Answers
Answer:
3, -1, 1 and 0
Step-by-step explanation:
An expression is undefined when the denominator is equal to 0 as you cannot divide by 0 in Mathematics. Therefore you are looking for the values of x which will result in either or both denominators equaling 0.
This simply means finding the solutions to the quadratics in the denominators.
First equation is [tex]x^{2} -2x-3[/tex].
One way you can solve this equation is using factorization (putting the equation into two sets of brackets which show the solutions) which puts the equation in the solvable form: (ax+b)(cx+d).
Firstly, we can deduct that a and c are both 1 as ax and cx multiply to give the x^2 term, the co-efficient of which is 1. Since only 1 and 1 can multiply to 1, a and c must both be 1.
Now, in order to work out b and d we need to find the possible factor combinations for -3 as b and d multiply to give the constant term. The only possible combination is 1x3, therefore b and d can either be -1 and 3, or -3 and 1.
To work this out we look at the x term. We see it is -2x. b and d will add to give the co-efficient.
Therefore we know that they are -3 and 1 as -3+1 = -2
We now have the equation: (x+1)(x-3)
Setting it to 0 gives us: [tex](x+1)(x-3)=0[/tex]
This tells us the solutions to this equation are x= -1 and x= 3 as substituting these values for x will result in a bracket adding to 0 so both those options can be selected as your answer.
The second equation [tex]2x^{2} +2x[/tex] can be approached with a slightly easier method. Both terms have a 2x, so we can condense it into a bracket by dividing both terms by the common factor and moving the factor outside. Factorizing this equation in this fashion gives us: [tex]2x(x+1)=0[/tex]
Now our solutions are x=0 and x=1.
Combined from both equations the correct options are: 3, -1, 1 and 0.
Hope this helped!
Related Questions
The mean amount of time it takes a kidney stone to pass is 12 days and the standard deviation is 4 days. Suppose that one individual is randomly chosen. Let X = time to pass the kidney stone. Round all answers to 4 decimal places where possible.
a. What is the distribution of X? X ~ N
b. Find the probability that a randomly selected person with a kidney stone will take longer than 16 days to pass it.
c. Find the minimum number for the upper quarter of the time to pass a kidney stone.
days.
Answers
The probability that a randomly selected person with a kidney stone will take longer than 16 days to pass it is 0.15866 , the minimum number for the upper quarter of the time to pass a kidney stone days is 14.4 .
What is Probability ?Probability is the measure of likeliness of an event to happen
Let X denote the time to pass the kidney stone.
The random variable X follows normal Distribution
mean = 12 days days
standard deviation = 4 days
The distribution of X is X - N ( 12 , 4)
The probability that a randomly selected person with a kidney stone will take longer than 16 days to pass it is
P ( X > 16) = 1 - P( X ≤ 16)
= 1 - P( Z ≤ (16-12)/4)
= 1 - P ( Z ≤ 1 )
= 1 - 0.84134
= 0.15866
P( X < x₀) = 0.75
[tex]\rm P ( \dfrac{x - \mu }{\sigma} < \dfrac{x_0 -13}{6}) = 0.75[/tex]
[tex]\rm \phi (\dfrac { x_o - 12}{4}) = 0.75[/tex]
Using the excel function the z score for the area 0.75 is
z - score = 0.6745
[tex]\rm \dfrac {x_o - 12}{4} = 0.6745[/tex]
x₀ = 0.6 * 4 + 12
x₀ = 14.4
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If AABC = ADEF, which congruences are true by CPCTC? Check all that
apply.
Answers
Answer: it's A, B, and D
Step-by-step explanation:
PLEASE HELP!! ANSWER AND EXPLANATION NEEDED URGENTLY!!
Answers
Using it's concept, it is found that the probability that the button is either pink or blue is:
[tex]p = \frac{26}{29}[/tex]
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, we have that:
There are x yellow buttons.There are y blue bottons.There are z pink buttons.There are six times as many pink buttons as yellow books, hence:
z = 6x.
