I am stuck on the graphing portion of this question, would it be formatted like A or like B?
Answers
To determine which option is a representation of the graph we need to make the numer line analysis; to make it we need to notice that the functions has zeros at the points:
[tex]\begin{gathered} x=2 \\ x=4 \\ x=-3 \\ x=0 \end{gathered}[/tex]once we know this we divide the number line in the following intervals:
now we need check the sign of the function in each interval, to do this we choose a value in them.
For the first interval let's take x=-4, then we have:
[tex]\begin{gathered} f(-4)=-(-4)^3(-4-2)^2(-4-4)(-4+3) \\ f(-4)=-(-64)(36)(-8)(-1) \\ f(-4)=(64)(36)(8) \\ f(-4)=18432 \end{gathered}[/tex]From the last expression we notice that the value of the function is positive at this point. Hence the firts interval have positive values for the function.
For the second interval let's take x=-1, then we have:
[tex]\begin{gathered} f(-1)=-(-1)^3(-1-2)^2(-1-4)(-1+3) \\ f(-1)=-(-1)(9)(-5)(2) \\ f(-1)=-90 \end{gathered}[/tex]From the result we conclude that the function is negative in this interval.
For the third interval, let's take x=1, we have:
[tex]\begin{gathered} f(1)=-(1)^3(1-2)^2(1-4)(1+3) \\ f(1)=-(1)(1)(-3)(-4) \\ f(1)=12 \end{gathered}[/tex]From the result we conclude that the function is positive in this interval.
For the fourth interval, let's take x=3. then we have:
[tex]\begin{gathered} f(3)=-(3)^3(3-2)^2(3-4)(3+3) \\ f(3)=-(27)(1)(-1)(6) \\ f(3)=162 \end{gathered}[/tex]Then the function is positive in this interval.
Finally, for the fifth interval let's take x=5, then we have:
[tex]\begin{gathered} f(5)=-(5)^3(5-2)^2(5-4)(5+3) \\ f(5)=-(125)(9)(1)(8) \\ f(1)=-9000 \end{gathered}[/tex]Then the function is negative in the last interval.
Hence the line analysis is:
The y-intercept of the function happens when x=0, then we have that:
[tex]\begin{gathered} f(0)=-(0)^3(0-2)^2(0-4)(0+3) \\ f(0)=0 \end{gathered}[/tex]Therefore the y-intercept of the function is 0.
Once we know the information from the line analysis and the y-intercept of the function we conclude that the sketch of the graph is option B.
Two graphs of the function (with different values for the y-axis) are shown below:
This graphs confirm that option B is an approximate sketch of the graph.
Related Questions
Can you teach me how to divide fractions?
Answers
We illustrate the division of fractions by taking the example below.
[tex]\frac{5}{7}\div\frac{25}{14}[/tex]The first step is to change the division sign to multiplication by changing the fraction after the division sign.
[tex]=\frac{5}{7}\times\frac{14}{25}[/tex]Next, we multiply the numerators together and the denominators together.
[tex]=\frac{5\times14}{7\times25}[/tex]You then simplify by dividing common factors.
[tex]\begin{gathered} \\ =\frac{5}{25}\times\frac{14}{7} \\ =\frac{1}{5}\times2 \\ =\frac{2}{5} \end{gathered}[/tex]An accident investigator measured the skid marks of one of the vehicles involved in an accident. The length of the skid marks was 245ft. Use the formula s=24d−−−√ to find the speed of the vehicle before the brakes were applied. Round your answer to the nearest tenth.
Answers
The vehicle speed is 53 units if s = 24d and d = 245ft
Given the formula for speed is = √24 d
s denotes the vehicle's speed.
d = the length of the skid marks
We need to find the speed of the vehicle.
We know that the displacement d is 117 ft
d = 117 ft
And also it is mentioned in the question to use the below-given formula.
s = √24d
Now substituting the value of displacement in the formula we get
=> s = √24 x 117
=> s = √2808
=> s = 52.99
Now approximating to the nearest value of the decimal, we get.
=> s = 53
Therefore the speed of the vehicle is 53 units.
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Ronny is selling coffee mugs for $4.00. So far, he has earned $344.00. Ronny needs to earn more than $392.00 in order to meet his sales goal. How many more coffee mugs, x, does Ronny need to sell in order to reach his sales goal?
