We get 2 complex answers
Quadratics can be defined as a polynomial equation of a second degree, which implies that it comprises a minimum of one term that is squared.
Given that F(x) = 3x2 - 40x + 180
Set F(x) to 0, and you get ax2 + bx + c = 3x2 -40x + 180.
[-b +/- (b2 -4ac)(1/2)] is the quadratic formula. / 2a.
The stuff under the square root / radical (b2 - 4ac) is the KEY to your answer, and it determines whether you have two real, one real, or two imaginary answers. The discriminant is the term (b2 - 4ac).
Obviously, if (b2 - 4ac) > 0, you have two real answers, because the square root of a positive number is also a (positive) real number. And -b multiplied by a real number (and divided by 2a) yields two (real) answers.
If (b2 - 4ac) = 0, you have one correct answer because the square root of 0 is zero. And -b multiplied by a 0 real number (and divided by 2a) yields 1 (real) answer.
(b2 - 4ac) 0 yields two fictitious answers, because the square root of a negative number is a fictitious number. And -b multiplied by an imaginary number (and divided by 2a) yields two (complex) answers.
In this case, (b2 - 4ac) = ((-40)2 - 4(3)(180)) = 1600 - 2160 0 As a result of the discriminant is negative, the quadratic formula yields two complex answers.
Therefore we get two complex answers
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Answer:
[tex]x=\dfrac{20 +2\sqrt{35}\:i}{3}, \quad x=\dfrac{20 -2\sqrt{35}\:i}{3}[/tex]
2 imaginary answers.
Step-by-step explanation:
Given quadratic function:
[tex]f(x) =3x^2 - 40x + 180[/tex]
The zeros of a quadratic function can be found when f(x) = 0:
[tex]\implies 3x^2 - 40x + 180=0[/tex]
[tex]\boxed{\begin{minipage}{3.6 cm}\underline{Quadratic Formula}\\\\$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\\\\when $ax^2+bx+c=0$ \\\end{minipage}}[/tex]
Therefore:
a = 3b = -40c = 180Substitute the values of a, b and c into the quadratic formula and solve for x:
[tex]\implies x=\dfrac{-(-40) \pm \sqrt{(-40)^2-4(3)(180)}}{2(3)}[/tex]
[tex]\implies x=\dfrac{40 \pm \sqrt{1600-2160}}{6}[/tex]
[tex]\implies x=\dfrac{40 \pm \sqrt{-560}}{6}[/tex]
[tex]\implies x=\dfrac{40 \pm \sqrt{16 \cdot 35 \cdot -1}}{6}[/tex]
[tex]\implies x=\dfrac{40 \pm \sqrt{16}\sqrt{35}\sqrt{-1}}{6}[/tex]
[tex]\implies x=\dfrac{40 \pm 4\sqrt{35}\sqrt{-1}}{6}[/tex]
Apply the imaginary number rule [tex]\sqrt{-1}=i[/tex]:
[tex]\implies x=\dfrac{40 \pm 4\sqrt{35}\:i}{6}[/tex]
[tex]\implies x=\dfrac{20 \pm 2\sqrt{35}\:i}{3}[/tex]
Therefore, the solution is 2 imaginary answers.
Imaginary numbers
Since there is no real number that squares to produce -1, the number [tex]\sqrt{-1}[/tex] is called an imaginary number, and is represented using the letter [tex]i[/tex].
An imaginary number is written in the form [tex]bi[/tex], where [tex]b \in \mathbb{R}[/tex].
If a cone has a volume of 100 cubic inches, what is the length of the radius? Round your answer to the nearest tenth.
The radius of the cone is 10√(3/πh) inches when the volume of the cone is 100 cubic inches.
According to the question,
We have the following information:
Volume of cone = 100 cubic inches
We know that the following formula is used to find the volume of cone:
Volume of cone = π[tex]r^{2}h/3[/tex] where r is the radius of the cone and h is the height of the cone
π[tex]r^{2}h/3[/tex] = 100
Now, using the cross multiplication method:
π[tex]r^{2}[/tex]h = 100*3
Dividing both sides of the equation by πh:
[tex]r^{2}[/tex] = 300/πh
r = 10√(3/πh) inches
We can also solve it further by putting the value of π.
Hence, the radius of the cone is 10√(3/πh) inches when the volume of the cone is 100 cubic inches.
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Graph the line with slope 1 passing through the point (-2 , -5)
Graph the line.
