Answers
Given the equation:
[tex]\sqrt[]{x}+1=x-\sqrt[]{x}-1[/tex]Solving for x:
[tex]\begin{gathered} \sqrt[]{x}+\sqrt[]{x}=x-1-1 \\ 2\sqrt[]{x}=x-2 \end{gathered}[/tex]Now, we take the square on both sides of the equation:
[tex]\begin{gathered} 4x=x^2-4x+4 \\ 0=x^2-8x+4 \end{gathered}[/tex]Now, using the general solution of quadratic equations:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]From the problem, we identify:
[tex]\begin{gathered} a=1 \\ b=-8 \\ c=4 \end{gathered}[/tex]Then, the solutions are:
[tex]\begin{gathered} x=\frac{-(-8)\pm\sqrt[]{(-8)^2-4\cdot1\cdot4}}{2\cdot1}=\frac{8\pm\sqrt[]{64-16}}{2} \\ x=\frac{8\pm4\sqrt[]{3}}{2}=4\pm2\sqrt[]{3} \end{gathered}[/tex]But the original equation √(x), so x can not be negative if we want a real equation. Then, the only real solution of the equation is:
[tex]x=4+2\sqrt[]{3}[/tex]Related Questions
Answers asap please
Answers
x ≥ 1 or x ≥ 3 is inequality of equations .
What do you mean by inequality?
The allocation of opportunities and resources among the people who make up a society in an unequal and/or unfair manner is known as inequality. Different persons and contexts may interpret the word "inequality" differently.The equals sign in the equation-like statement 5x 4 > 2x + 3 has been replaced by an arrowhead. It is an illustration of inequity. This indicates that the left half, 5x 4, is larger than the right part, 2x + 3, in the equation.9 - 4x ≥ 5
4x ≥ 9 - 5
4x ≥ 4
x ≥ 1
4( - 1 + x) -6 ≥ 2
-4 + 4x - 6 ≥ 2
4x ≥ 2 + 8
4x ≥ 10
x ≥ 10/4
x ≥ 5/2
x ≥ 2.5
x ≥ 1 or x ≥ 3
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A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment n=10, p=0.2, x=2
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The binomial probability of x successes is 0.302.
How to calculate the probability of x successes?Since we are dealing with a binomial probability experiment. We are going to use the binomial distribution formula for determining the probability of x successes:
P(x = r) = nCr . p^r . q^n-r
Given: n=10, p=0.2, x=2
The failures can be calculated using q = 1 - p = 1 - 0.2 = 0.8
P(x = 2) = 10C2 x 0.2² x 0.8¹⁰⁻²
= 10!/(10-2)! 2! x 0.2² x 0.8⁸
= 10!/(8!2!) x 0.2² x 0.8^8
= 10x9x8!/(8!2!) x 0.2² x 0.8⁸
= 45 x 0.2² x 0.8⁸
= 0.302
Therefore, the probability of x successes in 10 trials is 0.302
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The House of Pizza say that their pizzas are 14 inches wide, but when you measured it, the pizza was 12 inches. What is your percent error? Make sure to include your percent sign! (Round to 2 decimals)
Answers
The percent error of the house of the pizza would be 2.
How to calculate the percent error?Suppose the actual value and the estimated values after the measurement are obtained. Then we have:
Error = Actual value - Estimated value
To determine the percent error, we will measure how much percent of the actual value, the error is, in the estimated value.
We have been given that House of Pizza says that their pizzas are 14 inches wide, but when measured, the pizza was 12 inches.
WE know that Error = Actual value - Estimated value
Then Error = 14 - 12 = 2
Therefore, the percent error would be 2.
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3(2x+4) - 2(4x-1)=20A. x=5B. x=-5C. x=3D. x=-3
Answers
we have the following:
[tex]3(2x+4)-2\left(4x-1\right)=20[/tex]solving for x:
[tex]\begin{gathered} 3(2x+4)-2\left(4x-1\right)=20 \\ 6x+12-8x+2=20 \\ -2x=20-12-2 \\ -2x=6 \\ x=\frac{6}{-2} \\ x=-3 \end{gathered}[/tex]The answer is x = -3
This figure shows two similar polygons; DEFG∼TUVS. Find the value of x.
