The equation of the quartic function is f(x) = x⁴ - 18 · x² + 6 · x + 72.
How to find the possible equations for a quartic polynomial that passes through the x-axis at three points
Herein we must construct at least a polynomial that satisfies all conditions described in the statement. According to the fundamental theorem of algebra, quartic functions may have no real roots, two real roots or four real roots, which means that one of the roots must have a multiplicity of 2.
The root with a multiplicity of 2 is x = 3 and both x = - 4 and x = - 2 have only a multiplicity of 1, then we have the following expression by using the factor form of the definition of polynomials:
f(x) = (x - 3)² · (x + 4) · (x + 2)
Now we expand the expression to get the standard form:
f(x) = (x² - 6 · x + 9) · (x² + 6 · x + 8)
f(x) = x⁴ - 6 · x³ + 9 · x² + 6 · x³ - 36 · x² + 54 · x + 8 · x² - 48 · x + 72
f(x) = x⁴ - 18 · x² + 6 · x + 72
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Find the product of 2.1n(6n + 3.4).
12.6n + 3.4
8.1n + 3.4
8.1n2 + 7.14n
12.6n2 + 7.14n
A sphere has a radius of 5.4 yards. Find its a. volume and b. surface area. Use 3.14 for π. Round the answers to the nearest hundredth.
Answer:
sorry the drawing is messy, not used to drawing with just a finger haha! hope this helps<<3
You are building a ramp for your grandparent's house. The ramp will replace the steps that go
to their front door which is 3 feet off the ground. You want the ramp to start 10 ft from the
front door. How long will the ramp need to be?
Using right triangle, the length of the ramp is 10.44 ft.
How to find the length of the ramp using right triangle?The situation forms a right angle triangle.
The length of the ramp is the hypotenuse side of the right triangle.
Therefore, using Pythagoras theorem,
c² = a² + b²
where
a and b are the other legsc is the hypotenuse sideTherefore,
c² = 10² + 3²
c² = 100 + 9
c = √109
c = 10.4403065089
c = 10.44 ft
Therefore, the length of the ramp is 10.44 ft.
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Find the median for the scores 91, 69, 71, 82, 71, 95, 87, 74, 71, 89, 89, 95, 72, 75
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{What does \boxed{median} mean in math?}}[/tex]
[tex]\boxed{\text{Median}}\rightarrow\textsf{ is the number in the middle.}[/tex]
[tex]\huge\textbf{How do you find the \boxed{median}?}[/tex]
[tex]\text{You can found it by putting the numbers from \bf least to greatest.}[/tex]
[tex]\huge\textbf{Question reads....}[/tex]
[tex]\text{Find the median for the scores 91, 69, 71, 82, 71, 95, 87, 74, 71, 89, 89, 95,}\\\text{72, 75}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\text{91, 69, 71, 82, 71, 95, 87, 74, 71, 89, 89, 95, 72, 75}[/tex]
[tex]\huge\textbf{Rearrange the problems to:}[/tex]
[tex]\text{69,71,71,71,72,74,75,82,87, 89,89,91,95,95}[/tex]
[tex]\huge\textbf{The expression:}[/tex]
[tex]\mathsf{\dfrac{75 + 82}{2} = median}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{\dfrac{75 + 82}{2} = median}[/tex]
[tex]\mathsf{\dfrac{157}{2} = median}[/tex]
[tex]\mathsf{257\div2 = median}[/tex]
[tex]\mathsf{78.5 = median}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{78.5}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]Modules
Honorlock
An on-demand printing company has monthly overhead costs of $2,200 in rent, $380 in
electricity, S65 for phone service, and $240 for advertising and marketing. The printing
cost is $30 per thousand pages for paper and ink. The average cost for printing.x
thousand pages can be represented by the function
2,885 +30x
C(x)=
X
For a given month, if the printing company could print an unlimited number of pages,
what value would the average cost per thousand pages approach? What does this mean
in the context of the problem?
O The average cost would approach infinity. The more pages the company prints, the
higher the average cost.
o The average cost would approach $30 per thousand pages or
equivalently $0.03 per page. This is the cost per page in the absence
of fixed costs.
o The average cost would approach $2,885 per thousand pages. This is
the total of the fixed monthly costs.
o The average cost would approach $0 per thousand pages. The more
pages the company prints, the lower the average cost.
