The points plotted below are on the graph of a polynomial. How many roots
of the polynomial lie between x = -4 and x = 3?
URGENT
Answers
Given:
The graph of a polynomial.
To find:
The number of roots of the polynomial lie between x = -4 and x = 3.
Solution:
From the given graph it is clear that the graph is a downward U-shaped curve. It means the given graph represents a quadratic polynomial.
The graph of the polynomial is below the x-axis immediate before x=-2 and above the x-axis immediate after x=-2. It means the graph intersect the x-axis at x=-2.
The graph of the polynomial is above the x-axis immediate before x=2 and below the x-axis immediate after x=2. It means the graph intersect the x-axis at x=2.
Since the graph of the polynomial divides the x-axis two times between x = -4 and x = 3, therefore the two roots of the polynomial lie between x = -4 and x = 3.
Related Questions
Given two points P(sinθ+2, tanθ-2) and Q(4sin²θ+4sinθcosθ+2acosθ, 3sinθ-2cosθ+a). Find constant "a" and the corresponding value of θ when these two points coincide. (0 ≤ θ < 2π)
Show your work, thanks!
Answers
Answer:
[tex] \rm\displaystyle \displaystyle \displaystyle θ= {60}^{ \circ} , {300}^{ \circ} [/tex]
[tex] \rm \displaystyle a = - \frac{ \sqrt{3} }{2} - 1, \frac{\sqrt{3}}{2} - 1[/tex]
Step-by-step explanation:
we are given two coincident points
[tex] \displaystyle P( \sin(θ)+2, \tan(θ)-2) \: \text{and } \\ \displaystyle Q(4 \sin ^{2} (θ)+4 \sin(θ) \cos(θ)+2a \cos(θ), 3 \sin(θ)-2 \cos(θ)+a)[/tex]
since they are coincident points
[tex] \rm \displaystyle P( \sin(θ)+2, \tan(θ)-2) = \displaystyle Q(4 \sin ^{2} (θ)+4 \sin(θ )\cos(θ)+2a \cos(θ), 3 \sin(θ)-2 \cos(θ)+a)[/tex]
By order pair we obtain:
[tex] \begin{cases} \rm\displaystyle \displaystyle 4 \sin ^{2} (θ)+4 \sin(θ) \cos(θ)+2a \cos(θ) = \sin( \theta) + 2 \\ \\ \displaystyle 3 \sin( \theta) - 2 \cos( \theta) + a = \tan( \theta) - 2\end{cases}[/tex]
now we end up with a simultaneous equation as we have two variables
to figure out the simultaneous equation we can consider using substitution method
to do so, make a the subject of the equation.therefore from the second equation we acquire:
[tex] \begin{cases} \rm\displaystyle \displaystyle 4 \sin ^{2} (θ)+4 \sinθ \cos(θ)+2a \cos(θ )= \sin( \theta) + 2 \\ \\ \boxed{\displaystyle a = \tan( \theta) - 2 - 3 \sin( \theta) + 2 \cos( \theta) } \end{cases}[/tex]
now substitute:
[tex] \rm\displaystyle \displaystyle 4 \sin ^{2} (θ)+4 \sin(θ) \cos(θ)+2 \cos(θ) \{\tan( \theta) - 2 - 3 \sin( \theta) + 2 \cos( \theta) \}= \sin( \theta) + 2 [/tex]
distribute:
[tex]\rm\displaystyle \displaystyle 4 \sin ^{2}( θ)+4 \sin(θ) \cos(θ)+2 \sin(θ ) - 4\cos( \theta) - 6 \sin( \theta) \cos( \theta) + 4 \cos ^{2} ( \theta) = \sin( \theta) + 2 [/tex]
collect like terms:
[tex]\rm\displaystyle \displaystyle 4 \sin ^{2}( θ) - 2\sin(θ) \cos(θ)+2 \sin(θ ) - 4\cos( \theta) + 4 \cos ^{2} ( \theta) = \sin( \theta) + 2 [/tex]
rearrange:
[tex]\rm\displaystyle \displaystyle 4 \sin ^{2}( θ) + 4 \cos ^{2} ( \theta) - 2\sin(θ) \cos(θ)+2 \sin(θ ) - 4\cos( \theta) + = \sin( \theta) + 2 [/tex]
by Pythagorean theorem we obtain:
[tex]\rm\displaystyle \displaystyle 4 - 2\sin(θ) \cos(θ)+2 \sin(θ ) - 4\cos( \theta) = \sin( \theta) + 2 [/tex]
cancel 4 from both sides:
[tex]\rm\displaystyle \displaystyle - 2\sin(θ) \cos(θ)+2 \sin(θ ) - 4\cos( \theta) = \sin( \theta) - 2[/tex]