Answers
Answer:
25 more cups
Step-by-step explanation:
1. You need more than $636.00, but you already have $492.00. To find the needed amount of cups needed to sell, you need to find the difference of the two prices first. In other words, you need to subtract the total needed by the amount already raised.
2. You can get the equation, 636 - 492 = 144
3. Now that you have the amount needed, you can divide the number that you got (144) by 6. You divide it by 6 because that is the amount each cup costs.
4. After dividing 144 by 6, you should get 24. This gives your answer for getting EXACTLY 636. However, in this case, you need more to reach your goal. Since you cannot sell fractions of a cup, just raising it by one can reach your goal. We can add one to 24, making it 25.
In conclusion, you need to sell 25 more cups to reach your goal.
The height, h (in meters above ground), of a projectile at any time, t (in seconds), after the launch is defined by the function h(t) = −5t2 + 13t + 6. The graph of this function is shown below. When rounded to the nearest tenth, what is the maximum height reached by the projectile, how long did it take to reach its maximum height, and when did the projectile hit the ground?
Answers
As we can se from the graph, the maximum value of the function is almost 15 meters, it is reached between t=1s and t=2s, and the height is 0 again when the time is approximately 3 seconds.
We can find the exact values by using the equation.
First, find the zeroes of the function by setting h(t)=0 and solving the quadratic equation for t:
[tex]\begin{gathered} h(t)=-5t^2+13t+6=0 \\ \Rightarrow t=\frac{-13\pm\sqrt[]{13^2-4(6)(-5)}}{2(-5)} \\ \Rightarrow t_1=-0.4;t_2=3 \end{gathered}[/tex]Then, the projectile hits the ground at t=3s.
To find the time at which the projectile reaches its maximum height, find the average between both zeroes:
[tex]t_{\max }=\frac{t_1+t_2}{2}=\frac{-0.4s+3s}{2}=1.3s[/tex]To find the maximum height, evaluate h at t=1.3s:
[tex]h(1.3s)=-5(1.3)^2+13(1.3)+6=14.45[/tex]Therefore, to the nearest tenth, the projectile reached a maximum height of 14.5 meters in 1.3 seconds and it took 3.0 seconds for it to hit the ground.
The correct option is the second one.
Four years after paying $2700 for shares in a startup company, you sell the shares for $1300 (at a loss).
Answers
Based on the amount you paid for the shares and the selling price as well as the number of years, the total return would be -51.9%
The annual return would be -16.7%
How to find the total return?The total return on the stock can be found by finding the difference in stock prices for the 4 years and dividing by the buying price:
= (1,300 - 2,700) / 2,700 x 100%
= -1,400 / 2,700 x 100%
= 0.51851851851851851851851851851852 x 100%
= -51.9%
The annual return can be found as:
= ((1,300 / 2,700) ^ 1/4 - 1) x 100%
= -16.7%
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please Solve for brainliest and 20 points
Answers
Answer:
g=30
Step-by-step explanation:
Answer:
g = 28
Step-by-step explanation:
( n - 2 ) × 180
( 30 - 2 ) × 180
( 28 ) × 180 = 5040
6g × 30 = 180g
5040 = 180g
÷180 ÷180
--------------------
28 = g
I hope this helps!
An inverse variation includes the points (10, 2) and (n, 4). Find n.
Answers
SOLUTION
An inverse variation is given as
[tex]\begin{gathered} a\text{ }\propto\text{ }\frac{1}{b} \\ \text{Introducing a constant k, we have } \\ a\text{ = }\frac{k}{b} \end{gathered}[/tex]Putting a = 10 and b = 2, we have;
[tex]\begin{gathered} 10\text{ = }\frac{k}{2} \\ k\text{ = 10 x 2 = 20 } \end{gathered}[/tex]The relationship becomes
[tex]\begin{gathered} a\text{ = }\frac{20}{b} \\ \text{Putting a = n, and b = 4, we have } \\ n\text{ = }\frac{20}{4} \\ \\ n\text{ = 5} \end{gathered}[/tex]Therefore, n = 5
how can i find x and y in a triangle?