The equation of the line is y = x -3. The graph of the line is attached below.
What is a line?
A line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature. Since lines can exist in two, three, or higher dimensional environments, they are one-dimensional things. The term "line" can also be used to describe a line segment in daily life that contains two locations that serve as its ends.
Given that the slope of the line is 1.
Assume that the equation of the line is y = mx +c, where m is the slope of the line and c is y-intercepts.
Putting m = 1 in y = mx +c:
y = 1 × x +c
y = x +c
Since the line passes through the point (-2, -5), thus the point satisfies the given equation of line.
Putting x = -2 and y = -5 in y = x +c
-5 = -2 + c
c = -3
The equation of line is y = x - 3.
The points on the line are
(-2, -5), (0, -3), (3, 0).
Plot the points and join them:
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The effect of the time of day a science class is laught on test scores is being studied in an experiment. Giving every student in the experiment the same final exam is an example of which experimental design principle?
Giving every student in the experiment the same final exam is an example of A. Randomization.
What is an experimental design?The process of conducting research in an objective and controlled manner in order to maximize precision and draw specific conclusions about a hypothesis statement is known as experimental design.
The process in which participants in clinical trials are randomly assigned to separate groups that receive different treatments or other interventions. Neither the researcher nor the participant has any say in which treatment or intervention the participant receives.
A random process is a sequence of random variables that describe a process whose outcomes follow an evolution described by probability distributions. This was illustrated in the examination.
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Complete options
A. Randomization
B. Blocking
C. Direct control
D. Replication
Keala is making a new book cover before giving their favorite picture book to their little brother. The cover is 22 1 4 cm 22 4 1 cm22, start fraction, 1, divided by, 4, end fraction, start text, c, m, end text tall. It has a rectangular shape and an area of 890 cm 2 890cm 2 890, start text, c, m, end text, squared. How wide across is Keala's book cover? cm
The width across Keala book cover is 40cm
What is a rectangle?A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel. It is a four-sided polygon that has four angles, equal to 90 degrees
From the question,
The length of the cover
= 22 1/4
= 89/4
The area of the cover
=890 cm²
From the formula
Area of a Rectangle = Length x Breadth
890=89/4×Breadth
Breadth = 890×4/89
Breadth=40cm
Hence, the width of the book cover is 40cm
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create an x and y table of all 5 points in the picture (graphing)
The x and y table of all 5 points in this graph include the following:
x y
1 1
2 2
3 3
4 4
5 5
What is a graph?In Mathematics, a graph can be defined as a type of chart that is typically used for the graphical representation of data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis).
Additionally, the graph of any proportional relationship is always modeled by a straight line with the data points passing through the origin (0, 0).
In this scenario, we can reasonably and logically deduce that all of the data points in this graph are represented by the red symbols.
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Pls help question 9 and 10
The theorem that will prove similarity of triangle ΔGHS and ΔFES is AAA ( angle angle angle) theorem. The value of FE is 45m.
AAA theorem states that if two triangles have all three corresponding angles equal then they are similar triangles.
In the given figure FE║GE means FE is parallel to GE.
so ∠EFS = ∠HGS
and ∠FES = ∠GHS
also ∠S is common for both.
If two triangles are similar then ratio of corresponding sides are also same.
So, by applying this
[tex]\frac{FS}{GS}[/tex] = [tex]\frac{FE}{GH}[/tex]
54/24 = FE/20
( 54*20 ) / 24 = FE
FE = 45m.
Therefore the triangles will be similar by theorem AAA and the value of FE will be 45m.
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A resort has 380 rooms with space for 6 people. Estimate the greatest number of people who could be in these rooms at the same time. Explain your thinking to a friend or family member.
Using the multiplication operation, the greatest number of people who could be in the 380 rooms with space for 6 persons at the same time is 2,280.
What is multiplication operation?Multiplication operation is one of the basic mathematical operations, including subtraction, addition, and division.
A multiplication operation involves applying the multiplier to the multiplicand to result in a product.
The total number of rooms in the resort = 380
The number of people per room = 6
380 x 6 = 2,280
Thus, by multiplication, if 6 persons occupy each of the 380 rooms, the resort will have 2,280 persons at a time.
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why is not inverse function??
[tex]f(x) = x {}^{2} - 9[/tex]
The equation formed when x is the subject of the function f(x) = x² - 9, has two values of output for each input value to the function, therefore;
f(x) = x² - 9 does not have an inverse.
