The statement which best reflects the solutions of the equation; as given in the task content is; x = 3 is a valid solution and x = 2 is an extraneous solution.
What is the solution of the equation?It follows from the task content that the statement which represents the solution of the given equation be determined.
Since the given equation can be written algebraically as follows;
x/(x - 1) - 1/(x - 2) = (2x - 5) / (x² - 3x + 2)
By observation; (x - 1) (x - 2) = x² - 3x + 2.
Therefore, by multiplying through the equation by; x² - 3x + 2; we have;
x (x - 2) - 1 (x - 1) = 2x - 5
x² - 2x - x + 1 = 2x - 5
x² - 5x + 6 = 0.
Hence, the equation above can be solved quadratically so that we have;
(x - 3) (x - 2) = 0.
Therefore, the solution to the given equation is; x = -3 Or x = 2.
However, the solution x = 2 renders the equation undefined, hence, it is not a valid solution but an extraneous solution.
Therefore, the statement which reflects the solutions to the given equation is; x = 3.
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Without using a calculator, choose the statement that best describes the value of
Answer:
B
Step-by-step explanation:
Alright, to start off... we need to find a range of value that sqr 74 is between.
To do that, we can check by just trying some random numbers.
Let's try 8 -- 8^2 is 64. Let's try 9 -- 9^2 is 81. So the sqr 64 is 8 and sqr 81 is 9.
sqr 74 is between sqr 64 and sqr 81, so the statement is true. However, the multiple-choice has decimal numbers, meaning that they want us to be more specific.
First, we can cross out 9.5, because we don't want to expand our range, we want to keep it as accurate as possible.
That leaves us 8.5
To find if 8.5 fits the criteria, meaning that it can't be larger than sqr 74, we can use two methods.
The first method is preferred, you simply need to multiply them. I hope you know how to do that by hand. We get 72.25
The second method is less preferred but works. We need to approximate the value by finding the mean of 64 and 81, because 8.5 is the mean of 8 and 9. The approximate value should be very close to the true value. By doing (81+64)/2, we get 72.5
Now, double-check: is the 74 between 72.25 and 81? Yes, it is!
Hence, that gives us the answer that sqr74 is between 8.5 (sqr 72.25) and 9 (sqr 81)
Create an equivalent expression for (1.3 3/1.2 4)-6
1.2²4/1.3 18
1.2²/ 1.3 3
1.3 18/ 1.2 24
1.3 3 / 1.2²
The equivalent expression of [(1.3^3)/(1.2^4)]^-6 is (1.2^[24])/(1.3^[18]). So option(1) is correct.
Equivalent expressions are expressions that work the same way despite their appearance. When we plug in the same value(s) for the variable, two algebraic expressions have the same value (s).
Equivalent means that different terms and expressions with similar values are considered equal in mathematical form.
The given expression is
[(1.3^3)/(1.2^4)]^-6
Apply the indices power law to the above expression.
[(1.2^4)/(1.3^3)]^6
The exponents are then expanded using the power law of indices.
(1.2^[4x6])/(1.3^[3x6])
(1.2^[24])/(1.3^[18])
Hence, the equivalent expression of [(1.3^3)/(1.2^4)]^-6 is (1.2^[24])/(1.3^[18])
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Solve
n=5(m^2+D)
(It's a literal equation)
Step-by-step explanation:
are you sure there is no other given info? do you have to solve in terms of m and D?
Find the value of X
(Triangle Congruence)
Answer:
x = 139°
Step-by-step explanation:
The sum of the internal angles of a triangles is 180°
a + 59 + 80 = 180
a = 180 - 139
a = 41°
a and x are supplementary angles. Supplementary angles sum 180°.
Then:
a + x = 180
41 + x = 180
x = 180 - 41
x = 139°
Two number have a product of 7. One of the number i 4 2/3, what i the other number?
Answer:
1 1/2
Step-by-step explanation:
You want the other number when one of the two numbers that have a product of 7 is 4 2/3.
