Answers
Given the following equation:
[tex]\frac{x}{x-4}-\frac{4}{x}=\frac{3}{x-4}[/tex]First, we will identify the zeros of the denominator
So, the zeros are: x = {0,4}
Second, multiply the equation by x(x-4) to eliminate the denominators
[tex]x(x-4)*(\frac{x}{x-4}-\frac{4}{x})=x(x-4)*\frac{3}{x-4}[/tex]Simplify the equation:
[tex]x^2-4(x-4)=3x[/tex]Expand the equation and combine the like terms:
[tex]\begin{gathered} x^2-4x+16=3x \\ x^2-7x+16=0 \end{gathered}[/tex]The last quadratic equation will be solved using the quadratic rule:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]Substitute a = 1, b = -7, c = 16
[tex]\begin{gathered} x=\frac{7\pm\sqrt{(-7)^2-4(1)(16)}}{2(1)} \\ \\ x=\frac{7\pm\sqrt{-15}}{2}=\frac{7\pm i\sqrt{15}}{2} \\ \\ x=\lbrace\frac{7+i\sqrt{15}}{2};\frac{7-i\sqrt{15}}{2}\rbrace \end{gathered}[/tex]So, the answer will be:
[tex]x=\lbrace\frac{7+i\sqrt{15}}{2};\frac{7-i\sqrt{15}}{2}\rbrace[/tex]Related Questions
How would I convert 900,000km to miles?
Answers
EXPLANATION
Since we have 900,000 kilometers, and 1 kilometer is equivalent to 0.621371 kilometers, we can apply the unitary method in order to get the needed conversion as shown as follows:
[tex]\text{?miles}=900,000\operatorname{km}\cdot\frac{0.621371}{1\text{kilometer}}=559233\text{ miles}[/tex]?miles = 900,000 km * (0.621371/ 1 km) = 559,233 miles
The solution is 559,233 miles
Solve for x using trigonometry. Round to the nearest tenth. (hint: One decimal place) 17 x 19
Answers
By definition,
sin(angle) = opposite/hypotenuse
From the picture,
sin(x) = 17/19
x = arcsin(17/19)
x = 63.5°
A line passes through the point -8, -5 and has a slope of -3/2 Write an equation in slope-intercept form for this line.
Answers
Answer:
[tex]y = - \frac{3}{2} x - 17[/tex]
Step-by-step explanation:
[tex] - 5 = - \frac{3}{2} ( - 8) + b[/tex]
[tex] - 5 = 12 + b[/tex]
[tex]b = - 17[/tex]
[tex]y = - \frac{3}{2} x - 17[/tex]
Xavier wants to compare two websites based on customer ratings in order to decide on which website to make a big purchase. He creates a boxplot for each website with the same number of ratings. (look at the graph)What can Xavier NOT include?A. Website A has a higher median rating B. Website A has a larger interquartile range C. Website A has larger rangeD. Website A has a lower median rating E. Website A has a lower first quartile value
Answers
D.
Since the median of the blue box is upper from the orange one we conclude that the median is higher in website A.
Therefore, the wrong statement is D.
Given that sin(0)= 10/ 13 and 0 is in Quadrant II, what is cos(20)? Give an exact answer in the form of a fraction. ,
Answers
SOLUTION
Given the image in the question tab, the following are the solution steps to the answer
Step 1: Write out the function
[tex]\begin{gathered} \sin \theta=\frac{10}{13} \\ \text{since }\sin \theta=\frac{opp}{hyp} \\ \therefore opp=10,\text{ hyp=13} \end{gathered}[/tex]Step 2: Solve for the adjacent using the pythagoras theorem
[tex]\begin{gathered} \text{hyp}^2=opp^2+adj^2 \\ 13^2=10^2+adj^2 \\ \text{adj}^2=13^2-10^2 \\ \text{adj}=\sqrt[]{169-100} \\ \text{adj}=\sqrt[]{69} \end{gathered}[/tex]Step 3: Calculate the value of cos2Ф
[tex]\begin{gathered} cos2\theta=\cos ^2\theta-\sin ^2\theta \\ \cos 2\theta=(\frac{\text{adj}}{\text{hyp}})^2-(\frac{opp}{hyp})^2 \\ \cos 2\theta=(\frac{\sqrt[]{69}}{13})^2-(\frac{10}{13})^2 \\ \cos 2\theta=\frac{69}{169}-\frac{100}{169} \\ \cos 2\theta=-\frac{31}{169} \end{gathered}[/tex]Hence, the value of cos2Ф is -31/169.
