Step-by-step explanation:
The Rational Roots Test states that for a polynomial with integer coefficients, the factors of the constant / the factors of the leading coefficient are the possible rational roots.
Here, the constant (the value without an x attached to it) is -12 and the leading coefficient (the value that the x to the highest degree is multiplied by) is 1 as x⁴ is multiplied by 1. The factors of -12 are
±(1, 2, 3, 4, 6, 12), so the possible rational roots are ±(1, 2, 3, 4, 6, 12)/1 (as 1 is the only factor of 1).
Trying out a few roots until we get one that works using synthetic division, we can try
x+1 (the root is x=-1)
-1 | 1 1 -6 -14 -12
| -1 0 6 8
__________________________
1 0 -6 -8 -4
the remainder is -4, so this does not work
x+2 (the root is x=-2)
-2 | 1 1 -6 -14 -12
| -2 2 8 12
__________________________
1 -1 -4 -6 0
Therefore, x=-2 is a root and x+2 is a factor of the polynomial. The quotient of the polynomial and x+2 is
-6 + (-4)x + (-1)* x² + 1 * x³ = x³-x²-4x-6
Using the rational roots theorem, the possible roots of x³-x²-4x-6 are
±(1,2,3,6)
Starting with
x-1 (root is x=1), we have
1 | 1 -1 -4 -6
| 1 0 -4
_____________________
1 0 -4 -10
there is a remainder, so this is not a root
next, x-2 (root is x=2)
2 | 1 -1 -4 -6
| 2 2 -4
_____________________
1 1 -2 -10
there is a remainder, so this is not a root
next, x-3 (root is x=3)
3| 1 -1 -4 -6
| 3 6 6
_____________________
1 2 2 0
x-3 is a factor and 3 is a root. the quotient of (x³-x²-4x-6)/(x-3) is x²+2x+2
What action represents the "!" symbol on a TI 84 plus CE calculator for a Statistics problem??
Answer:
The "!" represents a factorial
Step-by-step explanation:
In math, a factorial when there is an ! followed by a number.
For example, 5! = 5 factorial.
To solve factorials, multiply every integer below the number before the factorial, including the number.
5! = 5 x 4 x 3 x 2 x 1 = 120.
This table shows the relationship of the total number of pieces of fruit to the number of bananas.
Why is StartFraction 6 Over 5 EndFraction not equivalent to Three-halves?
Given:
The table that shows the relationship of the total number of pieces of fruit to the number of bananas.
To find:
Why is [tex]\dfrac{6}{5}[/tex] not equivalent to [tex]\dfrac{3}{2}[/tex].
Solution:
If a, b, c are real numbers, then
[tex]\dfrac{a}{b}=\dfrac{a\times c}{b\times c}[/tex]
The given fraction is [tex]\dfrac{3}{2}[/tex]. It can be written as:
[tex]\dfrac{3\times 2}{2\times 2}=\dfrac{6}{4}[/tex]
The number 3 is multiplied by 2 to get 6. So, the 2 should also be multiplied by 2. The ratio should be [tex]\dfrac{6}{4}[/tex], not [tex]\dfrac{6}{5}[/tex].
Therefore, the correct option is A.
The median house price in Waterloo Region increased by 3.6% from Jan 1, 2018 to Jan 1, 2019. A home
was purchased in Waterloo Region on April 1, 2019 for $600,000.
(a) Assume this trend continues, write an exponential equation that models the Resale Value of this
home over time.
(b) At this rate, determine the date of the resale price of the home would reach $1 million (Show your
work to accurate to the nearest month)
(c) Use your exponential equation to determine the expected resale value of the home on April 1, 2020.
Answer:
The right answer is:
(a) [tex]P(t) = P_o \ e^{0.03536t}[/tex]
(b) [tex]t = 14 \ years \ 6 \ months[/tex]
(c) [tex]P(t) = =621,595.6[/tex] ($)
Step-by-step explanation:
Given:
House price increment rate,
= 3.6% annually
(a)
Let the exponential equation will be:
⇒ [tex]P(t) = P_o e^{Kt}[/tex]
here,
t = 0
P = P₀
t = 1 yr
then,
[tex]P(1) = P_o +3.6 \ persent \ P_o[/tex]
[tex]=1.036 \ P_o[/tex]
now,
⇒ [tex]1.036 P_o = P_o \ e^{K.1}[/tex]
[tex]ln(1.036) = K[/tex]
[tex]K = 0.03536[/tex]
Thus, the exponential equation will be "[tex]P(t) = P_o \ e^{0.03536t}[/tex]".
