Given:
The function is
[tex]f(x)=x^3-7x^2+10x[/tex]
To find:
The end behavior of its graph.
Solution:
We have,
[tex]f(x)=x^3-7x^2+10x[/tex]
Here, leading coefficient is 1 which is positive and degree of function is 3 which is odd.
For odd degree and positive leading coefficient, the end behavior is
[tex]f(x)\to \infty\text{ as }x\to \infty[/tex]
[tex]f(x)\to -\infty\text{ as }x\to -\infty[/tex]
Using this, we get
[tex]\text{As }x\to \infty, y\to \infty[/tex]
[tex]\text{As }x\to -\infty, y\to -\infty[/tex]
Therefore, the correct statements are A and D.
We want to study the end behavior of the given polynomial.
The two correct statements are A and D.
As x → ∞, y → ∞As x → −∞, y → −∞The polynomial is:
f(x) = x^3 - 7*x^2 + 10*x.
We can see that the degree of this polynomial is odd, this means that the behavior on the negative side is opposite to the one in the positive side.
In this case, the leading coefficient is one, so it is positive. This will mean that, for large positive values of x, f(x) will be positive.
For large (in absolute value) negative values of x, f(x) will be negative.
Then the end behavior is given by:
As x → ∞, y → ∞As x → −∞, y → −∞So the two correct statements are A and D.
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Find the equation of the linear function. Represented by the table below and slope intercept form.
i need help.
Answer:
the slope-intercept is minus 4
Step-by-step explanation:
y = mx + b
y = -4x+ -5
im pretty sure this is right bc im in highschool rn and i just did this last year so if i forgot than -_-
can someone help me please?
Answer:
9,10
Step-by-step explanation:
86 square root is 9.2
9 is less than 9.2
10 is bigger than 9.2
A flying object is moving at 150 m/s. It makes a complete and final stop in 12 seconds. Calculate the object’s acceleration.
Answer:
-12.5 m/s²
Step-by-step explanation:
v (final velocity) = 0
u (intial velocity) = 150 m/s
t = 12s
a= v-u/t
a = 0 - 150 / 12
a = -12.5 m/s²
A container of rain water is evaporating 1.2 centimeters a week. After 8 weeks what will be the change in rain water levels
Answer:
8.667
Step-by-step explanation:
After 8 weeks, the change in rainwater levels will be 9.6 centimeters.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
A container of rainwater is evaporating 1.2 centimeters a week.
After 8 weeks, the change in rainwater levels will be given as,
⇒ 1.2 x 8
⇒ 9.6 centimeters
After 8 weeks, the change in rainwater levels will be 9.6 centimeters.
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plz help im really bad at math
Answer: it is b i looked back at my notes and did the math
Step-by-step explanation
Where does -1/5 go on the number line
Answer:
-0.2
Step-by-step explanation:
-1/5 = -0.2
Depending on your scale, it would go at -0.2
if x = 5 and y = 3, then xy - 2x =
Answer:
5
Step-by-step explanation:
First, we will need to replace the x and ys with the values.
So the equation will be this:
(5) x (3) - 2(5)
Now, following PEMDAS, we will do the M in PEMDAS (aka multiplication left to right)
Now our simplified expression is this:
15 - 10
Now, following PEMDAS, we will do the S in PEMDAS (aka subtraction left to right)
Therefore, the answer is: 5
perimeter of an triangle
Answer:
hypotenuse + adjacent + opposite
Step-by-step explanation:
The three names of the sides on a triangle
Is my answer correct or wrong?
Which of the following is a step in multiplying 3/4 by 3/5? 2 А Adding 3 and 3 B. Finding the lowest common denominator of 4 and 5 C Multiplying 3 and 3 D Multiplying 3 and 5
=================================================
Explanation:
When you multiply fractions, you multiply the numerators together. So in this case we multiply 3 and 3 getting 9 as the updated numerator.
We also multiply the denominators together. The updated denominator is 4*5 = 20.
Overall, (3/4)*(3/5) = (3*3)/(4*5) = 9/20
The fraction 9/20 cannot be reduced because 9 and 20 do not have any common factors other than 1.
We don't have to worry about getting the LCD (lowest common denominator) since that is only applicable for adding and subtracting fractions.
(1). -4 – x=3x +6
(2). X – 4= -3x + 12
(3). -12 + 3x = -x + 8
(4). 3x – 10= -2x + 20
(5). -4 – x = 10- 3x
Answer:
2 over 5
Step-by-step explanation:
1.-4-x=3x+6
6+4=3x+x
10=4x
Which number can divide 10 and 4 and that number is 2.
