Answer:
A polynomial function f of least degree = f = x³ - 7x² + 36
The function in standard form = f = x³ - 7x² + 36
Step-by-step explanation:
As given, Leading coefficient of polynomial function = 1
Also given, zeroes of the function = -2, 3, 6
for root -2 : (x - (-2)) = (x + 2)
for root 3 : ( x - 3)
for root 6 : (x - 6)
Therefore, the polynomial function becomes -
f = 1(x+2)(x-3)(x-6)
⇒f = (x+2)(x² - 6x - 3x + 18)
⇒f = (x+2)(x² - 9x + 18)
⇒f = x³ - 9x² + 18x + 2x² - 18x + 36
⇒f = x³ - 7x² + 36
The polynomial function in standard form is [tex]f(x) = x^3 - 8x^2 +9x +18[/tex]
The zeros of the polynomial are given as:
[tex]Zeroes = -2,3,6[/tex]
Rewrite as:
[tex]x= -2,3,6[/tex]
Express the zeroes as an equation
[tex]x= -2[/tex], [tex]x =3[/tex] and [tex]x =6[/tex]
Equate to 0
[tex]x + 2 = 0[/tex], [tex]x -3 = 0[/tex] and [tex]x -6 = 0[/tex]
Multiply the equations
[tex](x + 1) \times (x - 3) \times (x - 6) = 0 \times 0 \times 0[/tex]
[tex](x + 1) \times (x - 3) \times (x - 6) = 0[/tex]
Expand
[tex](x^2 - 3x + x - 3) \times (x - 6) = 0[/tex]
[tex](x^2 - 2x - 3) \times (x - 6) = 0[/tex]
Expand
[tex]x^3 - 2x^2 - 3x -6x^2 +12x +18 = 0[/tex]
Collect like terms
[tex]x^3 - 2x^2 -6x^2 - 3x +12x +18 = 0[/tex]
[tex]x^3 - 8x^2 +9x +18 = 0[/tex]
Express as a function
[tex]f(x) = x^3 - 8x^2 +9x +18[/tex]
Hence, the function in standard form is [tex]f(x) = x^3 - 8x^2 +9x +18[/tex]
Read more about functions at:
https://brainly.com/question/20510856
What is the geometric sequence formula for 1/5, 1/25, 1/125, 1/625, ...
The Humphrey family is traveling 1,325 miles for their family vacation. Last year, they traveled 724 miles. They drove 420 miles earlier in the week and have driven 130 miles so far today. How many miles do they have left to travel?
Answer: They have 775 miles left to be traveled
Step-by-step explanation:
Miles required to travel for vacation = 1,325 miles
Miles already traveled = Miles driven this week + miles driven today
= 420 miles + 130 miles
-=550 miles
Miles remaining to be covered =Miles required to travel for vacation --- Miles already traveled
= 1,325 miles - 550 miles
= 775 miles
Answer:
1762 is the answer
Step-by-step explanation:
Add, Subtract, or Multiply, as indicated.
(5x^2+3x-7)+(6x+7)
2865 students participated in a competitive exam. There were 60 rooms in the
university. Equal number of students were placed in each room. How many students
were not seated in any one of the rooms?
Guided Practice
1. A manufacturer gets a shipment of 600 batteries of which 50 are
defective. The quality control manager tests a random sample of
30 batteries in each shipment. Simulate the test by generating random
numbers between 1 and 600. How well does your sample represent the
shipment? Explain. (Explore Activities 1 and 2)
Answer:
18.33
Step-by-step explanation:
600 -50 ÷ 30
550 ÷30 = 18.333
The Hollywood cats are a group of cats that have settled in along the Hollywood Beach in Florida. A group of volunteers feed them and care for them while trying to humanely reduce their numbers (as they are considered a nuisance). If there were 100 cats in the year 2012 and the rate of population change is given
Complete Question
The Hollywood cats are a group of cats that have settled in along the Hollywood Beach in Florida. A group of volunteers feed them and care for them while trying to humanely reduce their numbers (as they are considered a nuisance). If there were 100 cats in the year 2012 and the rate of population change is given
by [tex]-\frac{1}{4} t-2[/tex]
where t is measured in years, how many cats are projected to be in the group in 2020.
