Solve for 4/x+2 = 2/x x and determine if the solution is extraneous or not.
x = −2, extraneous
x = −2, non-extraneous
x = 2, extraneous
x = 2, non-extraneous
The given equation is:
4/(x + 2) = 2/x
First we get the value of x by doing cross multiplication so that all variables are in the numerator side:
4 x = 2 (x + 2)
4 x = 2 x + 4
2 x = 4
x = 2
An extraneous solution is one in which if we plug in the value of x back into the equation, the resulting values would be wrong.
Plug x = 2 back into the original equation:
4 / (2 + 2) = 2 / 2
4 / 4 = 2 / 2
1 = 1 (TRUE!)
Since the value of x = 2 satisfies the equation, then the solution is non-extraneous.
Answer:
x = 2, non-extraneous
Joyce is trying to solve the equation y = x2 − 8x + 7 using the quadratic formula. She has made an error in one of the steps below. Find the step where Joyce went wrong.
Step 1: x equals negative 8 plus or minus the square root of the quantity eight squared minus four times one times seven, end quantity, all over two times one.
Step 2: x equals negative 8 plus or minus the square root of sixty-four minus twenty-eight all over two times one.
Step 3: x equals negative 8 plus or minus the square root of thirty-six all over two times one.
Step 4: x equals negative 8 plus or minus six all over two.
Step 1
Step 2
Step 3
Step 4
What is the value of b in the equation below?
when dividing subtract the powers
so you would do 6-2 = 4
so b = 4
Answer:
The value of b is 4.
Step-by-step explanation:
The given equation is
[tex]\frac{5^6}{5^2}=a^b[/tex]
According to the property of exponent,
[tex]\frac{x^a}{x^b}=x^{a-b}[/tex]
Using this property of exponent, the given equation can be written as
[tex]5^{6-2}=a^b[/tex]
[tex]5^{4}=a^b[/tex]
On comparing both the sides, we get
[tex]a=5,b=4[/tex]
Therefore the value of b is 4.
a triangle has two sides of the lengths 8 and 10 what value could the length of the third side be
What is the equation of the graph below?
A graph shows a parabola that opens up and does not cross the x axis. The axis of symmetry is x equal negative 2. The parabola crosses through the points negative 1, 4 and negative 3, 4.
y = − (x − 2)2 + 3
y = (x + 2)2 + 3
y = − (x + 3)2 + 2
y = (x − 3)2 + 2
Identify a semicircle that contains C.
A.ABC
B.AC
C.CB
D. ACB
Answer: The correct option is (D). ACB.
Step-by-step explanation: We are given to identify a semi-circle that contains the point 'C'.
As shown in the figure, AB is the diameter of the circle with center 'O'.
So, there are two congruent semi-circles made by the diameter AB.
The point 'C' lies on the upper semi-circle made by the diameter AB.
Since the upper semi-circle contains the point 'C', so it is named as the semi-circle ACB.
Thus, the semi-circle ACB contains the point 'C'.
Option (D) is correct.
If GH is the angle bisector of FGI, which statement about the angle is true
The angle bisector of a given angle divides it into two equal parts. If GH is the angle bisector of FGI, angle FGH and angle HGI will be equal.
Explanation:If GH is the angle bisector of FGI, it means that it splits the angle FGI into two equal parts. Hence the angles FGH and HGI are equal.
For example, if angle FGI is 60 degrees, then the angle FGH and HGI (formed as a result of the bisector) would each be 30 degrees because the bisector divides the 60 degrees into two equal parts. This is the fundamental concept of an angle bisector in geometry.
Learn more about Angle Bisector here:https://brainly.com/question/37543581
#SPJ12
An isosceles triangle with equal sides of 5 inches and a base of 6 inches is inscribed in a circle. What is the radius, in inches, of the circle? Express your answer as a mixed number.
To find the radius of the circle inscribed in the isosceles triangle, we can use the formula for the inradius of a triangle. The inradius is given by the formula: inradius = (area of the triangle) / (semiperimeter of the triangle). First, we need to find the area and semiperimeter of the triangle. Then, we can calculate the inradius and find the radius of the circle.
