The best reflects solution of the equation is, There is only one solution: x = 3. The solution x = 2 is an extraneous solution.
What is extraneous solution?
An extraneous solution is a root of a converted equation that is not a root of the original equation because it was left out of the original equation's domain is referred to as a superfluous solution.
We are given the following equation,
(x / x - 1) - (1 / x - 2) = (2x - 5)/(x^2 - 3x + 2)
Solving the given equation we have,
(x^2 - 3x + 1) / (x^2 - 3x + 2) = (2x - 5) / (x^2 - 3x + 2)
x^2 - 3x + 1 = 2x - 5
x^2 - 5x + 6 = 0
x^2 - 3x - 2x + 6 = 0
x(x - 3) - 2(x - 3) = 0
(x - 3)(x - 2) = 0
(x - 3) = 0, (x - 2) = 0
x = 3, x = 2
At x = 2 the denominator of the equation will be 0. So solution of the equation is not valid at x = 2.
Therefore, x = 3 is the only one solution. The solution x = 2 is an extraneous solution.
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A small town has two local high schools. High School A currently has 900 studentsand is projected to grow by 50 students each year. High School B currently has 500students and is projected to grow by 100 students each year. Let A represent thenumber of students in High School A in t years, and let B represent the number ofstudents in High School B after t years. Graph each function and determine whichhigh school is projected to have more students in 4 years.
High School A currently has 900 students and is projected to grow by 50 students each year.
We can write an equation using the above information
[tex]A=900+50t[/tex]Where A represents the number of students in High School A in t years.
High School B currently has 500 students and is projected to grow by 100 students each year.
We can write an equation using the above information
[tex]B=500+100t[/tex]Where B represents the number of students in High School B in t years.
Let us graph these two equations
Determine which high school is projected to have more students in 4 years.
Let us substitute t = 4 into both equations
[tex]\begin{gathered} A=900+50t \\ A=900+50(4) \\ A=900+200 \\ A=1100 \end{gathered}[/tex]High school A is projected to have 1100 students in 4 years.
[tex]\begin{gathered} B=500+100t \\ B=500+100(4) \\ B=500+400 \\ B=900 \end{gathered}[/tex]High school B is projected to have 900 students in 4 years.
Therefore, high school A is projected to have more students (1100) as compared to high school B (900) in 4 years.
Scientists are conducting an experiment with a gas in a sealed container. The mass of the gas is measured, and the scientists realize that the gas is leaking over time in a linear way. Nine minutes since the experiment started, the gas had a mass of 68.4 grams. Thirteen minutes since the experiment started, the gas had a mass of 61.2 grams. At what rate is the gas leaking? Use g for grams and min for minutes.
the rate is:
[tex]m=\frac{61.2-68.4}{13-9}=-\frac{7.2}{4}=-1.8\frac{g}{\min }[/tex]What is the slope and y-intercept of the equation y = -2/3x + 1Group of answer choicesSlope = 2/3; y-intercept = 0Slope = 1; y-intercept = -2/3Slope = -2; y-intercept = 3Slope = -2/3; y-intercept = 1
The form of the linear equation is
[tex]y=mx+b[/tex]m is the slope
b is the y-intercept
The given equation is
[tex]y=-\frac{2}{3}x+1[/tex]Let us compare the given equation with the form above, then
[tex]m=-\frac{2}{3}[/tex]and the value of b is
[tex]b=1[/tex]The slope of the line is the coefficient of x
The y-intercept is the numerical term
The slope = -2/3
The y-intercept = 1
The right answer is D the last answer
In any question like that, put the equation in the form
y = m x + b
m is the slope
b is the y-intercept
In a nearby park, a field has been marked off for the neighborhood Pop Warner football team. If the field has a perimeter of 310 yd and an area of 4950 yd', what are the dimensions of the field?
Answer:
The dimension of the field is ( 110 x 45)
Exolanations:
Perimeter of the field, P = 310 yd
Area of the field, A = 4950 yd²
Note that the shape of a field is rectangular:
Perimeter of a rectangle, P = 2(L + B)
Area of a rectangle, A = L x B
Substituting the values of the perimeter, P, and the Area, A into the formulae above:
310 = 2(L + B)
310 / 2 = L + B
155 = L + B
L + B = 155...............................................(1)
4950 = L x B...............(2)
From equation (1), make L the subject of the formula:
L = 155 - B...................(3)
Substitute equation (3) into equation (2)
4950 = (155 - B) B
4950 = 155B - B²
B² - 155B + 4950 = 0
Solving the quadratic equation above:
B² - 110B - 45B + 4950 = 0
B (B - 110) - 45(B - 110) = 0
(B - 110) ( B - 45) = 0
B - 110 = 0
B = 110
B - 45 = 0
B = 45
Substitute the value of B into equation (3)
L = 155 - B
L = 155 - 45
L = 110
The dimension of the field is ( 110 x 45)
A normal distribution has a mean of 101 and a standard Deviation of 12. find the probability that a value selected at random is in the following interval.at most 13
Answer:
84.134%
Explanation:
First, determine the value of the z-score.
