The polynomial with a root 2i and exactly 2 real roots is F(x)=x³-x² + 4x-4
Factorizing polynomial functionsGiven the polynomial function below
F(x)=x³-x² + 4x-4
Group
F(x)=(x³-x²) + (4x-4)
f(x) = x²(x-1)+4(x-1)
f(x) = (x²+4)(x-1)
If f(x) = 0
x²+4 = 0 and x -1. = 0
x² = -4 and x = 1
x = ±2i and -1
Hence polynomial with a root 2i and exactly 2 real roots is F(x)=x³-x² + 4x-4
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State whether each of the following is an
open or closed question.
a) Why do you enjoy cooking?
b) What is your favourite fruit?
c) How tall are you?
d) Do you enjoy cooking?
e) What did you do on your holiday?
The following graph describes function 1, and the equation below it describes function 2. Determine which function has a greater maximum value, and provide the ordered pair. (1 point)
Function 1
graph of function f of x equals negative x squared plus 8 multiplied by x minus 15
Function 2
f(x) = −x2 + 2x − 3
Function 1 has the larger maximum at (1, 4).
Function 1 has the larger maximum at (4, 1).
Function 2 has the larger maximum at (1, −2).
Function 2 has the larger maximum at (−2, 1).
13.
Answer: Function 1 has the larger maximum at (4,1).
Step-by-step explanation:
The vertex of f(x) is at [tex]x=-\frac{2}{2(-1)}=1[/tex], and [tex]f(1)=-2[/tex].
For the graph, the maximum is obviously at (4,1).
So, Function 1 has the larger maximum at (4,1).
in the number pattern below, in which row is 2007
1
2. 3.
4. 5. 6.
....
The number 2007 is in the 63rd row
How to determine the number of row?The pattern is given as
1
2 3
4 5 6
The sum of n natural numbers is:
Sum = 0.5n(n + 1)
Assume n = 62
Sum = 0.5 * 62 * (62 + 1)
Sum = 1953
Assume = 63
Sum = 0.5 * 63 * (63 + 1)
Sum = 2016
2007 is between 1953 and 2016
Since 2016 is greater than 1953, we can conclude that 2007 is in row 63
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1. Calculate the area of the kite shown in the figure below:
9 cm
9 cm
35
Complete the following chart (check picture below)
The following requires the submission of the details of the parabola related to the equations.
What is a Parabola?A parabola, simply defined, is a plane curve that is created by a point that is moving such that it's distance from a fixed locus is equal to it's distance from a line that is fixed.
What are the details for equation y = -2(x-5)² + 3?Vertex → (5,3)Axis of Symmetry → x = 5Direction of Opening → Opens downMax or Min → (5, 3)Y-intercept → 25/8What are the details for equation y = (x + 2)²Vertex → (-2, 0)Axis of Symmetry → x = -2Direction of Opening → Opens UpMax or Min - (-2, 0)Y-intercept → (0,-47)Learn more about Parabola at;
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Given f(x) = 4x + 1 and g(x) = x^, choose
the expression for (fᵒg)(x).
Answer: 4x^2 + 1
Step-by-step explanation:
I am assuming g(x) = x^2
4(x^2) + 1
4x^2 + 1
Answer:
[tex](fog)(x)=4x^2+1[/tex]
Step-by-step explanation:
Assume [tex]g(x)=x^2[/tex]
[tex](fog)(x)[/tex] is a composition of two functions such that [tex](fog)(x)=f(g(x))[/tex].
Consider the function:
[tex]f(x)=4x+1[/tex]
Replace [tex]x[/tex] with [tex]g(x)[/tex] into the equation:
[tex]f(g(x))=4\cdot g(x)+1[/tex]
Substitute [tex]g(x)=x^2[/tex] on the right side of the equation:
[tex]f(g(x))=4\cdot x^2+1[/tex]
Therefore, the expression for [tex](fog)(x)[/tex] is [tex]4x^2+1[/tex].
Hi! Please help me find the slope of the line.
Answer:
3/2
Step-by-step explanation:
We can use the slope formula to find the slope of the line
m = ( y2-y1)/(x2-x1)
Using the points (0,-4) and (2,-1)
m = ( -1 - -4)/( 2 - 0)
= (-1+4)/ (2 -0)
= 3/2
State engineers have determined that a bridge cannot carry more than 700,000 pounds evenly dispersed.