Explanation:To find the radius of the circle inscribed in the isosceles triangle, we can use the formula for the inradius of a triangle. The inradius is given by the formula:
inradius = (area of the triangle) / (semiperimeter of the triangle)
First, we need to find the area of the triangle. Since it is an isosceles triangle with equal sides of 5 inches, we can split it into two congruent right triangles. The height of each right triangle can be found using the Pythagorean theorem:
height = sqrt(5^2 - (6/2)^2) = sqrt(25 - 9) = sqrt(16) = 4 inches
Now, we can find the area of the triangle:
area = (1/2) * base * height = (1/2) * 6 * 4 = 12 square inches
Next, we need to find the semiperimeter of the triangle:
semiperimeter = (5 + 5 + 6) / 2 = 16 inches
Finally, we can calculate the inradius:
inradius = 12 / 16 = 3/4 inches
Therefore, the radius of the circle is 3/4 inches.
The sum of the digits of a certain number is 12. When you reverse its digits you decrease the number by 36. Find the number
x+y=12
x*y =36
8+4=12, so make the digits 84, reverse to make it 48
84-48=36
the numbers are 8 & 4
a line perpendicular to a plane, would intersect the plane at one what
A line perpendicular to a plane, would intersect the plane at one point.
Perpendicular linesWhen a line is perpendicular directly away from the plane, the line will tend to intersect the plane at one points or single points.
The reason why the line intersect the plane is because the line cannot point to other places except directly away from the plane.
Therefore a line perpendicular to a plane, would intersect the plane at one point.
Learn more about Perpendicular lines here:https://brainly.com/question/1202004
#SPJ9
A farmer had 17 sheep. all but 9 died. how many live sheep were left
Use the following graph of the function f(x) = 2x^3 + x^2 - 3x + 1
What is the average rate of change from x = -1 to x = 1
A) -1
B) 1
C) 2
D) 4
Use the remainder theorem and the factor theorem to determine whether (b+4) is a factor of (b^3+3b^2-b + 12)
Solve the equation: h/9 = 7. A. h = 1 2/7 B. h = 63 C. h = –63 D. h = 7/9
Use the diagram of the right triangle above and round your answer to the nearest hundredth. If measure B= 60 degrees and a = 10 meters, find b.
Answer: A. 17.32m
Step-by-step explanation:
Just took edge test
Answer:A
Step-by-step explanation:
If the solution to 4 - 2x > x + 16 is x < a, what is the value of a?
A) 6
B) 4
C) 2
D) -4
E) -6
30 POINTS!!!!!!!
A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 99m long and 72m wide.
Find the area of the training field. Use the value 3.14 for π, and do not round your answer. Be sure to include the correct unit in your answer.
Answer:
1273 hola aaaaa oigan busco novia
Find the value of angle M
opposite angels = 180
so 6m+13 +4m+7 =180
combine like terms
10m+20=180
10m =160
m=160/10 = 16
Angle M = 6m = 6(16) = 96 degrees
What is the value of 64? 60 = 1 61 = 6 62 = 36 63 = 216
can someone help with factoring the trinomial below
What is the missing step in this proof?
The missing step in the proof is;
Statement: ∠1 ≅ ∠4 and ∠3 ≅ ∠5Reason: Alternate interior angle theorem.The correct answer choice is option C.
What is alternate interior angles theorem?Alternate angle theorem states that when two parallel lines are cut by a transversal, the resulting alternate interior or exterior angles are congruent.
It is used to prove that alternate interior angles are equal if two parallel lines are cut by a transversal,
Hence, angle 1 is congruent to angle 4 and angle 3 is congruent to angle 5.
Read more on alternate interior angle:
https://brainly.com/question/20344743
#SPJ3
A store sells two sizes of fresh wreaths. an? 18-inch wreath costs ?$1515?, and a? 22-inch wreath costs ?$3535. in one? day, the number of? 22-inch wreaths sold was fourfour more than twicetwice the number of? 18-inch wreaths, for a total of ?$820820. how many of each were? sold
The number of 18 inches of wreaths sold was 9 while 22 inches were 51.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
Let's say a number of 18 inches of wreaths is x while 12 inches is y.
Given that,
In one day, the number of 22-inch wreaths sold was six more than five times the number of 18-inch wreaths.
So,
y = 5x + 6
And
Total amount
15x + 35y = 1920
⇒ 3x + 7y = 384
By substitution,
3x + 7(5x + 6) = 384
38x = 342
x = 9
So y = 5(9) + 6 = 51
Hence "The number of 18 inches of wreaths sold was 9 while 22 inches were 51".
