I need help with thisIt asks to graph the functionIf you can, use Desmos to graph
Answers
Given the function
[tex]f(x)=\cot (x+\frac{\pi}{6})[/tex]The graph of the function is dhoe below
Related Questions
on a cold January day , Mavis noticed that the temperature dropped 21 degrees over the course of the day to -9C. Write and solve an equation to determine what the temperature was at the beginning of the day
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Answer:
Step-by-step explanation:
At the beginning of the day, the temperature was of x.
It dropped 21 degrees to -9C. So
x - 21 = -9
x =
Given A(-9, -12), B(-2, 2), C(x, 6).and D(-5, -2), find the value ofx so that AB || CD
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1) Given these line segments, let's find the slope of them. Let's begin with AB
[tex]m=\frac{2-(-12)}{-2-(-9)}=\frac{14}{-2+9}=\frac{14}{7}=2[/tex]2) Parallel lines have the same slope, so let's set this slope formula so that we can get the slope m=2. Bearing in mind CD:
[tex]\begin{gathered} 2=\frac{-2-6}{-5-x} \\ 2=\frac{-8}{-5-x} \\ 2(-5-x)=-8 \\ -10-2x=-8 \\ -2x=-8+10 \\ -2x=2 \\ x=-1 \end{gathered}[/tex]Thus, x=-1
RATIONAL FUNCTIONSSynthetic divisiontable buand write your answer in the following form: Quotient *
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The given polynomial is:
[tex]\frac{2x^4+4x^3-6x^2+3x+8}{x\text{ + 3}}[/tex]Using the long division method:
The equattion can be written in the form:
Quotient + Remainder / Divisor
[tex](2x^3-2x^2\text{ + 3) +}\frac{-1}{x+3}[/tex]Will mark as brainlist
Which of the following best represents R= A - B ?
Please help, it’s due soon!
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A.
Step-by-step explanation:This is a question of graphical operations with vectors. In order to get the answer, you must draw vector B with inverse direction, and place the tail of said vector on top of the arrow of vector A. Check the attached image.
Hence, the answer that better represent the resulting vector is answer A.
A.
Step-by-step explanation:This is a question of graphical operations with vectors. In order to get the answer, you must draw vector B with inverse direction, and place the tail of said vector on top of the arrow of vector A. Check the attached image.
Hence, the answer that better represent the resulting vector is answer A.
The figure is not drawn to scale. Find the unknown angle.
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ThereforeGiven the image, we can find the missing angle using the sum of angles at a point rule.
The sum of angles at a point is known to be 360 degrees.
Therfore,
[tex]\begin{gathered} a^0+315^0=360^0 \\ a^0=360^0-315^0 \\ a^0=45 \end{gathered}[/tex]Therefore, the measure of "a" is
Answer:
[tex]45^0^{}[/tex]An excursion boat traveled from the Ferry Dock to Shelter Cove. How many miles did ittravel?
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The situation forms a right triangle:
Where x is the distance traveled.
We can apply the Pythagorean theorem:
c^2 =a^2 + b^2
Where:
c= hypotenuse = x
a & b= the other 2 sides = 5 ,12
Replacing:
x^2 = 5^2 + 12^2
x^2 = 25+144
x^2 = 169
x= √169
x= 13
Distance traveled = 13 miles
Mark the drawing to show the given information and complete each congruence statement.∆acd=∆_____by______
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the triangle is ACD is equal to the triangle CBE so let write all the information we have in the figure so:
And for oposit angles we know that then angle BCE = to the angle ACD, so we have two angles and ine side equal so the triangles are similar
by: ASA
3.8% of a population are infected with a certain disease. There is a test for the disease, however the test is not completely accurate. 93.9% of those who have the disease test positive. However 4.1% of those who do not have the disease also test positive (false positives). A person is randomly selected and tested for the disease. What is the probability that the person has the disease given that the test result is positive? 0.475 0.038 0.525 0.905
Answers
ANSWER:
0.475
STEP-BY-STEP EXPLANATION:
The probability of a person has disease given the test is positive:
P (disease) = 3.8% = 0.038
P (positive | disease) = 93.9% = 0.939
P (positive | no disease) = 4.1% = 0.041
P (no disease) = 100% - 3.8% = 96.2% = 0.962
The probability that the person has the disease given that the test result is positive is calculated as follows:
[tex]\begin{gathered} \text{ P\lparen infected \mid test positive\rparen }=\frac{\text{ P\lparen positive \mid infected\rparen }\times\text{ \rbrack P \lparen infected\rparen}}{\text{ P \lparen positive\rparen}} \\ \\ \text{ P \lparen positive \mid infected\rparen }=\text{ P \lparen positive \mid disease\rparen = 0.939} \\ \\ \text{ P \lparen infected\rparen = P \lparen disease\rparen = 0.038} \\ \\ \text{ P \lparen positive\rparen = P \lparen positive \mid infected\rparen }\times\text{ P \lparen infected\rparen }+\text{ P \lparen positive \mid no infected\rparen}\times\text{ P \lparen no infected\rparen } \\ \\ \text{ P \lparen positive \mid infected\rparen =P \lparen positive \mid no disease\rparen = 0.041} \\ \\ \text{ P \lparen no infected\rparen = P \lparen no disease\rparen = 0.962} \\ \\ \text{ We replacing:} \\ \\ \text{ P \lparen positive\rparen = }0.038\cdot0.939+0.041\cdot0.962=0.075124 \\ \\ \text{ P\lparen infected \mid test positive\rparen }=\frac{0.038\cdot0.939}{0.075124} \\ \\ \text{ P\lparen infected \mid test positive\rparen = }\:0.47497=0.475 \end{gathered}[/tex]The correct answer is the first option: 0.475
In one study, it was found that the correlation between two variables is -.16 What statement is true? There is a weak positive association between the variables. There is a weak negative association between the variables. There is a strong positive association between the variables. There is a strong negative association between the variables.
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The correlation could be positive, meaning both variables move in the same direction,
If it is negative, meaning that when one variable's value increases, the other variables' values decrease.
Since the correlation between the 2 variables is -16
Since -16 is a negative value
Then The answer should be
There is a weak negative association between variables
The strong negative correlation should be between 0 and -1
I need help with this practice problem solving It is trigonometry I will send another picture with the graph that is included in the problem, it asks to use the graph to solve
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Given the function
[tex]f(x)=\sin (\pi x+\frac{\pi}{2})[/tex]The graph of the function is as shown below:
What is The volume of a cylinder 7 in height and 3 radius and a cone of 7 height and 3 radius together? So what is The volume of both together?
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In this case r =3, h= 7
[tex]\Rightarrow V_{cy}=\pi\times3^2\times7=63\pi=197.92unit^3[/tex][tex]\begin{gathered} \text{The Volume V}_{co\text{ }}of\text{ a cone with base radius r and height h is given by:} \\ V_{co}=\frac{1}{3}\times\pi\times r^2\times h \end{gathered}[/tex]In this case,
r=3, h=7
[tex]V_{co}=\frac{1}{3}\times\pi\times(3)^2\times7=21\pi=65.97unit^3[/tex][tex]\begin{gathered} \text{Therefore} \\ V_{cy}+V_{co}=63\pi+21\pi=84\pi=263.89unit^3 \end{gathered}[/tex]Hence
volume of cone + volume of cylinder = 263.89 cube units
What is the solution to the following system of equations. Enter your answer as an ordered pair.3x+2y=17and4x+6y=26As an ordered pairHelp me pls
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The system of equation are:
[tex]\begin{gathered} 3x+2y=17 \\ 4x+6y=26 \end{gathered}[/tex]to solve this problem we can solve the second equation for x so:
[tex]\begin{gathered} 4x=26-6y \\ x=6.5-1.5y \end{gathered}[/tex]Now we can replace x in the firt equation so:
[tex]3(6.5-1.5y)+2y=17[/tex]and we can solve for y so:
[tex]\begin{gathered} 19.5-4.5y+2y=17 \\ 19.5-17=2.5y \\ 2.5=2.5y \\ \frac{2.5}{2.5}=1=y \end{gathered}[/tex]Now we replace the value of y in the secon equation so:
[tex]\begin{gathered} x=6.5-1.5(1) \\ x=5 \end{gathered}[/tex]So the solution as a ordered pair is:
[tex](x,y)\to(5,1)[/tex]which function is best represented by this graphA) f(x) = x² - 3x + 8B) f(x) = x² - 3x - 8C) f(x) = x² + 6x + 8D) f(x) = x² + 6x - 8
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Solution:
Given the graph;
The axis of symmetry and vertex of the graph are;
[tex]\begin{gathered} x=-3 \\ (-3,-1) \end{gathered}[/tex]Also, the x-intercepts are;
[tex](-4,0),(-2,0)[/tex]And the y-intercep is;
[tex](0,8)[/tex]Thus, the function that best represents the graph is;
[tex]f(x)=x^2+6x+8[/tex]CORRECT OPTION: C
Maggie has $30 in an account. The interest rate is 10% compounded annually.To the nearest cent, how much will she have in 1 year?Use the formula B=p(1+r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
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Solution:
Using the formula;
[tex]\begin{gathered} B=p(1+r)^t \\ \\ \text{ Where }B=balance,p=principal,r=rate,t=time \end{gathered}[/tex][tex]p=30,r=10\text{ \%}=0.1,t=1[/tex]Thus;
[tex]\begin{gathered} B=30(1+0.1)^1 \\ \\ B=33 \end{gathered}[/tex]ANSWER: $33
If 10 = 1+4, then 1+9= 10substitution property symmetric property transitive propertyreflexive property8*1=8Multiplicative InverseMultiplicative IdentityMultiplicative Property of ZeroAdditive Identity Property
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Reflexive Property
In Math, especially in geometry, but also in other fiels.