MacBook Pro
Time Running
Attempt due: Jul
29 Minutes, 42
Answer:
Step-by-step explanation:
Comment
The formula used to figure out the costs is
C(x) = 2885 + 30x
2885 is the total of the fixed costs -
Rent 2200Electricity 380Phone 65Marketing 240Total 2885Now the problem gets sort of complicated. If the company could print an unlimited amount of pages, the 2885 remains the same, no matter what.
But x gets larger and larger. and so C(x) gets larger and larger.
Answer
Therefore the average cost would approach infinity.
A
What is the sum of the
HCF and
LCM of the
number
2³ x 3² x 5x7 and
2² x 5² x 11
Step-by-step explanation:
. Find the factors of 330.
(a)2 x 4 x 5 x 11
(b)2 x 3 x 7 x 13
(c)2 x 3 x 5 x 13
(d)2 x 3 x 5 x 11
Show Answer
2. Find the factors of 1122.
(a)3 x 9 x 17 x 2
(b)3 x 11 x 17 x 2
(c)9 x 9 x 17 x 2
(d)3 x 11 x 17 x 3
Show Answer
3. 252 can be expressed as a product of primes as
(a)2 x 2 x 3 x 3 x 7
(b)2 x 2 x 2 x 3 x 7
(c)3 x 3 x 3 x 3 x 7
(d)2 x 3 x 3 x 3 x 7
Show Answer
4. Which of the following has most number of divisors?
(a)99
(b)101
(c)176
(d)182
Show Answer
5. A number n is said to be perfect if the sum of all its divisors (excluding n itself) is equal to n. An example of perfect number is
(a)6
(b)9
(c)15
(d)21
Show Answer
6. 1095/1168 when expressed in simplest form is
(a)13 / 16
(b)15 / 16
(c)17 / 26
(d)25 / 26
Show Answer
7. Reduce 128352 / 238368 to its lowest terms
(a)3/4
(b)5/13
(c)7/13
(d)9/13
Show Answer
8. The simplest reduction to the lowest terms of 116,690,151 / 427,863,887 is
(a)3/11
(b)7/11
(c)11/3
(d)None of these
Show Answer
9. The highest common factor of 0 and 6 is
(a)0
(b)3
(c)6
(d)Undefined
Show Answer
10. The H.C.F. of 2² x 3³ x 5⁵, 2³ x 3² x 5² x 7 and 2⁴ x 3⁴ x 5 x 7² x 11 is
(a)2² x 3² x 5
(b)2² x 3² x 5 x 7 x 11
(c)2⁴ x 3⁴ x 5⁵
(d)2⁴ x 3⁴ x 5⁵ x 7 x 11
Show Answer
11. The H.C.F. of 2⁴ x 3² x 5³ x 7, 2³ x 3³ x 5² x 7² and 3 x 5 x 7 x 11 is
(a)105
(b)1155
(c)2310
(d)27720
Show Answer
12. H.C.F. of 4 x 27 x 3125, 8 x 9 x 25 x 7 & 16 x 81 x 5 x 11 x 49 is
(a)180
(b)360
(c)540
(d)1260
Show Answer
13. Find the highest common factor of 36 and 84.
(a)4
(b)6
(c)12
(d)18
Show Answer
14. Even numbers are formed by taking at least two at a time from the numbers 0, 4, 8, 9. Their H.C.F. is
(a)2
(b)4
(c)10
(d)None of these
Show Answer
Which of the following sets of numbers could not represent the three sides of a triangle?
Answer:
Step-by-step explanation:
Find the equation of the line
Answer:
Step-by-step explanation:
hello :
Solut i on :
1) A line that passes through A(0, -6 ) andB (8 ,- -8)
Hello : let A(0,-6) B(8,-8)
the slope is : (YB - YA)/(XB -XA)
(-8+6)/(8-0) = -2/8=-1/4
an equation is : y=ax+b a is a slope
y = (-1/4)x +b
the line through point A (0;-6) : -6 = (-1/4)(0)+b
b = -6 the equation is : y =(-1/)4x-6
Lesson Review
Directions: Factor the following trinomials containing negative numbers. Follow the rules for operations with signed numbers to identify the correct binomial factors.