Considering the ratio of yellow buttons to blue buttons, we have that:
[tex]\frac{x}{y} = \frac{3}{8}[/tex]
3y = 8x
[tex]y = \frac{8x}{3}[/tex]
The total number of buttons is given by:
[tex]T = x + \frac{8x}{3} + 6x[/tex]
[tex]T = \frac{29x}{3}[/tex]
The number of pink or blue is given by:
[tex]y + z = \frac{8x}{3} + 6x = \frac{26x}{3}[/tex]
Hence the probability is given by:
[tex]p = \frac{\frac{26x}{3}}{\frac{29x}{3}} = \frac{26}{29}[/tex]
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20
Apply the 50-30-20 Rule to the context below and determine how much money is left over.
You share an apartment with two friends, and the rent and utilities are split equally by all three tenants. Find the
amount left for savings if your bi-weekly net income is $1,391.50.
Total Rent: $1,100
Public Transportation: $88
Cell Phone: $68
Total Utilities: $327
Renter's Insurance: $48.20
Gym Membership: $50
Cable & Streaming Services: $175
Dining Out / Entertainment: $300
3% of Gross into a 401k Savings Plan
Credit Cards: $102
Student Loans: $150
1. Given this monthly budget, how much net income gets applied to each of the "Need/Wants/Debt-Savings"
categories?
50%
30%
20%
2. Subtract each deduction from the monies found in 1). How much remains in each category?
50%
30%
20%
3 How much money remains? What changes would you recommend to improve this budget?
Answers
Step-by-step explanationEl 50% para tus gastos más básicos, el 20% para ahorros y el 30% para tus gastos personales. Esta es la conocida como regla 50/20/30, la cual, se empieza a aplicar en distintos países, como Estados Unidos, siendo un hábito frecuente a la hora de distribuir los ingresos de cada uno.:
help please
what is
Answers
Option A. is correct for the given condition.
Lets solve it through steps of range and functions,
First of all, Solve the equation:
[tex]f(x) = |x|+5[/tex]
[tex]= > x = -5[/tex] (1)
[tex]= > x = 5[/tex] (2)
So these would be the ranges of X in between 5 and -5.
Hence option A. [tex]R{f(x)eR [f(x) < 5}[/tex] is correct.
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You deposit $400 in an account earning 2% interest compounded annually. How much will you have in the account in 20 years?
Answers
Answer:
Approximately $594.38
Step-by-step explanation:
Use the formula: y = a(1 + r)^t
a is the initial amount
r is the percent of interest in decimal form
t is the time in years
y is the money after t years
Substitute the values given in the problem into the equation:
400(1+0.02)^20
Use a calculator or solve manually
Around 594.38
Find the surface area of the composite figure
4 cm
13 cm
3 cm
4 cm
12 cm
SA = [?] cm²
5 cm
3 cm. Pls help
Answers
Question 11 (5 points) ✓ Saved Solve x² + 4x + 12 = 0 by completing the square. Ox= -2 + 2√2i, x=-2-2√/2i Ox= -2 +2i, x=-2-2/ O x = 0, -4 Ox= -2+ √2i, x=-2-√2i
Answers
The solution of the equation is x = -2±2i√2. The solution to the equation is found in the Sridharacharya formula.
What is the equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.
Given equation;
x² + 4x + 12 = 0
The solution to the equation is found as;
x² + 4x + 12 = 0
The solution to the equation is;
[tex]\rm x=-b \pm \frac{\sqrt{b^2-4ac}}{2a} \\\\ \rm x=-4 \pm \frac{\sqrt{4^2-4\times 4 \times 1}}{2\times 4} \\\\[/tex]
x = -2±2i√2
Hence the solution of the equation is x = -2±2i√2.
