Answers
Answer:
a = -2
p = 2
w = 3
Step-by-step explanation:
The degree of the polynomial is 6 as it has five turning points.
From inspection of the graph it appears that the curve touches
the x-axis at x = 1.
Therefore, a factor is (x - 1) with multiplicity of 2: (x - 1)²
The curve appears to cross the x-axis at x = 2.
Therefore, a factor is (x - 2), so p = 2
There appears to be a point of inflection at x = -1
Therefore, a factor is (x + 1)³, so w = 3
The y-intercept appears to be at (4, 0)
The product of the constants of the found factors is:
⇒ 1³ × (-1)² × (-2) = -2
Therefore, to find the value of a:
⇒ 4 = -2a
⇒ a = -2
Therefore, the polynomial function is:
f(x) = -2(x + 1)³ (x - 1)² (x - 2)
Related Questions
Wren recorded an outside temperature of –2°F at 8 a.m. When she checked the temperature again, it was 4°F at 12:00 p.m. If x represents the time and y represents the temperature in degrees Fahrenheit, what is the slope of the line through these two data points?
Answers
Answer:
Answer
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Assuming the time changes at a constant rate, the equation for this is linear (so has the equation y=mx +c)
8am = -2
9am = -0.5
10am = 1.0
11am = 2.5
12pm = 4
m = change in each value or the slope , for this it is m=1.5
c = the y intercept, we find this by: when x=8 y must = 1.5 , which it isn't , y has to = -2 . So c = -3.5
The equation then is: y= 1.5*x - 3.5
The gradient/slope/m value is 1.5. The answer is 1.5
Help me to answer this math please
Answers
The water consumption based on the information for three months will be 22267m³.
How to calculate the values?The total water consumption for the three months will be:
= 7219 + 7390 + 7658
= 22267m³
In conclusion, the information simply wants you to add the values of the water given.
Therefore, the water consumption based on the information for three months will be 22267m³.
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A hyperbola centered at the origin has a vertex at (0,−40) and a focus at (0, 41). which are the equations of the asymptotes? y = ±x y = ±x y = ±x y = ±x
Answers
The equations of the asymptotes of the given hyperbola are; y = ±(40/9)x
How to Interpret the equation of a hyperbola?We are given;
Vertex at (0,−40)
Focus at (0, 41).
Thus, the equation of the asymptote of the given hyperbola is;
y = ±(40/(√41 - (-40))
y = ±(40/(√81)
y = ±40/9
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MATH!!! find the volume of the pyramid. pleaseee answer correctly and tell me how you got your answer.
Answers
The area of polygons formulas to V=2.56m^2
We have to determine,
The volume of the pyramid.
What is the volume of the pyramid?The volume of a pyramid is found using the formula,
V = (1/3) Bh
where 'B' is the base area and 'h' is the height of the pyramid.
hight =2.4m
base=1.4+1.8
base=3.2m
V = (1/3) (3.2)(2.4)
V=2.56m^2
As we know the base of a pyramid is any polygon,
we can apply the area of polygons formulas to find 'B.
V=2.56m^2.
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help me plss ty in advance:))
Answers
Answer:
See below ~
Step-by-step explanation:
Q1
⇒ S = {1, 2, 3, 4, 5, 6}
===========================================================
Q2
⇒ No. of possible outcomes = 6
===========================================================
Q3
(a)
⇒ P(6) = Number of 6's / Total numbers
⇒ P(6) = 1/6
(b)
⇒ P (negative) = No. of negative numbers / Total numbers
⇒ P (negative) = 0/6
⇒ P (negative) = 0
(c)
⇒ P (odd) = No. of odd numbers / Total numbers
⇒ P (odd) = 3/6
⇒ P (odd) = 1/2
How many 1/12 pieces are in 3/3? 3/3 = __/12
Answers
Answer:
Is your teacher trying to confuse us or what?