The legal limit for 6-axle trucks is 100,000 pounds and the legal limit for Z-axle trucks is 34,000 pounds.
How many 6-axle trucks can travel on the bridge at one time? How many 2-axle trucks? (Assume that
there are no other vehicles on the bridge.) Write an inequality to solve the problem, then graph the solution.
The inequality of the bridge's legal limit 100000x + 34000y ≤ 700000
How to determine the inequalityThe given parameters are:
Maximum = 700,000 pounds6-axle trucks = 100,000 pounds2-axle trucks = 34,000 poundsRepresent the 6-axle trucks with x and the y-axle trucks with y.
So, we have the following inequality
100000x + 34000y ≤ 700000
The number of 6-axle trucks at one time
Here, we assume that y = 0.
So, we have:
100000x ≤ 700000
Divide by 100000
x ≤ 7
Hence, the number of 6-axle trucks at one time is 7
The number of 2-axle trucks at one time
Here, we assume that x = 0.
So, we have:
34000x ≤ 700000
Divide by 34000
x ≤ 20.58
Round down
x ≤ 20
Hence, the number of 2-axle trucks at one time is 20
See attachment for the inequality of 100000x + 34000y ≤ 700000
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Which of the following demonstrates the correct first step in copying an angle?
Create a line that intersects the angle.
Draw a ray with one endpoint.
Create a point outside of the angle.
Swing an arc that intersects the angle's rays.
"Draw a ray with one endpoint" demonstrates the correct first step in copying an angle. This is further explained below.
What is the angle?In general, the distance (which is sometimes stated as a degree) that occurs between two crossing lines or surfaces at or near the point where they meet. This distance might be positive or negative.
The formation of an angle is caused by the conjunction of two rays at a single point in space. The split or 'opening' that can be seen between these two rays is referred to as a 'angle,' and the symbol denotes this particular angle. The degree is the standard unit of measurement for angles, and its values include things like 60 degrees and 90 degrees, amongst other possible combinations.
In conclusion, "Draw a ray with one terminal" illustrates the correct first step in duplicating an angle. This step shows how to replicate an angle.
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Tasha wants to graph a line that is parallel to the line with equation y=3x. Give two examples of linear equations that represent lines she should draw: one that us above the original line and one that is below the original line
Answer:
y = 3x + a (a > 0) - above the original line
y = 3x + b (b < 0) - below the original line
Step-by-step explanation:
Pick any number you want for a or b, as long as the number meets the condition I wrote down.
Answer:
y=3x+1 and y=3x-1
Step-by-step explanation:
y=3x+1 is above because it has a positive slope (3) while y=3x-1 is below because it has a negative slope (-3).
Explain why you need to state the domain before simplifying a rational function. you should use at least one example in your explanation.
Knowing which x-values would result in division by zero can help you avoid using certain x-values. Finding the domains of rational functions is therefore likely to be your initial step.
What is a rational function?A function that measures two polynomials in comparison. Because one is divided by the other, just like a ratio, it is a "rational function."
All real numbers x, except those for which the denominator is 0, are included in the domain of a rational function. Equilibrate the denominator to zero and then solve for x to determine which x values are excluded from the scope of a rational function.
For instance, the set of all real numbers other than x=0 is the domain of the parent function f(x)=1/x.
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Guys I need help! You and your friend are rolling number cubes. Each cube has 6 sides with the numbers 1 to 6. If a sum of 7 is rolled, your friend gets 1 point.
If a 2, 3, or 4 is rolled, you get 1 point.
After 108 rolls each, what scores should you expect?
1. Friend: 54; You: 54
2. Friend: 54; You: 18
3. Friend: 18; You: 18
4. Friend: 18; You: 54
A ball of radius 14 has a round hole of radius 4 drilled through its center.
Find the volume of the resulting solid.
The volume of the spherical solid resulting of the drill is of 11,226 units³.
What is the volume of a sphere?The volume of a sphere of radius r is given as follows:
[tex]V = \frac{4\pi r^3}{3}[/tex]
In this problem, we have two spherical balls, one of radius 14 and other of radius 4, hence their volumes are given as follows:
[tex]V_1 = \frac{4\pi 14^3}{3} = 11494[/tex]
[tex]V_2 = \frac{4\pi 4^3}{3} = 268[/tex]
The volume of the resulting solid is the difference of the volumes, hence:
V = 11494 - 268 = 11,226 units³.
