What are the solutions of the system? Solve by graphing. y=x2-2x-1 y = -2
Answers
1. Rewrite the equations:
y=x²-2x-1 (i)
y=-2 (ii)
2. Then:
(i)=(ii)
-2=x²-2x-1
3. Now, you must order the terms and and factorize, as below:
(x-1)(x-1)=0
(x-1)²=0
4. The solution is:
x=1
You can see that the graphs attached touch each other in x=1. Therefore, the solution is x=1
Related Questions
Action wheels manufacturers models of antique cars for collectors. In August , it manufactured 300 model cars. In September, action wheels manufactured 5% fewer model cars than in August . What is the difference in the numbers of cars manufactured in August and September?
Answers
The difference in the number of cars manufactured in August and September is 15 cars.
The difference in the number of cars manufactured in August and September can be calculated as follows:
In August, Action Wheels manufactured 300 model cars.In September, they manufactured 5% fewer cars than in August, which means they made 95% of the cars they made in August.Calculating the number of cars manufactured in September: 300 * 0.95 = 285 cars.Therefore, the difference in the numbers of cars manufactured in August and September is 300 - 285 = 15 cars.A certain lottery has 3434 numbers. in how many different ways can 44 of the numbers beâ selected? (assume that order of selection is notâ important.)
Answers
A certain lottery has 34 numbers. in how many different ways can 4 of the numbers be selected? (assume that order of selection is not important.)
we know that
C=n!/[(n-r)!*r!]
n=34
r=4
then
C=34!/[(34-4)!*4!]=34*33*32*31/[4*3*2*1]=46376
the answer is 46376
Deposit $400 into an account that pays simple interest at rate of 4% per year how much interest will she be paid in the first 6 years
Answers
Simple interest = 4%
Simple interest for one year = 4% of $400 = 0.04 x 400 = $16
Simple interest for 6 years = 16 x 6 = $96
Total interest for 6 years is $96
HELP PLEASE!!!!!!!
Which of the following is equal to 4 and 1 over 2 divided by 2 and 2 over 3?
4 and 1 over 2 times 2 and 3 over 2
9 over 2 times 8 over 3
9 over 2 times 3 over 8
41 over 2 times 3 over 22
Answers
.. = (9/2)*(3/8) . . . . . . . . . . . . . . the 3rd selection
_____
A mixed number is converted to an improper fraction by
.. a +b/c = (ac +b)/c
Of course, dividing by a fraction is the same as multiplying by its inverse.
.. (a/b) / (c/d) = (a/b) * (d/c)
The mean of people in the sample of households of 7th-grade students is 4.3. The mean of people in the sample of households for 8th-grade students is 4.5. What might Principal Coleman infer or predict about the entire population based on the data?
Answers
Answer:
The mean of something is the "average"
For example, if the mean of people in the households of 7th-grade students is 4.3, this means that if you go to a random house of a 7th-grade student, you can expect around 4 people in there.
Now, for the 7th-grade students, the mean is 4.5, just a 0.2 bigger. (This means that, on average, there is more people in the 8th-grade student's households)
So Principal Coleman can infer that the amount of people in the households of 7th-grade students and 8th-grade students is almost the same, wherein the 8th-grade students there is a small chance of finding more people, but this difference is almost depreciable.
How many possible outcomes exist when Louisa spins the spinner below twice? The spinner is numbered from 1-8.
Answers
So for two spins there are 8*8=64 possible outcomes, order counts, i.e. 5-3 is different from 3-5.
Answer:
The total number of possible outcomes are:
64
Step-by-step explanation:
It is given that:
Louisa spins the spinner below twice.
The spinner is numbered from 1-8.
Now, on spinning the spinner twice we obtain the sample space as:
(1,1) (1,2)....................(1,8)
(2,1) (2,2)...................(2,8)
(3,1) (3,2)..................(3,8)
(4,1) (4,2)..................(4,8)
(5,1) (5,2)..................(5,8)
(6,1) (6,2)..................(6,8)
(7,1) (7,2)..................(7,8)
(8,1) (8,2)..................(8,8)
Hence, the total number of outcomes is equal to the number of elements in sample space.