1. x2 + 6x - 7
2. x2 - 5x + 6
3. x2 - 6x - 7
4. x2 + 5x - 6
5. x2 + x - 12
6. x2 - 2x - 8
7. x2 - 4x - 5
8. x2 + 2x - 3
9. x2 - 16
10. x2 - x - 12
11. x2 -9x + 18
12. x2 -5x - 14
13. x2 - 7x + 10
14. x2 -11x + 24
15. x2 - x - 30
Factorization implies the obtaining of the common factors in an expression.
What is factorization?The term factorization implies the obtaining of the common factors in an expression.
The factors of the expressions are as follows;
1) (x−1)(x+7)
2) (x−2)(x−3)
3) (x+1)(x−7)
4) (x−1)(x+6)
5) (x−3)(x+4)
6) (x+2)(x−4)
7) (x+1)(x−5)
8) (x−1)(x+3)
9) (x+4)(x−4)
10) (x+3)(x−4)
11) (x−3)(x−6)
12) (x+2)(x−7)
13) (x−2)(x−5)
14) (x−3)(x−8)
15) (x+5)(x−6)
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HELP ME WOTH THIS QUESTIONNN!!
Answer:
C
Step-by-step explanation:
For lines l and m and the transversal line that creates angles 6 and 18, angles 6 and 18 are corresponding angles of lines l and m. If they are congruent, lines l and m are parallel.
Answer: Choice C
In AABC, m/A = 15°, a = 9, and b = 12. Find c to the nearest tenth.
A. 20.0 B. 17.4 C. 8.4 D. 11.5
Answer:
Step-by-step explanation:
This is a Law of Sines problem. The expanded formula is
[tex]\frac{sinA}{a} =\frac{sinB}{b} =\frac{sinC}{c}[/tex] where the capital letters are the angles and the lowercase letters are the side lengths. We only use 2 of these ratios at a time. And in order to do that, we can only have one unknown per set of ratios. I have angle A and side a, so I'll use that ratio, but I don't have angle C to help me find side c. I also don't have angle B. But I do have side b, so I'll use the A and B sin stuff and then solve for C indirectly.
[tex]\frac{sin15}{9} =\frac{sinB}{12}[/tex] to solve for angle B. Cross multiply:
[tex]sinB=\frac{12sin15}{9}[/tex]
[tex]sinB=.3450926061[/tex] Use the inverse and sin keys on your calculator (in degree mode) to get that
B = 20.2°. Now that we have that, we can find the measure of angle C:
180 - 15 - 20.2 = 144.8°
Now we can use the sin ratio involving the angle C, side c (our unknown), and angle A and side a:
[tex]\frac{sin144.8}{c}=\frac{sin15}{9}[/tex] and cross multiply to solve for c:
[tex]c=\frac{9sin144.8}{sin15}[/tex] gives us that
c = 20.0
HELP ME PLEASE
LOOK AT IMAGE
Answer:
the answer is congruent making d midpoint
Alan is building a garden shaped like a rectangle with a semicircle attached to one short side. If he has 70 feet of fencing to go around it, what dimensions will give him the maximum area in the garden? Round the answers to the nearest tenth.
The dimension that would give the maximum area is 20.8569
How to solve for the maximum area
Let the shorter side be = x
Perimeter of the semi-circle is πx
Twice the Length of the longer side
[tex][70-(\pi )x -x][/tex]
Length = [tex][70-(1+\pi )x]/2[/tex]
Total area =
area of rectangle + area of the semi-circle.
Total area =
[tex]x[[70-(1+\pi )x]/2] + [(\pi )(x/2)^2]/2[/tex]
When we square it we would have
[tex]70x +[(\pi /4)-(1+\pi)]x^2[/tex]
This gives
[tex]70x - [3.3562]x^2[/tex]
From here we divide by 2
[tex]35x - 1.6781x^2[/tex]
The maximum side would be at
[tex]x = 35/2*1.6781[/tex]
This gives us 20.8569
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19) Write the scientific notation of 1
Answer:
1.0 x 10^0
Step-by-step explanation:
The above works because 10^0 = 1, and 1 x 1 = 1.
