete question is-
Which equations have the same value of x as Two-thirds (6 x + 12) = negative 24? Select two options.
4 x + 8 = negative 24
9 x + 18 = negative 24
4 x = negative 16
StartFraction 18 x + 36 over 2 EndFraction = negative 24
4 x = negative 32
What is the image of the point (-7,-6) after a rotation of 270° counterclockwise
about the origin?
Submit Answer
Drivsar Police Tormer Sondico
hp
attempt 2 out of 2
Answer:
(-6, 7)
Step-by-step explanation:
90 degrees counterclockwise / 270 degrees clockwise:
(x,y) -> (-y,x)
180 degrees counterclockwise / 180 degrees clockwise:
(x,y) -> (-x,-y)
270 degrees counterclockwise / 90 degrees clockwise:
(x,y) -> (y,-x)
I have 6 quarts of paint. How many shelves can be painted if each one takes one third of a quart.
Prove that:
( 1 - tan^4 A)cos^4 A = 1 - 2 sin^2 A
Here we go ~
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
[tex]\qquad \sf \dashrightarrow \: (1 - \tan {}^{4} (a) ) \cos {}^{4} (a) [/tex]
[tex]\qquad \sf \dashrightarrow \: (1 + \tan {}^{2} (a) )(1 - { \tan}^{2} (a)) \cos {}^{4}(a ) [/tex]
[ a² - b² = (a + b)(a - b) ]
[tex]\qquad \sf \dashrightarrow \: ( \sec {}^{2} (a) )(1 - ( \sec{}^{2} (a) - 1) )\cos {}^{4} (a) [/tex]
[ sec² a = 1 + tan² a, so : tan² a = sec²a - 1 ]
[tex]\qquad \sf \dashrightarrow \: \bigg( \dfrac{1}{{}cos^{2} (a)} \bigg)(2 - \sec{}^{2} (a) ) \cos {}^{4} (a) [/tex]
[tex]\qquad \sf \dashrightarrow \: \bigg(2 - \dfrac{1}{ \cos {}^{2} (a) } \bigg) \cos {}^{2} (a) [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{2 \cos {}^{2} (a) - 1}{ \cos {}^{2} (a) } \times \cos {}^{2} (a) [/tex]
[tex]\qquad \sf \dashrightarrow \: 2 \cos {}^{2} (a) - 1[/tex]
[tex]\qquad \sf \dashrightarrow \: 2(1 - \sin {}^{2} (a) ) - 1[/tex]
[ sin²a + cos² a = 1, hence sin²a = 1 - cos²a ]
[tex]\qquad \sf \dashrightarrow \: 2 - 2 \sin {}^{2} (a) - 1[/tex]
[tex]\qquad \sf \dashrightarrow \: 1 - 2 \sin {}^{2} (a) [/tex]
Answer:
See proof below
Step-by-step explanation:
Prove [tex]\left(\:1\:-\:tan^4A\right)cos^4A\:=\:1\:-\:2\:sin^2A[/tex]
[tex]\left(1-\tan ^4\left(A\right)\right)\cos ^4\left(A\right)[/tex] can be expressed in sin, cos terms
Use the trigonometric identity [tex]\tan \left(x\right)=\frac{\sin \left(x\right)}{\cos \left(x\right)}[/tex]
[tex]\left(1-\tan ^4\left(A\right)\right)\cos ^4\left(A\right) = \left(1-\left(\frac{\sin \left(A\right)}{\cos \left(A\right)}\right)^4\right)\cos ^4\left(A\right)[/tex]
[tex]\mathrm{Simplify}\:\left(1-\left(\frac{\sin \left(A\right)}{\cos \left(A\right)}\right)^4\right)\cos ^4\left(A\right)[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}[/tex]
= [tex]\left(1-\frac{\sin ^4\left(A\right)}{\cos ^4\left(A\right)}\right)\cos ^4\left(A\right)[/tex]
Multiplying the expression in parentheses by [tex]\cos ^4\left(A\right)[/tex] we get
[tex]\frac{\cos ^4\left(A\right)-\sin ^4\left(A\right)}{\cos ^4\left(A\right)}\cos ^4\left(A\right)[/tex]
Cancel the common factor [tex]\cos ^4\left(A\right)[/tex]
This gives us
[tex]\cos ^4\left(A\right)-\sin ^4\left(A\right)[/tex]
Now,
[tex]\sin ^4\left(A\right)=\left(\sin ^2\left(A\right)\right)^2[/tex]
[tex]\cos ^4\left(A\right)=\left(\cos ^2\left(A\right)\right)^2[/tex]
[tex]\:\cos ^4\left(A\right)-\sin ^4\left(A\right)[/tex] = [tex]\left(\cos ^2\left(A\right)\right)^2-\left(\sin ^2\left(A\right)\right)^2[/tex]
[tex]\mathrm{Apply\:Difference\:of\:Two\:Squares\:Formula:\:}x^2-y^2=\left(x+y\right)\left(x-y\right)[/tex]
[tex]\left(\cos ^2\left(A\right)\right)^2-\left(\sin ^2\left(A\right)\right)^2=\left(\cos ^2\left(A\right)+\sin ^2\left(A\right)\right)\left(\cos ^2\left(A\right)-\sin ^2\left(A\right)\right)[/tex]
= [tex]\cos ^2\left(A\right)-\sin ^2\left(A\right)[/tex] [tex]\textrm{ since }\cos ^2\left(A\right)+\sin ^2\left(A\right)[/tex] = 1
Using the fact that [tex]\cos ^2\left(A\right)=1-\sin ^2\left(A\right)[/tex]
we get
[tex]\cos ^2\left(A\right)-\sin ^2\left(A\right) = 1-\sin ^2\left(A\right)-\sin ^2\left(A\right)\\\\= 1-2\sin ^2\left(A\right)[/tex]
Proved
What is the area of the polygon if the side length of the square is 4
Answer:
16
Step-by-step explanation: This is because when we look at the square we realize by definition it is a 4-sided shape with 4 equal side lengths this means that if one side is 4 all the 4 sides of a square are also 4 and in this case, we would do length times width and get an answer of an area of 16 units.
