Using linear function concepts, it is found that:
a) The amount of lattes sold function is: N(p) = -240p + 1040.
b) The revenue function is: R(p) = -240p² + 1040p.
c) The revenue is maximized when p = $2.17.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the following rule:
y = mx + b
In which:
The coefficient m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis(x = 0).For this problem, we have a linear function with the points having the following format:
(price, lattes sold).
Hence two points are given as follows:
(2.50, 440), (2.75, 380).
The slope is given by change in y divided by change in x, hence:
m = -60/0.25 = -240.
Then:
N(p) = -240p + b.
When p = 2.50, N(p) = 440, hence we solve for b as follows:
440 = -240(2.5) + b
b = 1040.
Thus the function is:
N(p) = -240p + 1040.
The revenue function is:
R(p) = pN(p)
Hence:
R(p) = p(-240p + 1040)
R(p) = -240p² + 1040p.
Which is a concave down quadratic function, with a = -240 and b = 1040. A concave down quadratic function is maximized when:
p = -b/2a
Hence:
p = -1040/2(-240) = $2.17.
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What is the distance between points A(2,9) and B(-2,6)? Round to the nearest whole number.
The distance between the point is 5.
The formula to find the distance between two points (x1, y1) and (x2, y2)
distance = [tex]\sqrt{(x2-x1)^{2} + (\\ y2-y1)^{2} }[/tex]
Substituting points A(2,9) and B(-2,6), we get
distance = [tex]\sqrt{(-2-2)^{2} + ( 6-9)^{2} }[/tex]
=[tex]\sqrt{(-4)^{2} + (-3)^{2} }[/tex]
= [tex]\sqrt{16 + 9}[/tex]
=[tex]\sqrt{25}[/tex]
= 5
Therefore the distance between the two points is 5.
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Write the equation of the line in slope-intercept form.
The line is parallel to y + x = 3 and passes through the point (-12, 0).
Please help i will give big points
Answer:
The line is parallel to y + x =3
=> y = -x+3
the slope = -1
passes (-12, 0)
the equation would be :
y-0 = -1(x+12)
y = -x -12 Y=-x+12
Turn into mx+b form.
Y=-x+3
Plug in (-12,0)
0=-12+b
b=12
y=-x+12
It is negative X, because the slope has to be the same since it is paralle
Step-by-step explanation:
Protein bars come in a 4 pack box or a 12 pack box the 4 pack costs 7.68 and the 12 pack costs 22.32 which box is the better
Buying 12 pack is better as it is cheaper than 4 pack.
What is unitary method?A problem can be solved using the unitary method by first determining the value of a single unit, and then multiplying that value to determine the required value. The unitary method involves determining the value of a single unit before determining the value of the necessary quantity of units.
Given Data
Protein bars come in a 4 pack box or a 12 pack box
4 pack costs 7.68 and the 12 pack costs 22.32
In 4 pack
4 pack = 7.68
1 pack = 1.92
In 12 pack,
12 pack = 22.32
1 pack = 1.86
4 pack > 12 pack
Buying 12 pack is better as it is cheaper than 4 pack.
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Consider the following expression 2(x+3). Which of the following represents the correct use of the distributive property? A. 2x+3 B. 2x+6 C. X + 6 D. X^2 + 6x + 9
help me please!!!!!!11!
Answer:
[tex]y=x^2-4x-2[/tex]
Step-by-step explanation:
Standard Form of Quadratic:
[tex]y=ax^2+bx+c[/tex]
Vertex Form of Quadratic:
[tex]y=a(x-h)^2+k[/tex]
h = vertex x
k = vertex y
Think of h and k as the ordered pair (h,k).
Match this ordered pair to the vertex ordered pair.
(h,k) = (2, -6)
Plug in (h,k) into vertex form:
[tex]y = a(x-2)^2-6[/tex]
Use other point to solve for a.