Brainliest, please :)
CORRECT ANSWER PLEASE!!!!! 150 points
Answer: -7
Step-by-step explanation:
First, lets use the functions to find the answer to f(-8) and g(4)
f(-8) is the same as asking for the value of y when x is -8
Therefore, f(-8) = -5 (according to the graph)
Using the same rule, g(4) would be the value of y when x = 4 which,
according to the graph, g(4) = 3
Plug these values back into the original equation to get:
[tex]-1*f(-8)-4*g(4)=?\\=-1*-5-4*3\\[/tex]
using the order of operations, we will multiply the values first
[tex](-1*-5)+(-4*3)\\=5+(-12)\\=5-12\\=-7[/tex]
Therefore, our final answer is -7Answer:
-7
Step-by-step explanation:
find the maximum value of the function 7-2x-3x^2 and the equation of the axis of the curve
The maximum value of the function 7 - 2x - 3x² exists 22/3.
How to estimate the maximum value of the function 7 - 2x - 3x²?Given: 7 - 2x - 3x²
We must begin by estimating the first derivative:
Differentiating the equation above, we have:
dy/dx = 0 - 2 - 6x = - 2 - 6x
We know that dy/dx = 0 at maxima and minima
Therefore, we contain, - 2 - 6x = 0
6x = - 2
x = - 1/3
Substituting x = - 3 back into the equation of the curve yields the following result:
y = 7 - 2(-1/3) - 3(-1/3)² = 22/3
y = 22/3
Therefore, 22/3 exists the maximum value of y.
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help im low on my grade and it would help me alot
Answer:
3.5
Step-by-step explanation:
1 - (-2.5) = 1 + 2.5 = 3.5
Find the indicated side of the
right triangle.
60°
30°
X
x = 3√√√/[?]
3
Answer:
[tex]3\sqrt{3}[/tex]
Step-by-step explanation:
The given is a special right triangle with angle measures 30-60-90
The measure of side lengths for this special right triangle are represented with
a-a[tex]\sqrt{3}[/tex]-2a respectively
Now, since the side length that sees angle measure 30 is given as 3 (represented with a) then the measure of the side length that sees angle measure 60 would be [tex]3\sqrt{3}[/tex]
Find the volume of the triangular prism. 10 cm 8 cm Volume = 12 cm [?] cm³
Answer:
Step-by-step explanation:
volume of the triangular prism height times base times length so 10 times 8 times 12 = 960.
You can build two triangles that have the same side lengths but are not
congruent.
A. True
B. False
Answer: False .
Step-by-step explanation: mark me brainliest
Answer:
false because l don't know
Ray and Kelsey have summer internships at an engineering firm. As part of their internship, they get to assist in the planning of a brand new roller coaster. For this assignment, you help Ray and Kelsey as they tackle the math behind some simple curves in the coaster's track.
Part A
The first part of Ray and Kelsey's roller coaster is a curved pattern that can be represented by a polynomial function.
Ray and Kelsey are working to graph a third-degree polynomial function that represents the first pattern in the coaster plan. Ray says the third-degree polynomial has four intercepts. Kelsey argues the function can have as many as three zeros only. Is there a way for the both of them to be correct? Explain your answer.
Kelsey has a list of possible functions. Pick one of the g(x) functions below and then describe to Kelsey the key features of g(x), including the end behavior, y-intercept, and zeros.
g(x) = (x + 2)(x − 1)(x − 2)
g(x) = (x + 3)(x + 2)(x − 3)
g(x) = (x + 2)(x − 2)(x − 3)
g(x) = (x + 5)(x + 2)(x − 5)
g(x) = (x + 7)(x + 1)(x − 1)
Create a graph of the polynomial function you selected from Question 2.
From the information given about the polynomial function, It is correct to state that there is a way for both of them to be correct. See the explanation below and the attached for the graph related to the second question.
What is the explanation for the above?A polynomial could only have a number of zeros equal to its degree. A third degree polynomial can thus have three zeroes, but Ray claims the polynomial has four Intercepts.