(b)
We know,
[tex]P_o = 600,000[/tex] ($)
[tex]P(t) = 10,00,000[/tex] ($)
∵ [tex]P(t) = P_o \ e^{0.03536t}[/tex]
[tex]1000000=600000 \ e^{0.03536 t}[/tex]
[tex]\frac{5}{3}= e^{0.03536 t}[/tex]
[tex]ln(\frac{5}{3} )=0.03536 t[/tex]
[tex]\frac{\frac{0.5}{0825} }{0.03536} =t[/tex]
[tex]t = 14.45 \ years[/tex]
or,
[tex]t = 14 \ years \ 6 \ months[/tex]
(c)
[tex]P_o=600,000[/tex] ($)
[tex]t = 1 year[/tex]
Now,
⇒ [tex]P(t) = P_o \ e^{0.03536 t}[/tex]
[tex]=600000 \ e^{ 0.03536\times 1}[/tex]
[tex]=621,595.6[/tex] ($)
Identify the equation of the circle that has its center at (9, 12) and passes through the origin.
Answer:
(x-9)^2 +(y-12)^2 = 225
Step-by-step explanation:
First find the length of the radius
If is the distance from the center to the point
d = sqrt( (x2-x1)^2 + (y2-y1)^2 )
= sqrt( (0-9)^2 + (0-12)^2)
= sqrt ( 81+144)
= sqrt(225)
= 15
The equation for a circle is
( x-h) ^2+ (y-k)^2 = r^2
(x-9)^2 +(y-12)^2 = 15^2
(x-9)^2 +(y-12)^2 = 225
convert into power notation -1/81
Answer:
-1/9^2 is the power notation for your questions
Step-by-step explanations
A running track has two semi-circular ends with radius 27m and two straights of length 90.6m as shown.
Calculate the total distance around the track rounded to 1 DP.
Answer:
350.85
Step-by-step explanation:
90.6*2 = 181.2
27*2 = 54 (diameter)
54*pi = 169.646003294
169.646003294 + 181.2 = 350.846003294
350.846003294 = 350.85
need help with this!!
Answer:
{ 1,3,4,6,7}
Step-by-step explanation:
Do B∩C first
This is B intersect C which means what they have in common
B∩C = {3,6,7}
Then A∪(B∩C)
A union {3,6,7} which means join together ( combine with no duplicates) the two sets
{ 1,3,4,6,7}
Which is a y-intercept of the continuous function in the table? х – 4 -3 -2 -1 0 1 f(x) -10 0 0 – 4 -6 0 2 O (0,6) O (-2, 0) O (6,0) 0 (0, -2)
Plz Hurry
Answer:
x:-4,-3,-2,-1,0,1
f(x):-10,0,0,-4,-6,0
from the table we can see when x=0, y=-6
Therefore the y-intercept will be (0,-6)
OAmalOHopeO
The y intercept of the continuous function in the table is given by the relation f ( 0 ) = -6
What is a function rule?The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.
A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given data ,
Let the function be represented as A
Now , the value of A is
Let the values of x be x = { -4 , -3 , -2 , -1 , 0 }
Let the values of y be y = { -10 , 0 , 0 , -4 , -6 }
Now , the y intercept of the function is when the value of x = 0
So , when x = 0 , the value of y = -6
And , f ( 0 ) = -6
Therefore , the y intercept is ( 0 , -6 )
Hence , the y intercept of the function is ( 0 , -6 )
To learn more about function rule click :
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Evaluate:
18 (5n - 4) = [?]
Answer:
90n-72=0
Step-by-step explanation:
18×5n-18×4=0
Instructions: Find the measure of the missing angle using the Exterior Angle Sum
Theorem
Answer:
It's an isosceles triangle equal 2 sides so
it will be x+67 ° +67 ° =180° ( sum of angle in triangle)
x+134 °=180 °
x =180 - 134
x = 46 °
The measurement of the missing angles in the given triangle is 67.