SolutionLet x represent the unknown factor. Then we have ...
(4 2/3)x = 7
(14/3)x = 7 . . . . . . write as improper fraction
x = (3/14)(7) . . . . . multiply by the inverse of the coefficient of x
x = 3/2 = 1 1/2
The other number is 1 1/2.
Find an
for a line parallel to
4x + 5y + 2 = 0, with an
an x-intercept of 3
The equation of the parallel line is 4x + 5y - 12 = 0
How to determine the line equation?The equation is given as
4x + 5y + 2 = 0
The x-intercept is also given as
x-intercept = 3
We have
4x + 5y + 2 = 0
Make y the subject
5y = -4x - 2
Divide through by 5
y = -4x/5 - 2/5
The equation of a line can be represented as
y = mx + c
Where
slope = m
By comparing the equations, we have:
m = -4/5
This means that the slope of 4x + 5y + 2 = 0 is =4/5
The slopes of parallel lines are equal
This means that the slope of the other line is -4/5
The equation of the parallel line is then calculated as
y = m(x - x₁) +y₁
Where
m = -4/5
(x₁, y₁) = (3, 0) i.e. the x-intercept
So, we have
y = -4/5(x - 3) + 0
Multiply through by 5
5y = -4(x - 3)
Open the brackets and evaluate
5y = -4x + 12
This gives
4x + 5y - 12 = 0
Hence, the parallel line has an equation of 4x + 5y - 12 = 0
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Find the rectangular coordinates of the point whose spherical coordinates are given. (a) (1,0,0) (x, y, z) =( (b) (18, 1/3, 1/4) (X, Y, z)
The rectangular coordinates are
a. (1,0,0) ⇒ (x,y,z) = (0,0,1)
b. (18,1/3,1/4) ⇒ (x,y,z) = (11.022,11.022,9)
Let us take ( x, y, z ) as cartesian or rectangular coordinates and ( r, Θ, ∅ ) are the spherical coordinates, then
x = r.sinΘ.cos∅ → 1
y = r.sinΘ.sin∅ → 2
z = r.cosΘ → 3
According to the given problem,
a.) ( 1, 0, 0 ) = ( r, Θ, ∅ )
Substitute the values r = 1, Θ = 0 and ∅ = 0 in 1, 2, 3.
1 ⇒ x = r.sinΘ.cos∅
= 1.sin0.cos0
= 1.0.1
x = 0
2 ⇒ y = r.sinΘ.sin∅
= 1.sin0.sin0
= 1.0.0
y = 0
3 ⇒ z = r.cosΘ
= 1.cos0
= 1.1
z = 1
∴ ( x, y, z ) = ( 0, 0, 1 )
b.) ( 18, π/3, π/4 ) = ( r, Θ, ∅ )
Substitute the values r = 18, Θ = π/3 and ∅ = π/4 in 1, 2, 3.
1 ⇒ x = r.sinΘ.cos∅
= 18.sinπ/3.cosπ/4
= 18.√3/2.1/√2
x = 11.022
2 ⇒ y = r.sinΘ.sin∅
= 18.sinπ/3.sinπ/4
= 18.√3/2.1/√2
y = 11.022
3 ⇒ z = r.cosΘ
= 18.cosπ/3
= 18.1/2
z = 9
∴ ( x, y, z ) = ( 11.022, 11.022, 9 )
Therefore the rectangular coordinates for the spherical coordinates of
a. ( 1, 0, 0 ) is ( 0, 0, 1 )
b. ( 18, 1/3, 1/4 ) is ( 11.022, 11.022, 9 )
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(Please help quick!)
Which rectangle has the same area as the triangle
shown?
The rectangle with the sides 4 and 3 is the required rectangle.
The correct option is third shape.
What is area?Area is the amount of area occupied by an object's flat (2-D) surface or shape.
The area of the triangle,
= 1/2 x base x height
= 1/2 x 6 x 4
= 12 square millimeters.