Hence, the total number of possible outcomes are:
64
Find f '(0.3) for f of x equals the integral from 0 to x of the arccosine of t, dt
Answers
By the fundamental theorem of calculus,
[tex]\displaystyle\frac{\mathrm d}{\mathrm dx}\int_0^x\cos^{-1}t\,\mathrm dt=\cos^{-1}x[/tex]
so that
[tex]f'(0.3)=\cos^{-1}0.3\approx1.266[/tex]
Suppose p(x1) = .75 and p(y2 | x1) = .40. what is the joint probability of x1 and y2?
Answers
[tex]\mathbb P(Y_2\mid X_1)=\dfrac{\mathbb P(Y_2\cap X_1)}{\mathbb P(X_1)}[/tex]
so
[tex]\mathbb P(Y_2\cap X_1)=0.40\times0.75=0.3[/tex]
The joint probability of x1 and y2 is P (Y₂/X₁ ) = P(Y₂ ∩ X₁ )/ P (X₁) will be 0.3.
What is the probability about?In the joint probability of x1 and y2 is P (Y₂/X₁ )= P(Y₂ ∩ X₁ )/ P (X₁).
Therefore:
P(Y₂ ∩ X₁ )
=0.40 x 0.75
= 0.3
Therefore by following the law of conditional probability, the outcome of the The joint probability of x1 and y2 is P (Y₂/X₁ ) = P(Y₂ ∩ X₁ )/ P (X₁) will be 0.3.
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A biologist studied the populations of common guppies and Endler's guppies over a 6-year period. the biologist modeled the populations, in tens of thousands, with the following polynomials where x is time, in years.
common guppies: 3.1x^2+6x+0.3
Endler's guppies: 4.2x^2-5.2x+1
what polynomial models the total number of common and Endler's guppies
Answers
To get our answers we need to add those two polynomials. We add polynomials by adding their like terms. Like terms are those that have the same exponent.
[tex]3.1x^2+6x+0.3+4.2x^2-5.2x+1=\\=(3.1x^2+4.2x^2)+(6x-5.2x)+(0.3+1)=\\ =7.3x^2+0.8x+1.3[/tex]
So the total amount of guppies would be modeled using this polynomial:
[tex]7.3x^2+0.8x+1.3[/tex]
what polynomial models the total number of common and Endler's guppies
your answer will be:
7.3x^2+0.8+1.3
Step-by-step explanation:
this answer correct for 2022
4j-2/2=4j+5
4j minus 2 divided by 2 equals 4j plus 5 ?
Answers
[tex] \frac{4j - 2}{2} = 4j + 5[/tex]
then this is the answer:
[tex] \frac{4j - 2}{2} \times 2 = 2 \times (4j + 5)[/tex]
[tex]4j - 2 = 8j + 10[/tex]
4j - 2 - 4j = 8j + 10 - 4j
-2 = 4j + 10
-2 - 10 = 4j + 10 - 10
-12 = 4j
[tex] \frac{ - 12}{4} = \frac{4j}{4} [/tex]
-3 = j
j = -3
The solution to the equation (4j - 2) / 2 = 4j + 5 is j = -3. The equation was simplified by eliminating fractions and isolating the variable j through algebraic steps.
To solve the equation (4j - 2) / 2 = 4j + 5 for the variable j, you can follow these steps:
1. First, simplify both sides of the equation:
(4j - 2) / 2 = 4j + 5
2. Multiply both sides of the equation by 2 to eliminate the fraction:
4j - 2 = 2 * (4j + 5)
3. Distribute the 2 on the right side:
4j - 2 = 8j + 10
4. Move the variable terms to one side of the equation and the constants to the other side. You can do this by subtracting 8j from both sides:
4j - 8j - 2 = 10
5. Combine like terms:
-4j - 2 = 10
6. Add 2 to both sides to isolate the variable term:
-4j = 10 + 2
-4j = 12
7. Finally, divide both sides by -4 to solve for j:
j = 12 / -4
j = -3
So, the solution to the equation is j = -3.