Use the concept of isosceles triangle defined as:
A triangle with two equal-length sides is said to be isosceles.
An isosceles triangle has equal angles on either side of its equal sides.
In the given figure,
One angle is 67 degrees
And two sides are equal.
Let the missing angle is x°
Since the two sides of this triangle are equal,
So this is an isosceles triangle.
Then two opposite angles must be equal.
For a triangle,
The sum of interior angles = 180°
Therefore,
67° + 67° + x° = 180°
x° = 46°
Hence,
The measurement of the missing angle is 46°
To learn more about the triangle visit;
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Banks and other financial institutions offer incentives for people to keep their money in a savings account.
True or False?
it's true because it gives interset or compensation amount to the individuals or organizations which motivates people to save their money in a saving account
Which expressions are equivalent to the given expression?
Answer:
The answers are option B and E.
What could be the coefficient of x once the variable term is isolated on one side of the equation? Check all that apply.
3x - 6(5x + 3) = 9x + 6
1. Distribute: 3x - 30x - 18 = 9x + 6
2. Combine like terms: -27x - 18 = 9x + 6
–36
–27
–24
24
27
36
Answer:
-36,36
Step-by-step explanation:
3x - 6(5x + 3) = 9x + 6
Distribute:
3x - 30x - 18 = 9x + 6
Combine like terms:
-27x - 18 = 9x + 6
There are two possible ways to isolate x
On the left
Subtract 9x from each side
-27x - 18 -9x = 9x-9x + 6
-36x -18 = 6
On the right
Add 27x from each side
-27x - 18 +27x = 9x+27x + 6
-18 =36x+ 6
Find sin 0
A. 16/20
B. 12/16
C. 12/20
D. 16/12
Answer:
16/20
Step-by-step explanation:
Since this is a right triangle
sin theta = opp side / hypotenuse
sin theta = 16/20
Answer:
A.
[tex]{ \tt{ \sin( \theta) = \frac{opposite}{hypotenuse} }} \\ \\ { \tt{ \sin( \theta) = \frac{16}{20} }}[/tex]
“The length of a rectangle is two feet greater than twice its width. If the perimeter is 25 feet, find the width.” Which of the following translations is correct?
Answer:
b is the answer
Step-by-step explanation:
Picture is right there pls help
Answer: B
Step-by-step explanation:
Using slope formula, change in y (3) over change in x (2) is 3/2. So the equation would be y=3/2x.
Find the equation of the line that passes through (1,6) and (3,10).
y=2x+4
y=-2x+4
y=-24-4
Oy-23-4
Answer:
m = (y2 - y1) / (x2 - x1) = (10 - 6) / (3 - 1) = 2 slope of line
y = m x + b standard form of straight line
y = 2 x + b where b is the intercept at x = 0
b = y - 2 x
b = 6 - 2 = 4 from our first equation
Also, b = 10 - 6 = 4 check from second equation
y = 2 x + 4 is our equation
Check if y = 6 and x = 1 then
y = 2 * 1 + 4 = 6 verifying the first point given
Solve the equation by completing the square. Round to the nearest hundredth if necessary. x^2 - x = 25
Answer:
[tex]x1 = - 4.525[/tex]
[tex]x2 = 5.525[/tex]
Step-by-step explanation:
[tex]x1 = \frac{1 - \sqrt{101} }{2} [/tex]
[tex]x2 = \frac{1 + \sqrt{101} }{2} [/tex]
Does (x, y) satisfy an equation?
Answer:
Yeah
Step-by-step explanation:
please explain this to me.
Answer:
Equation of line:- y=2x-7
slope(m)=2
slope of parallel line (m)=2
∴ Equation of parallel line:- y=2x+b
it passes through the point (-3,6)
6=2(-3)+b 6+6=b
b=12
∴ y=2x+12
OAmalOHopeO
You are riding your bike. At 8:00am you have ridden your bike 23 miles. By 9:00pm you have ridden 179 miles. Find the rate of change in miles per hour. If needed, round your answer to the nearest whole number.