What we have here is the Reflexive Property, that states that
If a= b+c then b+c=a
Multiplicative Identity
The multiplicative identity is the number 1, so every number times 1 is equal to itself and this property is called multiplicative identity.
Given the focus and directrix shown on the graph, what is the vertex form of the equation of the parabola?
[tex]x\ =\ \frac{1}{10}(y\ -\ 3)^2\ -\ \frac{3}{2}[/tex]
[tex]x\ =\ 10(y\ +\ 3)^2\ +\ \frac{3}{2}[/tex]
[tex]x\ =\ \textrm{-}\frac{1}{10}(y\ -\ 3)^2\ -\ \frac{3}{2}[/tex]
[tex]y\ =\ \frac{1}{10}(x\ -\ 3)^2\ -\ \frac{3}{2}[/tex]
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The vertex-form equation of the parabola is given as follows:
y = 1/10(y - 3)² - 3/2.
What is the equation of a horizontal parabola?An horizontal parabola of vertex (h,k) is modeled as follows:
x = (1/4p)(y - k)² + h.
In which:
The directrix is x = h - p.The focus is (h + p, k).In the context of this problem, we have that:
The directrix is x = -4.The focus is: (1,3), hence k = 3.A system of equations is built for h and p as follows:
h - p = -4.h + p = 1.Hence:
2h = -3
h = -3/2.
p = 1 + 3/2 = 2.5.
Then the equation is:
y = 1/10(y - 3)² - 3/2. (first option).
Missing informationThe graph is given by the image at the end of the answer.
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This graph shows the amount of rain that falls in a given amount of time.
What is the slope of the line and what does it mean in this situation?
A line graph measuring time and amount of rain. The horizontal axis is labeled Time, hours, in intervals of 1 hour. The vertical axis is labeled Amount of rain, millimeters, in intervals of 1 millimeter. A line runs through coordinates 2 comma 5 and 4 comma 10.
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It is to be noted that the slope of the line is 5/2. This means that 5 mm of rain falls every 2 hours. See the calculation below.
What is a slope in math?In general, the slope of a line indicates its gradient and direction. The slope of a straight line between two locations, say (x₁,y₁) and (x₂,y₂), may be simply calculated by subtracting the coordinates of the places. The slope is often denoted by the letter 'm.'
To find the slope of the line in the graph, we use the following equation:
m = [y₂ - y₁]/[x₂-x₁]
Where (x1,y1) = coordinates of the first point in the line; and
(x₂,y₂) = coordinates of the second point in the line
Given that the points (2, 5) from the graph is (x₁, y₁) and the point on graph (4, 10) are (x₂,y₂) Hence,
m = [10-5]/[4-2]
The slope (m) = 5/2
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Full Question:
This is the complete question and the described graph is attached
This graph shows the amount of rain that falls in a given amount of time.
What is the slope of the line and what does it mean in this situation?
Select from the drop-down menus to correctly complete each statement
The slope of the line is ___
This means that ___ mm of rain falls every ___
Add or subtract the fractions. Write the answer in simplified form.-2/13+(-1/13)
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1) To add or subtract fractions, let's firstly check the denominators
In this case, the denominator is the same.
The plus before the bracket does not change the sign.
[tex]\begin{gathered} -\frac{2}{13}+(-\frac{1}{13}) \\ \frac{-2-1}{13} \\ \\ \frac{-3}{13} \end{gathered}[/tex]That is why we get to -3/13 as a result.
