Answer:
x=3 and x=-1
Step-by-step explanation:
Given Descartes' Rule of Signs, there is only one positive root and one negative root.
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient.
So P could be +1, -1, +3, or -3, while Q could be 1 or -1.
Therefore, P/Q could be +1, -1, +3, or -3.
Then we use synthetic division to find the correct factor(s):
1 | 1 -1 -5 -3
___ 1_0_ -5
1 0 -5 | -8
So (x-1) is not a factor
-1 | 1 -1 -5 -3
___-1_2_ 3
1 -2 -3 | 0
So (x+1) is a factor where the quotient is x^2-2x-3 or (x-3)(x+1)
3 | 1 -1 -5 -3
___ 3_6_ 3
1 2 1 | 0
So (x-3) is a factor where the quotient is x^2+2x+1 or (x+1)^2
Given (x-3) and (x+1) are factors, we now use the Zero Product Property:
(x-3)(x+1)=0
x-3=0
x=3
x+1=0
x=-1
So the roots are x=3 and x=-1
(15 points) Find the number of elements in A1∪A2∪A3 if there are 102 elements in A1, 992 elements in A2 and 9975 elements in A3 in each of the following situations:
(a) The sets are pairwise disjoint.
(b) A1⊆A2⊆A3.
(c) There are 14 elements common to each pair of sets and 4 elements in all three sets.
From the union operation between sets, we have that the number of elements for each case will be as follows:
a) 11069.
b) 9975.
c) 11031.
What is the union operation between sets?The union operation between sets is the set that contains all elements that belong to at least one of the sets.
In item a, if the sets are disjoint, all the elements belong to only one set, and the number of elements in A1∪A2∪A3 is given by:
102 + 992 + 9975 = 11069.
For item b, if they are all contained into A3, the number of elements is the cardinality of A3, given by 9975.
For item c, we have that:
There are 4 elements in all three sets.Hence 14 - 4 = 10 common to A1 and A2 but not A3.Hence 14 - 4 = 10 common to A1 and A3 but not A2.Hence 14 - 4 = 10 common to A2 and A3 but not A1.102 - (4 + 2 x 10) = 78 that belong to only A1.992 - (4 + 2 x 10) = 968 that belong to only A2.9975 - (4 + 2 x 10) = 9951 that belong to only A3.Hence:
n(A1∪A2∪A3) = 4 + 3 x 10 + 78 + 968 + 9951 = 11031.
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The ratio of boys to girls in math class is 2:4. If there are 24 students
in total in the class, how many boys and girls are there?
Answer:
8 boys and 16 girls
Step-by-step explanation:
2 boys plus 4 girls is six and six goes into 24 four times so 2 times four is eight and 4 times four is 16
Answer:
Step-by-step explanation: Since there are 24 students in total and the ratio is 2:4 then divide 24 by (2+4) which is 4. So the amount of boys is 2x4 which is 8. The amount of girls is 4x4 which is 16. 8+16=24
The product of a number and 10
please help me. I will give extra points and a Brainly.
Answer:
All I can think of is ¨pattern¨
help with theses answer please
Answer: correct me if I’m wrong
Step-by-step explanation:
How many rectangles (including squares) are there in a 4x4 square
Answer:
70 squares
Step-by-step explanation:
this is my answer to your question
Answer:
Hello,
100
Step-by-step explanation:
a square 4*4 : wide=4 , lenght=4
number of rectangles= wide*(wide+1)*lenght*(lenght+1) /4 = 4*5*4*5/4=100
Proof:
1 per 1 : 16 (rectangles )
1 per 2: 3*4=12
1 per 3: 2*4=8
1 per 4: 1*4=4 so 4*(4+3+2+1)=4*10=40
2 per 1: 4*3
2 per 2: 3*3
2 per 3: 2*3
2 per 4: 1*3 so 3*(4+3+2+1)=30
3 per 1: 4*2
3 per 2: 3*2
3 per 3: 2*2
3 per 4: 1*2 so 2*(4+3+2+1)=20
4 per 1: 4
4 per 2: 3
4 per 3: 2
4 per 4: 1 so 1*(4+3+2+1)=10
Total=40+30+20+10=(4+3+2+1)*(4+3+2+1)=100
What is an integer between -5. And -6
Answer:
does not exist
Step-by-step explanation:
You want an integer between -5 and -6.