[tex]3 = a(5-2)^2-6[/tex]
[tex]3=a(3)^2-6[/tex]
[tex]3=9a-6[/tex]
[tex]9=9a[/tex]
[tex]a=1[/tex]
Plug a back into vertex form and expand the expression into standard form:
[tex]y=(x-2)^2-6[/tex]
[tex]y=(x-2)(x-2)-6[/tex]
Use F.O.I.L. method to expand (x-2)(x-2).
F(first): [tex]x*x=x^2[/tex]
O(outer): [tex]x*-2=-2x[/tex]
I(inner): [tex]-2*x =-2x[/tex]
L(last): [tex]-2*-2=4[/tex]
[tex]y=x^2-2x-2x+4-6[/tex]
Combine like terms:
[tex]y=x^2-4x-2[/tex]
Drag and drop the number to match the division problem to its quotient.
Answer:
The correct number is -27.
Step-by-step explanation:
-81 ÷ 3 = -27
The data valo showed a mouse driven on a single day by random sample of 13 student calculate the 38th and the 60th percent all of the data
To get the percentile
Step 1: Write the formula
[tex]\begin{gathered} P_i=(\frac{i(n+1)}{100})^{th} \\ \\ \text{where n = 13} \end{gathered}[/tex]For the 38th percentile
[tex]P_{38}=(\frac{38(13+1)}{100})^{th}[/tex][tex]P_{38}=5.32^{th}\text{ number}[/tex]This means that the 38th percentile is between the 5th and 6th number
[tex]\begin{gathered} P_{38}=5^{th}\text{ observation}+0.32\lbrack6^{th}-5^{th}\rbrack \\ P_{38}=41+0.32(43-41)=41.64 \\ P_{38}=41.64 \end{gathered}[/tex]P38 = 41.64This means that approximately 38% of the data lie below 43, when the data are ranked
For the 60th percentile,
[tex]P_{60}=(\frac{60(13+1)}{100})^{th}[/tex][tex]P_{60}=8.4^{th\text{ }}n\nu mber[/tex]6089
[tex]P_{}=8^{th}\text{ observation}+0.4\lbrack9^{th}-8^{th}\rbrack[/tex][tex]\begin{gathered} P_{60}=56+0.4(58-56) \\ P_{60}=56.8 \end{gathered}[/tex]60
Please help me solve both a and b of this problem.
A. The relationship between number of towers and number of customers is proportional.
B. 12 customers.
What is a Proportional Relationship?A proportional relationship between two variables, x and y, is a relationship whereby the ratio y/x is the same all through the table of values.
Thus, the value of y/x is constant, and is referred to as the unit rate or constant of proportionality, k.
Part A:
Given the table of values, we have:
Constant of proportionality (k) = y/x = 252/5.25 = 300/6.25 = 348/7.25 = 444/9.25 = 48.
Therefore, it is a proportional relationship because it has a constant of proportionality, k = 48.
Part B:
Substitute k = 48 into y = kx (proportional relationship)
y = 48x.
The equation for the relationship is, y = 48x. Substitute y = 576 into the equation to find the value of x, number of customers:
576 = 48x
Divide both sides by 48
576/48 = 48x/48 [division property of equality]
12 = x
x = 12
The number of customers is 12.
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Algebra 2, 50 points, include steps please
(6-4i)(1+5i)-(3-i)
The simplified representation of the complex number expression is
23 + 37i
a + bi, where a and b are real numbers, can be used to represent any complex number.
A complex number is a component of a number system that includes an element with the symbol I, sometimes known as the imaginary unit, and that extends the real numbers by satisfying the equation i² = -1. i was described as an imaginary number by René Descartes since no real number can fulfil the aforementioned equation. The complex number a + bi is known as having real and imaginary parts, respectively, A and b. The group of complex numbers is denoted by the letter C.The complex number expression is (6-4i)(1+5i)-(3-i)
now let us simplify,
or, (6-4i)(1+5i)-(3-i)
or, 6 + 30i - 4i -20i² -3 + i
or, 6 + 36i + 20 - 3 + i (we know that i² = -1)
or, 23 + 37i
Therefore the simplified complex expression is 23 + 37i
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From a window 100 ft above the ground in building A, the top and bottom of building B are sighted so that the angels are 70 degrees and 30 degrees respectively. Find the height of building B?