Which number is not a solution to3(x+4)−2≥7?-2-12 1
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The inequality is:
[tex]3(x+4)-2\ge7[/tex]now we solve the inequality for x
[tex]\begin{gathered} 3(x+4)\ge7+2 \\ 3(x+4)\ge9 \\ x+4\ge\frac{9}{3} \\ x+4\ge3 \\ x\ge3-4 \\ x\ge-1 \end{gathered}[/tex]This means that all the number, from -1 to infinit are solution of the inequality, and the only option that is not a solution is a) -2
Irene is 54 ⅚ inches tall. Theresa is 1 ⅓ inches taller than Irene and Jane is 1 ¼ inches taller than Theresa How tall is Jane
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Let be "n" Irene's height (in inches), "t" Theresa's height (in inches) and "j" Jane's height (in inches).
You know Irene's height:
[tex]n=54\frac{5}{6}[/tex]You can write the Mixed number as an Improper fraction as following:
- Multiply the Whole number by the denominator.
- Add the product to the numerator.
- Use the same denominator.
Then:
[tex]\begin{gathered} n=\frac{(54)(6)+5}{6}=\frac{324+5}{6}=\frac{329}{6} \\ \end{gathered}[/tex]Now convert the other Mixed numbers to Improper fractions:
[tex]\begin{gathered} 1\frac{1}{3}=\frac{(1)(3)+1}{3}=\frac{4}{3} \\ \\ 1\frac{1}{4}=\frac{(1)(4)+1}{4}=\frac{5}{4} \end{gathered}[/tex]Based on the information given in the exercise, you can set up the following equation that represents Theresa's height:
[tex]t=\frac{329}{6}+\frac{4}{3}[/tex]Adding the fractions, you get:
[tex]t=\frac{337}{6}[/tex]Now you can set up this equation for Jane's height:
[tex]undefined[/tex]Enter a range of values for x.1416202x+109/15-5
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26
Here, we want to write a range of values for x.
The shape we have is not a parallelogram but we have two equal sides
If it was a complete parallelogram, the two marked angles will be equal
But since what we have is not a complete parallelogram,
then;
[tex]\begin{gathered} 2x\text{ + 10 < 62 } \\ 2x\text{ < 62 - 10} \\ \\ 2x\text{ < 52} \\ \\ x\text{ < }\frac{52}{2} \\ \\ x\text{ < 26} \end{gathered}[/tex]The System of PolynomialsYou are aware of the different types of numbers: natural numbers, integers, rational numbers, and real numbers. Now you will work with a property of the number system called the closure property. A set of numbers is closed for a specific mathematical operation if you can perform the operation on any two elements in the set and always get a result that is an element of the set.Consider the set of natural numbers. When you add two natural numbers, you will always get a natural number. For example, 3 + 4 = 7. So, the set of natural numbers is said to be closed under the operation of addition.Similarly, adding two integers or two rational numbers or two real numbers always produces an integer, or rational number, or a real number, respectively. So, all the systems of numbers are closed under the operation of addition.Think of polynomials as a system. For each of the following operations, determine whether the system is closed under the operation. In each case, explain why it is closed or provide an example showing that it isn’t.1)AdditionType your response here:2)SubtractionType your response here:3)MultiplicationType your response here:4)DivisionType your response here:5)Determine whether the systems of natural numbers, integers, rational numbers, irrational numbers, and real numbers are closed or not closed for addition, subtraction, multiplication, and division.Type your response here: 6)Addition Subtraction Multiplication Division natural numbers integers rational numbers irrational numbers real numbers When a rational and an irrational number are added, is the sum rational or irrational? Explain.Type your response here:7)When a nonzero rational and an irrational number are multiplied, is the product rational or irrational? Explain.Type your response here:8)Which system of numbers is most similar to the system of polynomials?Type your response here:9)For each of the operations—addition, subtraction, multiplication, and division—determine whether the set of polynomials of order 0 or 1 is closed or not closed. Consider any two polynomials of degree 0 or 1.Type your response here:10)Polynomial 1 Polynomial 2 Operation Expression Result Degree of Resultant Polynomial Conclusion addition subtraction multiplication division What operations would the set of quadratics be closed under? For each operation, explain why it is closed or provide an example showing that it isn’t.Type your response here:11)Is there a set of expressions that would be closed under all four operations? Explain.Type your response here:
Answers
The Solution To Question Number 10:
The question says what operations would the set of quadratics be closed under.