Answers
Using the sine formula;
sin 60 / x = sin 90 / 16
cross-multiply
x sin 90 = 16 sin 60
Divide both-side of the equation by sin 90
x = 16 sin 60 /sin 90
x= 13.86
To find y, we can simply use the Pythagoras theorem
opp² + adj² = hyp²
13.86² + y² = 16²
192.0996 + y² =256
subtract 192.0996 from both-side of the equation
y² = 256 - 192.0996
y² = 63.9004
Take the square root of both-side
y = 7.99
i want to plant 45 sunflower plants and 63 tomato plants in my garden. if i put the same number of plants in each row with only one type of plant in each row, what is the greatest number of plants i can put in one row? Show evidence
Answers
9 is the greatest number of plants in one row.
What is HCF?The HCF (Highest Common Factor) of two or more numbers is the highest number among all the common factors of the given numbers.
To find the greatest number of plants she can put in one row , need to find
HCF of 45 , 81 and 63
45 = 3× 3 × 5 = 3² ×5¹
63 = 3 ×3 × 7 = 3² × 7¹
HCF Highest common factor of given numbers is the largest factors which divides all the given numbers perfectly.
HCF = product of common factors of least power
HCF = 3² = 9
Hence greatest number of plants she can put in one row is 9
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daryl has 1/4 of a pound of chocolate he wants to divide it into 2 equal parts for his siblings how much will each sibling get
Answers
To divide the 1/4 of a pound into two equal parts, it is necessary to divide 1/4 by 2, as follow:
(1/4)/2
if 2 is written as 2/1, the previous quotient can be written as a product:
(1/4) (1/2) = 1/8
Now, to write a general expression that takes into account the number of siblings, you name the number of siblings as x. Thus, you have:
(1/4)/(x) = 1/(4x)
Delta Simply Fraction Exponent
Answers
the function shown is in the form y= ( x - h)² Determine the value of h.A) -1 B) 1C) 2D) -1/2
Answers
INFORMATION:
We have the graph of a function that has the form y = ( x - h)² and we must find the value of h.
STEP BY STEP EXPLANATION:
we can see that the graph is a parabola which its vertex is at the point (2, 0)
Now, having this point we can replace the values of its components in the formula of the function
Since the point is (2, 0), then x = 2 and y = 0
[tex]0=(2-h)^2[/tex]Finally, we must solve the equation for h
[tex]\begin{gathered} 0=(2-h)^{2} \\ \sqrt[]{0}=2-h \\ 0-2=-h \\ 2=h \\ h=2 \end{gathered}[/tex]ANSWER:
C) 2
What's the missing side
Answers
Therefore if we multiply 35 by 1.5 it would be:
52.5
1 ptsQuestion 22The point A(8,-6) has been transformed using the composition T-15) • r(180,0). Where is A?0 (71)o 17, -1)0 (-7,1)0 (-7, -1)+ Previous
Answers
You have to perform two transformations the first one is a 180º rotation with respect to the origin r(180º,O) and the second one is a translation of one unit left and 5 units up T(-1,5)
Given point A(8,-6)
To make a 180º rotation you have to invert the signs of both coordinates, following the rule:
[tex](x,y)\to(-x,-y)[/tex]For point A, the rotation is the following:
[tex]A(8,-6)\to A^{\prime}(-8,--6)=(-8,6)[/tex]Once you rotate the point, you have to perform the translation T(-1,5). The rule for the translation can be expressed as follows
[tex](x,y)\to(x-1,y+5)[/tex]So, the translation of point (-8,6) is:
[tex]A^{\prime}(-8,6)\to A^{\doubleprime}(-8-1,6+5)=(-9,11)[/tex]At the nearest wholesale store, 3 bags of cereal cost $21.75. Which equation represents the proportional relationship?
Answers
The cost of the 5 bags using proportionality method is: $36.25
What is proportionality?
In mathematics, the term proportionality can be defined by considering a two quantities in constant ratio. And the two quantities can be recognized as the variable y and x. Where, the variable y is defined as directly proportionate to the changes in the variable x which is based on its constant ratio.
According to the question, the given data states that 5 bags will cost $36.25.
By using proportionality method to solve the given statement. Put the price over the number of bags
21.75 x
---------- = ---------
3 bags 5 bags
Using cross products defined in standard mathematics,
21.75 * 5 = 3x
108.75 = 3x
Divide each side by 3
108.75/3 = 3x/3
36.25 =x
5 bags will cost 36.25
Hence, the cost of the 5 bags using proportionality method is: $36.25
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Correct Question:
At the nearest wholesale store, 3 bags of bulk cereal cost $21.75. At this rate, how much would 5 bags of bulk cereal cost?