Let's begin solving the problem by illustrating the problem using a diagram:
Let the height of building B be x
Re-drawing the triangles to show the unknown side:
Using trigonometric ratios and sine rule
Hence:
[tex]\begin{gathered} \frac{\sin110}{\frac{100}{\cos30}}\text{ = }\frac{\sin 40}{x} \\ \text{Cross}-\text{Multipy} \\ \text{x }\times\text{ sin110 }=\text{ sin40 }\times115.47 \\ \text{Divide both sides by sin110} \\ \text{x = }\frac{\sin 40\text{ }\times\text{ 115.47}}{\sin \text{ 110}} \\ x\text{ = 78.986} \\ x\text{ }\approx\text{ 79 ft} \end{gathered}[/tex]The height of the building B is 79 ft
The table represents a quadratic function. Write an equation of the function in
standard form.
X- -3,-2,-1,0
f(x)-6,0,-2,0
WILL GIVE BRAINLIEST
Answer:
[tex]y=2x^2+4x[/tex]
Step-by-step explanation:
Given table:
[tex]\begin{array}{|c|c|c|c|c|}\cline{1-5} x & -3 & -2 & -1 & 0\\\cline{1-5} f(x) & 6 & 0 & -2 & 0\\\cline{1-5}\end{array}[/tex]
The x-intercepts of a quadratic function are when f(x) = 0.
Therefore, the x-intercepts are: x = -2 and x = 0.
Intercept form of a quadratic equation
[tex]y=a(x-p)(x-q)[/tex]
where:
p and q are the x-intercepts.a is some constant.Substitute the found x-intercepts and one of the points from the table into the formula and solve for a:
[tex]\begin{aligned} y&=a(x-p)(x-q)\\\\\implies6&=a(-3-(-2))(-3-0)\\6&=a(-1)(-3)\\6&=3a\\a&=\dfrac{6}{3}\\\implies a&=2\end{aligned}[/tex]
Substitute the x-intercepts and the found value of a into the formula:
[tex]\implies y=2(x+2)(x-0)[/tex]
Expand to standard form:
[tex]\implies y=2(x+2)(x-0)[/tex]
[tex]\implies y=2x(x+2)[/tex]
[tex]\implies y=2x^2+4x[/tex]
what's the value of k
The sum of complementary angles = 90°
The angle shown is a right angle
Therefore:
k + 54.3 = 90
k = 90 - 54.3
k = 35.7°
The probability that a new machine will not need any repairs within t years from now is modeled by an exponential function of t. This probability is multiplied by 0.2 whenever the time period t is extended by 3 years as shown by the function belowf(t) = (0.2)^t/3 If the probability that the machine does not need repairs right now is 1, what is the probability that the machine will not need repairs within 12 years from now, according to the model? 0.8 0.05 0.008 0.0016
viven
t = time
function
[tex]f(t)=0.2^{t/3}[/tex]what is the probability that the machine will not need repairs within 12
rocedure
[tex]\begin{gathered} f(12)=0.2^{12/3} \\ f(12)=0.0016 \end{gathered}[/tex]
The probability would be 0.0016
A linear function is transformed from y = 3/4x + 1/2 to y = 3/4x + 5/2. What is the corresponding vertical change?A)The graph is shifted up 2 units,B)The graph is shifted down 2 units. C)The graph is shifted up 4 unitsD)The graph is shifted up 5/2 units
A. The graph is shifted up 2 units
Help! Please!!!!!!!!!?