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Which describes the slope of this line?
Number graph ranging from negative five to five on the x and y axes. A line is drawn on the graph that passes through (zero, negative three) and (two, one).
negative slope
positive slope
undefined slope
zero slope
Answers
The slope coefficient is S= (yb-ya)/(xb-xa)
S= (1-(-3))/(2-0) => S= (1+3)/2 = 4/2= +2 => S= +2
The correct answer is positive slope
Good luck!!!
a square has 4 right angle corners. give another shape with 4 right angle corners
Answers
find d for the arithmetic series with S17=-170 and a1=2
Answers
[tex]\bf \textit{ sum of a finite arithmetic sequence}\\\\ S_n=\cfrac{n(a_1+a_n)}{2}\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ ----------\\ n=17\\ S_{17}=-170\\ a_1=2 \end{cases} \\\\\\ -170=\cfrac{17(2+a_{17})}{2}\implies \cfrac{-170}{17}=\cfrac{(2+a_{17})}{2} \\\\\\ -10=\cfrac{(2+a_{17})}{2}\implies -20=2+a_{17}\implies -22=a_{17}[/tex]
well, since the 17th term is that much, let's check what "d" is then anyway,
[tex]\bf n^{th}\textit{ term of an arithmetic sequence}\\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference}\\ ----------\\ n=17\\ a_{17}=-22\\ a_1=2 \end{cases} \\\\\\ -22=2+(17-1)d\implies -22=2+16d\implies -24=16d \\\\\\ \cfrac{-24}{16}=d\implies -\cfrac{3}{2}=d[/tex]
In a circle with a radius of 26.9 m, an arc is intercepted by a central angle of 9π5 radians.
What is the arc length?
Use 3.14 for π and round your final answer to the nearest hundredth.
Make sure to show your calculations.
Answers
find the length of a circumference
L=2*pi*r-------------> 2*pi*26.9=53.8*pi m
Step 2
find the arc length
if 2*pi radians --------------> 53.8*pi m
(9/5)*pi radians------------> X
X=[(9/5)*pi*53.8*pi]/[2*pi]-------------> [9*53.8*pi]/[5*2]=152.04 m
the answer is 152.04 m
152.04 is right i just took the test
your welcome ;)
Use the distributive property to create an equivalent expression to 42+6x
Answers
6(7+x)
There's the answer:)
The expression 42 + 6x is already in its simplest form and does not have a common factor to apply the distributive property to simplify it. However, factoring out 6 would rewrite it as 6(7 + x), albeit without further simplification.
To create an equivalent expression to 42 + 6x using the distributive property, we need to factor out a common term from both parts of the expression. However, this expression does not have a common factor available in both terms. The distributive property typically comes into play when you have an expression in the form of a(b + c), where you would then distribute a to both b and c. The expression 42 + 6x is simplified as much as possible, given that one term is a constant and one term is a multiple of a variable. There is no factor that can be distributed to simplify the expression further.
However, if we wanted to factor out a number to potentially simplify the expression, we might choose to factor out 6, which would change the expression to 6(7 + x), although this does not simplify it further since the original expression is already in its simplest form.
It takes 212121 minutes for 555 people to paint 777 walls. How many minutes does it take 333 people to paint 555 walls?
Answers
Solution: We are given that:
5 people can paint 7 walls in 21 minutes
Therefore, 1 person can paint 7 walls in [tex] 21 \times 5=105 [/tex] minutes
Which means 1 person can paint 1 wall in [tex] \frac{105}{7} =15 [/tex] minutes
Now, 3 people can paint 1 wall in [tex] \frac{15}{3} =5 [/tex] minutes
Therefore, 3 people can paint 5 walls in [tex] 5 \times 5=25 [/tex] minutes
Answer:
25 :)
Step-by-step explanation:
for this job , Hayden earns an hourly rate of $30. For each hour he works over 40 hours, he earns 1.5 times his regular hourly rate. In a two-week period, Hayden earns $2175 by working 40 regular hours, plus overtime. How many overtime hours did Hayden work?
