Step-by-step explanation:
The factor of the polynomial is (x-2)
We know that dividing a third degree polynomial by a first degree factor will yield a quadratic of the form ax²+bx+c and possibly a remainder r,except that in this case r=0 since x-2 is a factor
We therefore equate
x³-4x²+3x+2=(x-2)(ax²+bx+c)+r
x³-4x²+3x+2=ax³+bx²+cx-2ax²-2bx-2c+r
We group terms on the RHS
x³-4x²+3x+2=ax³+x²(b-2a)+x(c-2b)-2c+r
By equating the terms on both sides,
ax³=x³,a=1
Next,
b-2a=-4
b-2(1)=-4
b-2=-4
b=-4+2
b=-2
Next,
c-2b=3
c-2(-2)=3
c+4=3
c=-1
Now we piece together our quotient quadratic using a=1,b=-2,c=-1 to obtain x²-2x-1
We now find the zeros of x²-2x-1
which are 1+√2 and 1-√2
The values of x are therefore 2,1+√2, and 1-√2
Note that I used this method in lieu of the famous polynomial division approach to teach someone also ;)
Answer:
2, 1 +/- sqrt2
or 2, 2.414, -0.414 (correct to the nearest thousandth).
Step-by-step explanation:
Let x = 2: then
f(2) = 8 - 16 + 6 + 2 = 0
So x = 2 is one of the zeros.
So one factor of the function is x-2.
If we divide the function by (x - 2) we get:
x-2)X^3-4x^2+3x+2(x^2-2x-1
x^3- 2x^2
-2x^2+3x
-2x^2+4x
-x+2
-x+2
.......
So x^2-2x-1= 0
x = [-(-2 +/- sqrt(4 - 4*-1)] / 2
x = (2 +/- sqrt8) / 2
= 1 +/-sqrt8/2
= 1 +/- sqrt2
A building is 1ft from an 11 ft fence that surrounds the property. A worker wants to wash a window in the building 14ft from the ground. He plans to place a ladder over the fence so it rests against the building. He decided he should place the ladder 11ft from the fence for stability. To the nearest tenth of a foot, how long a ladder will he need?
Answer:
L = 18,4 ft
Step-by-step explanation:
The building, the ground, and the ladder make up a right triangle, with legs:
The distance (a) between the bottom of the ladder and the building 12 ft
The distance (b) between the gound and the window 14 ft up
The hypothenuse is the length of the ladder (L)
According to Pythagoras theorem
L² = a² + b²
L = √ (12)² + (14)²
L = √ 144 + 196
L = √ 340
L = 18,4 ft
if two dice are rolled one time, find the probability of getting a sum less than or equal to 4
Answer:
The probability of getting a sum less than or equal to 4 is 1/6.
Step-by-step explanation:
When two dices are rolled, the number of outcomes are: 6*6 = 36 which is written in ordered pairs consisting of outcome of both dices.
When two dices are rolled, the number of sample space elements is:
[tex]n(S) = 36[/tex]
Let A be the event that the sum of outcomes is less than or equal to 4:
[tex]A = \{(1,1),(1,2),(1,3),(2,1),(2,2),(3,1)\}[/tex]
That implies
[tex]n(A) = 6[/tex]
The probability of getting sum less than or equal to 4 will be:
[tex]P(A) = \frac{n(A)}{n(S)} = \frac{6}{36} = \frac{1}{6}[/tex]
Hence,
The probability of getting a sum less than or equal to 4 is 1/6
The probability of getting a sum less than as well as equivalent to 4 will be "[tex]\frac{1}{6}[/tex]".
Probability:The probability that may be an outcome will happen together in random experiment. The greater the likelihood of such an occurrence, the further probable it will materialize.
Let,
The event that the sum less than as well as equivalent to 4 be "A".