10Estimate the solution to the following system of equations by graphingOA (1,7)OB. (-1,1)OC.OD. (-1,-1)
Answers
we have the system of equations
-4x + 5y =8
6x - y = 11
Using a graphing tool
Remember that
the solution is the intersection point of both lines
The answer is the option AIn 2001, Rodney Hampton earned $75,200 as a self-employed worker. He also earned $41,350 as an employee. How much FICA tax did he pay for both earnings? Note:Self-employed tax rate is 15.3% and the employee tax rate is 7.65%.$14,668.88$14,577.25$14,324.09$14,225.50None of these choices are correct.
Answers
Step 1: Rodney Hampton earned $75,200 as a self-employed worker
% tax rate for self employed = 15.3%
[tex]\begin{gathered} =15.3\text{ \% of \$75200} \\ =\frac{15.3}{100}\text{ x \$75200} \\ =11505.6 \\ =\text{ \$11505.6} \end{gathered}[/tex]Step 2: Rodney Hampton earned $41,350 as a employee worker
%tax rate for employee = 7.65%
[tex]\begin{gathered} =\text{ 7.65\% of \$41350} \\ =\text{ }\frac{7.65}{100}\text{ x \$41350} \\ =\text{ 3163.3} \\ =\text{ \$3163.3} \end{gathered}[/tex]Step 3: FICA tax paid for both earnings = $11505.6 + $3163.3
= $14668.875
=$14668.88
Hence FICA tax paid for both earnings = $14668.88
Math problem attached
Answers
2. 65 x 10⁶ ft³ of oil will be required to fill the pipe.
What is rounding off ?
Rounding off means a number is made into simpler form by keeping its value fixed but closer to the next number.
It is given that :
length of pipe l = 800 mi.
we know that :
1mi = 5280 ft.
8 mi = 5280 x 8 = 42240 ft.
also, diameter of pipe d = 48 in.
then, radius r = d/2 = 24in.
and, 1 in. = 0.833 ft.
24 in = 24 x0.833 ≈ 20 ft.
Now, volume of pipe V will be :
V = πr²l
V = 3.14 x (20)² x 42240
V = 2654017.5
V = 2. 65 x 10⁶ ft³
Therefore, 2. 65 x 10⁶ ft³ of oil will be required to fill the pipe.
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y 4 7(x-6)
x-intercept:
y-intercept:
PLEASE ANSWER FAST.
Answers
Answer: y-4=7(x-6)
x-intercept(s): (38/7,0)
y-intercept(s): (0,−38)
I believe this is right hope this helps
Step-by-step explanation:
The answers available are SSS SAS CPCTC and definition of congruence
Answers
Solution
The diagram below will be of help
From the above, we have two sides to be equal and an angle to be equal
Therefore, the answer Side, Angle, Side (SAS)
1. Caitlyn is going away to college and will need to rent a truck to helpmove. The cost of the truck is $35 plus $0.79 per mile. If her collegeis 85 miles away and she budgeted $100 for the rental, will she haveenough money?
Answers
1. Caitlyn is going away to college and will need to rent a truck to help
move. The cost of the truck is $35 plus $0.79 per mile. If her college
is 85 miles away and she budgeted $100 for the rental, will she have
enough money?
we know that
The equation in slope intercept form of this situation is
y=mx+b
where
m=$0.79 per mile
b=$35
y -----> is the total cost
x -----> the number of miles
so
y=0.79x+35
so
For x=85 miles
substitute
y=0.79(85)=35
y=$102.15
we have that
102.15 > 100
therefore
she not have enough moneyI am having so much trouble with my assignment. can you please help me with number 8 and 10.
Answers
We have to solve this system of equations by substitution.
8) First, we find the value of one of the variables in function of the other using one of the 2 equations (first equation, in this case). Then, we use the other equation and replace the variable we just cleared (x, int his case) and solve for the other variable (y).
Then, after calcualting y, we can use the first equation to calculate x.