[tex]\begin{gathered} Z=\frac{X-\mu}{\sigma} \\ =\frac{113-101}{12} \\ =\frac{12}{12} \\ z-score=1 \end{gathered}[/tex]Next, we determine the probability that a value selected at random is at most 113:
[tex]\begin{gathered} P(X\le113)=P(x\le1)_{} \\ =0.84134 \\ =84.134\% \end{gathered}[/tex]Thus, the probability that a value selected at random is in the given interval is 84.134%.
Determine whether the statement is true or false.
2E{x|XEN and x is odd}
Is the statement true or false?
O True
O False
The given statement exists as false. An expression, rule, or law in mathematics establishes the link between an independent variable and a dependent variable.
What is meant by function?An expression, rule, or law in mathematics establishes the link between an independent variable and a dependent variable (the dependent variable).
The characteristic that every input is associated with exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs.
A relation between a collection of inputs and outputs is known as a function. A function exists, to put it simply, a relationship between inputs in which each input exists connected to precisely one output.
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why are integers rational numbers? give an example
Integers are rational numbers because it consists of zero, positive and negative numbers till infinity only.
What is Rational number?This is referred to as a number which can be expressed as the quotient p/q of two integers such that q ≠ 0 and they are present till infinity due to the large numbers and examples include 2000, 25 etc.
Integers are rational numbers because they contain zero, positive and negative numbers. Decimals and fractions are not included in this context and an example is 12, 100 etc which is why the aforementioned above was chosen as the correct choice.
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find the slope of #1 y = 2x - 3#2 (-2,-4) (-1,-2)#3 y = 1/3x - 4# 4 (4,0) (4,1)
1. slope= 2
2. slope=2
3. slope= 1/3
4. slope indefinite, vertical line
Explanation
Step 1
[tex]\begin{gathered} y=\text{ 2x-3} \\ \end{gathered}[/tex]the equation is given in slope(m) - intercept(b)
[tex]\begin{gathered} y=\text{ mx+b} \\ \text{then} \\ mx+b=2x-3 \\ m=2 \\ \text{slope}=2 \end{gathered}[/tex]Step 2
when you have two points of a line, P1 and P2 the slope is given by:
[tex]\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ \text{where} \\ P1(x_1,y_1)andP2(x_2,y_2) \end{gathered}[/tex]Let
P1(-2,-4) P2(-1,-2)
replace
[tex]\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ \text{slope}=\frac{-2-(-4)}{-1-(-2)} \\ \text{slope}=\frac{-2+4}{-1+2}=\frac{2}{1}=2 \\ \text{slope}=2 \end{gathered}[/tex]Step 3
[tex]y=\frac{1}{3}x-4[/tex]similar to the #1. ,the equation is given in slope(m) - intercept(b)
[tex]\text{the slope = }\frac{1}{3}[/tex]Step 4
let
[tex]P1(4,0)\text{ and P2(4,1)}[/tex][tex]\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ \text{slope}=\frac{1-0}{4-4}=\frac{1}{0}=\text{indefined} \\ it\text{ means the line is vertical} \end{gathered}[/tex]Hi. I can send a picture. can you help? thank u
we have the equation
y=x^2-6x+2
this equation represents a vertical parabola open upward (because the leading coefficient is positive)
that means
the vertex is a minimum
Convert to vertex form
y=a(x-h)^2+k
where
(h,k) is the vertex
Complete the square
y=(x^2-6x+9)+2-9
y=(x-3)^2-7
therefore
the vertex is (3,-7)
the answer is the option Athe length of a rectangle is two more than the width. if the perimeter is 28, find the length and the width of the rectangle, let w represent the width and l represent the length.
You have that the perimeter of a rectangle is 28. In order to find the values of length and width of the rectangle, you take into account the following formula for the perimeter of a rectangle:
[tex]P=2w+2l[/tex]where w is the width and l is the length. You have that the length l is twice the width w of the rectangle, that is l=2w. By replacing this expression for l into theformula for the calculation of the perimeter you obtain:
[tex]P=2w+2(2w)=2w+4w=6w[/tex]Thus, you have that P = 6w. You solve this equation for w, and also replace the value of P, just as follow:
[tex]\begin{gathered} P=6w \\ w=\frac{P}{6}=\frac{28}{6}=\frac{14}{3}=4.66 \end{gathered}[/tex]Then, the width is 4.66. The length is:
[tex]l=2w=2(4.66)=9.33[/tex]length = 9.33
Determine if the following ordered pairs are solutions to the equation 3x + y = 12.