According to the question,
Whenever the 2 dices are rolled, the no. of outcomes will be:
= 6 × 6
= 36
and,
The no. of sample elements will be:
n(S) = 36
Now,
A = {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (3, 1)}
The probability be:
→ P(A) = [tex]\frac{n(A)}{n(S)}[/tex]
= [tex]\frac{6}{36}[/tex]
= [tex]\frac{1}{6}[/tex]
Thus the response above is correct.
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when the Dixon family traded in their old car, it had 53,790 miles on it. they had the car for 8.25 years. on average, how many miles did they drive per year?
Answer:
6,520 miles per year
Step-by-step explanation:
53,790 divided by 8.25 equals 6,520
P(A) = 0.8, P(B) = 0.55 and P(A and B) = 0.35.
What is P(A or B)?
Work Shown:
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = 0.8 + 0.55 - 0.35
P(A or B) = 1.35 - 0.35
P(A or B) = 1
A probability of 1 means there is 100% certainty the event happens. This must mean that there are only possible outcomes are: either event A happens, or B happens, or possibly both A and B happen simultaneously.
what's 9x - 7i > 3 (3x - 7u) ?
Step-by-step explanation:
9x-7i>9x-21u
-7i>-21u
i<3u
The solution to the given inequality 9x - 7i > 3(3x - 7u) is i < 3u.
Given that:
Inequality: 9x - 7i > 3 (3x - 7u)
To solve the inequality 9x - 7i > 3(3x - 7u), follow these steps:
Step 1: Distribute the 3 on the right side of the inequality as:
9x - 7i > 9x - 21u.
Step 2: Simplify the inequality.
9x - 9x - 7i > - 21u.
Step 3: Rewrite the inequality.
After cancelling out the 9x terms, we are left with -7i > -21u.
Step 4: Divide both sides by -7.
i < 3u
Therefore, the solution to the inequality 9x - 7i > 3(3x - 7u) is i < 3u.
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A triangle with side lengths of 10, 18, and 30 inches is similar to another triangle. The shortest side of the other triangle has length 3 inches. What is the perimeter, in inches, of the smaller triangle?
Perimeter = 9.5
Perimeter = 10.6
Perimeter = 15.2
Perimeter = 17.4
Answer:
wo similar figures have a ratio of 3:5. If 1 side of the smaller figure is 9 ... 12 in. What is the length of LM? x. = 12. 24. A. 13 in. C. 16 in. A. 10 ft. B. 14.4 ft ... How long is the corresponding side of the larger polygon? A. 18 cm. B. 24 cm ... 2. 10. An equilateral triangle has side lengths of 14 inches. Find the altitude of the
Step-by-step explanation:
The perimeter of the smaller triangle will be 17.4. Then the correct option is D.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
A triangle with side lengths of 10, 18, and 30 inches is similar to another triangle.
The shortest side of the other triangle has a length of 3 inches.
Then the perimeter of the smaller triangle will be
Let the other two sides of the smaller triangle be x and y. Then we have
3/10 = x/18 = y/30
From the first two terms, we have
3/10 = x/18
x = 5.4 inches
Then from the first and third terms, we have
y/30 = 3/10
y = 9
Then the perimeter of the triangle will be
P = 3 + 5.4 + 9
P = 17.4 inches
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5. A refrigerator is on sale for $1200. That is
25% off regular price. What was the original
price?
Answer: The original price is $4,800
Step-by-step explanation:
$1,200=25%
25%*4=100%
$1,200*4=$4,800=100%
Select a symbol to compare the numbers.
7/10
0.07
Answer:
7/10>0.07
Step-by-step explanation:
You can turn 7/10 into decimal and its 0.7.
0.7 is greater than 0.07 so you would put a > sign
so the answer is 7/10>0.07
pls mark brainliest
Help help please I really need it
jack was 8 years older than priscilla. together their ages totaled 154 years. what were their ages?