Answer:
The number of total cats left after 8 years T
[tex]T=76[/tex]
Step-by-step explanation:
From the question we are told that
Number of cats 2012 n=100
Number of years t=2012-2020=>8 years
Generally the equation of change in population is mathematically Given as
[tex]\frac{dp}{dt}= -\frac{1}{4} t-2[/tex]
[tex]\int dp=\int_0^8 (-\frac{1}{4} t-2)[/tex]
[tex]p=\frac{-64}{8} -16[/tex]
[tex]p=-24cats[/tex]
Therefore the number of total cats left after 8 years T is given as
[tex]T=100-24[/tex]
[tex]T=76[/tex]
The figure below is a square with dimensions given.
Part A: What is the perimeter of the square in terms of x?
2x - 1 in
Perimeter = ________
Part B: If the length of each side of the square is doubled, what would be the perimeter of this new square, in terms of x?
Perimeter = ________
Part C: If x = 5, what would be the ratio of the area of the original square to the area of the new square?
Answer: ____________________
Answer:
A: 8x-4
B: 16x-8
C: 1:2
Step-by-step explanation:
A dish washer manufacturer introduced a new type of dish washer and conducted a survey on the new product. The survey showed 40% of the consumers had seen an advertisement for the new product, 20% had tried the new product, and 15% had both seen an advertisement and tried the new product. Let event A denote that the consumers had seen an ad for the new product, and event B denote that the consumers had tried the new product. What is the probability a randomly selected consumer had either seen an advertisement or tried the new product
Answer:
[tex]P(A \cup B) =0.45[/tex]
Step-by-step explanation:
From the question we are told that
Consumers seen the soap [tex]P_A=40\% =0.40[/tex]
Consumers used the soap [tex]P_B=20\% =0.2[/tex]
Consumers seen/tried the soap [tex]P_x=15\% =0.15[/tex]
Generally the probability that consumers have seen and tried the soap is
[tex]P(A \cup B=P(A)+P(B)-P(A \cap B[/tex]
[tex]P(A \cup B=0.4+0.2-0.15[/tex]
[tex]P(A \cup B) =0.45[/tex]
Find the percent of a number 20% of 155
Hey there!
[tex]\text{The word \underline{of} means \underline{multiply} in \underline{mathematical terms}}[/tex]
[tex]\bold{Equation: 20\% \times 155}\\\bold{20\% = \dfrac{20}{100}=\dfrac{20\div20}{100\div20}=\dfrac{1}{5}}\\\bold{\dfrac{1}{5}\times 155=?}\\\bold{155\times1=155}\\\\\bold{\dfrac{155}{5}=31}\\\boxed{\boxed{\bold{Answer: 31}}}\huge\checkmark[/tex]
Good luck on your assignment and enjoy your day!
~[tex]\frak{Amphitrite1040:)}[/tex]
which of these numbers has exactly two factors, 7,8,9,10
Answer:
It's 7
Step-by-step explanation:
(x2 - 3)(x2 + 12) = 0
Answer:
x=1.7320508075688772 or x=−1.7320508075688772
Step-by-step explanation:
(x2−3)(x2+12)=0
x4+9x2−36=0
(x2−3)(x2+12)=0
x2−3=0 or x2+12=0
x=1.7320508075688772 or x=−1.7320508075688772
Please help and explain
True or False: The magnitude of a resultant vector will always be larger than individual vectors that are both in the first quadrant
Answer:true
Step-by-step explanation:
HELP QUICK ILL GIVE TOU BRAINLIEST
find the surface area...
Yousef saves $25 each month for a year. One year is 12 months. How much money does he save in one year?
Answer:
300
Step-by-step explanation:
25 x 12
Answer:300
Step-by-step explanation: its just 25 x 12
Drag Each expression to show whether it is equivalent to 6.7-(-2.5), 6.7+(-2.5), or neither.
Answer:
Step-by-step explanation:
6.7 – (-2.5)
2.5+6.7
6.7 + (-2.5)
-2.5+6.7
6.7-2.5
neither
-2.5-6.7
2.5-6.7
-6.7+2.5
4x² when x = 5/6 and 1/2
hat is the product of 4.01 × 10-5 and 2.56 ×108?