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6. Error Analysis A classmate says the endpoints of
the midsegment of the trapezoid in Problem 3 are
d+a
(2/2) and (dª). What is your classmate's
error? Explain.
M
R(2b, 2c) A(2d, 2c)
N
P(2a, 0)
Answer:
They used coordinates P(a,0), A(d,c), and R(b,c) instead of the given coordinates.
PLS HELP ME I PUT THIS OUT ONCE BUT DIDNT GET HELP !
Hope this helped!
This is just what I drew. I believe the answer for B could be somewhat different than what I drew.
Have a nice day!
Complete the sentence below. if (3x2 22x 7) ÷(x 7) = 3x 1, then (x 7)( ) = . the check of the polynomial division problem shows that the product of two polynomials is a polynomial. this supports the fact that the property is satisfied for polynomial multiplication.
The full set is;
(x + 7) (3x + 1) = 3x² + 22x + 7
This question introduces the concept of polynomial long division.
This is what we are
Given: (3x² + 22x + 7) ÷ (x + 7) = 3x + 1
Now, from the concept of polynomial long division, we can see that:
if, f (x) ÷ g (x) = h (x),
This means that we can write:
f (x) = g (x) × h (x)
Applying the same concept to the question, we can also say:
(3x² + 22x + 7) ÷ (x + 7) = 3x + 1,
Next; (x + 7) (3x + 1) = 3x² + 22x + 7
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Hi I need help with the question in the image. Step by step, thank you!
The exponential function is [tex]f(x) = 18(12)^{-x-4} + 2[/tex]
How to determine the equation?An exponential function is represented as:
y = b^x
Where b represents the base.
The base is given as:
b = 12
So, we have:
y = (12)^x
It is vertically compressed by a factor of 1/8.
So, we have:
y = 18(12)^x
When reflected across the y-axis, we have:
[tex]y = 18(12)^{-x}[/tex]
The horizontal asymptote is y = 2.
So, we have:
[tex]y = 18(12)^{-x} + 2[/tex]
It passes through the point (-3, 4).
So, we shift the function to the right by 4 units
[tex]y = 18(12)^{-x-4} + 2[/tex]
Express as a function
[tex]f(x) = 18(12)^{-x-4} + 2[/tex]
Hence, the exponential function is [tex]f(x) = 18(12)^{-x-4} + 2[/tex]
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TRUE or FALSE: The square root of R2 (the coefficient of determination) is r, the correlation coefficient. (remember that square roots are always positive)
The The square root of R² (the coefficient of determination) is not r, the correlation coefficient. Therefore, it's false.
What is a correlation coefficient?It should be noted that the correlation coefficient is used to measure how string the relationship between two variables are.
The correlation formula tells us the linear relationship between the variables. R² is the square of the correlation coefficient.
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What is EBC? ASAP please
We know that if [tex]m\angle ABD=2(m\angle DBC)[/tex], then [tex]m\angle ABD=\frac{2n}{3}[/tex] and [tex]m\angle DBC=\frac{n}{3}[/tex].
Since BE bisects [tex]\angle DBC[/tex], we know that [tex]\angle DBE \cong \angle EBC[/tex], and thus [tex]\angle EBC=\boxed{\frac{n}{6}}[/tex]
What is the value of x
Could someone help me out here and show the work for this question? Thank and this is much appreciated
Answer:
[tex]\boxed{\boxed{\bf x = 7}}[/tex]
Step-by-step explanation:
[tex] \sf \cfrac{4x - 4}{20} = \cfrac{30}{25} [/tex]
[tex]\sf 4x - 4 = \cfrac{(20)(30)}{25} [/tex]
[tex]\sf 4x - 4 = \cfrac{600}{25} [/tex]
[tex]\sf 4x - 4 = 24[/tex]
[tex]\sf 4x = 24 + 4[/tex]
[tex]\sf \cfrac{4x}{4} = \cfrac{28}{4} [/tex]
[tex]\sf x = 7[/tex]
----------------------------------The number of cars parked in a car park increases from 50 to 73. what is the percentage increase?
73 is a 46% increase of 50.
What is percentage ?
