Answer:
x³ - 6·x² + 6·x + 8 = (x - 4) × (x - (1 + √3)) × (x + 1 + √3)
Step-by-step explanation:
From the given graph of the polynomial, x³ - 6·x² + 6·x + 8, we have that one of the zeros of the polynomial, which is one point the graph cuts the x-axis is given as follows;
At a zero, we have, x = 4
∴ x - 4 = 0 is a factor of the polynomial
Dividing the given polynomial by (x - 4), gives;
x² - 2·x - 2
(x³ - 6·x² + 6·x + 8)÷(x - 4)
x³ -4·x²
-2·x² + 6·x + 8
-2·x² + 8·x
-2·x + 8
-2·x + 8
0
∴ (x³ - 6·x² + 6·x + 8)÷(x - 4) = x² - 2·x - 2
∴ (x - 4) × (x² - 2·x - 2) = x³ - 6·x² + 6·x + 8
Factorizing x² - 2·x - 2, gives;
x = (2 ± √((-2)² - 4×1×(-2)))/(2 × 1) = (2 ± 2·√(3)/(2) = (1 ± √(3)
Therefore, x = 1 + √3, (x - (1 + √3)) = 0 or x = 1 - √3, (x - (1 - √3)) = 0 which gives the factors, after factorizing completely as follows;
x³ - 6·x² + 6·x + 8 = (x - 4) × (x - (1 + √3)) × (x + 1 + √3)
Zeyad has a bag of 40 marbles. 10 of them are red. 12 are blue. 18 are white. He reaches into the bag without looking. What is the probability that Zeyad will select a white marble?
Answer:
9/20
Step-by-step explanation:
There are 40 marbles
18 are white
P( white marble) = number of white marbles / total number of marbles
= 18/40 = 9/20
Mandy gets 6 out of every 8 questions on a test correct. If she gets 27 questions correct, how many questions are on the test?
Answer:
36
Step-by-step explanation:
She gets 6 question right for every 8 question that means a ratio of 6/8 which is equal to 3/4
so we can say the ratio multiplied by the number of questions equals the correct answers
while x is the number of questions:
solve for x
3/4 * x = 27
x = 27 / (2/3) = 36
f(x) = x² , g(x) = x+1 find gof (2) , fog (2)
Answer:
Explanation:
Hey there!
Here;
f(X) = x²
and g(X) = X+1
To find: gof (2) and fog (2)
For gof (2),
gof = g{f(X)}
= g (x²)
= x²+1
Then;
gof(2) = 2²+1
= 4+1
= 5
Therefore, gof (2) is 5.
For fog(2),
fog (X) = f{g(X)}
= f(X+1)
= (x+1)²
= x²+2x+1
= x²+2x +1
Then;
fog(2) = 2²+2*2+1
= 4+4+1
= 9
Therefore, fog(2) = 9.
Hope it helps!
A company produce 6400 text book. The company packed 400 into each carton how many carton did they fill ?
Answer: 16
Step-by-step explanation: 6400 : 400 = 16
Find x to the nearest tenth.
Answer:
x = 11.3
Step-by-step explanation:
This is a right isosceles triangle
x² + x² = 16²
2x² = 256
x² = 128
x = 11.3
A guitar is originally priced at $80. The online retailer gives a discount and the guitar is now priced at $44. Enter the percentage discount for the cost of the guitar. (PLEASE ANSWER THIS I NEED THE ANSWER BY TODAY RIGHT NOW!!!)
Answer:
The percentage discount for the cost of the guitar is 45%.
Step-by-step explanation:
First let's find the difference between the original price and the new price.
80 - 44 = 36
So the actual discount got the price down by $36.
To find the percentage discount we need to ask ourselves the question
36 is what percent of 80?
36 = X percent of 80
In math, of means multiply.
36 = X percent * 80
So to get the "X percent" part alone we divide by 80 on both sides.
36 divided by 80 = 0.45
36 is 45 percent of 80.
The percentage discount for the cost of the guitar is 45%.
PLEASE HELP ASAP PLZZZZZZZZZZZZZZZZZZZZZZZ
Answer:
45%
Step-by-step explanation:
There are 450 people with over 3 people in their family. There are 1000 total people. 450/1000 is 45%
Simplify. pls pls pls helppp im really bad at math lol
a) 6 √3+ 4
b) 6 √6+ 3
c) 4 √3 + 6
Is this right PLEASE HELP ILL GIVE BRAINLY
Exquisite.
All are Correct
My doubts do come from your last answer.
I think the complement should be 60° too
what is the larger fraction 5/6 or 8/10
Answer:
5/6
Step-by-step explanation:
5/6=0.84, 8/10= 0.8
ABCD is a parallelogram in which cd = 7cm Ad = 5cm ND adc = 125.. Find correct to one decimal place the area of the parallelogram.