While the words "zeroes" and "intercepts" are sometimes used interchangeably, a zero is officially an x-intercept. A function can also have a y-intercept, therefore a cubic can have four intercepts in total, albeit only three will be zeroes.
The zeros of g(x)= x3-x2-4x+4 are -2,2, and 1. End behavior, the Y- intercept, the axis of symmetry, and the vertex are other important characteristics of polynomial functions.
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DEFG is a rumbus. Find the vaule
Step-by-step explanation:
in a rhombus (not rumbus !) all sides are equally long.
that means
7x - 4 = 3x + 12
4x = 8
x = 2
Answer:
Step-by-step explanation:
The sides of a square are equal to each other, it is with the same with rhombus.
With this information, we can Say that [tex]DE[/tex] is equal to line [tex]GD[/tex], with
[tex]DE =7x-4GD=3x+12[/tex]
[tex]7x-4=3x+12\\[/tex]
Take [tex]3x[/tex] from both sides.
[tex]4x-4=12[/tex]
Add 4 to isolate X
[tex]4x=16[/tex]
Divide by 4
[tex]x=4\\[/tex]
So we can say that the value of [tex]x[/tex] is 4
Amanda makes $40,000 and gets an annual raise of $3,000. Marie makes $45,000 and gets an annual raise of $2,500. How many years will it take Amanda and Marie to make the same salary?
Answer:
Six years
Step-by-step explanation:
because it will divided the twoo digit and mutiple it self
Evaluate 2a x 3 + b, if a = 5 and b = 1.
Answer:
31
Step-by-step explanation:
replace the values of a and b in the given term
=2a x 3 + b
2(5) x 3 + (1)
2x5 x 3 + 1
10 x 3 + 1
30 + 1
31
Kristina wants to invest $6200 in a savings account that pays 7.6% simple interest. How long will it take for this investment to double in value? Round your answer to the nearest tenth.
The number of years it would take the investment to double in value is 13.2 years.
How long will it take for the investment to double?When the amount doubles, the interest earned would be $6200.
Time = interest earned / (amount invested x simple interest)
$6200 / (6200 x 0.076) = 13.2 years
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Which is the graph of the function f(x) = 1/2x2 + 2x - 6?
Answer:i would need to see the graph but here is what i think you are talking about and it shows how to it popular- problems /Algebra/ 262080
Step-by-step explanation:
Answer: man i wish i knew
Step-by-step explanation:
how do you find the area and perimeter
area is multiplication
perimiter is adding the numbers on each side, for example, if the right side is 7, the left side will be 7. Add them and it will givey ou 14
What is the length of the apothem of the regular pentagon shown below? Round to one decimal place
Answer:
A
Step-by-step explanation:
Draw a diagonal line connecting the centre to a vertex at the bottom. This makes a triangle. It is a regular pentagon so the base of that triangle is 7.6 / 2, which is 3.8. You also know that the angle from the apothem to the base is 90 degrees. You also know that you could split the centre angle into 5 triangles. 360 / 5 = 72 and we have half of it so it is 36 degrees.
Let's see what we have so far:
The base of the triangle is 3.8
The angle at the bottom is 90
The angle at the top is 36
We now have the tan and the opposite and we need the adjacent so rearrange for adjacent.
This gives you adjacent = opposite / tan(angle)
adjacent = 3.8 / tan(36)
adjacent = 5.2m
Please help with this geometry question!
Answer:[tex]\sqrt{303.51}[/tex]
Step-by-step explanation:
The difference in the radii of the two circles is [tex]4.3-1.8=2.5[/tex] inches.
Since the tangent has a length of 2.5 inches, by the Pythagorean theorem, the required distance is
what the difference between graph and inequalities ?
what the difference between graphing lines and graphing inequalities?
You don't shade a region when graphing just a line, but you do when graphing an inequality.
It should be noted that a graph is a diagram representing a system of connections or interrelations among two or more things by a number of distinctive dots, lines, bars, etc.
How to illustrate the information?It should be noted that an inequality is a relation that makes a non-equal comparison between two numbers or other mathematical expressions.
This is used most often to compare the two numbers on the number line by their size.
On the other hand, the graphing inequalities shows what part of the number line contains values that will be able to satisfy the given inequality.
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