What is the inverse of a function?An inverse of a function is an anti function that reverses the values in the output into the input values thereby undoing the operations performed by the function.
A function f has an inverse if and only if it is bijective, such that there is a one to one correspondence between the set of the input elements and the set of the output elements
A function that has an inverse is said to be a bijective or invertible function or a function with one-to-one correspondence
The function in the question f(x) = x² - 9
Making x the subject of the function to verify if it has an inverse gives;
x² = f(x) + 9
[tex]x = \pm\sqrt{f(x) +9}[/tex]
Putting x = f⁻¹(x) gives;
[tex]f^{-1}(x) = \pm\sqrt{x +9}[/tex]
Therefore, each value of x gives two values of f⁻¹(x), such that the set of the output of inverse function, f⁻¹(x) does not have a one-to-one correspondence with the set of values of x.
The function f(x) = x² - 9 is not invertible and therefore does not have an inverse function.
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or
The equation of line k is y=
–
10x–8. Perpendicular to line k is line , which passes through the point (2,2). What is the equation of line ?
Considering the definition of perpendicular line, the equation of perpendicular line is y= -1/10x + 11/5.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Perpendicular linePerpendicular lines are lines that intersect at 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.
Equation of perpendicular line in this caseThe line is y= 10x -8.
The line has a slope of 10. If you multiply the slopes of two perpendicular lines, you get –1:
10× slope perpendicular line= -1
slope perpendicular line= (-1)÷ 10
slope perpendicular line= -1/10
The perpendicular line has a form of: y= -1/10x + b
The line passes through the point (2, 2). Then:
2= -1/10× (2) + b
2= -1/5+ b
2+ 1/5= b
11/5= b
Finally, the perpendicular line is y= -1/10x + 11/5.
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Warren likes to draw pictures of people and animals. In his notepad, he has drawn 2 pictures of people for every 5 pictures of animals.
If Warren has drawn 18 more pictures of animals than people in his notepad, how many pictures of animals has he drawn
By solving a linear equation, it is obtained that Warren has drawn 30 pictures of animals
What is linear equation?
At first it is important to know about equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Here, a linear equation needs to be solved
Let Warren has drawn 5x pictures of animals and 2x pictures of people
Warren has drawn 18 more pictures of animals than people in his notepad
By the problem,
5x - 2x = 18
3x = 18
x = [tex]\frac{18}{3}[/tex]
x = 6
Number of pictures of animals Warren has drawn = [tex]5 \times 6 = 30[/tex]
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The coordinates of the endpoints of
KL
are K(
–
16,10) and L(
–
9,
–
11). Point M is on
KL
and divides it such that KM:LM is 4:3.
What are the coordinates of M?
Write your answers as integers or decimals.
The coordinates M along the directed line segment is (-12, -2)
How to find the coordinates of the point along the directed line segment?The points are given as:
K = (-16, 10)
L = (-9, -11)
The ratio on the segment can be represented as;
KM : LM, m : n = 4 : 3
So, we have the coordinates of the point M that lies along the directed line segment to be
M = 1/(m + n) * (mx₂ + nx₁, my₂ + ny₁)
So, we have:
M = 1/(4 + 3) * (4 * -9 + 3 * -16, 4 * -11 + 3 * 10)
Evaluate
M = 1/7 * (-84, -14)
Evaluate
M = (-12, -2)
Hence, the coordinates of the point M is (-12, -2)
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What is the slope of the line that passes through the points (-6, -7) and (-3, -2)?
can somone help me with this will mark u brainliest
Answer:
686 cm^2
Step-by-step explanation:
First find the sides
7f = 49
4f = 28
To find a triangle area (right triangle), multiply each side like a rectangle, but divide it by two.
(49*28)/2 = 686
Answer:
67
Step-by-step explanation:
Alyssa is signing up for a gym membership with a one-time fee to join and
then a monthly fee to remain a member. Let C represent the total cost of the
gym membership over t months. The table below has select values showing
the linear relationship between t and C. Determine the one-time joining fee.
Answer: $
t
2
4
9
C
200
250
375
Submit Answer
The one time joining fee found from the linear relationship between total cost and the number of months of membership is $250
What is a linear relationship?A linear relationship is a relationship between two variables that has a straight line when graphed.