28.7cm²
Step-by-step explanation:
The sketch of the parallelogram is attached to this response.
As shown in the sketch,
h is the height of the parallelogram
ADC is 125°
AD = 5cm
CD = 7cm
Also
Since the adjacent angles of a parallelogram are supplementary (add up to 180°), it means that;
=> ADC + BCD = 180°
=> 125° + BCD = 180°
=> BCD = 180° - 125°
=> BCD = 55°
The area (A) of a parallelogram is given by;
A = b x h ----------(i)
Where
b = base of the parallelogram
h = height of the parallelogram
From the sketch,
b = CD = 7cm
h can be found by using the sine trigonometric function as follows
sin BCD = [tex]\frac{h}{BC}[/tex]
=> sin 55° = [tex]\frac{h}{5}[/tex]
=> h = 5 sin 55°
=> h = 5 x 0.8192
=> h = 4.096cm
Now, substitute the values of h and b into equation (i) as follows;
A = 7 x 4.096
A = 28.672
A ≅ 28.7 (to one decimal place)
Therefore, the area of the parallelogram is 28.7cm²
6,347.2184 to the nearest thousandth
Answer: 6347.218
Step-by-step explanation:
Answer:6,347.218
Step-by-step explanation:
look at the thousandths place and then look at the number next to it if the number was 5 and above the answer would be 6,347.219 but in this situation it's not so you would keep everything the same but subtract the 0.0004
Find the volume of the cone.
Either enter an exact answer in terms of π or use 3.14 for π and round your final answer to the nearest hundredth.
Answer:37.68
Step-by-step explanation:
Do yk the anwser to my question?
Write [4^ squareroot 81] 5^
Answer:
(⁴√81)⁵
= [tex]81^{\frac{5}{4} }[/tex]
[tex]81^{\frac{5}{4} }[/tex]
= 243
Step-by-step explanation:
(⁴√81)⁵
(3)⁵
= 243
Answer:
the answer is B 81^4/5 I HOPED THIS HELPED
How many four digit numbers cannot be divided by 5?
Answer:
2556
Step-by-step explanation:
FAST PLEASE
A standard deck of 52 playing cards contains 13 cards in each of four suits: hearts, diamonds, clubs, and spades. Four cards are drawn from the deck at random. What is the approximate probability that exactly three of the cards are diamonds? 1% 4% 11% 44%
=====================================================
Explanation:
We'll involve the nCr combination formula here. This is because order doesn't matter.
There are n = 13 diamonds and we want to select exactly r = 3 of them.
So,
[tex]_n C _r = \frac{n!}{r!*(n-r)!}\\\\_{13} C _{3} = \frac{13!}{3!*(13-3)!}\\\\_{13} C _{3} = \frac{13!}{3!*10!}\\\\_{13} C _{3} = \frac{13*12*11*10!}{3!*10!}\\\\_{13} C _{3} = \frac{13*12*11}{3!}\\\\_{13} C _{3} = \frac{13*12*11}{3*2*1}\\\\_{13} C _{3} = \frac{1716}{6}\\\\_{13} C _{3} = 286\\\\[/tex]
There are 286 ways to pick the three diamond cards. Then there are 52-13 = 39 ways to pick the fourth card that is either a spade, club of heart.
So we have 286*39 = 11,154 ways to pick the four cards given the conditions your teacher set.
This is out of 52C4 = 270,725 ways to pick four cards (use the nCr formula above with n = 52 and r = 4).
Divide the two values to get the answer:
(11,154)/(270,725) = 0.04120048019208
that rounds to 0.04 which converts to 4%
So there's roughly a 4% chance of getting exactly 3 diamond cards.
Answer:
4% (four percent)
Can someone help please (‘:
Answer:
exponent is -3, ceofficiant is 4
(d)
what are the factors of x^3-2x^2+x+2
Pleaseee HELP ASAP !!!
Answer:
A: (x-5.5)^2 + (y-4)^2=12.25
Step-by-step explanation:
Write 5 5/6 as an improper fraction
Answer:
the answer is 35/6 hope it helps:)
Answer:
The answer is 35/6
Step-by-step explanation:
Multiply the denominator by the whole number.
5 x 6 = 30
Then add the Numerator.
30 + 5 = 35
Now the answer is 35/6, you don't change the denominator.
!NOW! Bennett budgeted $6,000 to spend on food for the year. If he spent $400 each month,
which expression represents how much money Bennett had left after x months.