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According to the question, both polygons are similar. It means you can use proportions to find the value of x.
[tex]\frac{DE}{TU}=\frac{EF}{UV}[/tex]Replace for the given values in the picture
[tex]\begin{gathered} \frac{x}{6}=\frac{4}{12} \\ x=\frac{4}{12}\cdot6 \\ x=2 \end{gathered}[/tex]x has a value of 2.
Question 8 of 10According to this diagram, what is tan 62°?
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In this problem, we want to determine tangent of 62 degrees.
Recall the identity of tangent:
[tex]\tan\theta=\frac{\text{ opposite side}}{\text{ adjacent side}}[/tex]We are given the triangle:
Since we are referencing 62 degrees, the arrow pointing away from the 62 degrees is headed toward the opposite side. Therefore, the opposite side is 15, and the adjacent side is 8.
[tex]\tan62=\frac{15}{8}[/tex]Tangent of 62 degrees is 15/8.
Consider the following relation. y= 2x-4
Find four points contained in the inverse. Express your values as an integer or simplified fraction.
ASAP PLEASE¡
Answers
Four points that are contained in the inverse function include the following:
Point = (0, 4).Point = (1, 4.5).Point = (2, 5).Point = (4, 6).What is an inverse function?An inverse function refers to a type of function that is obtained by reversing a mathematical operation in a given function (f(x)).
In order to determine the inverse of the given function, we would interchange both the input value (x) and output value (y) as follows:
y = 2x - 4
x = 2y - 4
Subtracting 4 from both sides, we have:
x + 4 = 2y - 4 + 4
2y = x + 4
Dividing both sides by 2, we have:
y = (x + 4)/2
y = x/2 + 4
When x = 0, we have:
y = x/2 + 4
y = 0/2 + 4
y = 4
Point = (0, 4).
When x = 1, we have:
y = x/2 + 4
y = 1/2 + 4
y = 4.5
Point = (1, 4.5).
When x = 2, we have:
y = x/2 + 4
y = 2/2 + 4
y = 5
Point = (2, 5).
When x = 4, we have:
y = 4/2 + 4
y = 0/2 + 4
y = 6
Point = (4, 6).
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can you help me figure out the equation in the drop down menus
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To find:
The piecewise function for the graph.
Solution:
From the graph, it is clear that when x is less than -1, the graph passes through (-1, -3) and (-2, -5).
It is known that the equation of a line passes through two points is given by:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]So, the equation of line passing through (-1, -3) and (-2, -5) is:
[tex]\begin{gathered} y-(-3)=\frac{-5-(-3)}{-2-(-1)}(x-(-1)) \\ y+3=\frac{-2}{-1}(x+1) \\ y+3=2x+2 \\ y=2x-1 \end{gathered}[/tex]So, the first drop down is "2x - 1", and second drop down is "x is less than or equal to -1".
Now, the graph passes through (1, 5) and (2, 6). So, the equation of the line is:
[tex]\begin{gathered} y-5=\frac{6-5}{2-1}(x-1) \\ y-5=x-1 \\ y=x+4 \end{gathered}[/tex]So, the third drop down menu is "x + 4" and the fourth drop down menu is "x is greater than or equal to 1".
Kindly help with these questions.
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because the constant relationship between the x and y coordinates makes the point go through the origin and makes a straight line.
The answer of the second question is k
X is the x coordinate
Y is the y coordinate
so, K is the constant of proportionality.
I need help with a word problem in algebra 2 please
Answers
We were given the following information:
Plan 1
Cost = $175
It has unlimited call & texts as well as 15gb
Plan 2
Cost = $50 per month
It has unlimited call & texts as well as 6gb
After 6gb, data is charged $5 per gb
From this we have the following equations:
[tex]undefined[/tex]Given a standard normal curve, find the area under the curve between z =1.40 and z =2.13.