Let the sets of quadratics be
[tex]\begin{gathered} p(x)=ax^2+bx+c \\ q(x)=mx^2+nx+k \end{gathered}[/tex]The set of two quadratics (polynomials) is closed under Addition.
Explanation:
[tex]\begin{gathered} P(x)+q(x)=(ax^2+bx+c)+(mx^2+nx+k) \\ =(a+m)x^2+(b+n)x+(c+k) \\ \text{which is still a quadratic.} \\ \text{Hence, the set of quadratics is closed under Addition.} \end{gathered}[/tex]The set of two quadratics is closed under Subtraction.
[tex]\begin{gathered} P(x)-q(x)=(ax^2+bx+c)-(mx^2+nx+k) \\ =(a-m)x^2+(b-n)x+(c-k) \\ \text{which is still a quadratic, provided both a}\ne m,\text{ b}\ne n\text{ } \\ \text{Hence, the set of quadratics is closed under Subtraction.} \end{gathered}[/tex]The set of quadratics is not closed under Multiplication.
[tex]\begin{gathered} P(x)\text{.q(x)}=(ax^2+bx+c)(mx^2+nx+k)=amx^4+(bn+ak)x^2+ck+\cdots \\ \text{Which is not a quadratic.} \\ \text{Hence, the set of quadratics is not closed under multiplication.} \end{gathered}[/tex]The set of quadratics is not closed under Division.
[tex]\begin{gathered} \text{Let the sets be f(x)=8x}^2\text{ and} \\ h(x)=2x^2-1 \\ \text{ So,} \\ \frac{f(x)}{h(x)}=\frac{8x^2}{2x^2_{}-1} \\ \text{Which is not a quadratic.} \\ \text{Hence, the set is not closed under Division.} \end{gathered}[/tex]
11) a- 15 > 40-6 +3a) 12) 366b-1) > 18 - 3b a-151-46-67+1-useBay 9-15 124-12a atiza324+15 13a339 ay/9 13) 26 + m 2 5(-6 +3m) 14) 20-2p>-2lp
Answers
Answer
11) a > 3
12) b > (2/3)
Explanation
11) a - 15 > -4 (-6 + 3a)
a - 15 > 24 - 12a
a + 12a > 24 + 15
13a > 39
Divide both sides by 13
(13a/13) > (39/13)
a > 3
In graphing inequality equations, the first thing to note is that whenever the equation to be graphed has (< or >), the circle at the beginning of the arrow is usually unshaded.
But whenever the inequality has either (≤ or ≥), the circle at the beginning of the arrow will be shaded.
Then, the direction of the graph depends on the direction of the inequality sign, for example, the answer here says a is greater than 3. So, the graph will start with an unshaded circle and cover the numbers greater than 3.
12) 3 (6b - 2) > (8 - 3b)
18b - 6 > 8 - 3b
18b + 3b > 8 + 6
21b > 14
Divide both sides by 21
(21b/21) > (14/21)
b > (2/3)
This answer is similar to that of number 11. For the graph, it will start with an unshaded circle and move towards the numbers greater than (2/3)
Hope this Helps!!!
Is (x + 3) a factor of 7x4 + 25x³ + 13x² - 2x - 23?
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According to the factor theorem, if "a" is any real integer and "f(x)" is a polynomial of degree n larger than or equal to 1, then (x - a) is a factor of f(x) if f(a) = 0. Finding the polynomials' n roots and factoring them are two of their principal applications.
What is the remainder and factor theorem's formula?When p(x) is divided by xc, the result is p if p(x) is a polynomial of degree 1 or higher and c is a real number (c). For some polynomial q, p(x)=(xc)q(x) if xc is a factor of polynomial p. The factor theorem in algebra connects a polynomial's components and zeros. The polynomial remainder theorem has a specific instance in this situation. According to the factor theorem, f(x) has a factor if and only if f=0.The remainder will be 0 if the polynomial (x h) is a factor. In contrast, (x h) is a factor if the remainder is zero.The factor theorem is mostly used to factor polynomials and determine their n roots. Factoring is helpful in real life for comparing costs, splitting any amount into equal parts, exchanging money, and comprehending time.To learn more about Factor theorem refer to:
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Eduardo's school is selling tickets to a play. On the first day of ticket sales the school sold 4 adult tickets and 9 child tickets for a total of $108. The school took in $114 on the second day by selling 10 adult tickets and 3 child tickets. What is the price each of one adult ticket and one child ticket?