For more about the equation,
https://brainly.com/question/10413253
#SPJ2
The given question is incorrect, the correct question is ;
A store sells two sizes of fresh wreaths. An 18-inch wreath costs $15, and a 22-inch wreath costs $35. In one day, the number of 22-inch wreaths sold was six more than five times the number of 18-inch wreaths, for a total of $1920. How many of each were sold? .... The number of 18-inch wreaths sold was and the number of 22-inch wreaths sold was
In which case would it be best to use the “Factoring Method” to solve the trinomial equation?
x^2 + 4x = -5
4.3x^2 + 2.4x - 3 = 0
x^2 - 4x + 3 = 0
Using the Law of Cosines, in triangle DEF, if e=18yd, d=10yd, f=22yd, find measurement of angle D
Write “$4,915 for 72 shares of stock” as a unit rate. Round to the nearest hundredth if necessary.
divide
4915/72 = 68.2638
so $68.26 per stock is the unit rate
70 decreased by twice a number
Use The variable n to represent the unknown number
The required expression of the given statement is 70-2n.
Given that,
To determine the expression for the given statement 70 decreased by twice a number.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Let the number be n,
According to the question,
Number = n
70 decreased by twice the number,
So
= 70 - 2n
Thus, the required expression of the given statement is 70-2n.
Learn more about arithmetic here:
https://brainly.com/question/11424589
#SPJ2
Ryan spent $3.25 on lunch every day, Monday through Friday. If he had $20 at the start of the week, how much money will he have left after Friday?
The amount of money left after Friday is $3.75.
What is unitary method?The method in which first we find the value of one unit and then the value of the required number of units is known as the Unitary Method.
According to the given question.
Amount of money spent for the lunch every day is $3.25.
Total amount of money Ryan have is $20.
Now, number of total days from Monday to Friday is 5.
So,
The amount spent for lunch for 5 days by Ryan
= 5 × $ 3.25 = $16.25 (by unitary method)
Therefore,
The amount of money left after Friday
[tex]\$20 - \$16.25\\= \$3.75[/tex]
Hence, the amount of money left after Friday is $3.75.
Find out more information about unitary method here:
https://brainly.com/question/22056199
#SPJ2
The sum of three consecutive odd integers is 18 less than 5 times the middle number. Find the 3 integers. Use an algebraic solution
X +(x+2) + (x+4) = 5(x+2)-18
3x+6 = 5x+10-18
3x+6 = 5x-8
3x=5x-14
-2x=-14
x=7
(x+2) =9
(x+4) =11
7 + 9+ 11 =27
5(9)-18 =45-18 =27
3 numbers are 7, 9 & 11
The area of a book cover is 63.8 in². The width of the book is the difference of the length and 3 inches. Let x represent the book's length. Which quadratic equation represents the area of the book cover?
x(x - 3) = 63.8
x(3 - x) = 63.8
2x - 3 = 63.8
x + x - 3 = 63.8
The correct quadratic equation representing the area of the book cover is [tex]\( x(x - 3) = 63.8 \)[/tex].
To understand why this is the correct equation, let's break down the information given in the question:
1. The area of the book cover is given as 63.8 square inches.
2. The width of the book is the difference between the length and 3 inches. If we let [tex]\( x \)[/tex] represent the length of the book, then the width can be represented as [tex]\( x - 3 \)[/tex].
3. The area of a rectangle (which is the shape of the book cover) is calculated by multiplying its length by its width.
Using the information above, we can set up the equation for the area of the book cover as follows:
[tex]\[ \text{Area} = \text{length} \times \text{width} \][/tex]
[tex]\[ 63.8 = x \times (x - 3) \][/tex]
Expanding the right side of the equation, we get:
[tex]\[ 63.8 = x^2 - 3x \][/tex]
This is a quadratic equation in standard form. The other options given do not correctly represent the relationship between the length, width, and area of the book cover:
[tex]- \( x(3 - x) = 63.8 \)[/tex] incorrectly represents the width as [tex]\( 3 - x \)[/tex] instead of [tex]\( x - 3 \)[/tex].
[tex]- \( 2x - 3 = 63.8 \)[/tex] is a linear equation, not a quadratic one, and does not represent the area calculation.
[tex]- \( x + x - 3 = 63.8 \)[/tex] simplifies to [tex]\( 2x - 3 = 63.8 \)[/tex], which is also a linear equation and does not represent the area calculation.
Given that WXYZ is a rhombus, find the value of x. A. 15 B. 20 C. 30 D. 45
In this problem, we are given the equations of the two sides of a rhombus.
Equation 1 is 4 x – 10
Equation 2 is 2 x + 20
Since the given shape is a rhombus, therefore the two sides have equal sides. Hence, we can simply equate equation 1 and equation 2:
4 x – 10 = 2 x + 20
2 x = 30
x = 15
Therefore the answer is:
A. 15
4 x – 10 = 2 x + 20
2 x = 30
x = 15