here is a graph of a polynomial function with degree 4 what statements are true about the function?
Answers
It has 4 linear factors (the graph crosses the x-axis at 4 places)
One of the zeroes is x=2 (the graph crosses the x-axis at x=2)
The statements that are true about the functions are:
The leading coefficient is positive.
It has two relative maximums
It has four linear factors.
One of the zeroes is x = 2.
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
From the graph,
The graph passes through the following points on the graph.
x = -4
x = -2
x = 2
x = 6
This means the polynomial function is:
P(x) = (x + 4)(x + 2)(x - 2)(x - 6)
If we simplify the polynomial we get,
P(x) = (x² + 2x + 4x + 8) (x² + 6x - 2x + 12)
P(x) = [tex]x^{4}[/tex] + 6x³ - 2x³ + 12x² + 2x³ + 12x² - 4x² + 24x + 4x³ + 24x² - 8x² + 48x + 8x² + 48x - 16x + 96
P(x) =[tex]x^{4}[/tex] + 10x³ + 44x² + 104x + 96
The leading coefficient is positive 1 so it is positive.
The constant term is a positive number (96).
The relative maximum is a point on the graph where the function changes from increasing to decreasing.
So,
From the graph, there is only one point.
So only one relative maximum.
The relative minimum is a point on the graph where the function changes from decreasing to increasing.
So,
From the graph, there are two relative maximums.
The function has four linear factors
(x + 4), (x + 2), (x - 2), and (x - 6).
x = -4, x = -2, x = 2, and x = 6
Thus,
The statements that are true about the functions are:
The leading coefficient is positive.
It has two relative maximums
It has four linear factors.
One of the zeroes is x = 2.
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Related Questions
Find the slope of the line graphed below!!
Answers
Answer:
The slope is 3/2
Step-by-step explanation:
Rise = 3
Run = 2
Rise/Run = 3/2
In an unknown planet, a rock with a mass of 10 kg has a weight of 20 N. What is the gravitational acceleration of objects near the surface of the unknown planet?
Answers
Answer:
The gravitational force between a mass and the Earth is the object’s weight. Mass is considered a measure of an object’s inertia, and its weight is the force exerted on the object in a gravitational field. On the surface of the Earth, the two forces are related by the acceleration due to gravity: Fg = mg. Kilograms and slugs are units of mass; newtons and pounds are units of weight.
You can use Newton’s law of gravitation to get the acceleration due to gravity, g, on the surface of the Earth just by knowing the gravitational constant G, the radius of the Earth, and the mass of the Earth. The force on an object of mass m1 near the surface of the Earth is
F = m1g
This force is provided by gravity between the object and the Earth, according to Newton’s gravity formula, and so you can write
Step-by-step explanation:
For this graph, mark the statements that are true.
A. The range is the set of all real numbers.
7
B. The range is the set of all real numbers greater than or equal to
zero.
C. The domain is the set of all real numbers.
D. The domain is the set of all real numbers greater than or equal to
-2.
Answers
Answer:
B and C are true
Step-by-step explanation: range is y values the graph can have from 0 up
domain in x values the graph can have so all number in either direction left and right
Answer:
Step-by-step explanation: The answer is B and C because range is y and it is greater than 0 and domain is x and is go infinitely in both directions
5a+3a-4=36
Somebody please answer this
Answers
Answer:
a=4
Step-by-step explanation:
combine like terms
8a-4=36
add on both sides
8a-4+4=36+4
8a=32
divide
a=32/8
a=4
Answer:
a = 5
Step-by-step explanation:
5a+3a = 8a
8a - 4 = 36
8a - 4 + 4 = 36 + 4
8a = 40
a = 40 divied by 8
a = 5
The sum of the first 21 terms of the progression, - 18, - 15,-12.....is?
Answers
The sum of 21 terms is -1080.
What is Arithmetic Progression?A series in which the differences between each pair of following terms are the same is known as an arithmetic progression.An arithmetic progression is a sequence in which every phrase—aside from the initial term—is created by multiplying the previous term by a predetermined amount.given:
- 18, - 15,-12.....
First term, a= -18
common difference, d= -15 + 18= -3
So, [tex]S_{21[/tex] = 21/2 [ 2(-18)+ (21- 1) (-3)]
[tex]S_{21[/tex] = 21/2 [ -36 + (20) (-3)]
[tex]S_{21[/tex] = 21/2 [ -36 - 60]
[tex]S_{21[/tex] = 21/2 (-96)
[tex]S_{21[/tex] = 21 x (-48)
[tex]S_{21[/tex] = -1008
Hence, the sum of 21 terms is -1080.
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What would you do to both sides of the equation to solve for x?
10x=5
Answers
find the measures of the angles labeled in the figure on the right
Answers
Answer:
Step-by-step explanation:
EFD = 90* (straight line = 180, and other angle is 90)
EHF = 180-52 = 128* (again straight line)
HFG = 90-32 = 58* (its a right angle (can tell by the square angle) = 90*)
G = 180 - 52 - 58 = 70* (angles in triangle = 180)
E = 180 - 32 - 128 = 20* (angles in triangle = 180)
Meg will have
1 serving of frozen yogurt for dessert. One serving of frozen yogurt is
3/4 cup. Meg only has a 1/8 cup scoop. How many scoops should Meg use to get 1 serving?