Consider the relationship chart for the a fast-food restaurant,
Assume that the areas required for each department are:
Department Area Required (Square feet)
(CB) 300
(CF) 200
(PS) 200
(DD) 200
(CS) 300
Assume facility dimension of 6 (horizontal) by 8 (vertical) squares, where each square is 5 feet on a side. As a result, for example the CB department requires 12 squares. Develop a layout for the fast-food restaurant.
The layout of the fast-food restaurant of dimensions 6 by 8 5 feet squares is presented in the attached table created with Sheets.
How can the required layout be found?The dimensions of the facility are;
Horizontal = 6 squares
Vertical = 8 squares
The side length of each square = 5 feet
Therefore;
Area of each square = 5² ft.² = 25 ft.²
Number of squares, n, required by each dependent are therefore;
CB department, n = 300 ÷ 25 = 12 squares
CF department, n = 200 ÷ 25 = 8 squares
PS department, n = 8 squares
DD department, n = 8 squares
CS department, n = 12 squares
A layout for the fast-food restaurant is therefore;
The first three vertical columns of 8 squares each are occupied by the CF, PS, and DD departments. The remaining 3 by 8 squares are occupied by the CB department, (3 by 4 squares), and the CS department, (3 by 4 squares)Please see the attached table layout created using Sheets.
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Let D={12,15,17), E = {12,14,15,16) and F = {11,13,14,15,17).
List the elements in the set D UE.
DUE= (Use commas to separate answers.)
The elements that will be coming in the set D∪E will be {12, 14, 15, 16, 17}.
A set may be defined as a collection of letters or numbers that are written in order to depict a certain value or entity. A set is always represented by a capital letter symbol and is always written in curly brackets { }. Union of two sets may be defined as a new set which has the collection of all the elements of the two individual sets. Union of two sets is represented by the symbol '∪'. Union of two Indvidual sets, set A and set b is written as A∪B.
Now, according to the question set D is = {12, 15, 17} and set E is = {12, 14, 15, 16}.
The union of the two sets contains all the elements of the sets D and E.
Thus, D∪E will be given by {12, 14, 15, 16, 17}.
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Choose the estimate closest to the length of a woman's hand : 30 cm, 200mm, or 20 mm. Which is the correct answer?
Answer:
200mm
Step-by-step explanation:
200mm can be rewritten as 20 cm
a womans hand is on average 17.3 cm
this is the closest estimate out of the three
A small class has 9 students, 4 of whom are girls and 5 of whom are boys. The teacher is going to choose two of the students at random. What is the probability that the first student chosen will be a boy and the second will be a girl? Write your answer as a fraction in simplest form.
The probability that the first student chosen will be a boy and the second will be a girl is 0.28.
What is probability?Probability is also called the chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.
Total students = 9
Number of girls = 4
Number of boys = 5
Probability of choosing first boy = Number of boys / total students
⇒ 5/9
Now since 1 boy extract so remaining students = 9 - 1 = 8
Probability of choosing second girl = Number of girls / Total students
⇒ 4//8
Probability of A and B = P(A) × P(B)
Therefore,
The probability that the first student chosen will be a boy and the second will be a girl = (5/9) × (4/8) = 0.28
Hence "The probability that the first student chosen will be a boy and the second will be a girl is 0.28".
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a movie theater has a seating capacity of 329. the theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. there are half as many adults as there are children. if the total ticket sales was $ 2392, how many children, students, and adults attended?
Taking into account the definition of a system of linear equations, 178 children, 62 students and 89 adults attended to the movie theater.
System of linear equationsA system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values of the unknowns must be found, with which when are replaced in the equations, they must give the solution proposed.
This caseIn this case, a system of linear equations must be proposed taking into account that:
C is the number of children who attended the movie theater.S is the number of students who attended the movie theater.A is the number of adults who attended the movie theater.On the other hand, you know:
A movie theater has a seating capacity of 329. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. The total ticket sales was $ 2392.There are half as many adults as there are children.So, the system of equations to be solved consists of the following equations:
Equation 1: C + S + A= 329
Equation 2: 5C + 7S + 12A= 2392
Equation 3: A= C÷2= 1/2C
There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
Replacing equation 3 in equation 1 and isolating the variable S you get:
C + S + 1/2C= 329
3/2C + S= 329
S= 329 - 3/2C
Replacing this expression and equation 3 in equation 2 you get:
5C + 7(329 - 3/2C) + 12×1/2C= 2392
Solving:
5C + 7×329 - 7×3/2C + 12×1/2C= 2392
5C + 2303 - 21/2C + 6C= 2392
5C - 21/2C + 6C= 2392 -2303
1/2C= 89
C= 89÷ 1/2
C= 178
Remembering that S= 329 - 3/2C, you get S= 329 - 3/2×178 → S= 62
Finally, substituting the value of C in Equation 3: A= 1/2C= 1/2×178 → A=89
In summary, 178 children, 62 students and 89 adults attended to the movie theater.
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1. Let f be the function given by f(x)= X/ √x²-4 Find the domain of f.