move right hand side expression to left hand side and change its sign:
[tex]\rm\displaystyle \displaystyle - 2\sin(θ) \cos(θ)+\sin(θ ) - 4\cos( \theta) + 2 = 0[/tex]
factor out sin:
[tex]\rm\displaystyle \displaystyle \sin (θ) (- 2 \cos(θ)+1) - 4\cos( \theta) + 2 = 0[/tex]
factor out 2:
[tex]\rm\displaystyle \displaystyle \sin (θ) (- 2 \cos(θ)+1) + 2(- 2\cos( \theta) + 1 ) = 0[/tex]
group:
[tex]\rm\displaystyle \displaystyle ( \sin (θ) + 2)(- 2 \cos(θ)+1) = 0[/tex]
factor out -1:
[tex]\rm\displaystyle \displaystyle - ( \sin (θ) + 2)(2 \cos(θ) - 1) = 0[/tex]
divide both sides by -1:
[tex]\rm\displaystyle \displaystyle ( \sin (θ) + 2)(2 \cos(θ) - 1) = 0[/tex]
by Zero product property we acquire:
[tex] \begin{cases}\rm\displaystyle \displaystyle \sin (θ) + 2 = 0 \\ \displaystyle2 \cos(θ) - 1= 0 \end{cases}[/tex]
cancel 2 from the first equation and add 1 to the second equation since -1≤sinθ≤1 the first equation is false for any value of theta
[tex] \begin{cases}\rm\displaystyle \displaystyle \sin (θ) \neq - 2 \\ \displaystyle2 \cos(θ) = 1\end{cases}[/tex]
divide both sides by 2:
[tex] \rm\displaystyle \displaystyle \displaystyle \cos(θ) = \frac{1}{2}[/tex]
by unit circle we get:
[tex] \rm\displaystyle \displaystyle \displaystyle θ= {60}^{ \circ} , {300}^{ \circ} [/tex]
so when θ is 60° a is:
[tex] \rm \displaystyle a = \tan( {60}^{ \circ} ) - 2 - 3 \sin( {60}^{ \circ} ) + 2 \cos( {60}^{ \circ} ) [/tex]
recall unit circle:
[tex] \rm \displaystyle a = \sqrt{3} - 2 - \frac{ 3\sqrt{3} }{2} + 2 \cdot \frac{1}{2} [/tex]
simplify which yields:
[tex] \rm \displaystyle a = - \frac{ \sqrt{3} }{2} - 1[/tex]
when θ is 300°
[tex] \rm \displaystyle a = \tan( {300}^{ \circ} ) - 2 - 3 \sin( {300}^{ \circ} ) + 2 \cos( {300}^{ \circ} ) [/tex]
remember unit circle:
[tex] \rm \displaystyle a = - \sqrt{3} - 2 + \frac{3\sqrt{ 3} }{2} + 2 \cdot \frac{1}{2} [/tex]
simplify which yields:
[tex] \rm \displaystyle a = \frac{ \sqrt{3} }{2} - 1[/tex]
and we are done!
disclaimer: also refer the attachment I did it first before answering the question
Joe tried to prove that the sum of a triangle's interior angle measures is 180°
Answers
Answer: Angles ∠4 and∠2 are not alternate interior angles and neither are ∠1 and ∠5
Step-by-step explanation: Khan Academy
Joe made the mistake by guessing Angles ∠4 and∠2 are not alternate interior angles and neither are ∠1 and ∠5.
The correct option is (b).
What is Parallel line?The fundamental characteristics listed below make it simple to recognise parallel lines.
Straight lines that are always the same distance apart from one another are called parallel lines.No matter how far apart they are from one another, parallel lines can never intersect.Given:
WE have to prove that the sum of a triangle's interior angle measures is 180°
According to the figure <1 and <4 are the alternate interior angle and <2 and <5 are alternate interior angle.
So, Joe made the mistake by guessing Angles ∠4 and∠2 and ∠1 and ∠5 are alternate interior angles.
Learn more about parallel lines here:
https://brainly.com/question/16701300
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(NO LINKS OR else your be reported)
Pls help me if your good at math I’ll mark brainliest I
~couldn’t get the whole picture in:(~
A pair of parallel lines are translated.which of these could be the result?
Answers
Answer:
B
Step-by-step explanation:
Which graph shows the line y = 4x - 2?