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find the midpoint A and B where A has a coordinates (2, 7) and B has coordinates (6,3)
Answers
Answer:
(2+6)/2= 4 (x-coordinate of midpoint)
(7+3)/2= 5(y=coordinate of midpoint)
Answer:
Hope it will help you:)
Step-by-step explanation:
Solution:
here,
A(2,7)-([tex]x_{1,}y_{1[/tex])
B(6,3)-([tex]x_{2},y_{2[/tex])
Now using midpoint formula,
midpoint of ab=(x1 + x2)/2, (y1 + y2)/2
=(2+6)/2,(7+3)/2
=(8/2,10/2)
=(4,5)
The midpoint of AB is(4,5).
4Days 7hours 16 minutes
Answers
Answer:
6190
Step-by-step explanation:
you multiply 4 days by 24 because a day have 24 hrs,then you will multiply the answer by 60 ,then after multiplying by 60 you will add 16 minutes and if you want to put is in seconds you multiply by 60 again that's what I know
Consider the algebraic expression √ 7 x 18 + 12.1 x 15 + π 4 x 6 + 1 9 . What is the degree of this polynomial? Identify the leading coefficient. Identify the leading term.
Answers
The degree of the provided polynomial is 18, and the leading term is √7.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have given an expression:
[tex]= \rm \sqrt{7}x ^{18} + 12.1x^{ 15} + \pi 4 x^ 6 + 1 9[/tex]
As we can see in the expression the greatest degree is 18.
So the degree of the polynomial is 18
And the coefficient of the variable which has a height degree is the leading term.
The leading term = √7
Thus, the degree of the provided polynomial is 18, and the leading term is √7.
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find the missing number in ?/4 = 27/36
Answers
[tex]\text{First I would recommend replacing the question mark with x}\\\text{We have two ratios, }\\\text{and we need to solve that hard-looking equation}\\\text{in terms of x}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\text{We can multiply x times 36:: 36x}\\\text{We can multiply 4 times 27:: 108}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\text{Now it's easier to solve for x:: 36x=108; x=3}\\\text{ (we divided by 36 on both sides of the = sign)}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\text{The missing number is 3}[/tex]
Determine a, given that A = 63°, C = 49°, and c = 3. Round answers to the nearest whole number. Do not use a decimal point or extra spaces in the answer or it will be marked incorrect. a =
Answers
The value of a given that A = 63°, C = 49°, and c = 3 is 4 units
How to determine the value of a?The given parameters are:
A = 63°, C = 49°, and c = 3
Using the law of sines, we have:
a/sin(A) = c/sin(C)
So, we have:
a/sin(63) = 3/sin(49)
Multiply both sides by sin(63)
a = sin(63) * 3/sin(49)
Evaluate the product
a = 4
Hence, the value of a is 4 units
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The graph below have the same shape. What is the equation of the red graph
Answers
Answer:
G(x)=x³-1
because it intersect at the negative side of y
Answer:
g(x) = x³ - 1
(option C)
Step-by-step explanation:
We know that the shape of the graph has not changed, as stated in the question, meaning that the change has not happened as a direct change to x (like 2x³ instead of x³).
The entire graph has been moved down and not left/right, which would have happened inside the parenthesis (like g(x) = (x³ - 3)).
Because it has been shifted down (as evident by the y-intercept), and we know that the shape has not changed, we know that the original function was shifted down 1 --which can be expressed by the equation g(x) = x³-1
Show how to solve it step by step
tan(x)cot(x)=1
Answers
There are two ways to confirm the identity.
Method 1
[tex]\tan(x)\cot(x) = 1\\\\\tan(x)\frac{1}{\tan(x)} = 1\\\\\frac{\tan(x)}{\tan(x)} = 1\\\\1 = 1 \ \ \checkmark\\\\[/tex]
--------------------------------------------
Method 2
[tex]\tan(x)\cot(x) = 1\\\\\left(\frac{\sin(x)}{\cos(x)}\right)\left(\frac{\cos(x)}{\sin(x)}\right) = 1\\\\\frac{\sin(x)\cos(x)}{\cos(x)\sin(x)} = 1\\\\\frac{\sin(x)}{\sin(x)} = 1\\\\1 = 1 \ \ \checkmark\\\\[/tex]
The average of 4 numbers is 9. If one of the numbers is 7, What is the sun of the other 3 numbers?