Step-by-step explanation:
well 3/3 is full so it's just like 12/12, so 12 pieces of 1/12 piece are in 3/3
Please help! 20 points if u answer
Answers
Answer:
find the measure of J
180-45=135
find the measure of K
360-135=225
Part A: In your own words, describe the relationship between the temperature of the city and the number of ice cream cones sold. (5 points)
Part B: Describe how you can make the line of best fit. Write the approximate slope and y-intercept of the line of best fit. Show your work, including the points that you use to calculate slope and y-intercept. (5 points)
Answers
Part A: The amount of ice cream increases as the temperature increases. Part B: the slope is 2 and the y-intercept will be 5.
What is the slope of a line which passes through points ( p,q) and (x,y)?Its slope would be:
[tex]m = \dfrac{y-q}{x-p}[/tex]
Part A: The relationship between the temperature of the city and the number of ice cream cones sold.
From the graph, the dots on the graph increase in the up-right direction.
Thus, The amount of ice cream increases as the temperature increases.
Part B: The line of best fit
First, if we draw a line through the points
we select any 2 points on the line:
( p,q) and (x,y) as (15, 35) and (0, 5).
The slope (m) is:
[tex]m = \dfrac{y-q}{x-p}[/tex]
[tex]m = \dfrac{5 - 35}{0-15}\\\\m = 2[/tex]
So, the line of best fit is:
y = mx + c
y = 2(x - 0) + 5
y = 2x + 5
The y-intercept will be when x = 0
y = 2x + 5
y = 0 + 5
y = 5
Thus, the slope is 2 and the y-intercept will be 5.
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Chris needs a clever pattern for Math class tomorrow. He comes up with this pattern: 8, 4, 12, 6, 16, 8, 20, 10, ___, __.
What is his rule for this pattern
A. each set of 4 numbers adds to 36.
B. each set of four numbers adds up to 30.
C. each set of 2 numbers makes up a prime number.
D. the first number in each set of 2 numbers is 4 more than the last first number, and the second number is ½ of the first.
Answers
Answer:
D
Step-by-step explanation:
can't really explain it just is the answer
hope this helps!
The equation of a circle is x^2 + y^2 =16 if the circle is translated 2 units up, what is the equation of the new circle?
Answers
The equation of the circle with the new point will be x² + ( y - 2 )² = 16.
What is a circle?The circle is defined as the locus of the point traces around a fixed point called the centre and is equidistant from the outer trace.
Given that:-
The circle is translated as 2 units up.The equation of the circle will be formed as:-
We know that the general form of the circle is given as
( x - h )² + ( y - k )² = r²,
where ( h, k ) is the centre and r is the radius. When the circle is shifted 2 units up it means that now its centre will be ( 0, 2). So the equation will be:-
x² + ( y - 2 )² = 16
Therefore the equation of the circle with the new point will be x² + ( y - 2 )² = 16.
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The lengths of 10 ribbons are 100 cm, 110 cm, 95 cm, 60 cm, 20 cm, 60 cm, 110 cm,
88 cm, 102 cm and 120 cm.
(i) State the modal lengths of the ribbons.
(ii) If a ribbon of length 110 cm is removed, what will be the new modal length of
the ribbons?
Answers
The modal lengths of the ribbons are 60 cm and 110cm.
If the length 110 is removed, the new model length would be 60 cm.
What is the mode?
Mode refers to a value that appears most frequently in a data set. Mode is a measure of central tendency. 110 and 60cm occur twice in the dataset. Thus, they are the mode lengths.
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At Dairy Freeze, 2 of the last 10 sundaes sold had nuts. Considering this data, how many of the next 20 sundaes sold would you expect to have nuts?
sundaes
Answers
What is 2x^2+3x-9? i need help finding this answer
Answers
(2x−3)(x+3)
HAVE A NICE DAY!
Answer:
x=3/2 or x=-3
Step-by-step explanation:
first off equate the equation to zero
2x²+3x-9=0
then using factorisation method multiply 2 and -9 to get -18.
factors of -18 include +6 and -3
2x²+6x-3x-9=0
then factorise it
2x(x+3)-3(x+3)
(2x-3)(x+3)=0
2x=3 x+3=0
x=3/2 or -3
given lim x→0 f(x)=4. what is lim x→0 1/4 [f(x)]^4?