Answers
Given:
z = 1.40 and z = 2.13
Let's find the area under the standard normal curve.
Let's find the score using the standard normal distribution table:
NORMSDIST(1.40) = 0.9192
NORMSDIST(2.13) = 0.9834
To find the area between them, we have:
P(1.40 < Z < 2.13) = P(Z<2.13) - P(Z<1.40) = 0.9834 - 0.9192 = 0.0642
Therefore, the area under the curve between z=1.40 and z=2.13 is 0.0642
ANSWER:
0.0642
(h) through (5,0), y-intercepto 0
Answers
We first need to calculate the slope of the line.
m=(0-0)/(5-0)=0 since the slope is equal to zero we have that the line is horizontal.Then the equation is
[tex](y-0)=0(x-0)\Rightarrow y=0[/tex]the equation is y=0
one month Mark measure the rainfall each day the data is shown below which statement is true about the two sets of data
Answers
Given
Data from graph
Procedure
It is more likely to rain on the first 15 days of the month
Fill in the missing values to make the equations true.(a) log, 9-log, 11 = log5(b) log45 + log4 = log, 45(c) 5log72 = log7
Answers
(a)
[tex]\log _59-\log _511=\log _{5_{}}(\frac{9}{11})\text{ (}\because\log a-\log b=\log (\frac{a}{b})[/tex]Thus, the required value in the blank in 9/11/
(b)
[tex]\log _45+\log _4(9)=\log _445\text{ (}\because\log a+\log b=\log ab)[/tex]Thus, the required value in the blank is 9.
(c)
[tex]\begin{gathered} 5\log _72=\log _72^5(\because a\log b=\log b^a) \\ =\log _732 \end{gathered}[/tex]Thus, the requried value in the blank is 32.
Missed this day of class and have no idea how to solve this last problem on my homework
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From the given expression
a) The linear system of a matrix form is
[tex](AX=B)[/tex]The linear system of the given matrix will be
[tex]\begin{gathered} 2x+y+z-4w=3 \\ x+2y+0z-7w=-7 \\ -x+0y+oz+w=10 \\ 0x+0y-z+3w=-9 \end{gathered}[/tex]b) The entries in A of the matrix is
[tex]\begin{gathered} \text{For }a_{22}=2 \\ a_{32}=0 \\ a_{43}=-1 \\ a_{55}\text{ is undefined} \end{gathered}[/tex]c) The dimensions of A, X and B are
[tex]\begin{gathered} A\mathrm{}X=B \\ \begin{bmatrix}{2} & 1 & {1} & -4 \\ {1} & {2} & {0} & {-7} \\ {-1} & {0} & {0} & {1} \\ {0} & {0} & {-1} & {3}\end{bmatrix}\begin{bmatrix}x{} & {} & {} & {} \\ {}y & {} & {} & {} \\ {}z & {} & {} & {} \\ {}w & {} & {} & {}\end{bmatrix}=\begin{bmatrix}3{} & {} & {} & {} \\ {}-7 & {} & {} & {} \\ {}10 & {} & {} & {} \\ {}-9 & {} & {} & {}\end{bmatrix} \end{gathered}[/tex]Brenda is preparing food for a picnic. She must make at least 6 sandwiches and at least 3 dozen cookies. It takes her 4 minutes to make a sandwich
Answers
For 6 sandwiches and 3 dozen cookies, the total time taken by Brenda would be 33 minutes.
What is a mathematical function, equation and expression?function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.equation modelling : Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis and results of the given problemGiven is Brenda who must make at least 6 sandwiches and at least 3 dozen cookies. It takes her 4 minutes to make a sandwich, and 45 minutes to make a dozen cookies.