Answers
Answer:
Hi, there the answer is Graph A because the y-intercept and I did rise over run
Step-by-step explanation:
Hope this helps :)
Help!! Thank you so much
Answers
Answer:
336 cm²
Step-by-step explanation:
rectangle area:
b×h = 24×7,5=180 cm²
" " = 6,5×24=156 cm²
total area: 180+156=336 cm²
when i post these questions just solve them for my brother will ya plz he will give thanks to who ever does it
Answers
Answer:
1/4 or 5/20
Step-by-step explanation:
You find how many numbers are above 10. Then find the frequency and add them together, that will be your numerator. The total number of tries is 200, that is your denominator.
What are simultaneous equations
Answers
Answer:
Simultaneous equations are equations involving two or more unknowns that are to have the same values in each equation.
10. A map uses the scale of ã of an inch to represent 3
miles. If the actual distance between two cities is
25 miles, then what is the length on the map?
Answers
please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!!!!
Answers
Answer:
∠ G ≈ 8.3°
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan G = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{HI}{GI}[/tex] = [tex]\frac{1.1}{7.5}[/tex] , then
∠ G = [tex]tan^{-1}[/tex] ([tex]\frac{1.1}{7.5}[/tex] ) ≈ 8.3° ( to the nearest tenth )
Building A is 490 feet tall and Building B is 754 feet tall. If the angle of depression from the top of Building B to the top of Building A is 46°, how far apart are the buildings?
Answers
Answer: [tex]254.94\ ft[/tex]
Step-by-step explanation:
Given
Building A is 490 feet tall and building B is 754 ft tall.
If the angle of depression from building B to the top of building A is [tex]46^{\circ}[/tex]
Difference in the height of the two buildings is [tex]754-490=264\ ft[/tex]
If the difference between them is [tex]x[/tex]
From the figure, we can write
[tex]\Rightarrow \tan 46^{\circ}=\dfrac{264}{x}\\\\\Rightarrow x=\dfrac{264}{\tan 46^{\circ}}\\\\\Rightarrow x=254.94\ ft[/tex]
Therefore, the two buildings are [tex]254.94\ ft[/tex] apart.
In how many different
ways can 5 bicycles be
parked if there are 7
available parking
spaces?
pls pasagot
Answers
5 bicycles can be parked in=7*5
=35
Therefore 5 bicycles can be parked in 35 different ways
Question 4 pls thanks, I will mark Brainliest
Answers
the second one.
Step-by-step explanation:
sjisidjdododpdpddod
(13.01 LC) What is the value of the expression 7 +(16 - 7) = 3 + 8? (2 points) O 12 O 15 O 17 O 18 Question 3
Answers
Answer:
16 > 11
Step-by-step explanation:
7 + (16 - 7) = 3 + 8
7 + 9 = 3 + 8
16 = 3 + 8
16 ≠ 11
or
16 > 11
The length of a rectangular piece of
construction paper is 8 inches and the width
is 17 inches. Vincent folded the piece of
paper along its diagonal. Which
measurement is closest to the length of the
diagonal in inches?
A. 5 in.
B. 18.79 in
C. 15 in
D. 25 in.
Answers
Answer:
B 18.79
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Evaluate 1/3m-1-1/2n when m=21 and n=12
Answers
Answer:
12
Step-by-step explanation:
Here are the city gas mileages for 13 different midsized cars in 2008. 16, 15, 22, 21, 24, 19, 20, 20, 21, 27, 18, 21, 48 What is the first quartile?
Answers
Answer:
Q1 --> 18.5
Step-by-step explanation:
2. Which equation describes a line that has
a slope of and a y-intercept of ?
A) 5y + 4x = 2
C) Sy - 4x = 2
B) 4x5y = 2
D) -5y - 4x = 2
Answers
Answer:
What?
Step-by-step explanation:
G8ve me more info and Ill answer again
Lydia was doing her homework. She did math for 3/5 of an hour. She did science for 2/3 of an hour, half an hour for art sketches, and 1/10 of an hour for French. and How much time did she spend on her homework? How much time would she have spent if she took 10 minutes break between each subject? Show your work.
Answers
Answer:
82 minutes
102 minutes with breaks
Step-by-step explanation:
So there are 60 minutes in an hour. 3/5 of 60 is 36. 2/3 of 60 is 40. And 1/10 of 60 is 6. So adding all those numbers up 36+40+6=82 minutes.
Now if she spent 10 minute breaks in between her assignments then she did 36+10+40+10+6=102 minutes with breaks in between Math and Art also Art and French
Which statement about rectangles and rhombuses is always true?
Answers
Answer:
B
Step-by-step explanation:
B...............................
mark me the brainliest plzzzzzzzz
The statement about rectangles and rhombuses that is always true is that both figures are quadrilaterals.
What is a quadrilateral?A quadrilateral is a closed, two-dimensional shape which has four straight sides.