A percentage is a relative value that represents the hundredth part of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entire amount and 200 percent specifies twice the given amount.
Percentage is defined as a specific part or amount out of a hundred. It is a fraction with the denominator 100 and is denoted by the symbol "percent."
The percent increase formula is as follows:
Percent increase = [(new value - original value)/original value] * 100.
Number of car parking (original value)=50
Number of car parking(new value)=73
The Percentage increase =[(73-50)/50]*100
= [(23)/50]*100
=.46*100
=46%
73 is a 46% increase of 50.
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On a coordinate plane, a curved line labeled f of x with a minimum value of (1.9, negative 5.7) and a maximum value of (0, 2), crosses the x-axis at (negative 0.7, 0), (0.76, 0), and (2.5, 0), and crosses the y-axis at (0, 2).
Which statement is true about the graphed function?
F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5).
F(x) > 0 over the intervals (-∞, -0.7) and (0.76, 2.5).
F(x) < 0 over the intervals (-0.7, 0.76) and (2.5, ∞).
F(x) > 0 over the intervals (-0.7, 0.76) and (0.76, ∞).
Answer:
(a) F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5)
Step-by-step explanation:
Wherever the function crosses the x-axis, its sign changes. This lets us make a map of the signs of the function, and identify intervals where it is positive and negative.
Sign changesThe x-intercepts are said to be at x ∈ {-0.7, 0.76, 2.5}. These three crossing points divide the graph into four (4) intervals. The sign of the function is given as positive at x=0 and negative at x = 1.9. So, our sign map is ...
< -0.7 . . . . . negative
-0.7 to 0.76 . . . . . positive (2 at x=0, for example)
0.76 to 2.5 . . . . . negative (-5.7 at 1.9, for example)
> 2.5 . . . . . positive
Choosing from the descriptions, the one that matches is ...
F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5)
Can someone help with this geometry question? It’s urgent
Answer:
Step-by-step explanation:
So if you look at the first photo I sent you'll see I marked three points. So the first point is going to be the two lines meet and the other two are going to be at 0 degrees and 48 degrees. After that you're going to draw a line to connect 2 of the dots to the middle one or the one connecting the two. After this you're going to put the protractor back on the triangle and line it up and then draw a point at 24 degrees (half of 48 degrees) and then draw a line to it. And this will be the bisector. And then after that label all the points. Also for the congruency thing just do the same thing except without an angle bisector through it.
Which inequality is true? 1.5 greater-than 2 and one-half
One-half greater-than 0.5
Negative 2.5 greater-than negative 1.5
Negative 3 and one-half greater-than negative 4.5
The inequality negative 3 and one-half greater-than negative 4.5 or -3.5 > -4.5 is true.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
We have inequalities given:
[tex]1.5 > 2\dfrac{1}{2}[/tex]
or
1.5 > 2.5 (false)
1/2 > 0.5
0.5 > 0.5 (false)
-2.5 > -1.5 (false)
[tex]-3 \dfrac{1}{2} > -4.5[/tex]
-3.5 > -4.5 (true)
Thus, the inequality negative 3 and one-half greater-than negative 4.5 or -3.5 > -4.5 is true.
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What are the zeros of g(x)= x³ + 6x² - 9x-54?
Answer:
3,-3
Step-by-step explanation:
g(3)= (3)³+6(3)²-9(3)-54
= 27+54-27-54
=81-81
= 0
g(-3) = (-3)³+6(-3)²-9(-3)-54
= -27+54+27-54
= 27-27
= 0
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Find a linear inequality with the following solution set. Each grid line represents one unit.
Answer:
y≤-x+1
Step-by-step explanation:
Since the line is slanted down and crossing through a point every one unit the slope is negative one. The line is also crossing 1 on the y-axis. This is the y-intercept. The last thing we need to know is which sign to use, less than, greater than, less than or equal to, greater than or equal to. We can immediately cross out less than and greater than because it is a solid line. The sign used on the graph is less than or equal to because it is a solid line shaded to the left. Now, we can use the formula with the information we have found to create the linear inequality.
Formula: y≤x+b
I put the less than or equal to sign there instead of the equal sign because the line graphed is less than or equal to. Plug in the information we have.
y≤-x+1
Using function notation.
f(x)≤-x+1
I have also attached a picture for you to see it is correct.
Hope this helps!
If not, I am sorry.