IntegersThe integers -5 and -6 are consecutive integers. There are no integers between these values. (That's what "consecutive" means.)
If f(x)=−7ex, find f(2) rounded to the nearest tenth.
Answer:
Step-by-step explanation:
f(x)=-7ex
f(2)=-7e(2)
f(2)=-10
a light bulb consumes 2400 watts-hour per day. how many watts-hour does it consume in 5 days and 12 hours
The number of watts it will consume is 436.32
How the calculate the number of watts ?A light bulb consumes 2400 watts/hour
The number of watts it will consume in 5 days 12 hours can be calculated as follows
The first step is to change 5 days 12 hours to hours
120 hours + 12 hours
= 132 hours
The bulb consumes 2400 watts per hour
= 2400/132
= 18.18
The number of watts consumed in 5 days 12 hours is
= 24 × 18.18
= 436.32
Hence the light bulb will consume 436.32 watt-hour in 5 days 12 hours
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+87 + (4 + 8) = (7 + 4) + what property is
Answer:
87+(4+8)=(7+4)+x
87+12=11+x
87+12-11=x
88=x
Goofy ahh questions are hard
Answer:
True sometimes when it is stressful.
Step-by-step explanation:
Answer:
Step-by-step explanation:
your very right
[tex] \rm\sum \limits_{n = 2}^{ \infty } \frac{1}{( {n}^{2} - 1 {)}^{2} } \\ [/tex]
Partial fractions:
[tex]\displaystyle \frac1{(n^2-1)^2} = \dfrac14 \left(\frac1{n+1} - \frac1{n-1} + \frac1{(n+1)^2} + \frac1{(n-1)^2}\right)[/tex]
Now evaluate the sums. The first two terms form a telescoping sum,
[tex]\displaystyle \sum_{n=2}^\infty \left(\frac1{n+1} - \frac1{n-1}\right) = \sum_{n=1}^\infty \left(\frac1{n+2} - \frac1n\right) \\\\ ~~~~~~~~ = \lim_{N\to\infty} \sum_{n=1}^N \left(\frac1{n+2} - \frac1n\right) \\\\ ~~~~~~~~ = \lim_{N\to\infty} \left(\frac1{N+2} + \frac1{N+1} - 1 - \frac12\right) \\\\ ~~~~~~~~= -\frac32[/tex]
The others are flavors of [tex]\zeta(2)[/tex].
[tex]\displaystyle \sum_{n=2}^\infty \frac1{(n+1)^2} = \sum_{n=3}^\infty \frac1{n^2} \\\\ ~~~~~~~~~~~~~~~~~ = \sum_{n=1}^\infty \frac1{n^2} - 1 - \frac1{2^2} \\\\ ~~~~~~~~~~~~~~~~~ = \frac{\pi^2}6 - \frac54[/tex]
[tex]\displaystyle \sum_{n=2}^\infty \frac1{(n-1)^2} = \sum_{n=1}^\infty \frac1{n^2} \\\\ ~~~~~~~~~~~~~~~~~ = \frac{\pi^2}6[/tex]
It follows that
[tex]\displaystyle \sum_{n=2}^\infty \frac1{(n^2-1)^2} = \frac14 \left(-\frac32 + \left(\frac{\pi^2}6 - \frac54\right) + \frac{\pi^2}6\right) = \boxed{\frac{\pi^2}{12} - \frac{11}{16}}[/tex]
A rectangle has side lengths of 7units and (x + 4) units. When multiplied the area is 70 units². Write and solve an equation that will allow you to find the value of x.
Answer:
7(x + 4) = 70
x = 6
Step-by-step explanation:
7(x + 4) = 70 Distribute the 7. Multiply everything inside the parentheses by 7
7x + 28 =70 Subtract 28 from both sides of the equation
7x = 42 Divide both sides by 7
x = 6
if two intersecting lines are not perpendicular, then they form which two types of angles
Square root of 16 multiply by 35
Answer:
140
Step-by-step explanation:
the square root of 16 is 4 so do that times 35
The Sugar Sweet Company will choose from two companies to transport its sugar to market. The first company charges $5500 to rent trucks plus an additional fee of $200.25 for each ton of sugar. The second company charges $5041 to rent trucks plus an additional fee of $225.75 for each ton of sugar.