Answers
Answer:
Step-by-step explanation:
Comment
If 4 numbers have an average of 9, then total of the 4 numbers is 4 * 9 = 36.
If one of the 4 numbers is a 7, then
7 + x = 36 where x is the sum of the other 3 numbers.
7 + x = 36 Subtract 7 from both sides
7- 7 +x = 36 - 7
x = 29
Answer 29
Ahmed is three times as old as Suad. Deeqa is three times o Ahmed. If Deeqa is 39 years old. How old is Suad?
Answers
Answer:
Suad is 4.333 years old.
Step-by-Step explanation:
let x = Suad's age
let y = Deeqa's age
let z = Ahmed's age
y = 3x
z = 3y = 3(3x)
but z = 39
3(3x) = 39
x = 4.33333
A cliff on the seashore is eroding at the rate of 17 cm per year. Write and solve an equation to find the number of years in which the cliff will erode 85cm.
Answers
Answer: 0.2 years
Step-by-step explanation:
you loaned a friend $100 and will charge him 5% annual simple interest when he pay it back
Answers
The amount of interest after 3 years will be $15.
The complete question is given below.
You loaned a friend $100 and will charge him 5% annual simple interest when he pay it back. What is the amount of interest after 3 years?
What is simple interest?Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.
The interest is given as
I = (P × R × T) / 100
Where, P is the initial amount, R is simple interest rate, and T is the time.
We have
P = $100
R = 5%
T = 3 years
Then the interest will be
I = (100 × 5 × 3) / 100
I = $15
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in case of severe pathologic hypersecretory conditions a physician may order ZantacR up to 6 g/day if the patient is to be given 1.5 g/day divided into four doses what is the amount to administer per dose?
Answers
Step-by-step explanation:
sorry sorry ^$£%£$¥#^÷£=₩€%¥=£=;÷¥÷¥9=
Determine the value of x.
Answers
Answer: 75
Step-by-step explanation:
For the lines to be parallel, this means the given angles have to be congruent (because then the lines will be parallel by the converse of the corresponding angles theorem)
2x - 45 = x + 30 [congruent angles have equal measure]x - 45 = 30 [subtract x from both sides]x = 75 [add 45 to both sides]A menu has five choices of appetizers
Answers
The number of the meals possible is 350.
The complete question is given below:-
A menu has 5 choices of appetizers, ten main courses, and seven desserts. How many meals are possible?
What is the combination?The arrangement of the different things or numbers in a number of ways is called the combination.
Given that:-
A menu has 5 choices of appetizers, ten main courses, and seven desserts.The number of the combination of the meals will be calculated as:-
N = 5 x 10 x 7
N = 350
Therefore the number of the meals possible is 350.
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Ratio 6 to 5 of 20000
Answers
Answer:
24000
Step-by-step explanation:
6/5×20000
=24000
If P(n) and Q(n) are polynomials of degree j and k, respectively, then the series
Infinite
Σ P(n)/Q(n)
n=1
converges if j < k − 1 and diverges if j ≥ k – 1.
Use the polynomial test given above to determine whether the series converges or diverges.
Infinite
Σ 1/(n)^8 +7
n=1
O converges
Odiverges
Answers
Answer:
converges
Step-by-step explanation:
well the two polynomials in the series are 1 and n^8 (I'm assuming the +7 is not in the decimal but it seems to not matter). The degree of the polynomial 1 is 0 which can be represented by 1x^0. The second polynomial in the denominator has a degree of 8. So j = 0 and k = 8. Since 0 < (8-1)
0 < 7 the series converges
A manufacturing company regularly conducts quality control checks at specified periods on the products it manufactures. Historically, the failure rate for LED light bulbs that the company
manufactures is 14%. Suppose a random sample of 10 LED light bulbs is selected. Complete parts (a) through (d) below.
a. What is the probability that none of the LED light bulbs are defective?