Answer:
35.1 and 276.48
Step-by-step explanation:
Answer:
The correct answer is: 1.0266 ×104
Step-by-step explanation:
The government of Japan between World War I and World War II can best
be described as *
democratic
communist
militaristic
Nazi
Answer:
I believe communist just because or there influences in world war I and world war II they were on the communist side and part of the USSR at the time
HELP PLZZZ EASY AREA MATH
Answer:
4,400
Step-by-step explanation:
help me please :)
iiiiiiiiiiiiiiiiiiiiiiiiiiiiii
Answer:
[tex]x = \frac{5}{3}[/tex]
Step-by-step explanation:
The expression under the square root is [tex]\sqrt{4x^2 - 20x + 25}[/tex]
This is equivalent of [tex](2x-5)^2[/tex]
We can check this by using the formula
[tex](a+b)^2 = a^2 + 2ab + b^2[/tex]
where [tex]\\a = 2x so a^2 = (2x)^2 = 4x^2\\\\b = -5 so b^2 = (-5)^2 = 25\\\\2ab = (2)(2x)(-5) = -20x\\[/tex]
So
[tex]\sqrt{4x^2 - 20x + 25} = \sqrt{(2x-5)^2}[/tex] which is [tex](2x-5)[/tex]
(The square root of the square of an expression is the expression itself)
So that gives us
[tex]2x - 5 = 5-2x\\[/tex]
Collecting like terms on each side gives us
[tex]2x + 2x = 5 -(-5)\\\\4x = 10\\\\x = 10/4 = 5/3[/tex]
Plz guys I rlly need help
Given points A(2,1,3) and B(0,5,0), find a point C in the xy-plane that creates an isosceles right triangle such that:_______
a. AB and BC are the legs of the right triangle
b. AB is the hypotenuse of the right triangle (for part ii, just doing all the set-up work is sufficient; you do not need to solve and find the points)
Answer:
a.)Point C will be either (4.82, 7.41) or ( -4.82, 2.59)
b.) -x² + 2x + 6y - y² - 5= 0 , 8y - 4x = 11
Step-by-step explanation:
As given A(2,1,3) and B(0,5,0)
a.)
We have to find C in the xy-plane
⇒ C is of the form (x, y, 0) ( Because in xy plane , z coordinate is zero)
Now, given AB and BC are the legs of the right triangle .
AB = (0, 5, 0) - (2, 1, 3) = ( -2, 4, -3)
BC = (x, y, 0) - (0, 5, 0) = ( x, y-5, 0)
As AB and BC are legs of triangle
⇒AB is perpendicular to BC
⇒(AB).(BC) = 0
⇒( -2, 4, -3).( x, y-5, 0) = 0
⇒ -2x + 4(y-5) -0 = 0
⇒ -2x + 4y- 20 = 0
⇒ -x + 2y- 10 = 0
⇒ 2y = 10 + x
⇒ y = 5 + [tex]\frac{x}{2}[/tex] ......(1)
As ABC is making an isosceles right triangle
It means two sides of the triangle are equal
Now,
|AB| = √(-2)² + (4)² + (-3)² = √4+16+9 = √29
|BC| = √(x)² + (y-5)² + 0² = √(x)² + (y-5)²
Now,
AS AB = BC
⇒|AB| = |BC|
⇒|AB|² = |BC|²
⇒29 = (x)² + (y-5)²
⇒29 = (x)² + (5 + [tex]\frac{x}{2}[/tex] -5)²
⇒29 = (x)² + ( [tex]\frac{x}{2}[/tex] )²
⇒29 = x²( 1 + [tex]\frac{1}{4}[/tex] ) = x²( [tex]\frac{5}{4}[/tex] )
⇒ x² = [tex]\frac{116}{5}[/tex] = 23.2
⇒ x = 4.82 , -4.82
⇒y = 7.41 , 2.59
so, Point C will be either (4.82, 7.41) or ( -4.82, 2.59)
b.)