The computation shows that the tons of sugar when they'll have same price is 18 tons.
How to compute the value?The first company charges $5500 to rent trucks plus an additional fee of $200.25. Thai will be:
= 5500 + (200.25 × s)
= 5500 + 200.25s
where s = tons of sugar
The second company charges $5041 to rent trucks plus an additional fee of $225.75 for each ton of sugar. This will be:
5041 + 225.75s
Then we will equate both of them. This will be:
5500 + 200.25s = 5041 + 225.75s
5500 - 5041 = 225.75d - 200.25s
459 = 25.5s
s = 459/25.5
s = 18
At 18 tons, they'll have same price.
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The Sugar Sweet Company will choose from two companies to transport its sugar to market. The first company charges $5500 to rent trucks plus an additional fee of $200.25 for each ton of sugar. The second company charges $5041 to rent trucks plus an additional fee of $225.75 for each ton of sugar. For want mount if sugar do they charge the same price.
Subtract the polynomials. Indicate the degree of the resulting polynomial.
(10x^4y^2-9x^3y-9y)-(5x^4^y2+10x^3y+12y-8x)
The degree of the resulting polynomial, 5x^4^y² - x^3y - 12y + 8x, after subtraction is: degree 4.
How to Subtract Polynomials?Given, (10x^4y^2 - 9x^3y - 9y) - (5x^4^y2 + 10x^3y + 12y - 8x), to subtract, open the parentheses using the distributive property.
10x^4y^2 - 9x^3y - 9y - 5x^4^y² - 10x^3y - 12y + 8x
Combine like terms together
10x^4y^2 - 5x^4^y² - 9x^3y - 10x^3y - 9y - 12y + 8x
5x^4^y² - x^3y - 12y + 8x
The highest degree is 4. This determines the degree of a polynomial.
Therefore, the degree of the resulting polynomial, 5x^4^y² - x^3y - 12y + 8x, after subtraction is: degree 4.
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p^2+3p+1=0 using completing the square method
Answer:
Answer is in the picture attached
In a photograph, allison stands next to her brother caleb
The actual height of Caleb based on the ratio in the photograph and actual is 48 inches.
What are the ratio and proportion?The ratio is the division of the two numbers.
Proportion is the relation of a variable with another. It could be direct or inverse.
Let's say Allison and Caleb's height in the photograph is A' and C' while in actuality it is A and C.
Since the ratio of height in the photograph will same as the ratio in actual life.
Thereby,
C/A = C'/A'
C/60 = 3.2/4
C = 192/4
C = 48 inches.
Hence "The actual height of Caleb based on the ratio in the photograph and actual is 48 inches".
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Given question is incomplete complete question follows ;
In a photograph, Alison stands next to her brother Caleb. Alison is 4 cm tall in the photograph. Her actual height is 60 in. Caleb is 3.2 cm tall in the photograph.
What is his actual height?
(Show your work)
PLEASE HELP ASAP!
What is the upper bound of the function?
f(x)= 3x^4 -7x^3 +5x -3
( ^4 and ^3 are exponents)
The term of highest degree is given as 3x⁴,and it has a positive coefficient. The upper bound is +∞.
What is the degree of a polynomial ?To determine the degree of a polynomial just observe the highest power of the given variable.
We have polynomial given by f(x) = 3x⁴ - 7x³ +5x -3
Here we can see that it is a polynomial in of degree 4.
We know that a polynomial of degree has n number of roots so it is obvious a polynomial of degree 4 has 4 roots.
The function that tends to infinity as x goes in both the positive and negative directions.
The term of highest degree is given as 3x⁴,and it has a positive coefficient.
The upper bound is +∞.
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Panchito walks 9.75 kilometers in 90 minutes what is the unit rate in kilometers per hour
Answer:
6.5 kilometers per hour
Step-by-step explanation:
90 minutes is 1 1/2 hours.
to find the unit rate you would divide the distance by the time so you would divide 9.75 by 1.5 (1.5 is the decimal version of 1 1/2) which would give you 6.5 kilometers per hour
Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 5 more than 4 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 95 ?
Mark has 18 and Don has 77 number of marble to sell.