Answers
Given that
[tex]\displaystyle \lim_{x\to0} f(x) = 4[/tex]
we can use the properties of limits to show
[tex]\displaystyle \lim_{x\to0} \frac14 f(x)^4 = \frac14 \lim_{x\to0} f(x)^4 = \frac14 \left(\lim_{x\to0} f(x)\right)^4 = \frac14 \times 4^4 = 4^3 = \boxed{64}[/tex]
Let's see
[tex]\\ \rm\Rrightarrow \lim_{x\to 0}\dfrac{1}{4}f(x)^4[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{1}{4}\lim_{x\to 0}f(x)^4[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{1}{4}\times 4^4[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{256}{4}[/tex]
[tex]\\ \rm\Rrightarrow 64[/tex]
A table of data is given.x(-2,-1,0,1,2)f(x)(71,13,3,0.6,0.1) which exponential model best represents the data
Answers
The equation of the exponential model is f(x) = 3 * 0.2^x
How to determine the exponential model?The table of data is given as:
x(-2,-1,0,1,2)
f(x)(71,13,3,0.6,0.1)
An exponential model is represented as:
f(x) = ab^x
When x= 0 and f(x) = 3;
We have:
ab^0 = 3
This gives
a = 3
When x= 1 and f(x) = 0.6
We have:
ab^1 = 0.6
This gives
ab = 0.6
Substitute 3 for a
3b = 0.6
Divide both sides by 3
b = 0.2
Substitute b = 0.2 and a =3 in f(x) = ab^x
f(x) = 3 * 0.2^x
Hence, the equation of the exponential model is f(x) = 3 * 0.2^x
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Estimate a 20% tip on a dinner bill of $161.86 by first rounding the bill amount to the nearest ten dollars.
Answers
Answer:
See below
Step-by-step explanation:
If you just want the tip
[tex]0.20*161.86\approx\frac{1}{5}*160=32[/tex]
If you want the total bill
[tex]1.20*161.86\approx160+32=192[/tex]
what adds to -288 and adds to -41?
Answers
Answer: -329 sorry if i'm not right
70 is what percent
of 350?
Answers
Answer:
20
Step-by-step explanation:
it is easy first think but besides which school are you from
The equation y - 5 = 6(x+1) is written in point-stope form. What is the equation written in slope-intercept form?
A. y = 6x + 11
B. y = 6x - 1
C. y = 6x - 4
D. y = 6x + 6
Answers
Answer:
A
Step-by-step explanation:y-5=6(x+1)
y-5=6x+6 Combine like terms so you add -5 to +6 which would be y=6x+11
6. Emily rides her bike with a constant speed of
12 miles per hour. How far can she travel in 3
1/2 hours?
Answers
Answer:
42 miles
Step-by-step explanation:
If it's a constant 12 miles per hour then it would be
12 mph x 3 hours = 36
then you would add that with the 1/2 hour for
12 mph x 1/2 hours = 6
36 + 6 = 42 miles traveled
Garrett throws a dart at a circular dart board. the dart board has a radius of 16 inches and the bull's eye in the center of the dart board has a radius of 6 inches. what is the probability that a dart thrown at random within the dartboard will hit the bull's eye? round your answer to the nearest tenth, if necessary
Answers
Answer:14.1%
Step-by-step explanation:
The volume of a pyramid whose base is a
right triangle is 680 units. if the two legs
of the right triangle measure 15 units and
16 units, find the height of the pyramid.
Answers
The height of the prism is 5.67 units
How to determine height of the pyramid?
The given parameters are:
Volume = 680 cubic unitsBase dimensions = 15 and 16 unitsThe volume of a right triangle pyramid is:
Volume = 0.5 * Height * Base dimensions
So, we have;
680 = 0.5 * Height * 15 * 16
Evaluate
Height = 5.67
Hence, the height of the prism is 5.67 units
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How can you represent writing a check of$10 as an integer
Answers
Answer:
Step-by-step explanation:
La cantidad numérica es donde escribes la cantidad del cheque con números/dígitos. Escribe los dólares en forma numérica y luego indica los centavos después del punto decimal. En el ejemplo a continuación, los dólares son ciento veinticinco (125) y los centavos son setenta y cinco (. 75).
i will ask alot of questions again sorry
Answers
Answer:
7.5 m = 0.0075 km (Correct)
0.31 = 310 mm (Correct)
46 m = 4,600 cm (Correct)
457 mm =4.57 cm (Incorrect)
0.6 km = 6,000 m (Incorrect)
Step-by-step explanation:
Tell me if something is wrong.