Answers
can someone do this for me please
Answers
Answer:
Step-by-step explanation:
2(2+3) =9+1
let me know if you get it right
solve for r to find the missing term in geometric sequence.
—
hi can someone please answer my question, thank you ❤️
Answers
Answer:
20 18. on the answer is 18 and 20 give me the brainlyest
Answer:
8, 16, 32, 64, 128,...Step-by-step explanation:
We observe the terms increase twice, therefore r = 2.
The missing terms are:
32/2 = 1616/2 = 8Part 1 - Application
Give a convincing argument with logical explanations that the contrapositive of a conditional is the
same as the converse of the inverse of the conditional
Answers
Answer:
see explanation. (I did this exact assignment this morning, and this is very similar to what I submitted)
Step-by-step explanation:
The contrapositive of a conditional is the same as the converse of the inverse of the conditional.
The best way to prove/support this statement is to create an example. You should start by creating a conditional; you can then form the conditional's converse, inverse, and contrapositive. Here is an example:
Conditional: If C, then D. (starting statement)
Converse: If D, then C. (conditional reversed)
Inverse: If not C, then not D. (opposite of the conditional)
Contrapositive: If not D, then not C. (reversed opposite of the conditional)
Based on the information from the example you gave, you can conclude:
The converse of the inverse: If not D, then not C. (reversed opposite of the conditional)
Because: The converse is the conditional reversed (If D, then C). The inverse of the converse, in this case, would then make it the opposite (If not D, then not C).
I have not yet received a grade on this assignment, but I know the information is correct; the amount of explanation you need to give really depends on how your teacher grades. Personally, I just submitted an example (similar to the one above) that was color-coded to help show the different parts of each statement.
I hope this helps! :)
Find the value of x.
Answers
Find the perimeter of triangle ABC
Answers
Answer:
20 units
Step-by-step explanation:
to solve this equation you need the pythagorean theorem: a^2 + b^2 = c^2
2^2 + 7^2 = 53; square root of 53 is 7.28010989; or about 7.3 units (line AC)
2^2 + 6^2 = 40; square root of 40 is 6.32455532; or about 6.3 units (line BC)
4^2 + 5^2 = 41; square root of 41 is 6.40312424; or about 6.4 units (line AB)
7.3 + 6.3 + 6.4 = 20
20 units
PLEAS EHELP ME I AM BEGGING YOU!!!!!!! EXTRA POINTS AND BRAINLIEST
Answers
1. v= 0.013m/s
t = 60 seconds
d = v×t
= 0.013×60
= *0.78 m*
2. v= 17.6 m/s
d= 100m
t = d/t
= 100/17.6
= *5.68 s*
PLEASE HELP, ITS URGENT!!
A sum of money is shared amongst three friends, Shai, Toni, and Mara in the ratio 6:5:9 respectively. If Toni received $160, how much money did Shai and Mara receive?
Answers
Answer:
Shai received $192 while Mara received $288.
Step-by-step explanation:
Let u be 1 unit.
5u=$160
u=$160÷5
=$32
6u=$32×6
=$192
9u=$32×9
=$288
9/20 - 7/15=
help guys plsss need na now .,.
Answers
Answer:
-1/60
Step-by-step explanation:
9/20-7/15=27/60-28/60
=-1/60
Answer:
-1/60
Step-by-step explanation:
The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.
LCD(9/20, 7/15) = 60
Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.
(9/20×33)−(7/15×44)
Complete the multiplication and the equation becomes
27/60−28/60
The two fractions now have like denominators so you can subtract the numerators.
Then:
27−28/60=−1/60
This fraction cannot be reduced.
Therefore:
9/20−7/15=−1/60
Order the number \pi ,3, and \sqrt(11 )from least to greatest
Answers
Firstly, let's write these out to help us see:
[tex]\pi[/tex] = 3.1415
3
[tex]\sqrt{11}[/tex] = 3.3166
We can see that [tex]\sqrt{11}[/tex] is 0.3166 greater than 3, and 0.1751 greater than pi. Therefore, it's the biggest number.
Pi is second biggest because it is less than [tex]\sqrt{11}[/tex] but greater than 3.
Therefore, your order would be:
3, [tex]\pi[/tex], [tex]\sqrt{11}[/tex]
Hope this helps! :)
If Tristan wants to stretch the spring by 9 inches, how many kilograms of weight must he apply to it?
Answers
Answer:
Step-by-step explanation:
Substitute y = 9 into the equation y = 3x, or locate the answer on the graph:
y = 3x
9 = 3x.
Divide both sides of the equation by 3:
[tex]\frac{9}{3}[/tex] = [tex]\frac{3x}{3}[/tex]
3 = x
The spring stretches 9 inches with 3 kilograms of weight attached to it.
(You toss two dimes 24 times and record the results use the table to find the experimental probability of the event.)