Answer:
Jack is 81, Priscilla is 73
Step-by-step explanation:
Because their age difference is 8 years, we can subtract 8 from the total 154 years to get 146. Then we divide by 2 to get 73, so Priscilla is 73. Jack is 8 years older, so therefore he is 81. We can check this by adding 81 + 73 = 154.
Students from Texas, New York, Washington, Florida, and Utah identified their area of concentration at various universities. The results are listed in the table.
One of these students is selected at random. What is the probability that the student is from the state of Washington under the condition that the student studies history?
Enter a number in the box.
The probability of a random student who is from Washington and studies history is [tex]\frac{5}{33}[/tex].
What is probability?Probability is the chance of happening an incident or event. A probability is calculated by the ratio of the possible outcomes to total number of outcomes.
Given, the total number of students of History
= (30 + 17 + 20 + 32 + 33) = 132
The number of students from Washington who studies history = 20.
Therefore, the probability that the student is from the state of Washington under the condition that the student studies history is = [tex]\frac{20}{132} = \frac{5}{33}[/tex] .
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How do you say hi in chamoru?
Answer:
Step-by-step explanation:
To say Hi in Chamoru you say, "Håfa Adai" (Chamorro for "Hello").
Hope this helped!
Elizabeth spins each spinner once.
What is the probability the arrows will land on a consonant and the number 2?
20% is the answer
Hope this helps
A coordinate plane with 2 lines. The first line is labeled y equals f(x) and passes through (0, 4) and (1, 1) The second line is labeled y - g(x) and is horizontal passing through (negative 2, 2), (0, 2), and (2, 2). The lines intersect at a point that is slightly to the right of (0.5, 2).
If f(x) = −3x + 4 and g(x) = 2, solve for the value of x for which f(x) = g(x) is true.
x = ______
Answer:
2/3
Step-by-step explanation:
cuz it is
Answer:
2/3
Step-by-step explanation:
4.9 divided by 3581.9
Just help me
Answer:
.00136799
Step-by-step explanation:
4.9/3581.9 into a calculator
Answer:
.00136798905
Step-by-step explanation:
Used a calculator!
1. Which equation represents the relationship shown in the table below? (1 point)
y = -x - 3
y=x-3
y = 2x - 3
y=-2x + 3
The equation representing the relationship in the table is y = 2x - 3. The correct option is C.
What is an equation?The equation in mathematics is the relationship between the variables and the number and establishes the relationship between two or more variables.
Given data in the table:-
x y
0 -3
1 -1
2 1
3 3
The equation satisfying the values of the table will be:-
y = 2x - 3
-3 = 2 x 0 - 3=-3
-1 = 2 x 1 - 3 =-1
1 = 2 x 2 - 3 = 1
3 = 2 x 3 - 3 = 3
Therefore, the equation representing the relationship in the table is y = 2x - 3. The correct option is C.
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f(x)=0.5-2xsquared find the value of f(x) when x=0
Answer:
f(0) = 0.5
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Function NotationStep-by-step explanation:
Step 1: Define
f(x) = 0.5 - 2x²
x = 0
Step 2: Evaluate
Substitute in x: f(0) = 0.5 - 2(0)²Exponents: f(0) = 0.5 - 2(0)Multiply: f(0) = 0.5 - 0Subtract: f(0) = 0.5Answer:
f ( 0 ) = 0.5
Step-by-step explanation:
Step 1:
f ( x ) = 0.5 - 2x² Function
Step 2:
x = 0 Given
Step 3:
f ( 0 ) = 0.5 - ( 2 ( 0 ) )² Multiply
Answer:
f ( 0 ) = 0.5
Hope This Helps :)
Which situation cannot be represented by the equation 15 + x = 25?
Victor and Raul donated 25 cans of fruit to their local food bank. Victor donated 15 cans. What is, x, the number of cans Raul donated?
The day's low temperature read 15ºF. The day's high temperature read 25ºF. What is x, the amount of degrees the temperature increased throughout the day?