If she makes [x] sandwiches and [y] dozen cookies, then the total time she would take to make them can be written as -
t = 4x + 3y
For 6 sandwiches and 3 dozen cookies, we can write -
t(6, 3) = 4 x 6 + 3 x 3 = 24 + 9 = 33 minutes
t(6, 3) = 33 minutes
Therefore, for 6 sandwiches and 3 dozen cookies, the total time taken by Brenda would be 33 minutes.
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{Complete question is given below -
She must make at least 6 sandwiches and at least 3 dozen cookies. It takes her 4 minutes to make a sandwich, x, and 45 minutes to make a dozen cookies, y.}
1. A coat at the Utopian Coat factory cost $99.99. The sales tax is 7%. Find the sales tax and the total cost of the jacket. (Round to the nearest cent).
Answers
The Solution:
Given that a coat costs $99.99 and the sales tax is $75.
We are required to find the actual sales tax and the total cost of the coat.
Step 1:
We shall find the sales tax.
[tex]\begin{gathered} \text{ Cost of the coat=\$99.99} \\ \\ \text{Sales tax of 7\% }=\frac{7}{100}\times99.99=0.07\times99.99 \\ \\ =6.999\approx\text{ \$7.00 (or 700 cent)} \end{gathered}[/tex]Thus, the sales tax is $7.00 or 700 cents.
Step 2:
We shall find the total cost of the coat.
The total cost of the coat is the sum of the coat's cost and the sales tax.
[tex]\text{ The total cost=99.99+6.999=106.989}\approx\text{ \$106.99}[/tex]Therefore, the correct answers are:
Sales tax =$7.00 or 700 cents.
Total cost = $106.99 or 10699 cents..99 or 10699 cents.
Which expressions simplify to a rational answer.
Question is attached below
Answers
The expression that simplify to rational number are as follows:
1 / 4 + 1 / 2 2.√9 3.7.(1 / 3) 7. √81 How to find rational numbers?A rational number is a number that is in the form of p/q, where p and q are integers, and q is not equal to 0.
In a simpler terms, If a number can be expressed as a fraction where both the numerator and the denominator are integers, the number is a rational number.
Rational numbers can also be expressed in decimal form.
Rational numbers have terminating decimals.
Therefore, let's find the rational simplification in the options.
1 / 4 + 1 / 2 = 3 / 4 2.√9 = 2 × 3 = 93.7.(1 / 3) = 21 × 1 / 3 = 77. √81 = 7 × 9 = 72learn more on rational numbers here:https://brainly.com/question/7129080
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Which graph represents the equation X =2?
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ANSWER and EXPLANATION
We are given x = 2.
To plot the graph of x = 2, it is important to note that the value of x does not change for this equation.
x is always 2 regardless of the value of y.
This means that we are going to plot a straight line that will straight up (and down as well) at x = 2.
The graph therefore is:
Which of the following functions is graphed below?
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So, y is a system two distinct exponential functions.
The function on the bottom is a cubic function with a y-intercept of -3, and the full dot means that point is included in the domain.
y = x^3 - 3, x ≤ 2
The other function is a quadratic function with a currently unknown y-intercept. The hollow dot on point 2 means that the point is not included in the domain of the function.
y = x^2 + b, x > 2
So, given that there is only one option that matches this, even with the unknown b value, we know:
[tex]y = \left \{ {{x^3 - 3, x\leq 2} \atop {x^2 + 6, x > 2}} \right.[/tex]
So the answer is C.
The wholesale price for a pair of shoes is $3.50. A certain department store marks up the wholesale price by 60%. Find the price of the pair of shoes in the department store
Answers
Given
Wholesale price for a pair of shoes = $3.50.
Wholesale price by 60%.
Find
price of the pair of shoes in the department store
Explanation
Price in deparrtmental store is 60% more than wholesale
[tex](1+60\%\text{ \rparen of wholesale }[/tex]so ,
[tex]\begin{gathered} 1.6\times3.50 \\ 5.60 \end{gathered}[/tex]Final Answer
Therefore , the price of the pair of shoes in the department store is $5.60.