[tex]\begin{gathered} x+4y=0 \\ x=-4y \end{gathered}[/tex][tex]\begin{gathered} 3x+2y=20 \\ 3(-4y)+2y=20 \\ -12y+2y=20 \\ -10y=20 \\ y=\frac{20}{-10} \\ y=-2 \end{gathered}[/tex][tex]\begin{gathered} x=-4y=-4(-2) \\ x=8 \end{gathered}[/tex]Answer: x=8, y=-2.
10)
[tex]\begin{gathered} x-3y=-2 \\ x=3y-2 \end{gathered}[/tex][tex]\begin{gathered} 10x+8y=-20 \\ 10(3y-2)+8y=-20 \\ 30y-20+8y=-20 \\ 38y=-20+20 \\ 38y=0 \\ y=0 \end{gathered}[/tex][tex]x=3y-2=3\cdot0-2=0-2=-2[/tex]Answer: x=-2, y=0
Please help me
I give brainliest
worth 15 points
The amount of money in a bank account is given by the function y = 200(1+0.05), where y is in dollars and t is measured in months since the account was opened.
What is the percent rate of growth of the bank account?
Enter your answer in the box.
Answers
Answer:
60% annual rate
Step-by-step explanation:
Your equation is incorrect
It should be Y = 200 (1+.05)^t
T is the number of compounding periods per year (12 to a year)
.05 is the periodic interest rate ( 1/12 th of the annual)
.05 * 12 = .6 Which is 60% <=====REALLY high annual rate!
A quadrilateral has two angles that measure 110° and 120°. The other two angles are in aratio of 6:7. What are the measures of those two angles?andSubmit
Answers
From the problem, two angles in a quadrilateral are 110 and 120 degrees.
Note that the sum of interior angles in a quadrilateral is 360 degrees.
Then the sum of the other two angles will be :
[tex]360-(110+120)=130[/tex]And the angles are in a ratio of 6 : 7.
Multiply the ratio by a common factor "x"
[tex]6x\colon7x[/tex]Then take the sum and equate it to 130 degrees.
[tex]6x+7x=130[/tex]Solve for x :
[tex]\begin{gathered} 13x=130 \\ x=\frac{130}{13} \\ x=10 \end{gathered}[/tex]Now, substitute x = 10 to the ratio.
[tex]\begin{gathered} 6(10)\colon7(10) \\ 60\colon70 \end{gathered}[/tex]Therefore, the other two angles are 60 and 70 degrees.
ANSWER :
60 and 70 degrees
Hi, can you help me answer this question please, thank you!
Answers
From the problem we have
[tex]\begin{gathered} n_1=50 \\ n_2=30 \\ \bar{x_1}=2.31 \\ \bar{x_2}=2.02 \\ s_1=0.89 \\ s_2=0.61 \end{gathered}[/tex]We replace in t
[tex]\begin{gathered} t=\frac{(2.31-2.02)}{\sqrt[]{\frac{(0.89)^2_{}}{50_{}}+\frac{(0.61)^2_{}}{30_{}}_{}}} \\ t=\frac{0.29}{\sqrt[]{0.028245_{}_{}}} \\ t=1.725 \\ t=1.73 \end{gathered}[/tex]The answer is t=1.73Write an equivalent fraction with the given denominator. (Only input numerator in final answer.) 2/3 = /24
Answers
Write an equivalent fraction with the given denominator. (Only input numerator in final answer.) 2/3 = /24
we have 2/3
Multiply by 8/8
(2/3)(8/8)=16/24
therefore
the answer is 16Which inequalities are shown on the graph?Find your inequalities in the grid below. Check the ONE box that pairs the two correct inequalitiesY-3-1 y>-**-172-**-1 y<-**-1<3+3y>+3y< <+3y2 ++3D D D DOOOO"OOOOPreviousPauseO Search for anything0-
Answers
From the graph we could see that y = x + 3 for the first line . The shaded line is where y is less than or equals to x + 3.
For the second line we can see that y = x - 1 . The shaded line is where y is greater than or equals to x - 1 . Therefore, the inequalities are as follows
[tex]\begin{gathered} y\leq x+3 \\ y\ge x-1 \end{gathered}[/tex]A triangular road sign has a base of 30 inches and a height of 40 inches. What is it’s area?