Jean has $25. She found $15 of the amount in her wallet and the rest in her coat pocket. What is x, the amount of money in her coat pocket?
Elizabeth worked 15 hours. Josh worked 25 hours. What is x, the amount of hours they worked together?
Answer:
the last answer about the jobs
Step-by-step explanation:
the point that doesn't lie to a straight line y=-4x+12 is
Answer:
12?
Step-by-step explanation:
Generally those who are less active have no opportunities to exercise
Answer:
False
Step-by-step explanation:
Edge 2021
remove it please......
what do you need removing? I'll try to help
4. Tom and Bina read 34 books in a month. Bina and Weiming read 58 books in the
same month. Weimning read twice as many books as Tom. How many books did
Bina read in that month?
Answer:
92
Step-by-step explanation:
the question is only asking how many books Bina read, so the amount of books Weimning read is irrelevant.
to get the answer, you have to add both the amount of books bina read in the month.
hope this helped :)
May you please help ill give out brainlyist ..
Answer:
C. is your answer dear
Step-by-step explanation:
2^3 = 8
1 = 1
Find the Length of AC. Round answers to the nearest hundredth (2 decimal places)
Answer:
32.78
Step-by-step explanation:
Assuming that we have two right triangles joined together, with one having adjacent side a, with a side of 12 ft opposite reference angle 30°, and the other one having adjacent side b, with a side of 12 ft opposite reference angle 45°. Thus, a + b = length of AC.
Let's find a and b.
Finding a:
Reference angle = 30°
Opp = 12 ft
Adj = a
Using trigonometric ratio formula, we have:
tan(30) = 12/a
Multiply both sides by a
a*tan(30) = 12
Divide both sides by tan(30)
a = 12/tan(30)
a = 20.78 (nearest hundredth)
Finding b:
Reference angle = 45°
Opp = 12 ft
Adj = b
Using trigonometric ratio formula, we have:
tan(45) = 12/b
Multiply both sides by a
b*tan(45) = 12
Divide both sides by tan(45)
b = 12/tan(45)
a = 12
Length of AC = 20.78 + 12 = 32.78
The ages of three teachers are consecutive even integers. Three times the age of the youngest teacher is 48 years more than the older teacher’s age. What is the age of the youngest teacher?A.14 B.18 C.22 D.26
Answer:
B
Step-by-step explanation:
In a company, the ratio of the number cashiers is 20:3. If there are 120 workers in the company,
how many cashiers are there ?
(A)17
(B)18
(C)21
(D) 23
9514 1404 393
Answer:
(B) 18
Step-by-step explanation:
Multiply each of the numbers in the ratio by 6.
workers : cashiers = 20 : 3 = 120 : 18
There are 18 cashiers for 120 workers.
For the state of Indiana, there are 181,560 businesses that are open during the pandemic. If this makes up only 68% of all businesses, how many total business are there in the state?
Answer:
267,000
Step-by-step explanation:
Numbers Of pizza to order
What is the slope of the line
The length of a rectangle exceeds its width by 1
inch and the area is 132 square inches. What
are the length and width of the rectangle?
Answer:
Width equals 11, and length equals 12.
Step-by-step explanation: It is helpful to memorize your multiplication tables up to 12. I personally couldn't figure out a formula for this, but I knew that 12 x 11 equals 132, and the length is greater than the width, so length is 12 and width is 11. Hopefully somebody else can figure it out. P.S. I meant the formula, not the answer, my answer is correct.
Answer:
[tex]l(l - 1) = 132[/tex]
[tex] {l }^{2} - l - 132 = 0 [/tex]
[tex](l - 12)(l + 11) = 0[/tex]
[tex]l = 12 \: or \: l = - 11[/tex]
[tex]length \: must \: be \: postive[/tex]
[tex]integers[/tex]
[tex]l = 12 \: and \: w = l - 1 = 11[/tex]
plato
Hii I need the 7th and 8th question asap will mark brainliest 100% to who ever answers first and right thank you