Geometry)
Given the circle with center O and with m angle ROQ=144^o , find the measure of minor arc PR.
Answer choices…
72^o
216^o
36^o
18^o
(Picture is below) Thank you!
AMSWER :
Just remove the given angle from 180°
since , a straight line makes a angle of 180°
hence,
ROQ + ROP = 180°
144° + ROP = 180°
ROP = 180° - 144° = 36°
.
.
________________________________
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Given that is the angle bisector of A, determine the length of x. (SHOW YOUR WORK PLEASE!!!)
The length of x will be 4 cm if is the angle bisector of A.
What is an angle bisector?A straight line that splits an angle in a triangle into two congruent angles is known as the angle bisector.
Given sides;
AB=12
AE=8
BD=6
DE=x
From the triangle angle bisector theorem;
[tex]\rm \frac{BD}{DE} = \frac{AB}{AE} \\\\ \frac{6}{x} =\frac{12}{8} \\\\ x=4[/tex]
Hence the length of x will be 4 cm.
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Consider [tex]$\triangle ABC$ such that $BC = 3AC$ and $\angle A = \pi/6$[/tex]
What are [tex]\[12 \sin(\angle B), 12 \sin(\angle C)\][/tex] in that order?
The answer to the question is,
12 sin(∠B) = 2, 12 sin(∠C) = √3+√35
Sin rule is,
sin(A)/BC = sin(B)/AC = sin(C)/AB
sin(B) = (sin(A)×AC)/BC
sin(C) =(sin(B)×AB)/AC
To solve this question we apply sin rule,
Now we take
12 sin(∠B) =12 (sin(∠A)×AC)/BC
12 sin(∠B) =12 (sin(π/6)×(x/3x)) where ∠A =π/6 and AC=x, BC =3x
12 sin(∠B) =12 ((1/2)×(1/3))
12 sin(∠B) =12/6 = 2
12 sin(∠B) = 2
now we find the value of 12 sin(∠C)
12 sin(∠C) = 12(sin B)×(AB/BC)
now put the value of 12 sin(∠B) = 2
12 sin(∠C) = 2×(AB/BC)
12 sin(∠C) = (2/AC)×[AC×(cos(π/6))+BC×(cos B)]
12 sin(∠C) = 2×[cos(π/6)+(BC/AC)×(cos B)]
cos (π/6) = √3/2 and BC/AC =3
then
12 sin(∠C) = 2×[(√3/2)+3×(cos B)]
cos B= √1-sin²B
12 sin(∠C) = 2×[(√3/2)+3×√(1-sin²B)]
12 sin(∠B) = 2
sin B = 1/6
12 sin(∠C) = 2×[(√3/2)+3×√(1-(1/6)²]
12 sin(∠C) = 2×[(√3/2)+3×√1-(1/36)]
12 sin(∠C) = 2×[(√3/2)+3×√(36-1)/36]
12 sin(∠C) = 2×[(√3/2)+3×√(35/36)]
12 sin(∠C) = 2×[(√3/2)+(3/6)×√35]
12 sin(∠C) = 2×[(√3/2)+(1/2)×√35]
12 sin(∠C) = 2×[(1/2)(√3+√35)]
12 sin(∠C) = √3+√35
Hence the answer is,
12 sin(∠B) = 2, 12 sin(∠C) = √3+√35
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Elvira College has an enrollment of 1,000 students and is located in a small Midwestern town named Johnsonville. Johnsonville has a total population of 2,500 people. The nearest town is 20 miles away. Most of the residents shop locally, but they travel about once a month to the larger city and pick up the large-ticket items. Johnsonville has one fairly good-size supply store named Jameson's Grocery. The only other place in town where you might buy supplies is at the gas station/convenience store located on the edge of town. What competitive situation is Jameson's Grocery experiencing?
Since there are only two (2) sellers in the town with many buyers, the competitive situation which Jameson's Grocery is experiencing is an oligopoly.
What is an oligopoly?An oligopoly can be defined as a market structure which comprises a small number of business firms (sellers) that are offering identical (similar) products to many buyers, wherein none of the sellers can limit the significant influence of others.
In this scenario, we can infer and logically deduce that the competitive situation which Jameson's Grocery is experiencing is an oligopoly because there are only two (2) sellers in the town with many buyers (1,000 students).
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