The estimates for [tex]6\frac{1}{9}. 1\frac{5}{7}[/tex] is [tex]10\frac{10}{21}[/tex]
The actual answer of [tex]6\frac{1}{9}. 1\frac{5}{7}[/tex] is [tex]10\frac{30}{63}[/tex]
How to estimate fractions?The estimated answer of the fraction can be done as follows:
[tex]6\frac{1}{9}. 1\frac{5}{7}[/tex]
Hence,
[tex]6\frac{1}{9} = \frac{55}{9}[/tex]
[tex]1\frac{5}{7} = \frac{12}{7}[/tex]
Therefore, the actual answer of the fractions is as follows:
[tex]\frac{55}{9}.\frac{12}{7} = \frac{660}{63} = 10\frac{30}{63}[/tex]
Hence, the estimated answer of the fractions can be calculated as follows
[tex]\frac{55}{9}.\frac{12}{7} = \frac{660}{63} = \frac{220}{21} = 10\frac{10}{21}[/tex]
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What is the correct answer
The measure of angle B in triangle ABC is 158°.
What is meant by the triangle?A triangle is a 2-dimensional closed shape with three sides, three angles, and three vertices. A triangle would be a category of polygon.
The sum of a triangle's three interior angles is always 180.The sum of any two triangle sides is always bigger than this same length of a third side.A triangle's area is equal to half the product of it's own base and height.For the given angles of the triangle ABC.
∠BAC = 78° , ∠CAD = 46° and ∠ADB = 110°.
Now,
∠BAC = ∠BAD + ∠DAC
Put the values;
78° = ∠BAD + 46°
∠BAD = 78° - 46°
∠BAD = 32°
Now, in a triangle; the sum of all three angles is 180°.
In triangle ADB
∠ABD + ∠BAD + ∠BDA = 180°
Put the values;
∠ABD + 32° + 110° = 180°
∠ABD = 180° - 142°
∠ABD = 158°
Thus, the measure of angle B is 158°.
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What is the answer to the question
From the right triangle, and using the definitions of the tangent and the cosine functions, we have:
[tex]\begin{gathered} \tan B=\frac{AC}{BC}=\frac{b}{a}\Rightarrow b=a\cdot\tan B...(1) \\ \\ \cos B=\frac{BC}{AB}=\frac{a}{c}\Rightarrow c=\frac{a}{\cos B}...(2) \end{gathered}[/tex]From the problem, we identify:
[tex]\begin{gathered} B=55.7\degree \\ a=266\text{ km} \end{gathered}[/tex]Finally, using these values, we can find b and c.
Using (1):
[tex]\begin{gathered} b=266\cdot\tan55.7\degree \\ \\ \therefore b=389.941\text{ km} \end{gathered}[/tex]Using (2):
[tex]\begin{gathered} c=\frac{266}{\cos55.7\degree} \\ \\ \therefore c=472.028\text{ km} \end{gathered}[/tex]Choose the most convenient method to graph the line y=-1/4x+3
The graph for the function (y = -(1/4)x + 3) is given in the attached image. See the explanation below.
Step 1 Find (x,y) pairs
Step 2: plot the points
Step 3 Draw the line on the graph.
Let's look at Step 1.
Using the graph as an example, our first pair of x,y is (0, 3)
This is obtained by substituting 0 in the equation y = -(1/4)x + 3
⇒ y = -(1/4)0 + 3
y = 0 +3
y = 3, where x = 0
If we repeat this process with x = 1, x = 2, x = 3, we will get the corresponding y for case.
Step 2: Plotting the x,y pairs will give us points on the graph.
Step 3: connecting the dots will give us the same line in the graph that is attached.
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8=3+2i and z9 = 4+3i.
Answer:
8 - 3 = 5
5 divided by 2 = 2.5
i = 2.5
3 x 2.5 = 7.5
4 + 7.5 = 11.5
11.5 divided by 9 = 1.277
z = 1.277
Hope this helps!
AlphaFay
(05.03 MC)
Two families visited an amusement park. The first family bought 3 hot dogs and 5 bottles of waters, which totaled $20. The second family bought 6 hot dogs and 3 bottles of
waters, which totaled $33. How much did one hot dog cost?