And rectangle has the same area as the triangle.
The rectangle with the sides 4 and 3 is the required.
Therefore, the rectangle with the sides 4 and 3 is the required rectangle.
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What’s the unit rate for three dollars for 2 1/2 hours of work
The unit rate of three dollars for 2 1/2 hours of work is 1.2.
The rate is a ratio of change in one quantity with respect to other. The unit rate is a rate such that the denominator of the rate must be one. An item's unit rate is its rate for one of them. How many units of the first type of quantity are needed to make up one unit of the second type is expressed using a unit rate (or unit ratio).
Now, finding the unit rate for three dollars for 2 1/2 hours of work,
Unit rate [tex]=\frac{3}{2.5}[/tex]
= 1.2
Therefore, the unit rate of three dollars for 2 1/2 hours of work is 1.2.
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HELP WHATS IS A multi step equation that has a variable on both side that equals 10
Answer:
Step-by-step explanation:
an equation that takes two or more steps to solve is called a multi-step equation. let's take a multi-step equation that will satisfy the given condition:
4x - 8 = 22 + x
4x -x = 22 + 8
3x = 30
x = 10
Find the Area of the figure below, composed of a rectangle with a semicircle removed from it. Round to the nearest tenths place.
4
6
is a stockbroker. earns 12% commission each week. Last week, sold 7200$ worth of stocks. How much did make last week in commission? If averages that same amount each week, how much did make in commission in 2011?
The amount earned as commission in 2011 is $44928
How to determine the amount earned as commission?From the question, we have the following parameters that can be used in our computation:
Commission percentage = 12%
Average sales per week = $7200
The amount earned as commission in the 2011 is then calculated as
Amount = Commission percentage x Average sales per week x Number of weeks
Substitute the known values in the above equation
So, we have
Amount = 12% x 7200 x 52
Evaluate
Amount = 44928
Hence, the commission amount is $44928
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A container releases fuel at a rate of 5 gallons per second. If y represents the amount of fuel remaining in the container and x represents the number of seconds that have passed since the fuel started dispensing, then x and y satisfy a linear relationship. If the tank begins with 103 gallons, how many gallons will remain after 2 seconds?
By evaluating a linear equation, we will see that after two seconds there are 93 gallons of fuel.
How many gallons will remain after two seconds?We know that the tank initially has 103 galons of fuel, and we know that it releases 5 gallons per second at a constant rate.
So, after x seconds, the amount of fuel inside the container is:
F(x) = 103 - x*5
so we have a linear equation.
The amount of fuel in the tank after 2 seconds is given by:
F(2)= 103 - 2*5 = 103 - 10 = 93
After 2 seconds there are 93 gallons of fuel.
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In the first week of July, a record 1,040 people went to the local swimming pool. In the second week, 110 fewer people went to the pool than in the first week. In the third week, 130 more people went to the pool than in the second week. In the fourth week, 332 fewer people went to the pool than in the third week. What is the percent decrease in the number of people who went to the pool over these four weeks?
Answer:
ok
Step-by-step explanation:
A woman who is 64 inches tall has a shoulder width of 16 inches.
Write an equation relating the height h to the width w. Find the height
of a woman who has a shoulder width of 18.5 inches. I know we have to multiply 18.5x4 but why?
The height of woman who has a shoulder width of 18.5 inches is 74 inches.
What is Proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
According to the concept of proportion, two ratios are in proportion when they are equal.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
Height of woman = 64 inches
Shoulder width = 16 inches
So, ratio = Height : shoulder width = 64:16
let the height of a woman who has a shoulder width of 18.5 inches be x.
So, x:18.5.
Now,
64 / 16 = x/ 18.5
4= x/18.5
x= 74
Hence, the height of woman who has a shoulder width of 18.5 inches is 74 inches.