Answers
Answer:
600ft
Step-by-step explanation:
Because a triangle is half of a rectangle, the area can be found by taking the base times height and dividing by 2.
A = (b * h)/2
A = (40 * 30)/2
A = 1200/2
A = 600ft
Eric is a software salesman. His base salary is 2300, and he makes an additional $90 for every copy of History is Fun sells. Let P represent his total pay (in dollars) and let N represent the number of copies of History is Fun he sells. Write an equation relating P to N. Then use this equation to find his total pay if he sells 23 copies of History is Fun.
Answers
Equation
P = 2300 + 90(N)
Total payment after selling 23 copies of History is Fun.
P= 2300 + 90(23)
P= 2300 + 2070 (Multiplying)
P= 4370 (Adding)
The answer is $4370
27. If figure A and figure B are similar with a ratio of similarity of 2, and the perimeter of figure A is 28 units,what is the perimeter of figure B?
Answers
SOLUTION
Since the two shapes are similar, that is A and B similar with a ratio of 2, then we have that
[tex]\begin{gathered} \frac{length\text{ A}}{lemgth\text{ B}}=\frac{2}{1}=\frac{perimeter\text{ A}}{perimeter\text{ B}} \\ \frac{2}{1}=\frac{perimeter\text{ A}}{perimeter\text{ B}} \\ \frac{2}{1}=\frac{28}{perimeter\text{ B}} \end{gathered}[/tex]Cross multiplying we have
[tex]\begin{gathered} 2Perimeter\text{ B = 28} \\ Perimeter\text{ B = }\frac{28}{2} \\ =14\text{ units } \end{gathered}[/tex]hence the answer is 14 units
Which expression is equivalent to (2-3x) (2+3x) ?
Answers
Answer:
[tex]4-9x^{2}[/tex]
Step-by-step explanation:
in the first parenthesis, multiply the FIRST number (2 - 3x) by the numbers in the OTHER parenthesis. (2 + 3x)
[tex](2-3x)(2+3x)[/tex]
it would look like:
[tex]2(2) = 4\\2(3x) = 6x[/tex]
Next, multiply the SECOND number (2 - 3x) by the numbers in the OTHER parenthesis. (2 + 3x)
[tex]-3x(2) = -6x\\-3x(3x) = 9x^2[/tex]
Now, add like terms. Your answer should either be:
[tex]4+6x-6x+9^2[/tex] OR [tex]4 -9x^2[/tex]
The current in a simple electrical circuit is inversely proportional to the resistance. If thecurrent is 30 amperes (an ampere is a unit for measuring current) when the resistance is 5ohms, find the current when the resistance is 7.8 ohms.
Answers
Hello there. To solve this question, we'll have to remember some properties about inversely proportional terms.
Let's start labeling the terms:
Say Current is given by I, Resistance is given by R and voltage is given by V.
By Ohm's Law, we know that:
[tex]V=R\cdot I[/tex]In fact, this is the definition we need to find the answer.
But, to understand why the question mention the fact that they are inversely proportional, note:
We say two numbers x and y are inversely proportional when:
[tex]x\cdot y=k[/tex]Their product is equal to a constant. k is the constant (of proportionality).
Now, using the given values in the question, we can solve this question.
If the current is 30 ampère when the resistance is 5 ohms, we have to find the current when the resistance is 7.8 ohms.
First scenery:
[tex]V=30\cdot5[/tex]Multiply the numbers
[tex]V=150[/tex]Second scenery:
[tex]V=7.8\cdot I[/tex]Plugging V = 150, we get:
[tex]150=7.8\cdot I[/tex]Divide both sides of the equation by a factor of 7.8
[tex]I=\frac{150}{7.8}[/tex]Simplify the fraction by a factor of 2
[tex]I=\frac{75}{3.9}[/tex]Using a calculator, we get the following approximation
[tex]I\approx19.2\text{ A}[/tex]A is for Ampère.
The expression (222)(x?) is equivalent to z What is the value of p?
Answers
SOLUTION;
Step 1:
[tex]undefined[/tex]Find the solutions of the given system of equations: x2 + y2 = 68 and y = 4x.