4. Tossing two tails.
5. Tossing on head and one tail.
6. Not tossing 2 heads.
7. Tossing all heads or all tails.
Answers
2. 15/24
3. 5/24
4. 9/24
3.7 - 1.8 - 3.67 + 4.4 - 1.34
Answers
Answer:
1.29
Step-by-step explanation:
Answer:
The person above me is correct, the answer would be 1.29. ^ .^
Step-by-step explanation:
plz help me solving me math questions
Answers
Q3).
0.4x + 0.3y = 1.7
0.7x - 0.2y = 0.8
Solve it by using substitution method.
Answers
Step-by-step explanation:
[tex] \green{\large\underline{\sf{Solution-}}}[/tex]
Given pair of linear equations are
[tex]\rm :\longmapsto\:0.4x + 0.3y = 1.7 \\ \\ \rm :\longmapsto\:0.7x - 0.2y = 0.8[/tex]
can be rewritten as on multiply by 10,
[tex]\rm :\longmapsto\:4x + 3y = 17 - - - - (1)\\ \\ \rm :\longmapsto\:7x - 2y = 8 - - - - - (2)[/tex]
From equation (2)[tex]\rm :\longmapsto\:2y = 7x - 8[/tex]
[tex]\rm\implies \:\boxed{\tt{ y = \frac{7x - 8}{2}}} - - - - (3) [/tex]
On substituting the value of y in equation (1), we get
[tex]\rm :\longmapsto\:4x + 3\bigg( \dfrac{7x - 8}{2} \bigg) = 17[/tex]
[tex]\rm :\longmapsto\:\dfrac{8x + 21x - 24}{2} = 17[/tex]
[tex]\rm :\longmapsto\:29x - 24 = 34[/tex]
[tex]\rm :\longmapsto\:29x = 34 + 24[/tex]
[tex]\rm :\longmapsto\:29x = 58[/tex]
[tex]\bf\implies \:x = 2 - - - - (4)[/tex]
On substituting x = 2 in equation (3), we get
[tex]\rm :\longmapsto\:y = \dfrac{7 \times 2 - 8}{2} [/tex]
[tex]\rm :\longmapsto\:y = \dfrac{14 - 8}{2} [/tex]
[tex]\rm :\longmapsto\:y = \dfrac{6}{2} [/tex]
[tex]\bf\implies \:y = 3[/tex]
So, we get
[tex]\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:\begin{cases} &\bf{x = 2} \\ \\ &\bf{y = 3} \end{cases}\end{gathered}\end{gathered}[/tex]
VerificationFrom equation (1),
[tex]\rm :\longmapsto\:0.4x + 0.3y = 1.7[/tex]
On substituting the value of x and y, we get
[tex]\rm :\longmapsto\:0.4(2) + 0.3(3) = 1.7[/tex]
[tex]\rm :\longmapsto\:0.8 + 0.9 = 1.7[/tex]
[tex]\rm :\longmapsto\:1.7 = 1.7[/tex]
Hence, Verified▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
Basic Concept :-To solve systems using Method of Substitution, follow this procedure:
1. Select one equation and solve it for one of its variables.
2. In the other equation, substitute the value of one variable evaluated in step 1 to reduced the equation to one variable.
3. Solve the equation to get the value of this variable
4. Substitute the value found in to first equation involving both variables and solve for the other variable.
if i make 50 dollars a month and need 600 dollars how many months will it take to get 600 dollars
Answers
Answer:
It will take 12 months to get $600 dollars.
Step-by-step explanation:
All you have to do is 600/50 and 600/50 is 12.
Hope I Helped!
Examples: Which type of triangle is graphed? Classify by Side and Angle. Then find the perimeter of each
(round to the nearest tenth if necessary)
Answers
i need help with my math homework
Answers
Answer:
x=3
Step-by-step explanation:
g(x)=2x+1,
When g(x)=7
g(x)=2x+1,
7=2x+1
7-1=2x
x=6/2
x=3
What is the value of the 3 in this number?
5,400,387,214
is the value of this number.
Answers
Answer:
The value of 3 is in the three-hundred thousands place
300,000
Help!!! I'll give brainly to whoever does it correctly and first
Answers
Answer:-7x but don’t look at me if it’s wrong cuz I finally did not search this up so
Step-by-step explanation:
Answer this please because I need help nowwwww
Answers
Answer:
[tex]3(x + 4) = 3x + 11 \\ 3x + 12 = 3x + 11 \\ 3x - 3x = 12 - 11 \\ 0 = 1[/tex]
So; Not solution
could a triangle have angle measures of 112° 57° and 11°? explain hw u know
Answers
The additional of a triangle's degree measure will always equal 180˚
When the question asks you if a triangle with 112˚, 57˚, and 11˚, you have to add them up and make sure they equal to 180˚
In this case, 112˚ + 57˚ + 11˚ DO add up to 180˚, and is indeed a triangle.
A company is downsizing its employees by 11%. If the company has 200 employees how many staff members are left?
Answers
Answer:
178
Step-by-step explanation:
200*11%
200*.11
22 employees will leave
200-22 = 178 left