One weekend, 5,780 people saw a new movie at 17 different theaters. Each theater sold tickets at $7.50 a piece. If each theater received the same number of moviegoers, how much did each theater make?
Answers
The amount that each theater make if they received the same number of moviegoers will be $2550.
How to calculate the amount?From the information, 5,780 people saw a new movie at 17 different theaters and each theater sold tickets at $7.50 a piece.
Therefore, the amount that each theater make if they received the same number of moviegoers will be:
= (5780 × $7.50) / 17
= $43350 / 17
= $2550
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Find the equation (in slope-intercept form) of the line with the given slope that passes through the point with the given coordinates.
Slope: 0
Ordered Pair: (-9,7)
Answers
The equation of the line woth slope 0 and passing through (-9,7) in slope-intercept form is y = 7.
If a line L has a slope M and it has the intercept c, then the equation of the line L can be written in the point slope form as,
L : y = Mx + c
This above equation of line is known as slope-intercept form of line.
Here, we have to find the equation of line which has slope m equal to zero and passing through (-9,7).
putting the known values in y = mx+c
y = (0)x+ c
y = c
Putting the value of y = 7
c = 7
Here, we have,
y = 7
So, the equation of the required line is y=7.
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a square flowerbed has an area of 12 sq feet.find length of pne side of the square in ft/in rounded to the nearest in.
Answers
Area of square = L x L
12sq feet =L x L
[tex]\begin{gathered} L=\sqrt[]{12} \\ L=3.46\approx3\text{ f}eet \end{gathered}[/tex]Find a solution for the equation. x^2-6x-8=0
Answers
Given:
[tex]x^2-6x-8=0[/tex]Required:
To find the solution of the given equation.
Explanation:
From the given equation,
[tex]\begin{gathered} a=1 \\ b=-6 \\ c=-8 \end{gathered}[/tex]Now
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]Therefore,
[tex]x=\frac{-(-6)\pm\sqrt{(-6)^2-4(1)(-8)}}{2(1)}[/tex][tex]\begin{gathered} x=\frac{6\pm\sqrt{36+32}}{2} \\ \\ =\frac{6\pm\sqrt{68}}{2} \\ \\ =\frac{6\pm2\sqrt{17}}{2} \\ \\ =\frac{2(3\pm\sqrt{17)}}{2} \\ \\ =3\pm\sqrt{17} \end{gathered}[/tex]Final Answer:
The solutions are
[tex]x=3+\sqrt{17},3-\sqrt{17}[/tex]What number can be divided into 9 equal groups without a remainder?
A. 256
B. 387
C. 424
D. 532
Answers
Answer:
B
Step-by-step explanation:
387/9 = 43
How many ways can you arrange 4 books on a shelf?
Answers
In order to find the number of ways, we must simply calculate:
4! = 4*3*2*1 = 24
24 possible ways.
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YOU WILL GET 100 POINTS IF YOU HELP! QUESTION DOWN BELOW!!!!!
THIS IS MY LAST QUESTION!!
Answers
Answer:
Step-by-step explanation:
statement:
1 = 2
reason:
since 1 and 4 are equal to each other and because lines AB and CD are parallel, any line crossing both lines will create the same angles in the same areas, thus connecting 4 and 2 together. And since 4 is equal to 1, it is also equal to 2.
I hope this helps!
Answer:
statement is 1=2
reason: since 1 and 4 are eqaul to eachothers and beacause lines AB CD are parelle, any line crossing both lines will create the same angels and same area
Gross Income 3 Ted gets paid a monthly salary of $5,000 and receives 6% commission on all sales over $8000. 1 point Which of the following is an equation that can be gross income? y = 5000+ 6(x - 8000) y = 5000+.06 (x - 8000) y = 8000 +.06 (x - 5000) O y = 5000+.06 (8000 - 2) Previous 3 4
Answers
Given that,
base salary = b = 5000$
Comission rate = 6% = 0.06
Let's say, the sales are = x
As given in the question, he receives 6% commission on all sales over $8000.