STATEMENTREASON1. DBC - RST1. Given2. ZABC - ZDBC+ ABD2. Angle addition therom3.3. Ifa=b+cand c>0,thena > b4. ABC > RST4. SubstitutionWhich of the following statements would complete the proof in line 3?O ZABC> ZABDO LABC> DBCO ZDBC> ZABD
Answers
Answer
Option B is correct.
Angle ABC > Angle DBC
Explanation
Since it's been proven that
Angle ABC = Angle ABD + Angle DBC
Since Angle ABD > 0,
Angle ABC > Angle DBC is the part that completes the proof that
Angle ABC > Angle RST
Hope this Helps!!!
Northeast Hospital’s Radiology Department is considering replacing an old inefficient X-ray machine with a state-of-the-art digital X-ray machine. The new machine would provide higher quality X-rays in less time and at a lower cost per X-ray. It would also require less power and would use a color laser printer to produce easily readable X-ray images. Instead of investing the funds in the new X-ray machine, the Laboratory Department is lobbying the hospital’s management to buy a new DNA analyzer.
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The classification of each cost item as a differential cost, a sunk cost, an opportunity cost, or None, is as follows:
Cost Classification1. Cost of the old X-ray machine Sunk cost
2. The salary of the head of the Radiology Dept. None
3. The salary of the head of the Laboratory Dept. None
4. Cost of the new color laser printer Differential cost
5. Rent on the space occupied by Radiology None
6. The cost of maintaining the old machine Differential cost
7. Benefits from a new DNA analyzer Opportunity cost
8. Cost of electricity to run the X-ray machines Differential cost
9. Cost of X-ray film used in the old machine Sunk cost
What are differential cost, sunk cost, and opportunity cost?A differential cost is a cost that arises as the cost difference between two alternatives.
A sunk cost is an irrelevant cost in managerial decisions because it has been incurred already and future decisions cannot overturn it.
An opportunity cost is a benefit that is lost when an alternative is not chosen.
Thus, the above cost classifications depend on the decision to replace the old X-ray machine with a new machine (new X-ray or new DNA analyzer).
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Question Completion:Required Classify each item as a differential cost, a sunk cost, or an opportunity cost in the decision to replace the old X-ray machine with a new machine. If none of the categories apply for a particular item, select "None".
1. Cost of the old X-ray machine
2. The salary of the head of the Radiology Department
3. The salary of the head of the Laboratory Department
4. Cost of the new color laser printer
5. Rent on the space occupied by Radiology
6. The cost of maintaining the old machine
7. Benefits from a new DNA analyzer
8. Cost of electricity to run the X-ray machines
9. Cost of X-ray film used in the old machine
Claim: The mean pulse rate (in beats per minute) of adult males is equal to bpm. For a random sample of adult males, the mean pulse rate is bpm and the standard deviation is bpm. Find the value of the test statistic.
Answers
For solving this question, you should apply the equation:
The question gives
Next step - replace the values in the equation
[tex]z_T=\frac{70.4-69}{\frac{10.8}{\sqrt[]{129}}}=\frac{1.4}{\frac{10.8}{\sqrt{129}}}=1.47[/tex]4. Ifline m has the equation y = 3x - 1, and line k is perpendicular to m and goes through the point (-4,3), find the equation of line k.
Answers
Answer:
The equation of the line k is
[tex]y=-\frac{1}{3}x+\frac{5}{3}[/tex]Explanation:
Given that k is perpendicular to line m, defined as:
y = 3x - 1
the slope of k is the negative reciprocal of the slope of line m.
The slope of m is 3
The negative reciprocal of m is -1/3 (this is the slope of k)
Therefore, k is in the form
[tex]y=-\frac{1}{3}x+b[/tex]Since this line passes through the point (x, y) = (-4, 3), we can use this to obtain the value for the y-intercept, b
[tex]\begin{gathered} 3=-\frac{1}{3}(-4)+b \\ \\ 3=\frac{4}{3}+b \end{gathered}[/tex]Solving for b by subtracting 4/3 from both sides
[tex]\begin{gathered} b=3-\frac{4}{3} \\ \\ =\frac{5}{3} \end{gathered}[/tex]The equation is therefore,
[tex]y=-\frac{1}{3}x+\frac{5}{3}[/tex]Why can the Vertical Angle Theorem NEVER be used to prove two triangles are congruent?