Answers
Extra hour rate is 1.5×30=$45
given that he earned $2175 by working 40 regular hours, the number of overtime hours he worked will be given as follows;
let the number of overtime be x
hence total amount earned will be:
(40×30)+(45×x)=2175
1200+45x=2175
45x=2175-1200
45x=975
solving for x we get
x=975/45
x=65/3=21 2/3 hours
Three student teams collected 65 books for the school library. The first team collected 10 fewer books than the second team and the third team collected 30% of the number of books collected by first and second teams together. How many books did each team collect?
Answers
3 student teams
65 total number of books collected
first team collected 10 fewer books than the second team
the third team collected 30% of the number of books collected by first and second teams together
Let x represent the books collected by the 2nd team.
1st team: (x - 10)
2nd team: x
3rd team: 30%[x + (x-10)]
(x-10) + x + 30%[x + (x - 10)] = 65
x - 10 + x + 0.3x + 0.3x - 3 = 65
x + x + 0.3x + 0.3x = 65 + 10 + 3
2.6x = 78
x = 78/2.6
x = 30
1st team: x - 10 → 30 - 10 = 20
2nd team: x → 30
3rd team: 30%[x + (x-10)] → 0.3(30 + 30 - 10) = 0.30 (50) = 15
20 + 30 + 15 = 65
1st team got 20 books.
2nd team got 30 books.
3rd team got 15 books.
For a total of 65 books.
Team 1 -x
Team 2- x+ 10
As team 2 collected 10 books more than team 1
Team 3 -30% of (x + x+ 10)
Team 3 collected 30% of the books that team 1 and team 2 collected in total
The equation for the total number of books is;
x + x + 10 + 0.3(2x+10) = 65
2x + 10 + 0.6x + 3 = 65
2.6x +13 = 65
2.6x = 52
x = 20
Team 1-20 books
Team 2 -30 books and
Team 3 - 15 books
glenn raced his motorcycle 30 times last season. he finished first 12 times, second 5 times and crashed in 9 races. what percent of races did he crash? set up a proportion and solve.
Answers
Final answer:
Glenn crashed in 30% of the races.
Explanation:
To find the percentage of races Glenn crashed, you can set up a proportion. A proportion is an equation that states that two ratios are equivalent. Since Glenn raced 30 times and crashed 9 times, the ratio of crashes to total races is 9 crashes out of 30 races.
You can set up the proportion as follows:
Crashes / Total Races = Percentage of Crashes / 100
Plugging in the known values gives us this:
9 / 30 = Percentage of Crashes / 100
To solve for the percentage of crashes, you multiply both sides of the equation by 100:
(9 / 30)
100 = Percentage of Crashes
Simplifying gives us:
(9/3) 10 = Percentage of Crashes
Hence, the percentage of races that Glenn crashed is 30%.
Write a while loop that adjusts uservalue while uservalue is less than 0 or greater than 80. if uservalue is greater than 80, then subtract 5 from uservalue. if uservalue is less than 0, then add 10 to uservalue.
Answers
A 'while loop' can be programmed with conditions to adjust a 'user value'. If 'user value' is greater than 80, 5 would be subtracted from it. If it is less than 0, 10 would be added to it. This loop continues until 'user value' does not meet either condition.
Explanation:The question asks for a while loop in programming that modifies a value (user value) based on these conditions: if the user value is less than 0, it should be increased by 10 and if it's greater than 80, it should be decreased by 5. Here's a representative code for that:
while(user value < 0 || user value > 80) {
if(user value > 80) {user value -= 5; } else if(user value < 0) {user valuable += 10;}
This loop will continue to execute until the user value is not less than 0 or greater than 80.