Answer:
12 miles/hour
Step-by-step explanation:
8am to 9pm = 13 hours
in that time we were driving 179-23 = 156 miles.
so, our speed was 156 miles / 13 hours.
now simplify it to our standard miles/hour format :
156/13 = 12
therefore, or standardized speed was
12 miles/hour
Find the BD in the image below
Answer:
x = 10
The both line crosses with a little hyphen, meaning those are same
Answered by GAUTHMATH
Which of the following is a characteristic of science?
Answer:d
Step-by-step explanation:
Answer:
D
explanation:
i got it right on the test
An acute angle of a right triangle measures 30°, and the length of the triangle's hypotenuse is 10 ft. Find the missing angle measure and side lengths.
Answer:
missing angle <60 and side lengths 5, 5[tex]\sqrt{3}[/tex]
Step-by-step explanation:
we understand from the given information that the triangle in question is a special right triangle
and since this is a special triangle the side lengths follows :
the side length that sees <90 is represented by 2x
the side length that sees <60 is represented by x[tex]\sqrt{3}[/tex]
and the side length that sees <30 is represented by x
2x = 10 so x = 5 and x[tex]\sqrt{3}[/tex] = 5[tex]\sqrt{3}[/tex]
asap answer pls ----------------
Answer:
C
Step-by-step explanation:
PLS ANSWER YA'LL!
A house owner wishes to cover their roof with solar panels. Each solar panel is of the following size.
->The roof section is rectangular 7.2 m by 4.4 m.
->Each solar panel measures 1400 mm by 850 mm.
There needs to be at least a 30 cm gap left at each edge of the roof section. The house owner thinks he can have at least 15 solar panels fitted to the roof section.
Can u agree? If yes, show the working. (Hint: He can rotate the solar panel)
Answer:
Yes
Step-by-step explanation:
The roof is Rectangular :
Dimension of roof section : 7.2 m by 4.4 m
Area of roof = length * width
Area of roof = 7.2 * 4.4 = 31.68 m²
Dimension of solar panels = 1400 mm by 850 mm
Converting to m:
1000mm = 1 m
1400/1000 by 850/1000 = 1.4 m by 0.85 m
Area each solar panel = 1.4 * 0.85 = 1.19 m²
Gap left at each edge :
30cm gap about the 4 edges gives a square with side length 30cm:
30cm = 30/100 = 0.3m
Area of gap left = 0.3² = 0.09 m²
Total area that can be covered = (31.68 - 0.09) m² = 31.59 m²
Maximum number of panels that can be placed on roof section :
Total area that can be covered / area of panel
31.59 m² / 1.19 m²
= 26.54 panels
Which of the following is most likely the next step in the series?
| || H
Oat И
O B. #
och
#
D.
Answer:
D makes sense. I think the answer is D.
A researcher decides to find out whether giving students positive
reinforcement improves or impairs their grades. The researcher's sample
group consists of the following 8 students:
0 Jack
1 Tucker
2 Susie
3 Jill
4 Charianna
5 Trey
6 Ashton
7 Jordan
52197 66082 97867 49397 47924 78900 59414 64755 48733
Which of the following represents a 5-person group selected for the
treatment group using the first number in the line from a table of random
numbers above?
A. Charianna, Tucker, Jack, nobody, Ashton
B. Tucker, Susie, Trey, Ashton, Jordan
C. Trey, Susie, Tucker, Jordan, Ashton
D. Charianna, Tucker, Jack, Ashton, Trey
Answer: C. Trey, Susie, Tucker, Jordan, Ashton
========================================================
Explanation:
The random sub-sequence 52197 66082 helps directly determine who we pick.
The digit 5 is first of that sequence, so we pick Trey first (as he's the 5th student). Then we pick student #2 next, who is Susie.
Up next is student #1, and that would be Tucker
Up next is student #9, but the list only goes high as 7. So we skip over 9
Jordan is next up since 7 is the next digit
Finally, the last selection is Ashton because 6 follows after.
--------------
In other words, the sequence 52197 6 will lead to these selections in the order provided.
5 = Trey2 = Susie1 = Tucker9 = skip, since it's not on the list7 = Jordan6 = AshtonSide note: if we wanted a 6th student, then we'd have to skip over the next 6 since we cannot pick Ashton twice. The 6th selection would be Jack since he's student #0
Graph the inequality.
1
Answer:
hope it helps
Step-by-step explanation:
simplify:-a). (-5a²)²(6ab²)(-3ab²)