Answers
Solution
Why can the Vertical Angle Theorem NEVER be used to prove two triangles are congruent?
The Vertical angle theorem states that vertical angles are always congruent.
We can't use this to proof congruence between two triangles because this theorem not provide enough evidence to obtain the SSS, ASA, SAS, AAS, HHL. For this reason is not appropiate to use it for this case.
What is the scale factor for AXYZ to AUVW?O A1/1O B. 1/1/20OC. 2OD. 4371620A A837-105353X 6 Z12
Answers
SOLUTION:
We want to know the scale factor of the transformation from;
[tex]\Delta XYZ\rightarrow\Delta UVW[/tex]We do this by taking ratios of corresponding sides, they should be the same in either case;
Thus , the scale factor is;
[tex]\frac{20}{10}=\frac{12}{6}=\frac{16}{8}=2[/tex]Thus, the scale factor is 2.
Jacob opened his piggy bank and found Nickels, Dimes, and Quarters totaling 81 coins. The total value of the coins was $7.90. The number of Dimes was 7 less than triple the number of Quarters. Write a system of equations that represents this situation. Use N, D, and Q.
Answers
A Nickel is 5 cents = 5/100 = $0.05
A dime is 10 cents = 10/100 = $0.1
A quarter is 25 cents = 25/100 = $0.25
Let N represent the number of nickels
Let D represent the number of dimes
Let Q represent the number of quarters
Jacob opened his piggy bank and found Nickels, Dimes, and Quarters totaling 81 coins. It means that
N + D + Q = 81
The total value of the coins was $7.90. It means that
0.05N + 0.1D + 0.25Q = 7.9
The number of Dimes was 7 less than triple the number of Quarters. It means that
D = 3Q - 7
The system of equations is
N + D + Q = 81
0.05N + 0.1D + 0.25Q = 7.9
D = 3Q - 7
In the given figure, find the mesure of angle BCD
Answers
Since the sum of angles in a triangle is 180°, it follows that;
[tex]\begin{gathered} 4x+3x+2x=180 \\ 9x=180 \\ \text{ Divide both sides of the equation by }9 \\ \frac{9x}{9}=\frac{180}{9} \\ x=20 \end{gathered}[/tex]Since line segment AB is parallel to the line segment CD, it follows from the Corresponding angles theorem that:
[tex]\begin{gathered} \angle{B}=\angle{BCD} \\ \text{ Therefore:} \\ \angle{BCD}=4x \\ \text{ Substitute }x=20\text{ into the equation} \\ \angle{BCD}=4\times20=80 \end{gathered}[/tex]Therefore, The req
Bob wants to build an ice skating rink in his backyard, but his wife says he can only use the part beyond the wood chipped path running through their yard. What wouldbe the area of his rink if it is triangular-shaped with sides of length 18 feet, 20 feet, and 22 feet? Round to the nearest square foot.
Answers
In order to calculate the area of the triangle, given the length of its three sides, we can use Heron's formula:
[tex]A=\sqrt{p\left(p-a\right)\left(p-b\right)\left(p-c\right)}[/tex]Where p is the semi-perimeter.
So, calculating the value of p and then the area of the triangle, we have:
[tex]\begin{gathered} p=\frac{a+b+c}{2}=\frac{18+20+22}{2}=\frac{60}{2}=30 \\ A=\sqrt{30\left(12\right)\left(10\right)\left(8\right)} \\ A=\sqrt{28800} \\ A=169.7\text{ ft^^b2} \end{gathered}[/tex]Rounding to the nearest square foot, the area is 170 ft².