The total cost of the gym membership = C
The number of months of membership = t
The table in the question is presented as follows;
t (Time in months) [tex]{}[/tex] C (Total cost)
2 [tex]{}[/tex] 200
4 [tex]{}[/tex] 250
9 [tex]{}[/tex] 375
The linear equation that represents the value in the table is found as follows;
Slope of the line, m = (375 - 250)/(9 - 4) = 25
The equation of the line in point and slope form is therefore;
(C - 375) = 25·(t - 9)
C = 25·(t - 9) + 375
C = 25·t - 225 + 375 = 25·t + 250
C = 25·t + 250
The joining fee is the amount paid at the start when t = 0, therefore;
Joining fee = 25 × 0 + 250 = 250
The one time joining fee is $250
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The graph shows Derek’s pay compared to the hours he has worked.
What is Derek’s hourly rate of pay?
Charlie earns $52.25 in 5 hours of work. What is Charlie’s hourly rate of pay?
Who gets paid more per hour? How much more?
Derek's hourly rate is $10 and Charlie's hourly rate is $10.45, Charlie's earns $0.45 more per hour than Derek.
What is unit rate?A unit rate means a rate for one of something.
Given that, a graph which shows Derek's earning hourly, and Charlie earns $52.25 in 5 hours of work,
Derek's earns $10 for an hour
Charlie's earning for an hour = 52.25/ 5 = $10.45
Hence, Charlie's hourly rate is $10.45, and he earns $0.45 more per hour than Derek.
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mass
density
volume
2.23 kg of oxygen gas has a volume of 1.56 x 106 cm³.
Calculate the density of the oxygen gas in g/cm³.
Give your answer in standard form to 3 significant figures.
Answer:
density = 1.43 × 10⁻³ g/cm³
Step-by-step explanation:
We are told that oxygen gas of mass 2.23 kg has a volume of 1.56 × 10⁶ cm³, and we are told to find its density in g/cm³.
To do this we have to first convert the mass, which is given in kg, to g:
mass = 2.23 kg = 2.23 kg × 1000 [tex]\mathrm{_\frac{g}{kg}}[/tex]
= 2230 g
Next, we can find the density of the gas using the following formula:
[tex]\boxed{density = \frac{mass}{volume}}[/tex]
⇒ density = [tex]\mathrm{\frac{2230 \ g}{1.56 \times 10^{6} \ cm^3}}[/tex]
= 1.43 × 10⁻³ g/cm³
Therefore, the density of the oxygen gas is 1.43 × 10⁻³ g/cm³.
Determine the value of each expression. |-2-8|-|−5|
Answer:
5
Step-by-step explanation:
:)
Answer:5
Step-by-step explanation:|-10|-|-5|
10-5
5
Name a plane in the image.
A
•C
B
Answer:
ABCStep-by-step explanation:
A is a point
AB is a line
ABC is a plane
Therefore, ABC is a plane.
__________________
Hope this helps!
Have a great day!
How many numbers are there from 10 to 99 in which the difference between the largest digit and the smallest digit equals 4?
For example 15 and 51, where 5 – 1 = 4.
There are 9 numbers from the range with the difference of 4 in the digits
How to determine the frequency of the numbers with the properties?The properties of the numbers are given as
Difference: Largest - Smallest = 4
Range: 10 to 99
The numbers with above properties are as follows
15, 26, 37, 48, 59, 62, 73, 84 and 95
When these numbers are counted, we have
Frequency = 9
This means that there are 9 of such numbers from 10 to 99
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Simon bought a $48 table on sale at 30% off.
Select from the drop-down menu to correctly complete the sentence
0.03(50)
0.3(50)
3(50)
30(50).
Simon bought a $48 table on sale. The price of the table can be estimated by $50.
The sale propose 30% off, then an estimate for the discount can be calculated using proportion:
$50 -- 100%,
$x -- 30%
that is mathematically
Find x:
Answer: correct choice is B
Graph The any form equation 3(-2x-4y-3) = 5(x - 5y + 10) Build equation with the given information (2) slope = m = -5 point (-3,-2) 3 point 1 (-5,-3) point2 (-7,-9) Build an equation parallel to the given equation and passing through The point 47 y = - ³²/²x-4 point (-7,5)
Here is what i did
I used a graphing calculator
If Ø (theta) is an angle in standard position and its terminal side passes through the point (-9,5), find the exact value of sec Ø (theta) in simplest radical form.
For the given data, ∅ is the given angle in standard position, terminal side passes through (-9,5) then the exact value of sec∅= ( - √106/ 9 ) in simplest radical form.