$3
$4
$5
$6
The cost of one hotdog based on the given situation is $5
The correct answer option is Option C
How to find the cost of one hotdog?let
Cost of hotdogs = hCost of bottle water = wFamily A:
3h + 5w = 20
Family B:
6h + 3w = 33
Solve the two equations simultaneously:
3h + 5w = 20
6h + 3w = 33
Multiply (1) by 2
6h + 10w = 40
6h + 3w = 33
Substract the equations to eliminate h
10w - 3w = 40 - 33
7w = 7
divide both sides by 7
w = 7/7
w = 1
Substitute w = 1 into
3h + 5w = 20
3h + 5(1) = 20
3h + 5 = 20
3h = 20 - 5
3h = 15
divide both sides by 3
h = 15/3
h = 5
So therefore, the cost of one hotdog and one bottle water is $5 and $1 respectively.
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Answer: the answer is 5 dollars
Step-by-step explanation:
Mrs. Parkow gives her class clues
about a 5-digit mystery number,
• The 3 is in a place that is 100 times
greater than the place of the 4,
The 2 is in a place that is 10 times
less than the place of the 3.
The 8 is in a place that is 10 times
less than the place of the 4.
The 7 is in a place that is 100 times
greater than the 2
•
•
What is Mrs. Parkow's
5-digit mystery number?
Mrs. Parkow's 5-digit mystery number is 73248.
What are Numbers up to 5-Digits?Ten thousand is the starting point for five-digit numbers, which go up to ninety-nine million, nine hundred and ninety-nine. Integers are present in the places of ones, tens, hundreds, thousands, and ten thousands in these numbers. Any positive number may be placed at these places, with the exception of 0 at the ten thousands place.
A general 5-digit number can be written as:
a×10000 + b×1000 + c×100 + d×10 + e where a, b, c, and d are single-digit numbers.
a is the ten thousands digit
b is the thousands digit
c is the hundreds digit
d is the tens digit
e is the units digit.
Let 8 be at one's place that is e
Now, it is given that 8 is in a place that is 10 times less than the place of the 4.
This implies 4 is at the ten's place that is d.
Next, it is given that 3 is in a place that is 100 times greater than the place of the 4.
That is 100×10 = 1000 place
So, 3 is at the place of b.
The 2 is in a place that is 10 times less than the place of the 3. So, 2 is at the place of c.
The 7 is in a place that is 100 times greater than the 2. That is 100×100 = 10,000 place.
Thus, 7 is at the place of a.
Thus, we obtain
a= 7
b= 3
c= 2
d= 4
e= 8
Therefore, the 5-digit mystery number is 73248.
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29-(11-2³)+6²÷4 simplify each Expression
The simplified form of the expression 29 - ( 11 - 2³ ) + 6² ÷ 4 is 35
What is the simplified form of the given expression?Given the expression in the question;
29 - ( 11 - 2³ ) + 6² ÷ 4
To simply, replace 2 raised to the power of 3 with 8 and 6 raised to the power of 2 by 36
29 - ( 11 - 2³ ) + 6² ÷ 4
29 - ( 11 - 8 ) + 36 ÷ 4
Now, remove the parenthesis by performing the operation inside the parenthesis.
29 - ( 11 - 8 ) + 36 ÷ 4
29 - 3 + 36 ÷ 4
Now, divide 36 by 4
29 - 3 + 36 ÷ 4
29 - 3 + 9
Next, add -3 and 9
29 + 6
Add 29 and 6
35
Therefore, 35 is the simplified form of the expression.
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Find all angles, osO<360, that satisfy the equation below, to thenearest 10th of a degree.cos(0) =-1/6
The cosine of the angle given is negative.
