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.
Learn more about polynomials here:
https://brainly.com/question/2284746
#SPJ2
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?
9/20 - 7/15=
help guys plsss need na now .,.
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
solve for r to find the missing term in geometric sequence.
—
hi can someone please answer my question, thank you ❤️
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 = 8PLEASE 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?
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
The sum of the first 21 terms of the progression, - 18, - 15,-12.....is?
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.
Learn more about Arithmetic progression here:
https://brainly.com/question/16947807
#SPJ5
Find the slope of the line graphed below!!
Answer:
The slope is 3/2
Step-by-step explanation:
Rise = 3
Run = 2
Rise/Run = 3/2
PLEAS EHELP ME I AM BEGGING YOU!!!!!!! EXTRA POINTS AND BRAINLIEST
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*
Find the perimeter of triangle ABC
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
Part 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
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! :)
What would you do to both sides of the equation to solve for x?
10x=5
If Tristan wants to stretch the spring by 9 inches, how many kilograms of weight must he apply to it?
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.
Find the value of x.
Q3).
0.4x + 0.3y = 1.7
0.7x - 0.2y = 0.8
Solve it by using substitution method.
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.
can someone do this for me please
Answer:
Step-by-step explanation:
2(2+3) =9+1
let me know if you get it right
plz help me solving me math questions
Help!!! I'll give brainly to whoever does it correctly and first
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:
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?
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:
5a+3a-4=36
Somebody please answer this
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
(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.
What is the value of the 3 in this number?
5,400,387,214
is the value of this number.
Answer:
The value of 3 is in the three-hundred thousands place
300,000
could a triangle have angle measures of 112° 57° and 11°? explain hw u know
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.
find the measures of the angles labeled in the figure on the right
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)
Answer this please because I need help nowwwww
Answer:
[tex]3(x + 4) = 3x + 11 \\ 3x + 12 = 3x + 11 \\ 3x - 3x = 12 - 11 \\ 0 = 1[/tex]
So; Not solution
A company is downsizing its employees by 11%. If the company has 200 employees how many staff members are left?
Answer:
178
Step-by-step explanation:
200*11%
200*.11
22 employees will leave
200-22 = 178 left
if i make 50 dollars a month and need 600 dollars how many months will it take to get 600 dollars
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!
Order the number \pi ,3, and \sqrt(11 )from least to greatest
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! :)
i need help with my math homework
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
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.
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
3.7 - 1.8 - 3.67 + 4.4 - 1.34
Answer:
1.29
Step-by-step explanation:
Answer:
The person above me is correct, the answer would be 1.29. ^ .^
Step-by-step explanation:
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)