As given in the question,
For the given angle ∅ (theta) in standard position:
Terminal side of ∅ is passes through the point ( -9, 5 )
( -9 , 5 ) represents ∅ is in the second quadrant.
In second quadrant sine in positive and cosine is negative.
Base is negative and altitude is positive.
Base = -9
Altitude = 5
Using Pythagoras theorem,
Hypotenuse² = (-9)² + (5)²
⇒ Hypotenuse = √106
cos ∅ = -9 / √106
sec ∅ = 1/ cos ∅
= - √106/9 ( simplest radical form )
Therefore, for the given data, ∅ is the given angle in standard position, terminal side passes through (-9,5) then the exact value of
sec∅= ( - √106/ 9 ) in simplest radical form.
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Determine the interval(s) on which the function is (strictly) increasing.
Write your answer as an interval or list of intervals.
When writing a list of intervals, make sure to separate each interval with a comma and to use as few intervals as possible.
Click on "None" if applicable.
Answer:1341
Step-by-step explanation:
1342123
how to find perimeter of a triangle?
Answer:
Just add the 3 sides together
Step-by-step explanation:
if a triangle has the side values of 3, 4, 6. Then you would simply add them together!
3+4+6=13
therefor that triangles perimeter is 13
hope this helps!
manuel wishes to purchase 25cent and 30 cent stamps. he decides to buy 10 fewer 30 cent stamps. How many of each can he buy for no more than $19.00
Using the simplification, Manuel buy 15 stamps of 25 cents and 5 stamps of 30 cent.
In the given question,
Manuel wishes to purchase 25 cent and 30 cent stamps.
He decides to buy 10 fewer 30 cent stamps.
We have to find how many of each can he buy for no more than $19.00.
Let he buy x stamps of 25 cent.
He want to buy 10 fewer 30 cent stamps.
So he buy x−10 stamps of 30 cent.
But he have to buy total stamps of $19.
So the equation is
x+x−10 = 19
Simplifying
2x−10=19
Add 10 on both side
2x−10+10=19+10
2x=29
Divide by 2 on both side
2/2 x =29/2
x=14.5
x≈15
Hence, he buy 15 stamps of 25 cent.
Now finding the number of 30 cent.
he buy x−10 stamps of 30 cent.
So 15−10=5.
So he buy 5 stamps of 30 cent.
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Mary Granola consumes tomatoes and nectarines. Mary's indifference curves are kinky. When she is consuming more tomatoes than nectarines, she is just willing to trade 3 tomatoes for 1 nectarines. When she is consuming more nectarines than tomatoes, she is just willing to trade 4 nectarines for 1 tomatoes. Let P₁ be the price of nectarines and P₂ the price of tomatoes. Mary maximizes her utility subject to her budget constraint. Which is true? (Hint: Sketch one of her indifference curves.)
When P₁ >3P₂ she must consume only tomatoes.
What are indifference curves ?
An indifference curve is a graph that illustrates numerous pairings of two goods or commodities that leave the customer equally well off or satisfied—hence indifferent—when it comes to owning any pairing of the two items that is represented along the curve.
Mary do trading 3 tomatoes for 1 nectarine.
So, MRS=3
P₁ >3P₂
P₁/P₂ > 3
P₁/P₂ < -3
This satisfies MRS=3
P₁ >3P₂ shows budget constraint
consumer specializes in tomatoes consumption.
if P₂ > 4 P₁ , consumer specializes in nectarine consumption. option is not there.
So, When P₁ >3P₂ she must consume only tomatoes.
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2(4 - 2w) - 8 = -4
w = ?
Use the distributive property to multiply 2 times 4−2w.
8 - 4w - 8 = -4Subtract 8 from 8 to get 0.
-4w = -4Divide both sides by −4.
w = -4/-4Divide −4 by −4 to get 1.
w = 1Answer:
w = 1
Step-by-step explanation:
2(4 - 2w) - 8 = -4
(2*4 + 2*-2w) - 8 = -4
(8 - 4w) - 8 = -4
-4w + 8 - 8 = -4
-4w = -4
w = -4/-4
w = 1
Check:
2(4 - 2*1) - 8 = -4
2(4-2) -8 = -4
2(2) - 8 = -4
4 - 8 = -4
On April 1, 2022 the balance in inventory is 220 units at $50 each
April 5, 2022 purchased 100 units at $60 each
Purchased 50 units at $45 each on April 10, 2022
Sold 300 units at $80 each on April 16, 2022
Sold 20 units at $95 each on April 25, 2022
Purchased 200 units at $40 each on April 30, 2022
The calculation of the ending inventory and the cost of goods sold using FIFO and LIFO methods for ABC Inc. is as follows:
FIFO LIFO
Ending inventory $10,250 $12,800
Cost of goods sold $17,000 $14,450
How does FIFO differ from LIFO?FIFO (First-in, First-out) assumes that the physical flow of goods sold depends on the chronological order of acquisition.