Answers
Given the system of equations:
[tex]\begin{gathered} x^2+y^2=68 \\ y=4x \end{gathered}[/tex]We can solve it by substituting the second equation into the first as follows:
[tex]\begin{gathered} x^2+(4x)^2=68 \\ \\ Operating: \\ \\ x^2+16x^2=68 \\ 17x^2=68 \end{gathered}[/tex]Dividing by 17:
[tex]x^2=\frac{68}{17}=4[/tex]Applying square root on both sides:
[tex]\begin{gathered} x=\pm\sqrt{4} \\ x=\pm2 \end{gathered}[/tex]There are two solutions for x and they produce two solutions for y.
For x = 2
y = 4*2 = 8
For x = -2
y = 4*(-2) = -8
Thus, the solutions are:
(2,8) and (-2, -8)
A point is chosen at random in the square shown below. Find the probability that the point is in the shaded circular region. Each side of the square is 6in, and the radius of the circle is 3in.Use the value 3.14 for π. Round your answer to the nearest hundredth.
Answers
We will have the following:
First, we determine the area of the square and of the shaded region, that is:
[tex]\begin{gathered} A_s=6in^2\Rightarrow A_s=36in^2 \\ \\ A_c=\pi(3)^2\Rightarrow A_c=9\pi in^2 \end{gathered}[/tex]Now, we will have that the probability will be of:
[tex]P=\frac{9\pi}{36}\Rightarrow P=\frac{\pi}{4}\Rightarrow P\approx0.79[/tex]So, the probability is approximately 79%.
Which of the following is a valid application of the distributive property?
A. 5.2+3=5 (2+3)
B. 5 2+3=5 (2) +5. (3)
ONeither A nor B
OB only
O A only
O Both A and B
Answers
5 2+3=5 (2) +5. (3) is a valid application of the distributive property.
What is a distributive property?
According to this property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
Given that,
A. 5.2+3=5 (2+3)
B. 5 2+3=5 (2) +5. (3)
Distributive property
a*(b+c) = a*b+a*c
In option A the RHS part is not correct.
In option B both part is correct.
5*(2+3)= 5*2+5*3
5*5 = 10+15
25 = 25
LHS = RHS
Hence, Option B is correct.
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the equation 5x+7=4x+8+x-1 is true for all real numbers substitute a few real numbers for x to see that this is so and then try solving the equation
Answers
The equation 5x+7 = 4x+8+x-1 is true for all real numbers.
Solution for the equation is 5x + 7 = 5x + 7.
Given,
The equation; 5x+7 = 4x+8+x-1
We have to find the solution for this equation.
Here,
5x + 7 = 4x + 8 + x - 1 = 5x + 7
The equation is true for all real numbers;
Lets check;
x = 65 x 6+7 = 4 x 6 + 8 + 6 - 1
30 + 7 = 24 + 13
37 = 37
x = 155 x 15 + 7 = 4 x 15 + 8 + 15 - 1
75 + 7 = 60 + 22
82 = 82
That is,
The equation 5x + 7 = 4x + 8 + x - 1 is true for all real numbers.
The solution for the equation is 5x + 7 = 5x + 7.
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PLEASE HELP I WILL MARK BRAINLIEST!!Which of the following equations is a linear function?A) 2x + 3y = 6B) y = x^2 + 1C) y=x^3D) x^2 + y^2 = 9
Answers
Given data:
The given sets of equations.
The polynomial in which degree of the variable is 1 is said to be linear expression.
The first option 2x+3y=6 is only linear function.
Thus, the option (A) is correct.
3) An experiment is designed to compare the average salaries in a particular Position in two competing companies. The null hypothesis is assumed to be that there is no difference in the average salaries of empoty employees in a particular position in the two companies. What is the alternative hypothesis?
Answers
Given:
There are two competing companies.
Required:
We need to find the alternative hypothesis
Explanation:
If the null hypothesis assumes equal average salaries (i.e. no difference), then the alternative can take on three cases:
A)
One mean is greater than the other
B)
One mean smaller than the other
C)
The means are not equal
Now here A and B sound the same, so I shoukd be more precise,
Two numbers sum to 61. Twice the first subtracted from the second is 1. Find the numbers.
Answers
x + y = 61
y - 2x = 1
y = 2x + 1
x + (2x + 1) = 61
3x + 1 = 61
3x = 60
x = 20
y = 61 - 20 = 41