In other word, a quadrilateral is a plane figure that has four sides or edges, and also has four corners or vertices.
Quadrilateral has four sides.
Rhombuses and rectangles have four sides. Therefore, they are both quadrilaterals.
learn more on quadrilateral here: https://brainly.com/question/10388790
plss help me answer this
Answers
Answer:
c≈5.2
Step-by-step explanation:
c=a2+b2=1.412+52≈5.19501
find the range of the data 52 40 49 48 62 54 44 58 and 39 range is what
Answers
Answer:
Hi! The answer to your question is the range is 23
Step-by-step explanation:
Subtract the minimum data value from the maximum data value to find the data range. In this case, the data range is 62-39=23
VOCAB:
Minumum Data = Smallest Number
Maximum Data = Largest Number
Data Range = The set of y-values that a function passes through, Also the right coordinate in a coordinate pair.
In statistics, the difference between the largest number and the smallest numbers in a data set.
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☁Brainliest is greatly appreciated!☁
Hope this helps!!
- Brooklynn Deka
what are the steps in 3-√x-2 =0 ? (to find x)
Answers
Answer:
x=1
Step-by-step explanation:
3-√x-2 =0
-√x=2-3
√x=1
x=1²=1
Solve the following quadratic function
by utilizing the square root method.
y = 25x2 - 100
X = +[?]
Answers
Answer
25(x2−4)
Rewrite 4
as 22.25(x2−22)
Find the perimeter of the figure.
Answers
Answer:
26 meters
Step-by-step explanation: Ez. First add all the data you already have. You should end up with 19. Then, you want to find the length of the missing side. Well, we know it's 7 meters since its opposite is 7, and these lengths are in the same square. So 19+7 is 26 meters.
Answer:
[tex]26[/tex]
Step-by-step explanation:
perimeter= AB + BC + CE + DE + AD
AB= DE = 7
BC = 5
EC= 3
DE = 7
AD = 4
So, perimeter = 7+ 5+ 3+ 7+ 4
→ 12+ 10 +4
→ 24+ 4
→26
So, 26 is your answer
[tex]----------[/tex]
hope it helps..
have a great day!!
Find the length of the third side. If necessary, round to the nearest tenth.2 5
Answers
Answer:
b= 4.6
Step-by-step explanation:
use the pythagorean theorem.
Answer:
4.6
Step-by-step explanation:
solve for x in the diagram below
Answers
Answer:
x=20
Step-by-step explanation:
3x+80+2x=180(being linear pair)
5x=180-80
x=100/5
x=20
3x=3*x =3*20 =60
2x=2*x =2*20 =40
Complete the square to find
the vertex of this parabola.
x^2 - 4x + y + 10 = 0
([?], [ ])
Answers
Answer: 2,-6
Step-by-step explanation:
The vertex of the parabola defined by the equation x² - 4x + y + 10 = 0 is (2, -6).
To maintain the equality of the equation, we need to add and subtract 4 within the parentheses.
3. Rewrite the equation by adding and subtracting 4 within the parentheses: x² - 4x + 4 + y = -10 + 4.
Now, we can factor the perfect square trinomial (x - 2)² and simplify the right side of the equation.
4. Factor the perfect square trinomial: (x - 2)² + y = -6.
The equation is now in the form (x - h)² + k = y, where (h, k) represents the vertex of the parabola. Therefore, the vertex of the parabola is (2, -6).
To learn more about parabolas;
https://brainly.com/question/21685473
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The complete question:
Complete the square to find
the vertex of this parabola.
x² - 4x + y + 10 = 0
foods that build up the immune system
Answers
Answer:
1. Citrus fruits · 2. Red bell peppers · 3. Broccoli · 4. Garlic · 5. Ginger · 6. Spinach · 7. Yogurt · 8. Almonds.
Step-by-step explanation:
Answer:
Citrus fruits.
Red bell peppers.
Broccoli.
Garlic.
Ginger.
Spinach.
Yogurt.
Almonds.
Step-by-step explanation:
please answer fast help me i have thgis math problem
Answers
Answer:
[tex]x = 152[/tex]
because these angles are infront of each other
Answer:
x = 152
Step-by-step explanation:
x and 152° are vertical angles and are congruent , then
x = 152
To solve this system of equations by elimination you should begin by... x+y=10 2x-3y=6 A) adding the two equations together. B) multiplying the first equation by 2, then add them together. C)multiplying the first equation by 3, then add them together. D) subtracting the first equation from the second equation
Answers
Answer:
C. Multiply 1st equation by 3, then add together
Step-by-step explanation:
X+y=10
3(x+y)=3(10)multiply by 3
3x+3y=30 add to following equation
2x-3y=6
5x=36