Cosine is negative in the second and third quadrant
[tex]\begin{gathered} 0\leq x\leq360 \\ \cos (\theta)=-\frac{1}{6} \\ \theta=\cos ^{-1}(\frac{1}{6}) \\ \theta=80.41^0 \\ \theta=80.4^0\text{ (to the nearest tenth)} \\ \end{gathered}[/tex]In the second quadrant,
[tex]\begin{gathered} 180-\theta \\ 180-80.4=99.6 \\ \theta=99.6^0 \end{gathered}[/tex]In the third quadrant,
[tex]\begin{gathered} 180+\theta \\ 180+80.4=260.4 \\ \theta=260.4^0 \end{gathered}[/tex]Therefore, the values that satisfy the equation are 99.6 and 260.4 degrees.
Use the confidence level and sample data to find a confidence interval for estimating the population μ. Round your answer to the same number of decimal places as the sample mean.
A group of 59 randomly selected students have a mean score of 29.5 with a standard deviation of 5.2 on a placement test. What is the 90% confidence interval for the mean score, μ, of all students taking the test?
The 90% confidence interval for the mean score, μ, of all students taking the test is; CI = (28.36, 30.64)
What is the Confidence Interval?
The formula for confidence interval is;
CI = x' ± z(s/√n)
where;
CI = Confidence Interval
x' is sample mean
z is critical value at confidence level
s is standard deviation
n is sample size
We are given;
n = 59
x' = 29.5
s = 5.2
z at CL 0f 90% = 1.645
Thus;
CI = 29.5 ± 1.645(5.2/√59)
CI = 29.5 ± 1.136
CI = (28.36, 30.64)
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The telephone company offers two billing plans for local calls. Plan 1 charges $29 per month for unlimited calls and plan 2 charges $17 per month plus $0.03 per call. Use and inequality to find the number of monthly calls for which plan is more economically than plan 2
Calls greater than 400 would be more economical in plan 1 than plan 2 and the inequality is 29 < 17 + 0.03x
How to determine the more economical plan?The given parameters are:
Plan 1
Charges per month = $29Plan 2
Charges per month = $17Monthly rate = $0.03Let the number of months be x.
So, we have the following equation
Plan 1: 29
Plan 2: 17 + 0.03x
For plan 1 to be more economical plan than plan 2, then we have the following inequality
Plan 1 < Plan 2
This is represented as
29 < 17 + 0.03x
Subtract 0.03x from both sides of the inequality
So, we have
0.03x > 12
Divide both sides by 0.03
x > 400
How to interpret the result in (a)?
In (a), we have
x > 400
This means that the number of calls for the plan 1 to be more economical than plan 2, then the number of calls must be greater than 400
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Triangle A has a height of 8 inches and a base of 2 inches. Triangle B has a height of 16 inches, what is the base?
The base of Triangle B is 1 inches.
Given,
Triangle A has a height of 8 inches
and base of Triangle is 2 inches
Let's Find the Area of Triangle A
We know that the formula of Area of Triangle
Area of Triangle = [tex]\frac{1}{2}[/tex] × b × h
where, b is the base and h is the height of triangle.
Plug the values of base and height in above formula.
Area of Triangle A = [tex]\frac{1}{2}[/tex] × 2 × 8
Hence, Area of Triangle A is 8 sq. inches
In this question, Some part is missing that is:
Triangle A is similar to Triangle B
Now, For Triangle B is given:
Triangle B has a height of 16 inches
and, to find the base of the triangle.
We know, Area of Triangle A is 8 sq. inches.
Area of Triangle B = [tex]\frac{1}{2}[/tex] × b × h
8 = [tex]\frac{1}{2}[/tex] × b × 16
8 = 8b
b = 1 inches
Hence, The base of Triangle B is 1 inches.