(2,5)
(4,0)
(0,6)
Is (2,5) a solution to the equation 3x+y=12? Select the correct choice below and fill in the answer box to complete your
choice.
OA. Yes, because when 2 is substituted for x and 5 is substituted for y, simplifying the left side results in.
equals the right side.
OB. No, because when 2 is substituted for x and 5 is substituted for y, simplifying the left side results in
does not equal the right side.
A. Yes, because when 4 is substituted for x and 0 is substituted for y, simplifying the left side results in
equals the right side.
which
Is (4,0) a solution to the equation 3x + y = 12? Select the correct choice below and fill in the answer box to complete your
choice.
OB. No, because when 4 is substituted for x and 0 is substituted for y, simplifying the left side results in
does not equal the right side.
which
which
which
Is (0,6) a solution to the equation 3x+y=12? Select the correct choice below and fill in the answer box to complete your
choice.
OA. Yes, because when 0 is substituted for x and 6 is substituted for y, simplifying the left side results in
which
We can conclude that (4,0) is the solution of the equation 3x + y = 12 with the correct option (A).
What exactly are equations?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign.So, the ordered pair of the equation 3x + y = 12:
(A) When (2,5):
3x + y = 123(2) + 5 = 126 + 5 = 1211 ≠ 12(B) When (4,0):
3x + y = 123(4) + 0 = 1212 + 0 = 1212 = 12(C) When (0,6):
3x + y = 123(0) + 6 = 120 + 6 = 126 ≠ 12Therefore, we can conclude that (4,0) is the solution of the equation 3x + y = 12 with the correct option (A).
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Angelina has 10 yards of fabric. She needs ⅓ yard of fabric for each purse she will sew. How many purses will she be able to make?
Divide the total amount of fabric by the amount needed to create a purse to find how many purses will she be able to make.
Since she has 10 yards of fabric and each purse requires 1/3 of a yard, then, divide 10 over 1/3:
[tex]10\div\frac{1}{3}=\frac{10}{1}\div\frac{1}{3}=\frac{10\times3}{1\times1}=\frac{30}{1}=30[/tex]Therefore, Angelina will be able to make 30 purses using 10 yards of fabric.
Triangle UVW, with vertices U(-5,5), V(-4,7), and W(-9,8), is drawn on the coordinate grid below.
The area formula of a triangle given the coordinates of the vertices :
[tex]U(-5,5),V(-4,7),W(-9,8)[/tex][tex]A=\lvert\frac{U_x(V_y-W_y)+V_x(W_y-U_y)+W_x(U_y-V_y)}{2}\rvert[/tex]Using the formula above, the area will be :
[tex]\begin{gathered} A=\lvert\frac{-5(7-8)-4(8-5)-9(5-7)}{2}\rvert \\ A=\lvert\frac{5-12+18}{2}\rvert \\ A=\lvert\frac{11}{2}\rvert \\ A=\lvert5.5\rvert \\ A=5.5 \end{gathered}[/tex]The answer is 5.5 square units
Solve for w. 3w + 2w - 3w = 8
Answer
w = 4
Explanation
We are asked to solve for w
3w + 2w - 3w = 8
5w - 3w = 8
2w = 8
Divide both sides by 2
(2w/2) = (8/2)
w = 4
Hope this Helps!!!
Question number 3: which of the following is equal to 18x*7 y*6?
Solution:
Given:
[tex]\sqrt{18x^7y^6}[/tex]Splitting the expressions further to get the perfect squares out:
[tex]\begin{gathered} \sqrt{18x^7y^6}=\sqrt{9\times2\times(x^6\cdot x)\times(y^3)^2} \\ =\sqrt{9\times2\times(x^3)^2\cdot x\times(y^3)^2} \end{gathered}[/tex][tex]\begin{gathered} \sqrt{18x^7y^6}=\sqrt{9\times2\times(x^3)^2\cdot x\times(y^3)^2} \\ =3x^3y^3\sqrt{2x} \end{gathered}[/tex]Therefore, the correct answer is:
[tex]3x^3y^3\sqrt{2x}[/tex]Part of a manufacturing plant packages tissues in boxes. Each box contains 250 tissues. Part A: Write an algebraic expression that can be used to find the total number of tissues packaged one day. Describe what the variable stands for in your expression. Part B: In one hour, 87,500 tissues are packaged into boxes. How many boxes of tissues are packaged? Show your work. Answer: boxes
Given
A manufacturing plant packages tissues in boxes and each box contains 250 tissues.