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Statement Let V be any vector space and let x, y, z be in V. Prove that if x + z = y + z, then x = y. Proof Suppose for full generality that V is any vector space and x, y, z are any vectors in V. Suppose x+z= y + z. Show that x = y. Since z is in V, there exists a vector —z in V such that z+(-2) = 0 because implies Thus, x +z = y + z (x + 2) + (-2) = (y + 2) + (-2) and thus x+(2+(-2)) = y + (z + (-2)) because X+0 = y + 0 because and thus X = y by properties of the zero vector. Therefore, x +z = y + z implies x = y, and V has the cancellation property
By the zero vector property x=y.
Suppose for full generality that V is any vector space and x,y,z is any vector in V. Suppose, x+z = y+z. Show that x=y. Since z is in v, there exists a vector z in v, such that
= z + (-z) = 0, because x+y=y+z
Thus x+z=y+z
= (x+z)+(-z) = (y+z)+(-z) and thus
= x+(z+(-z)) = y + (z+(-z)) because addition is associative in vector
= x+0 = y+0 because additive inverse exists in a vector
= and thus x=y by the properties of zero vector
Also according to the question, it is now proved that x+z=y+z implies x=y and v has the cancellation property.
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Which is an equation of the line that passes through the points (0, 0) and (1,
4)?
y = x + 1
y = 4x + 1
y = x
y = 4x
slope = m = (4 - 0) / (1 - 0) = 4
y = mx + b
y = 4x + b
substitute (0, 0) to find b
b = 0
y = 4x
a construction worker is pouring concrete stairs. the first step requires 1.8 cubic feet of concrete, and the first 5 steps require a total of 27 cubic feet. if the steps follow an arithmetic series, how much concrete is required for the first 12 steps?
If the steps follow an arithmetic series, the concrete required for the first 12 steps is 140.4.
Given, the first term of the arithmetic series, a=1.8 and the sum of first five terms that is s5=27, we have to find the sum of first 12 steps.
The formula to calculate the sum of the terms in AP is
Sn = n/2 {2a + (n - 1) d}
S5=5/2(2(1.8) +(5-1)d)
27=2.5(3.6+ 4d)
27=9+10d
27-9=10d
18=10d
d=18/10
d=1.8
The common difference d is 1.8.
Now we have to find S12,
S12=12/2(2(1.8) +(12-1)1.8)
= 6(3.6+19.8)
=6(23.4)
=140.4
S12=140.4
Therefore, the concrete required for the first 12 steps is 140.4.
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f(x)=-x^2-7x please answer
Answer:
[tex]f( x) = x2 - 7 x[/tex]
3) a² + 3a - 10 = 0
I don’t know how to do this and I need to solve it by quadratic formula
A quadratic equation in one unknown;
[tex]ax^2+bx+c=0[/tex]has two roots. In order to determine these roots, we need to apply certain operations. We can get information about the existence of these roots by discrimination. Below is the discrimination formula.
[tex]D=b^2-4ac[/tex]If we apply discriminant for the above equation, we obtain the following expression;
[tex]D=(3)^2-4(1)(-10)[/tex][tex]D=9+40[/tex][tex]D=49[/tex]If the discriminant number is greater than [tex]0[/tex], the equation has two real and distinct roots.
[tex]D > 0,[/tex] [tex]x_{1}\neq x_{2}[/tex][tex]D=0,[/tex] [tex]x_{1}=x_{2}[/tex][tex]D < 0,[/tex] [tex]No[/tex] [tex]Root[/tex] [tex]in[/tex] [tex]Real[/tex] [tex]Numbers.[/tex]Now let's remember our formula for finding the roots and solve the problem using the discriminant value.
[tex]x_{1}=\frac{-b-\sqrt{D} }{2a},[/tex] [tex]x_{2}=\frac{-b+\sqrt{D} }{2a}.[/tex]Therefore;
[tex]x_{1}=\frac{-3-\sqrt{49} }{2}[/tex][tex]x_{1}=-5[/tex]Other root is;
[tex]x_{2}=\frac{-3+\sqrt{49} }{2}[/tex][tex]x_{2}=2[/tex]There are 10 squares and 2 circles. What is the simplest ratio of circles to squares?