Write an expression that represents “divide 0.04 by n''
Answers
Answer:.04/n
Step-by-step explanation:solidus represents division
Which is the completely factored form of 12x3 – 60x2 + 4x – 20?
Answers
Answer:
[tex]4(x-5)(3{x}^{2}+1)[/tex]
Step-by-step explanation:
1) Find the Greatest Common Factor (GCF).
1 - What is the largest number that divides evenly into [tex]12x^3,-60x^2,4x,[/tex] and [tex]-20[/tex] ?
It is [tex]4.[/tex]
2 - What is the highest degree of [tex]x[/tex] that divides evenly into [tex]12x^3,-60x^2,4x,[/tex] and [tex]-20[/tex] ?
It is 1, since [tex]x[/tex] is not in every term.
3 - Multiplying the results above,
The GCF is 4.
2) Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
[tex]4(\frac{12{x}^{3}}{4}+\frac{-60{x}^{2}}{4}+\frac{4x}{4}-\frac{20}{4})[/tex]
3) Simplify each term in parentheses.
[tex]4(3{x}^{3}-15{x}^{2}+x-5)[/tex]
4) Factor out common terms in the first two terms, then in the last two terms.
[tex]4(3{x}^{2}(x-5)+(x-5))[/tex]
5) Factor out the common term [tex]x-5[/tex].
[tex]4(x-5)(3{x}^{2}+1)[/tex]
Transform this equation to slope-intercept form: 6x + 4y = 8.
O y=3/2x+4
○ y=-3/2x+4
○ y =3/4 x+2
○y=-3/2x+2
Answers
Answer:
last option
Step-by-step explanation:
[tex]6x + 4y = 8 [/tex]
[tex]4y = 8 - 6x[/tex]
[tex]y = \frac{8 - 6x}{4} \\ [/tex]
[tex]y = \frac{8}{4} - \frac{6x}{4} \\ [/tex]
[tex]y = 2 - \frac{3x}{2} \\ [/tex]
[tex]y = - \frac{ 3x}{2} + 2 \\ [/tex]
y = -3/2x + 2
A penny, nickel, and dime are simultaneously flipped. What is the probability that heads are showing on at least 6 cents worth of coins
Answers
Answer:
5/8
Step-by-step explanation:
The number of possible outcomes after flipping 3 coins is $2 \times 2 \times 2 = 8$. If the dime isn't heads, we need both the penny and nickel to be heads. If the dime is heads, the other two could be anything. So there are a total of $1+(2 \times 2)=5$ ways for us to get at least 6 cents. The answer is $\boxed{\dfrac58}.$
The given equation has been solved in the table.
Step Statement
1
2
3
4
5
In which step was the subtraction property of equality applied?
A.
step 2
B.
step 3
C.
step 4
D.
The subtraction property of equality was not applied to solve this equation.
Answers
From the steps shown in the table given, we can conclude that: D. in solving the equation, the subtraction property of equality was not applied.
What is the Subtraction Property of Equality?If a + b = c, to apply the subtraction property of equality so that b is moved to the other side of the equation, we would have:
a + b - b = c - b
a = c - b
Thus, from the table given, the none of the steps showed that the subtraction property of equality was applied in solving the equation, so, the answer is: D.
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Graph the inequality p < - 8. Also ignore my dirty iPad
Answers
Step-by-step explanation:
it is just a line covering all values smaller than -8 (that means left of -8).
so, it is a line starting at -8 and going all the way to the left (to the arrow on the left). and you make an empty (hollow) dot at -8, because the value -8 is not included (otherwise it would be p <= -8, and it would be a filled dot at -8).