Required
We need to find an algebraic expression that illustrates the number of tissues packed per day.
Explanation
Let x be the number of boxes manufactured in one day
Then total number of tissues manufactured on that day is 250x
This answers our first part.
Now in one hour 87500 tissues are manufactured
Let the number of boxes packed in one hour be y
Then
[tex]y=\frac{number\text{ }of\text{ }tissues\text{ }in\text{ }one\text{ }hour}{number\text{ }of\text{ }tissues\text{ }in\text{ }each\text{ }box}=\frac{87500}{250}=350\text{ boxes}[/tex]So the answer to second part is 350 boxes.
Peri earned $55 for 5 dog walks. If Peri earned $22, how many times did she walk her neighbor's dog?
Answer:
2
Step-by-step explanation:
55÷5=11
22÷11=2
complete the square to writey= x2 + 4x +9 in graphing form.
In order to express y = x² + 4x +9 in graphing form and graphing it we can follow these steps:
1. complete squares to express the equation in the form y = (x - p)² + q
We have to add and subtract (b/2)² on the right, where b is the coefficient of the second term of the equation
y = x² + 4x +9 + (4/2)² - (4/2)²
y = x² + 4x +9 + (2)² - (2)²
We can gorup and factor some terms of the equation by applying the following formula:
(x + a)² = x² + 2ax + a²
then by writing 4x as 2×2x we get:
y = x² + 2×2x + (2)² - (2)² +9
y = (x + 2)² - (2)² + 9
y = (x + 2)² - 4 + 9
y = (x + 2)² + 5
For an equation of the form y = (x - p)² + q, the vertex is (q, p), then, the vertex of the parabola is (-2, 5)
2. Determine the x-intercepts by replacing 0 for y and solving for x, like this:
0 = (x + 2)² + 5
0 - 5 = (x + 2)² + 5 - 5
-5 = (x + 2)²
±√-5 = √(x + 2)²
±√-5 = x + 2
x = -2 ± √-5
As you can see, on the right side the argument of the square root is a negative number, which makes the solution of this equation a complex number, then which means that the parabola won't intercept the x-axis.
3. Find the y-intercept by replacing 0 for x:
y = (0 + 2)² + 5
y = (2)² + 5
y = 4 + 5
y = 9
Then, the y-intercept of this parabola is (0, 9)
By graphing the vertex (-2, 5) and the y-intercept (0, 9) and joining them with the parabola we get the following graph:
5x+y=4x-y=2GRAPHINGI need The Two slopes and The Two y- intercepts pleaseeeee
Given the equations:
5x + y = 4
x - y = 2
Convert the standard from to the slope intercept from
The slope intercept form is : y = mx + c
Where m is the slope and c is y-intercept
So, for the equation 5x + y = 4
the slope intercept form will be:
[tex]y=-5x+4[/tex]so, the slope = m = -5
and y-intercept = c = 4
The graph of the line will be as following:
For the second equation: x - y = 2
The slope intercept form is :
[tex]y=x-2[/tex]The slope of the line = 1
and the y-intercept = -2
The graph of the line will be as following :
Do you see my messages ?
a
Help math help math
What is this answer?
Answer:
24/25
Step-by-step explanation:
We are dividing 3/10 by 5/16
The domain of f(g(x)) is:
Answer:
x ≥ 0
Explanation:
Given the function f(x) and g(x) defined below:
[tex]f(x)=3x-1,g(x)=\sqrt{x}[/tex]The composite function f(g(x)) is:
[tex]f(g(x))=3\sqrt[]{x}-1[/tex]The domain of the function is the value at which the value under the square root sign is non-negative.
Therefore:
[tex]\text{Domain of f(g(x)): }x\ge0[/tex]The first option is correct.
How would the fraction71-√√√5using difference of squares?OA. 7-7√56OB. 7+7√56O c. 7+7√5OD. -7+7√5← PREVIOUSbe rewritten if its denominator is rationalizedSUBMIT
1) Examining that ratio, we can perform the following:
[tex]\begin{gathered} \frac{7}{1-\sqrt{5}} \\ \\ \frac{7\left(1+\sqrt{5}\right)}{\left(1-\sqrt{5}\right)\left(1+\sqrt{5}\right)} \\ \\ \frac{7+7\sqrt{5}}{1^2-(\sqrt{5})^2} \\ \\ \frac{7(1+\sqrt{5})}{-4} \\ \\ -\frac{7(1+\sqrt{5})}{4} \end{gathered}[/tex]2) Note that when we multiply that ratio by their conjugates, that yields a difference between two squares. Note that on the top, there is the expanded version of this expression.