Answer: 5:1
Step-by-step explanation: 10:2 can be simplified by dividing both by 2, making it 5:1
Rewrite the following equation in slope-intercept form.
y + 6 = 9(x − 8)
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
y = 9x -78
Step-by-step explanation:
You want the equation y + 6 = 9(x − 8) written in slope-intercept form.
SolutionSolve for y and simplify.
y +6 = 9x -72 . . . . . . . . eliminate parentheses
y = 9x -78 . . . . . . . . . subtract 6
__
Additional comment
The given equation is written in point-slope form. It has a slope of 9 and goes through the point (8, -6).
Slope-intercept form is ...
y = mx +b
where m is the slope and b is the y-intercept.
Find the unit vector in the direction of < 5, −7 >
The vector <5√74 / 74, - 7√74 / 74> is the unit vector in the direction of <5, - 7>.
How to determine the unit vector in the direction of a given vector
Vectors are described by two features: (i) magnitude, (ii) direction. The magnitude is the quantity associated with a vector and determine by Pythagorean theorem, and the direction indicates the "distribution" of the magnitude along the ortogonal axes of the vector. Unit vectors are vectors of magnitude 1 and we can determine it by using the following definition:
[tex]\vec u[/tex] = <x, y> / ||<x, y>||
Where ||<x, y>|| = √(x² + y²)
Please notice that [tex]\vec u[/tex] represents the unit vector.
If we know that <x, y> = <5, - 7>, then the unit vector is:
Magnitude
||<x, y>|| = √[5² + (- 7)²]
||<x, y>|| = √74
Unit vector
[tex]\vec u[/tex] = <5, - 7> / √74
[tex]\vec u[/tex] = <5 / √74, - 7 / √74>
[tex]\vec u[/tex] = <5√74 / 74, - 7√74 / 74>
<5√74 / 74, - 7√74 / 74> is the unit vector in the direction of <5, - 7>.
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least common
Denominator of 7/2 &
3/10
Answer: 10
Step-by-step explanation: The least common denominator is 10 because both integers 2 and 10 have a LCM OF 10. Your welcome. :’j
Answer: 10
Step-by-step explanation: The least common denominator is 10, cuz it is the lowest common multiple of 10 and 2, 2 × 5 =10, 10× 1 = 10. they r both common multiples.
Add the fractions. **Remember to have a common denominator.**
1/4 + 1/3
Answer:
[tex] \sf \: \frac{7}{12} [/tex]
Step-by-step explanation:
Given problem,
[tex] \sf \rightarrow \: \frac{1}{4} + \frac{1}{3} [/tex]
Let's solve the problem,
[tex] \sf \rightarrow \: \frac{1}{4} + \frac{1}{3} [/tex]
[tex] \sf \rightarrow \: \frac{(1) \times 3}{(4) \times 3} + \frac{(1) \times 4}{(3) \times 4} [/tex]
[tex] \sf \rightarrow \: \frac{3}{12} + \frac{4}{12} [/tex]
[tex] \sf \rightarrow \: \frac{(3 + 4)}{12} [/tex]
[tex] \sf \rightarrow \: \frac{7}{12} [/tex]
Hence, the answer is 7/12.
The relative frequency table describes the relationship between students who completed an exam review and their performance on the exam
Passed exam Did not pass exam Row Totals
Completed exam review
55%
10%
65%
Did not complete exam review
20%
15%
35%
Column Totals
75%
25%
100%
Part A: What is the percentage of students who completed the exam review, given that they passed the exam? Round to the nearest percentage. (2 points)
Part B: What is the percentage of students who completed the exam review, given that they failed the exam? Round to the nearest percentage (2 points)
Part C: Is there an association between completing the exam review and passing the exam? Justify your answer. (2 points)
From the given relative frequency table , answer of the following questions are as follow:
a. Percentage of students those who have completed the exam review with the condition that they have passed the exam is given by 55%.
b. Percentage of students those who have completed the exam review with the condition that they have failed the exam is given by 10%.
c. Yes, there is association between the two completing the exam review and passing the exam is only 55%.