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what is the gcf of the numerator and denominator of the rational expression
3x-15/x^2-x-20
A: x-5
B: x+4
C: 4
D: 5
Answers
The only common factor is (x -5).
Selection A is appropriate.
the number of sentence is an example of which multiplication property
Answers
Make a comparison between the government’s roles in a capitalist economic system versus a socialist or communist economic system.
Answers
In a Capitalist Economic System, the government is expected to guarantee the respect to private property, promulgate laws that defend economic freedom, and is an intermediary between the private sector and society. In this economic system, the government is reduced an doesn't intervene in the free market.
In a Socialist or Communist Economic System, the government redistributes goods and services, takes the means of production (private property) from their owners to put them in service of the working class, promulgate laws that limit economic freedom and heavily intervenes in the market and economy.
Have a nice day!
A capitalist economic system is built on the respect of private property and competition. Hard work and free enterprise benefit citizens more than the government can. For the most part, government intervention is reduced. However, the government does provide security and some basic services, like infrastructure, to its citizens.
Socialist and communist systems endure more government control. Citizens of these economies have a limited amount of freedom by law. The government controls the market place and the production of most goods and services.
^ My answer from Edge
What fraction is equivalent to the fraction 0/6
Answers
Since this is equal to zero, the answer could actually be any number in the demoninator and zero in the numerator.
Hope this helps!
9xa+9xb write as a product
Answers
To write the expression 9xa+9xb as a product, factor out the common factor 9x to get 9x(a+b), which is the simplified product form.
The student has presented an algebraic expression: 9xa+9xb and is requesting to rewrite it as a product. To simplify this expression, we can factor out the common factor which is present in both terms. The common factor here is 9x. When we factor out 9x, we combine the terms within the parentheses.
Here is the step-by-step simplification:
Identify the common factor in both terms, which is 9x.Factor out the 9x, resulting in 9x(a+b).This is the simplified product form of the given expression.A stop sign is a regular octagon. Each side of the sign is 12.6 in. long. The area of the stop sign is 770 in.^2. What is the length of the apothem to the nearest whole number?
Answers
hope this help
Final answer:
To determine the length of the apothem of a regular octagonal stop sign given its side length and area, use the formula for the area of a regular polygon, solve for the apothem, and then calculate it to be approximately 15 inches when rounded to the nearest whole number.
Explanation:
The student is asking how to find the length of the apothem of a regular octagonal stop sign with side lengths of 12.6 inches and a total area of 770 square inches. The apothem of a regular polygon is a line from the center to the midpoint of one of its sides and is also the radius of the inscribed circle within the polygon.
To find the apothem's length, we can use the formula for the area of a regular polygon: Area = (1/2) × Perimeter × Apothem. The perimeter (P) of the octagon is the length of one side multiplied by 8 (since an octagon has eight sides). Therefore, the perimeter is 12.6 in × 8 = 100.8 in.
We can rearrange the area formula to solve for the apothem (a): Area = (1/2) × P × a becomes a = Area × 2 / P. Substituting the known values, we get: a = 770 in² × 2 / 100.8 in, which calculates to an apothem length of approximately 15.24 inches. Round this to the nearest whole number to get an apothem length of 15 inches.
Fiona is serving iced tea and lemonade at a picnic. She has only 44 cups in which to serve the drinks. If x represents the number of glasses of iced tea and y represents the number of glasses of lemonade, which equation represents the number of glasses of iced tea she can serve?
Answers
will compute the number of glasses of tea Fiona can serve based on the number of cups used for lemonade.
Answer:
[tex]x=44-y[/tex]
Step-by-step explanation:
Let x represents the number of glasses of iced tea .
Let y represents the number of glasses of lemonade.
Now we are given that She has only 44 cups in which to serve the drinks
Since y is the number of glasses of lemonade out of 44 glasses
So, remaining glasses = [tex]44-y[/tex]
So, remaining glasses is for iced tea .