Thus, the answer is D
Solve. 2x – 5=-3x + 15
Explanation:
First we have to add 3x on both sides of the equation:
[tex]\begin{gathered} 2x-5+3x=-3x+3x+15 \\ 5x-5=15 \end{gathered}[/tex]Now add 5 on both sides:
[tex]\begin{gathered} 5x-5+5=15+5 \\ 5x=20 \end{gathered}[/tex]And finally divide both sides by 5:
[tex]\begin{gathered} \frac{5x}{5}=\frac{20}{5} \\ x=4 \end{gathered}[/tex]Answer:
x = 5
Answer:
[tex] \sf \: x = 4[/tex]
Step-by-step explanation:
Given equation,
→ 2x - 5 = -3x + 15
Now the value of x will be,
→ 2x - 5 = -3x + 15
→ 2x + 3x = 15 + 5
→ 5x = 20
→ x = 20 ÷ 5
→ [ x = 4 ]
Hence, the value of x is 4.
Tran is in charge of the school's Awards Dinner. She set up the multi-purpose room with a stage in front and round tables for parents, students, and family members to sit around for dinner. Below is the floorplan that she drew for the eventStageHow many people can be seated as the tables are arranged right now? (In the box below, type your answer as a number only
Tran has made a plan with 12 tables for 8 people each of them. Then, we have 12 tables * 8 ( amount of chairs each of them) = 96. So 96 people can be seated.
the sum of the reciprocal of two consecutive positive integers is 17/72. Write an equation that can be used to find the two integers. What are the integers?
Answer:
[tex]\frac{1}{x}+\frac{1}{x+1}=\frac{17}{72}[/tex]The two consecutive positive integers are 8 and 9.
Explanation:
Let the 1st positive integer be x and the 2nd be x + 1, so their reciprocal will be 1/x and 1/x+1.
The equation can then be written as;
[tex]\frac{1}{x}+\frac{1}{x+1}=\frac{17}{72}[/tex]To solve for x, the 1st step is to find the LCM of the left-hand side of the equation;
[tex]\begin{gathered} \frac{(x+1)+x}{x(x+1)}=\frac{17}{72} \\ \frac{2x+1}{x(x+1)}=\frac{17}{72} \end{gathered}[/tex]We can equate the numerators and solve for x as shown below;
[tex]\begin{gathered} 2x+1=17 \\ 2x=17-1 \\ x=\frac{16}{2} \\ x=8 \end{gathered}[/tex]If the 1st positive integer, x, is 8, therefore the 2nd integer, x + 1, will be;
[tex]x+1=8+1=9[/tex]Write the equation for a line that is perpendicular to the given line and contain the following points. 12. X=-11Contains the point (-5, -7)equation:____
Purple line is perpendicular to given line (x = -11), and the equation for this lines is y = -7
Solve the equation by working backward through the number trick.
x = 3
Explanations:The given equation is:
[tex]\frac{4(x+3)-6}{2}=\text{ 9}[/tex]Step 1: Cross multiply
4 ( x + 3) - 6 = 9(2)
Step 2: Remove the brackets by expanding the equation
4x + 12 - 6 = 18
4x + 6 = 18
Step 3: Collect like terms
4x = 18 - 6
4x = 12
Step 4: Divide both sides by 4
4x / 4 = 12 / 4
x = 3
Camera has Alyssa price of $768.95 before tax the sales tax rate is 8.25% final total find the total cost of the camera with sales tax included round your answer to the nearest cent as necessary
We know that the listed price of the camera is $768.95 and the tax rate is 8.25%.
To find the total cost we must use the next formula
[tex]\text{Total cost }=\text{listed price before tax+(listed price before tax }\cdot\text{rate tax)}[/tex]Now, we must replace the values in the formula using that 8.25% = 0.0825
[tex]\text{Total cost}=768.95+(768.95\cdot0.0825)[/tex]Simplifying,
[tex]\text{Total cost}=832.39[/tex]ANSWER:
$O32
6. Tyrion's hourly rate is $16 an hour. He worked for 30 hours this week. 5 of those hours wereon a holiday, and his company pays twice the hourly rate for holidays. What was the total on hispaycheck? Show your calculations.
If f(x)=2x+1, what is f(2)?
f(2) means that we must substitute the value 2 in the place of x, that is
[tex]f(2)=2\cdot2+1[/tex]which gives f(2)=5.