Answer:
Y=6000-400x
Step-by-step explanation:
Y=6000-400x where 6000 is beginning total, x represents how many months have passed, and 400x reduces the total by 400 for x number of months.
What is the length of b?
What’s the least number of faces a polyhedron can have? And why?
Answer:
The minimum number of faces a polyhedron can have is 4 faces.
Step-by-step explanation:
We know that a polyhedron is a shape surrounded by polygons. We also know that we need at least 3 sides to make a polygon. So, at the minimum a polyhedron can be made by using only triangular faces but in order to make a closed figure we need at least four triangular faces (which is a tetrahedron).
Left parenthesis 5 plus 2 square root of 6 right parenthesis squared = a plus b square root of 6 then the value of a and b are
Answer:
The values of [tex]a[/tex] and [tex]b[/tex] are [tex]33[/tex] and [tex]\frac{20\sqrt{3}}{3}[/tex], respectively.
Step-by-step explanation:
The statement is equivalent to the following mathematic expression:
[tex]\left(5 + 2\sqrt{2})^{2} = a + b\cdot \sqrt{6}[/tex] (1)
By definition of the perfect square trinomial:
[tex]25 + 20\cdot \sqrt{2} + 8 = a + b\cdot \sqrt{6}[/tex]
[tex]33 + 20\sqrt{2} = a + b\cdot \sqrt{6}[/tex]
And by direct comparison we have the following system:
[tex]a = 33[/tex] (2)
[tex]b\cdot \sqrt{6} = 20\sqrt{2}[/tex] (3)
By (3), we solve for [tex]b[/tex]:
[tex]b = \frac{20}{\sqrt{3}}[/tex]
[tex]b = \frac{20\sqrt{3}}{3}[/tex]
The values of [tex]a[/tex] and [tex]b[/tex] are [tex]33[/tex] and [tex]\frac{20\sqrt{3}}{3}[/tex], respectively.
David bought a chain of fast food restaurants that operated 200 stores in 2009. The number of restaurants has grown at a rate of 12% annually
Complete Question
David bought a chain of fast food restaurants that operated 200 stores in 2009. The number of restaurants has grown at a rate of 12% annually.how many stores does the restaurant operate in 2020?
Answer:
[tex]N_{11} \approx 749[/tex]
Step-by-step explanation:
From the question we are told that:
Number of Fast Food Restaurants [tex]P=200[/tex]
Number of years [tex]t=11yrs[/tex]
Rate [tex]r=12%[/tex]
Generally the equation for the Number of restaurant in operation in 2020 is mathematically given by
[tex]N(t)=Pe^{rt}[/tex]
Therefore
For t=11
[tex]N_{11}=200*e^{0.12*11}[/tex]
[tex]N_{11}=748.7[/tex]
[tex]N_{11} \approx 749[/tex]
for each type of division problem, decide if the quotient is positive or negative
complete the statement
Answer:
positive divided by positive = positive
negative divided by positive = negative
positive divided by negative = negative
negative divided by negative = positive
Step-by-step explanation:
Examples;
8 ÷ 2 = 4
-8 ÷ 2 = -4
8 ÷ -2 = -4
-8 ÷ -2 = 4
You can try these on a calculator
1. positive
2. negative
3. negative
4. positive
What is quotient?The number resulting from the division of one number by another.
The given quotient can be positive or negative can be decide by the facts given below:
1) positive divided by positive = positive
2) negative divided by positive = negative
3) positive divided by negative = negative
4) negative divided by negative = positive
Examples;
16÷ 4 = 4-6 ÷ 2 = -310 ÷ -2 = -5-10 ÷ -5 = 2Learn more about quotient here:
https://brainly.com/question/27796160
#SPJ2
When finding the length of the hypotenuse of a right triangle, why might you approximate the answer? I NEED THIS ASAP I AM TIMED
Answer:
You would approximate because the hypotenuse might not be a perfect square.
Step-by-step explanation:
solve the equation:x²y²–x²–y⁴+y²=0
According to a survey, 15% of city workers take the bus to work. Donatella randomly surveys 10 workers. What is the probability that exactly 6 workers take the bus to work? Round the answer to the nearest thousandth. P (k successes) = Subscript n Baseline C Subscript k Baseline p Superscript k Baseline (1 minus p) Superscript n minus k. Subscript n Baseline C Subscript k Baseline = StartFraction n factorial Over (n minus k) factorial times k factorial EndFraction
1) 0.001
2) 0.002
3) 0.128
4) 0.899
Answer:
.899
Step-by-step explanation:
[algebra 2, word problems and expressions] hai! please help!
Answer:
The first one, f+2g+3t! :)
Step-by-step explanation:
F is worth 1 point so you don't need to add a number, g is worth 2 points, and t is worth 3 points.