The probability that none of the LED light bulbs are defective is
(Type an integer or a decint. Round to four decimal places as needed.)
Answers
A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. The probability that none of the LED light bulbs are defective is 0.2213.
What is Binomial distribution?A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,
P(x) = ⁿCₓ (pˣ) (q⁽ⁿ⁻ˣ⁾)
Where,
x is the number of successes needed,
n is the number of trials or sample size,
p is the probability of a single success, and
q is the probability of a single failure.
Given the probability of a bulb being a failure is 14%, therefore, the probability of bulb passing the quality check is 86%.
Let the probability of success be defined as 0.14 for binomial distribution, and the probability for failure be 0.86. Therefore, The probability that none of the LED light bulbs are defective is
P(x=0) = ¹⁰C₀ (0.14)⁰ (0.86)¹⁰ = 0.2213
Hence, The probability that none of the LED light bulbs are defective is 0.2213.
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What is the length of the line?
Answers
If ur talking about vectors It’s (6,1)
Find all (a, b, c, d) in R4
such that the given set is orthogonal.
{(1, 2, 1, 0), (1, −1, 1, 3), (2, −1, 0, 1), (a, b, c, d)}
Answers
Answer:
[tex]\left[\begin{array}{}0&\\1&\\-2&\\1&\end{array}\right][/tex] t in R Correct option (B)
Step-by-step explanation:
Orthogonal vectors : We say that 2 vectors are orthogonal if they are perpendicular to each other. i.e. the dot product of the two vectors is zero.
Dot product : The dot product of two vectors is equal to the sum of the products of the individual components of the two vectors.
for the given vector (a, b, c, d) to be orthogonal its dot product with each vector must be 0
therefore (1, 2, 1, 0).(a, b, c, d) = 0
a + 2b+ c+ 0 = 0 -------- (i)
similarly (1, -1, 1, 3 ).(a, b, c, d) = 0
a - b + c + 3d = 0 -------- (ii)
(2, -1, 0, 1).(a, b, c, d) = 0
2a - b + 0 + d = 0 ---------- (iii)
subtracting equation (i) from (ii)
a - b + c + 3d - a - 2b - c - 0 = 0
-3b + 3d = 0
b = d
substituting b = d in (iii)
2a + b + 0 + b = 0
2a + 2b = 0
a = 0
substituting a = 0 , b = d in (i)
0 + 2d + c + 0 = 0
c = -2d
thus for any t ∈ R, vector(0, t, -2t, t) will make the given set orthogonal
the above vector can also be written as (0, 1, -2, 1)
therefor option B is correct
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Neil started a stamp collection with 12 stamps. Every week, he adds 4 more stamps to the collection. Which function f represents the relationship between the number of stamps (s) and the number of weeks (w)?
A.
s = f(w) = 12 + 4w
B.
w = f(s) = 12s + 4
C.
s = f(w) = 12 + 4s
D.
w = f(s) = 12w + s
E.
s = f(w) = s – 12
Answers
The function s = f(w) = 12 + 4w represents the relationship between the number of stamps (s) and the number of weeks (w) option (A) is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have:
Neil started a stamp collection with 12 stamps. Every week, he adds 4 more stamps to the collection.
The number of stamps is s and the number of weeks is w.
s = f(w) = 12 + 4w
Because Every week, he adds 4 more stamps to the collection
Thus, the function s = f(w) = 12 + 4w represents the relationship between the number of stamps (s) and the number of weeks (w) option (A) is correct.
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What is the product?
3.[1 -4 5-7]
Answers
Answer:
-26
Step-by-step explanation:
Multiply -4 by 7
1-20-7
Subtract 20 from 1
-19-7
Subtract 7 from -19
-26
Fill in the blank to make the tw
7
9
||
0
54
X
Answers
Answer:
lol
79*540=lol haha
Step-by-step explanation:
then lol lala lol hahahaha hahaha ten another big lol get it lollalol