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I need to know which is the best estimate for rabbit population after 5 years
Answer:
[tex]\text{ B: 800 rabbits}[/tex]Explanation:
Here, we want to estimate the rabbit population after 5 years
From the question, there was an approximate increase in the rabbit population by 150 (from 150 to 300) in a space of 2 years
Let us have an exponential relationship for this:
[tex]P=I.a^t[/tex]Let us get the value of t
P is the current population at 300
I is the initial
a is ?
t is the number of years which is 2
Mathematically, we have it that:
[tex]\begin{gathered} 300\text{ =150 }\times a^2 \\ a^2\text{ = 2} \\ a\text{ = }\sqrt[]{2} \end{gathered}[/tex]Now, for the 5 years tenor, we substitute 5 for t
We have that as:
[tex]\begin{gathered} P\text{ = 150}\times\text{ (}\sqrt[]{2})^5 \\ P\text{ = 849} \end{gathered}[/tex]From the option, we have an approximate value of 800 rabbits
Simplify the quantity 8 minus one third times the square root of 9 end quantity squared plus the quantity 1 minus 5 end quantity squared.
The statement quantity 8 minus one third times the square root of 9 end quantity squared plus the quantity 1 minus 5 end quantity squared is simplified to 65
What are fractions?Fractions are defined as parts of a whole element, set or number.
There are various types of fractions, which includes;
Complex fractionsProper fractionsSimple fractionsMixed fractionsImproper fractionsBased on the information provided, we have;
8 minus one third times the square root of 9 = 8 - 1/3(√9)1 minus 5 end quantity squared = (1 - 5)²Now, substitute the values
(8 - 1/3(√9))² + (1 - 5)²
Find the square root
(8 - 1/3(3))²+ (-4)²
Find the square
(8 - 1)² + 16
7² + 16
49 + 16
Add the values
65
Hence, the value of the expression is 65
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The degree of the polynomial function f(x) is 3.
The roots of the equation f(x) = 0 are -1, 0, and 4.
Which graph could be the graph of f(x)?
The graph of the polynomial function x³ - 3x² - 4x = 0 is shown if figure.
What is Polynomial function?
A mathematical expression of algebraic terms each of which consists of a constant multiplied by one or more variables raised to a nonnegative integral power.
Given that;
The degree of the polynomial function f(x) is 3.
And, The roots of the equation f(x) = 0 are -1, 0, and 4.
Now, The polynomial function are calculated as;
f (x) = 0
(x + 1) (x - 0) (x - 4) = 0
x (x + 1) (x - 4) = 0
x (x² - 4x + x - 4) = 0
x (x² - 3x - 4) = 0
x³ - 3x² - 4x = 0
Thus, The polynomial function is;
x³ - 3x² - 4x = 0
Therefore, The graph of the polynomial function x³ - 3x² - 4x = 0 is shown if figure.
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what is the standard algorithm for 72 / 3
Long division gives the answer of 24 when 72 is divided by 3.
What is long division calculator?Long division in mathematics is a strategy for breaking down complicated division problems into a series of simpler steps. It is the approach that division-based issues are typically solved using. The dividend, the quotient, the remainder, and the divisor can all be seen in the following long division.
So as we know:
Start by arranging it so that the dividend 72 is on the right side and the divisor 3 is on the left:
3 ⟌ 7 2
Start by arranging it so that the dividend 72 is on the right side and the divisor 3 is on the left:
2
3 ⟌ 7 2
Write the result (3 x 2 = 6) underneath the dividend after multiplying the divisor by the outcome from the previous step.
2
3 ⟌ 7 2
6
Write the solution below after subtracting the result from the previous step from the dividend's first digit (7 - 6 = 1).
Reduce the dividend's second digit (2) as follows:
2
3 ⟌ 7 2
- 6
1 2
The bottom number (12) is multiplied by the divisor (3) four times (s). Put 4 thus on top
Subtract the result of the previous step (3 x 4) from the divisor to get the solution (12), which you should write at the bottom:
2 4
3 ⟌ 7 2
- 6
1 2
1 2
Take the number above it and deduct the outcome from the preceding calculation. Write the response at the bottom after calculating (12 - 12 = 0).
The top number is the solution, and the remaining value is the bottom one.
Therefore, the result of 72 divided by 3 using long division is 24.
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