Let’s say Mark has x number of marble and Don’s marble number is y.
According to this problem we have,
Y = 4x +5
And x + y = 95
Or, x + 4x + 5 = 95
Or, 5x = 90
Or, x = 18 and y = 77
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Convert 1/2 into a fraction whose denominator is 10. Then write the corresponding decimal number
Answer:
• 5/10
• 0.5
Step-by-step explanation:
1.) if you multiply the numerator by 5 and the denominator by 5 you are left with a fraction of 5/10.
2.) the fraction line represents division. So 5 ÷ 10 = 0.5.
1. A market research survey in which 60 consumers were contacted states that 65% of all consumers of a certain product were motivated by the product's advertising. Find the confidence limits for the proportion of consumers motivated by advertising in the population, given a confidence level equal to 0.95.
The confidence limits for the proportion of consumers motivated by advertising in the population, given a confidence level equal to 0.95. is; CI = (0.47, 0.77)
How to find confidence Interval of Proportions?We are given;
Sample Size; n = 60
sample proportion; p' = 65% = 0.65
Confidence level = 0.95
Now, formula for confidence interval of proportion is;
CI = p' ± z√(p(1 - p)/n)
At CL of 95%, z = 1.96Thus;
CI = 0.65 ± 1.96√(0.65(1 - 0.65)/60)
CI = 0.65 ± 1.96√0.00379167
CI = 0.65 ± 0.12
CI = (0.65 - 0.12), (0.65 + 0.12)
CI = (0.47, 0.77)
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HELP ME WITH THISSSS
Using it's concept, the probability that a randomly selected boy attended the dance is:
7/9.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
From the table, we have that:
There are 49 + 14 = 63 boys.Of those, 49 attended the dance.Hence the probability that a randomly selected boy attended the dance is given as follows:
p = 49/63 = 7/9.
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A survey of 800 school employees yielded the following information 430 were instructors 595 were full time faculty and 340 of the instructors were full time
Which of these could be an option after high school for Jon, an active person, who is interested in higher education but who doesn't want to take out student loans?
O Sign up for the military
O Apply for college
O
Take a reflection year
Attend a technical school
The option after high school for Jon, an active person, who is interested in higher education but who doesn't want to take out student loans is to take a reflection year.
How to illustrate the information?It should be noted that based on the information, the inference has to do with the conclusion that one gets from the information or evidence that is given earlier.
In this instance, it should be mentioned that Jon, an energetic individual interested in further education but unwilling to take out student debt, has the choice to take a reflection year following high school.
In conclusion, the correct option is C.
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If angle YXZ measures 90 degrees, which statement is true?
O. segment XZ is perpendicular to segment WY
O. WX =XY
O. segment XZ is a perpendicular bisector of segment WY
O. X is the midpoint of segment WY
Answer:
its the first alternative
the odle show the fraction 2/3 a student uses the model to find the product of 5/2 and 2/3
It should be noted that the product of the fractions 5/2 and 2/3 will be 5/3.
What is a fraction?It should be noted that this is a number that is expressed as a quotient, in which a numerator is divided by a denominator.
Therefore, it should be noted that the product of the fractions 5/2 and 2/3 will be illustrated as thus:
= 5/2 × 2/3
= 5/3.
Therefore, the product of the fractions 5/2 and 2/3 will be 5/3.
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rofessor Frank Nabarro insists that all senior physics majors take his notorious physics aptitude test. The test is so tough that anyone not going on to a career in physics has no hope of passing, whereas 55% of the seniors who do go on to a career in physics still fail the test. Further, 75% of all senior physics majors in fact go on to a career in physics. Assuming that you fail the test, what is the probability that you will not go on to a career in physics? (Round your answer to four decimal places.)
The probability that you will not go on to a career in physics is 0.215.
How to calculate the probability?From the information, the test is so tough that anyone not going on to a career in physics has no hope of passing, whereas 55% of the seniors who do go on to a career in physics still fail the test and 75% of all senior physics majors in fact go on to a career in physics.
Therefore, the probability that you will not go on to a career in physics will be:
= (1 - 0.75) / (0.75 × 0.55) + (0.75)
= 0.25 / (1.1625)
= 0.215
Therefore, the probability that you will not go on to a career in physics is 0.215.
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