Hence, the commissionable amount is (x - 8000) '.' x - 8000 shows the amount greater than 8000, which receives a commission.
hence, gross income will be
base salary + commission * (commisonable amount)
=> 5000 + 0.06 * (x - 8000)
Speed is calculated by the equation S = d/t, where S = speed, d = distance, and t = time travelled. For what amount of time (in hours) did a car travel if its speed was 75 miles per hour and it travelled a distance of 187.5 miles?
Answers
We get from the question the following equation:
S = d/t
We have the following informations:
Speed(S) = 75 miles /h
Distance(d) = 187.5 miles
If you plug those informations into the formula, you'll get the following:
75 miles/h = 185.5 miles/ t
Now, you just have to solve for "t". If you invert the equation, you'll get(I'm going to omit the units, to make it clearer, but don't forget about them!)
1/75 = t / 185.5
If you multiply both sides by 185.5, you'll get
185.5/75 = t
Solving this calculation, we get the final solution!
t = 185.5/75 hours = 2.47 hours
A machine used to paint white lines on a road uses 250 litres of paint for
each 8km of road marked. Calculate:
a how many litres of paint would be needed for 200km of road
b what length of road could be marked with 4000 litres of paint.
Answers
a) Amount of paint needed for 200 km road = 6250 litres
b) Length of road that can be painted by using 4000 litres of paint = 128 km
Amount of paint used for painting white lines on road= 250 litres
Length which was painted = 8 km
By using unitary method;
Thus for 1 km amount of paint required = 250/8
= 31.25 litres
a) Amount of paint needed for 200 km road = 31.25 × 200
= 6250 litres.
therefore, Amount of paint needed for 200 km road = 6250 litres
b) Since for 1 km 31.25 liters paint is required this implies with 1 liter = 1/ 31.25 = 0.032 km can be covered.
Length of road that can be painted by using 4000 litres of paint = 4000× 0.032
= 128 km
Thus, Length of road that can be painted by using 4000 litres of paint = 128 km
What is unitary method?A single or unique unit is referred to as unitary. Determining values in relation to a single unit is the goal of this strategy. For instance, we can use the unitary technique to determine how many kilometers a car will go on one litre of gas if it travels 44 km on two litres of fuel.
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What is the surface area of the cube below?
A. 96 units²
B. 120 units²
C. 64 units²
D. 80 units²
Answers
Answer:
C. 64 units squared
Step-by-step explanation:
do 4•4•4 so 4 • 4 = 16 then 16 • 4 = 64 and since its surface area square it. so the answer would actually be 4096 units
Determine if the function below is continuous.A. not continuous, >2 holesOB. not continuous, 1 holeOC. not continuous, 2 holesOD. continuousReset Selection
Answers
Given:
A graph
To determine if the given function is continuous, we first note that the given function has gaps or holes. As we can see, the function has two holes.
We must also remember that a function that has any hole or break in its graph is known as a discontinuous function.
Therefore, the answer is:
[tex]C.\text{ not continuous, 2 holes}[/tex]
Given the right △△DEF, DE = 30, EF = 72 and DF = 78. Find the cos F=
Answers
see the figure below to better understand the problem
cos(F)=EF/DF --------> by CAH
substitute given values
cos(F)=72/78
simplify
cos(F)=12/13Option C"I just made a purchase of $130.00 but, once I got to my car and looked at the receipt, I realized that the salesperson who helped me did not apply the 15% discount."
Employee: "I sincerely apologize for our oversight. I will refund __________ back to your credit card."
Answers
Answer:
19.5
all you had to do was divide 15% with 130.00
What is the square root of 225As I am new to thisPlease answer step by step in the easiest form possible
Answers
Given:
[tex]225[/tex]To Determine: The square root of the given number
Solution
Step 1: Express 225 as the product pf its prime factors of 225
[tex]\begin{gathered} 225=3\times3\times5\times5 \\ 225=3^2\times5^2 \end{gathered}[/tex]Step 2: Separate the factors into their own square root
[tex]\begin{gathered} \sqrt{225}=\sqrt{3^2\times5^2} \\ \sqrt{225}=\sqrt{3^2}\times\sqrt{5^2} \end{gathered}[/tex]Step 3: Solve the individual's squares
[tex]\begin{gathered} \sqrt{225}=\sqrt{3^2}\times\sqrt{5^2} \\ \sqrt{225}=3\times5=15 \end{gathered}[/tex]Hence, the square root of 225 is 15