As given AB is the hypotenuse of the right triangle
S, AC and CB will perpendicular to each other
Now,
AC = (x, y, 0) - ( 2, 1, 3) = ( x-2, y-1, -3)
CB = (0, 5, 0) - (x, y, 0) = (-x, 5-y, 0)
As, AC and CB is perpendicular
⇒(AC).(CB) = 0
⇒( x-2, y-1, -3).(-x, 5-y, 0) = 0
⇒(x-2)(-x) + (y-1)(5-y) - 0 = 0
⇒-x² + 2x + 5y - y² - 5 + y = 0
⇒-x² + 2x + 6y - y² - 5= 0 ..........(2)
As ABC is making an isosceles right triangle
It means two sides of the triangle are equal
Now,
|AC| = √(x-2)² + (y-1)² + (0-3)² = √(x-2)² + (y-1)² + 9
|BC| = √(x)² + (y-5)² + 0² = √(x)² + (y-5)²
Now,
AS AC = BC
⇒|AC| = |BC|
⇒|AC|² = |BC|²
⇒(x-2)² + (y-1)² + 9 = (x)² + (y-5)²
⇒x² + 4 - 4x + y² + 1 - 2y + 9 = x² + y² + 25 - 10y
⇒ 4 - 4x + 1 - 2y + 9 = 25 - 10y
⇒14 - 4x - 2y = 25 - 10y
⇒10y - 2y - 4x = 25 - 14
⇒8y - 4x = 11 ........(3)
Now, we have 2 equations
-x² + 2x + 6y - y² - 5= 0 , 8y - 4x = 11
Solve these equations to find x, y
Write the linear equation in slope-intercept form if
Slope = 1/2
y-intercept is -7
Working together, it takes two computers 12 minutes to send out a company's email. If it takes the slower computer 30 minutes to do the job on its own, how
long will it take the faster computer to do the job on its own?
Do not do any rounding?
Answer:
The faster computer will complete the job in 20 minutes alone.
Step-by-step explanation:
Given that:
Time taken by both computers = 12 minutes
Time taken by slower computer = 30 minutes
Let,
x be the time taken by faster computer.
[tex]\frac{1}{x}+\frac{1}{30} = \frac{1}{12}[/tex]
[tex]\frac{1}{x} = \frac{1}{12}-\frac{1}{30}\\\\\frac{1}{x} = \frac{5-2}{60}\\\\\frac{1}{x} = \frac{3}{60}\\\\\frac{1}{x} = \frac{1}{20}\\\\x= 20[/tex]
Hence,
The faster computer will complete the job in 20 minutes alone.
х
0
100
200
300
у
1.5
36.5 71.5 106.5
Answer:
oh
Step-by-step explanation:
Answer:
y = 0.335x + 1.5
Step-by-step explanation:
First, find the slope using two of the given pairs, say, (0, 1.5) and (100, 36.5):
Slope (m) = [tex] \frac{y_2 - y_1}{x_2 - x_1} = \frac{36.5 - 1.5}{100 - 0} = \frac{35}{100} = 0.35 [/tex]
find the y-intercept (b):
y-intercept (b) is 1.5. At y = 1.5, the value of x is 0. Thus, the y-axis is intercepted by the line.
b = 1.5.
✔️Substitute m = 0.35 and b = 1.5 into y = mx + b.
y = 0.35x + 1.5
Find the length of side x in simplest radical form with a rational denominator.
Answer:
[tex] x = 6\sqrt{2}[/tex]
Step-by-step explanation:
Reference angle = 45°
Adjacent side = 6
Hypotenuse = x
Applying trigonometric ratio, we have:
[tex] cos(45) = \frac{6}{x} [/tex]
Multiply both sides by x
[tex] x*cos(45) = 6 [/tex]
Divide both sides by cos(45)
[tex] x = \frac{6}{cos(45)} [/tex]
[tex] x = \frac{6}{\frac{\sqrt{2}}{2} [/tex] (cos 45 = √2/2)
[tex] x = \frac{6}*{\frac{2}{\sqrt{2}} [/tex]
[tex] x = \frac{12}{\sqrt{2}} [/tex]
Rationalize
[tex] x = \frac{12*\sqrt{2}}{\sqrt{2}*\sqrt{2} [/tex]
[tex] x = \frac{12*\sqrt{2}}{2} [/tex]
[tex] x = \frac{6*\sqrt{2}}{1} [/tex]
[tex] x = 6\sqrt{2}[/tex]
true false or not enough information??
Answer:
True.
Step-by-step explanation:
The range of the 10 values is 10 - 3 = 7 so that is true.
The median will be the mean of the 2 middle values so that is possible also. The distribution could be, for example:
3 3 3 4 4 4 7 8 8 10 when the median = (4 + 4) / 2 = 4.
Answer:
True.
Step-by-step explanation:
the range of 10 values is 10-3 = 7 so that is true
A candy bar is 9/15 of an inch long. If it is divided into pieces that are 1/5 of an inch long, then how many pieces is that?
Answer:
3 pieces
Step-by-step explanation:
Solve.
log6x+log6(x−1)=1
Enter your answer in the box.
x = ?
Answer:
7
Step-by-step explanation:
hhfndbdbdbueheheheheheheh
Solve the absolute
[x] - 7 =-3