As given in the question,
From the given relative frequency table , answer of the following questions are as follow:
Total percentage of students completing the exam review = 65%
a. Completed the exam review with the condition that they have passed the exam = 55%
b. Completed the exam review with the condition that they have failed the exam = 10%
c. Yes, there is association between the two completing the exam review and passing the exam is only 55% and those who have completing the exam review but failed are 10%.
Therefore, from the given relative frequency table , answer of the following questions are as follow:
a. Percentage of students those who have completed the exam review with the condition that they have passed the exam is given by 55%.
b. Percentage of students those who have completed the exam review with the condition that they have failed the exam is given by 10%.
c. Yes, there is association between the two completing the exam review and passing the exam is only 55%.
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Sharon spent #13.60 on baseball Cards. She bought 16 packs How much did each pack cost?
Answer:
#0.85
Step by step:
13.60/16 = #0.85
pls give me brainliest
pls:(
Which transformation can be applied to the blue figure to create the red figure?
The sequence of transformations that we should apply is the one that appears on the top left option:
Reflection across the y-axis followed by a rotation of 90° counterclockwise.
Which sequence of transformations map the blue figure into the red one?We can see that the blue figure is on the third quadrant, and the "spiral" part is pointing upwards.
First, we would want to apply a rotation of 90° clockwise, this will move the blue figure to the second quadrant, and now the "spiral" part will point thowards the right.
Now you can see that the red figure is a reflection along the y-axis of the blue figure, so we need to apply that transformation.
Concluding, the sequence of transformations is:
rotation of 90° clockwise.reflection across the y-axis.Notice that this is equivalent to:
Reflection across the y-axis.rotation of 90° counterclockwise.Then the correct option is the one in the top left corner.
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i will mark brainliest pls help it was due last week
Answer:
[tex]y=\frac{1}{2}x-5[/tex]
B: smaller rate of change but night y intercept
Step-by-step explanation:
y intercept is -5 because when x is zero y is -5
Now to find slope
-1-(-3)/8-4
-1+3/4
2/4
1/2
Now we can put it in an equation
y=1/2x-5
2nd question
-6-4/0-2
-10/-2
5
-6 is greater then -10 so the y intercept is bigger
So B is correct
Answer: i'm writeing this so you can mark the other person brainliest
Step-by-step explanation:
Using the completing-the-square method, find the vertex of the function f(x)=-2x^2+12x+5 and indicate whether it is a minimum or a maximum and at what point.
Using the completing-the-square method, find the vertex of the function f(x)=-2x^2+12x+5 and indicate whether it is a minimum or a maximum and at what point.
Given function is: [tex]f(x) = -2x^{2}+12x+5[/tex]
[tex]f(x) = a(x-h)^{2} +k[/tex] , where (h,k) is the vertex
Apply completing the square method to find vertex
[tex]f(x) = -2x^{2}+12x+5\\\\f(x) = -2(x^{2}-6x)+5[/tex]
Lets take half of coefficient of x is -6
divide by 2 that is -3
square it [tex](-3)^{2}[/tex] that is 9
Add and subtract 9
[tex]f(x) = -2(x^{2}-6x+9-9)+5[/tex]
Take out -9 and multiply by -2
[tex]f(x) = -2(x^{2}-6x+9)+18+5\\\\f(x) = -2(x^{2}-6x+9)+23[/tex]
Now factor the parenthesis part
[tex]f(x) = -2(x-3)^{2} +23[/tex]
The value of h=3 and k=23
So vertex is (3,23)
The value of 'a' is -2, it means the parabola is upside down. so vertex is maximum
Hence the answer is the vertex is maximum at (3,23)
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