So, No. of iced tea glasses = [tex]x=44-y[/tex]
Hence She can serve [tex]x=44-y[/tex] number of glasses of iced tea serve.
Use euler's theorem to find a number x between 0 and 28 with x85 congruent to 6 modulo 35.
Answers
By Fermat-Euler theorem:
If a and n are coprime, i.e. (a,n)=1, then
a^phi(n) ≡ 1 mod n
where phi(n)=totient function, the number of positive integers less than n that is coprime with n.
for n=35, phi(35)=24 calculated as follows:
There are 10 positive integers from 1 to 34 which are NOT coprime with 35, namely {5,7,10,14,15,20,21,25,28,30}.Therefore phi(35)=34-10=24
From Fermat-Euler theorem,
x^(phi(35) = x^24 ≡ 1 modulo 35 since (24,35)=1, i.e. 24 and 35 are coprime.
=>
x^12 ≡ ± 1 modulo 35. ...........(1)
and
x^85 ≡ x^(85-3*24) ≡ x^(85-72) ≡ x^(13) ≡ 6 mod 35 ............(2)
Substituting (1) in (2)
x^(12)*x ≡ 6 mod 35
=>
(+1)*x = 6 mod 35 or (-1)*x ≡ 6 mod 35
x ≡ 6 mod 35 x ≡ -6 mod 35 (rejected)
=> x=6
So
6^85 ≡ 6 mod 35
If any clarifications are needed or if you find any errors, please post.
To find a number x between 0 and 28 with x ≡ 6 (mod 35) using Euler's theorem, we can use Euler's totient function to find the power x^24 that is congruent to 1 (mod 35). The value x = 1 satisfies the congruence, so it is a possible solution.
Explanation:To use Euler's theorem to find a number x between 0 and 28 with x ≡ 6 (mod 35), we need to find the value of x that satisfies the congruence. Euler's theorem states that if a and n are coprime positive integers, then a^φ(n) ≡ 1 (mod n), where φ(n) is the Euler's totient function of n. In this case, we need to find x such that x^φ(35) ≡ 1 (mod 35). The Euler's totient function of 35 is φ(35) = φ(5) * φ(7) = 4 * 6 = 24. Therefore, we need to find x such that x^24 ≡ 1 (mod 35).
We can start by examining the powers of x modulo 35:
x ≡ x (mod 35)
x2 ≡ x² (mod 35)
x³ ≡ x³ (mod 35)
...
x^24 ≡ 1 (mod 35)
From this, we can see that x = 1 satisfies the congruence x^24 ≡ 1 (mod 35).
Therefore, a possible value of x between 0 and 28 that satisfies x ≡ 6 (mod 35) is x = 1.
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Matt Miller, age 28, takes out $50,000 of straight-life insurance. His annual premium is $418.20. Using
the tables in the Business Math Handbook that accompanies the course textbook, determine the cash value
of his policy at the end of 20 years.
A. $13,250
B. $26,000
C. $30,000
D. $26,500
Answers
50,000/1,000 = 50 will be multiplied with 265 to get 265*50 = 13,250
So the cash value of this policy is $13,250
Ava bought a rectangular rug for her hallway. The rug is 23 yards wide and 234 yards long. What is the area of the rug as a mixed number in simplest form?
Answers
5,382 is in the simplest form
this is not a fraction, so i don't see where the simplest form comes in
The area of Ava's rectangular rug is 5382 square yards, calculated by multiplying the width (23 yards) and the length (234 yards).
To find the area of Ava's rectangular rug, we need to multiply its length and width:
Area = length × width
Using the given dimensions: 23 yards wide and 234 yards long:
Area = 23 × 234
First, let's perform the multiplication:
23 × 234 = 5382 square yards
Thus, the area of the rug is 5382 square yards as an improper fraction, which cannot be simplified further as a mixed number. Since the measurements are whole numbers, converting to a mixed number doesn't apply in this case.