Answers
The price of one adult ticket is $9 and the price of child ticket is $8
First day of ticket sales the school sold 4 adult tickets and 9 child tickets for a total of $108
Consider the price of adult ticket as x and child ticket as y
Then the equation will be
4x+9y = 108
Similarly the school took in $114 on the second day by selling 10 adult tickets and 3 child tickets
10x+3y = 114
Here we have to use the elimination method
Multiply the first equation by 10 and second equation by 4
40x+90y = 1080
40x+12y = 456
Subtract the equation 2 from equation 1
90y-12y = 1080-456
78y = 624
y = 624/78
y = $8
Substitute the value of y in any equation
10x+3y =114
10x+3×8 =114
10x +24 =114
10x = 90
x = 90/10
x = $9
Hence, the price of one adult ticket is $9 and the price of child ticket is $8
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In ACDE, m/C= (5x+18), m/D= (3x+2), and m/B= (2+16)°.
Answers
Angle (D) = m(D) = 50°, CDE provides the following: 3. angles
m=C=(5x+18), m=D=(3x+2), and m=E=(x+16)°.The total of the angles in a triangle is 180°What are angles?An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.CDE provides the following: 3. angles
m<C=(5x+18),m<D=(3x+2), andm<E=(x+16)degree.The total of the angles in a triangle is 180 degrees, so:
"mC + mD + mE = 180°"(5x+18)° + (3x+2)° + (x+16)° = 180°5x + 18 + 3x + 2 + x + 16 = 180°5x + 3x + x + 18 + 2 + 16 = 180°9x +36= 180°From both sides, deduct 36 as follows:
9x + 36 - 36 = 180° - 36°9x = 144°x = 144°/9x = 16From the aforementioned query, we are requested to determine:
angular D (m<D)Hence:
m∠D=(3x+2)°m∠D=( 3 × 16 + 2)°m∠D=(48 + 2)°m∠D= 50°Therefore, angle (D) = m(D) = 50°, CDE provides the following: 3. angles
m=C=(5x+18), m=D=(3x+2), and m=E=(x+16)°.The total of the angles in a triangle is 180°To learn more about angles, refer to:
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Iq scores were gathered for group of college students at a local university. What is the level of measurement of dataNominal, ordinal, interval, ratio
Answers
Nominal data refers to non numerical data, for example categories, colors, etc...
Ordinal data refers to numerical data with a natural order, it comprehends real numbers.
Intervals comprehends data with equal distance between the values and no meaningful zero
Ratios comprehends data with equal distance between the values and a meaningul zero value.
With this in mind, the IQ scores of the college students represent numerical data, with a natural order, and the distance between the values is not equal, so you can classify the data as "ordinal"
Match each piece of the function with its domain.(6, oo)(-00, 1)(1,00)(-oo, -2)(-00, 6)(-2, 6)(3,00)(1, 4)
Answers
Explanation
The question wants us to select all the domains in the set of functions graphed.
The domain of a function is the set of all possible inputs for the function.
To do so, we have to be aware that there are 3 pieces of functions
These are shown below
These are
[tex]\begin{gathered} (-\infty,-2) \\ \\ (-2,6) \\ \\ (6,\infty) \end{gathered}[/tex]
Shanice has 4 times as much many pairs of shoes as does her brother Ron. If Shanice gives Ron 12 pairs of shoes, she will have twice as many pairs of shoes as Ron does. How many pairs of shoes will Shanice have left after she gives Ron the shoes?
Answers
Let's define:
x: pairs of shoes of Shanice
y: pairs of shoes of Ron
Shanice has 4 times as much many pairs of shoes as does her brother Ron, means:
x = 4y (eq. 1)
If Shanice gives Ron 12 pairs of shoes, she will have twice as many pairs of shoes as Ron does, means:
x - 12 = 2y (eq. 2)
Replacing equation 1 into equation 2:
4y - 12 = 2y
4y - 2y = 12
2y = 12
y = 12/2
y = 6
and
x = 4*6 = 24
After she gives Ron the shoes, she will have left 24-12 = 12 pairs of shoes
may ou solve the system of linear equations by substitution
Answers
y= 11 + 4x
3x +2y = 0
Put the first equation into the second one. (replace the value of y)
3x +2 (11 + 4x) = 0
Solve for x:
3x + 22 + 8x = 0
3x+8x = -22
11x = -22
x = -22/11
x = -2
Replace x=-2 in the first equation and solve for y
y= 11 + 4 (-2)
y= 11-8
y= 3
Solution:
x= -2 , y=3