LIFO (Last-in, First-out) assumes that the cost of goods sold should be based on the latest inventory purchases.
Date Description Units Unit Costs Total Cost
April 1 Beginning inventory 220 $50 $11,000
April 5 Purchases 100 $60 6,000
April 10 Purchases 50 $45 2,250
April 16 Sales -300 $80
April 25 Sales -20 $95
April 30 Purchases 200 $40 8,000
Total 570 $27,250
Units sold 320
Ending inventory 250
FIFO:
Ending Inventory = $10,250 (200 x $40 + 50 x $45)
Cost of goods sold = $17,000 ($27,250 - $10,250)
LIFO:
Ending Inventory = $12,800 (220 x $50 + 30 x $60)
Cost of goods sold = $14,450 ($27,250 - $12,800)
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Question Completion:Calculate Ending Inventory And COGS Using FIFO And LIFO Methods For ABC Inc.
A quarterback threw a football from a height of 6 feet with an initial velocity of 20 feet per second. The height, h, of the ball at time t seconds can be represented by
the equation h (t)=-16t² + 20t+6.
True or False?
The ball was in the air for 1.5 seconds before hitting the ground.
The ball was in the air for 1.5 seconds. The answer is true.
What is a quadratic equation?The equation of the form ax² + bx +c is known as a quadratic equation.
The given equation is h(t) = -16t² + 20t + 6.
To find the time for which the ball was in the air, substitute h(t) =0.
0 = -16t² + 20t + 6
Use the quadratic formula to solve the equation:
[tex]t= \frac{- 20 \pm\sqrt{20^2 - 4(-16)(6)}}{2(-16)}\\t=\frac{- 20 \pm\sqrt{400+384}}{-32}\\t=\frac{- 20 \pm\sqrt{400+384}}{-32}\\t=\frac{- 20 \pm\sqrt{784}}{-32}\\\\t= \frac{- 20 \pm28}{-32}[/tex]
t = (-20 + 28)/(-32) or t = (-20-28)/(-32)
t = -0.25 or t = 1.5
Since time cannot be negative, discard the negative value.
Hence, the ball was in the air for 1.5 seconds. The answer is true.
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What is the end behavior of the graph?
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As x approaches infinity, f(x) approaches negative infinity.
As x approaches negative infinity, f(x) approaches negative infinity.
As x approaches infinity, f open argument x close argument approaches negative infinity., , As x approaches negative infinity, f open argument x close argument approaches negative infinity., , ,
As x approaches infinity, f(x) approaches infinity.
As x approaches negative infinity, f(x) approaches infinity.
As x approaches infinity, f open argument x close argument approaches infinity., , As x approaches negative infinity, f open argument x close argument approaches infinity., , ,
As x approaches infinity, f(x) approaches negative infinity.
As x approaches negative infinity, f(x) approaches infinity.
As x approaches infinity, f open argument x close argument approaches negative infinity., , As x approaches negative infinity, f open argument x close argument approaches infinity., , ,
As x approaches infinity, f(x) approaches infinity.
As x approaches negative infinity, f(x) approaches negative infinity.
The end of the graph is
As x approaches infinity, f open argument x close argument approaches negative infinity., , As x approaches negative infinity, f open argument x close argument approaches infinity
as x tends to ∞, f(x) tends to -∞as x tends to -∞, f(x) tends to ∞What is end behavior?The end behavior of function typically says the characteristics of the function at the ends
How to find the end behavior of polynomial functionThis is determined by examining the graph and the coordinates.
The graph shows as at the positive side of the x coordinate, as x tends to ∞ the curve is pointing down - ∞The graph shows as at the negative side of the x coordinate as x tends to - ∞ the curve is pointing up ∞The end behavior is can be written as
x ⇒ ∞ f(x) ⇒ -∞
x ⇒ -∞ f(x) ⇒ ∞
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