2 divided by 5.
A rectangular prism is 15 inches long, 8 inches wide, and 6 inches high. What is the volume of a pyramid that has the same height as the prism.
Answer:
[tex]240 in^3[/tex]
Step-by-step explanation:
I'm assuming the pyramid base has to fit the prism, else the answer would be "as big as you want.
Now if you compare the formulas for the volume of a pyramid and a prism, you notice that the only difference is a factor of 1/3 (it will take 3 pyramids to fill a prism).
Volume of the prism is the product of the sides, ie [tex]15\cdot8\cdot6 = 720 in^3[/tex]. Volume of the pyramid will be 1/3rd of that, or [tex]240 in^3[/tex]
Helppppp pleaseeeee
Answer:
3.75
Step-by-step explanation:
5 tables every 2 months,then 30 days (30 days in 1 month) / 8 ordes = 3.75
what are the coordinates of the image of point B after the triangle is rotated 270 On the Origin
Answer:
(4,2) hopefuly right hope that helps u out
Step-by-step explanation:
PLEASE HELP! I WILL MAKE YOU BRAINLIST
Answer:
A. y = 5x
Step-by-step explanation:
In order to find the answer, all you have to do is see the unit rate, which is the number of balls per minute, and if you look at the chart, it shows that for every 1 minute that passes, 5 balls are thrown, therefore, the answer would be:
y = 5x
Hope this helps :)
Answer:
y=5xStep-by-step explanation:
y=5x
if you put the graph as a table :
x y
1 5
2 10
3 15
4 20
constant is y/x=5/1=10/2=15/3=20/4=5
Find the perimeter of a rectangular block of land 3p metres long and 4Q metres wide
Answer:
86 is the correct answer
1. Approximate the value of
√
√
Answer:
[tex]\sqrt{3} =1.7\\\sqrt{3/48} =0.04\\\sqrt{48} =6.9\\\frac{\sqrt{3} }{\sqrt{48} } =0.25[/tex]
Step-by-step explanation:
I wasn't sure which one you were referring to
3 in.
Find the volume of the sphere. Round your answer to the nearest tenth. Use 3.14 for at.
The volume of the sphere is about
in?
Answer:
Step-by-step explanation:
Remark
That word about is a killer. It's a good thing they tell you they want the answer rounded to the nearest tenth, otherwise you'd be stuck.
Givens
pi = 3.14
r = 3
Formula
V = (4/3) pi r^3
V = (4/3) * 3.14 * 3^3
V = (4/3) * 3.14 * 27
V = (4/3) * 84.78
Answer: V = 113.0 in^3
Juan is walking a hill at 130 3/4 feet above sea level when he kicks a pebble. If the pebble falls to the base of the hill, which is 18.5 feet below sea level, what is the vertical distance that the pebble fell?
Choose the correct equation and answer to solve for x shown below
Answer:
it would be 3^2+4^2=x^2 and x=5
Step-by-step explanation:
3^2+4^2=c^2
9+16=c^2
25=c^2
c=5
A student’s work to simplify a radical is shown below. Select the statement which best applies to the sample mathematical work.
Answer:
the answer is B
Answer:
B
Step-by-step explanation:
[tex]\sqrt[4]{80} =\sqrt[4]{16 \cdot 5}[/tex]
[tex]\sqrt[4]{16 \cdot 5} =\sqrt[4]{16} \sqrt[4]{5} =2\sqrt[4]{5}[/tex]
The second line is incorrect as [tex]\sqrt[4]{16} =2[/tex]
Each person in a group of students was identified by year and asked when he or she preferred taking classes: in the morning, afternoon, or evening. The results are shown in the table. Find the probability that the student preferred morning classes given he or she is a freshman. Round your answer to the nearest thousandth.
Freshman Sophomore Junior Senior
Morning: 19 2 6 16
Afternoon: 17 3 13 15
Evening: 8 14 9 7
A. 0.105
B. 0.182
C. 0.386
D. 0.432
Answer: 0.432
Step-by-step explanation: I just took the test!
The probability that the student preferred morning classes given he or she is a freshman is 0.432. Option D. is the right choice.
What do we mean by the Probability of an event?The probability of an event is the fractional value showing how likely an event is to occur. It is determined by the formula,
The probability of an event
= number of outcomes favorable to the event/total number of outcomes
How do we solve the given question?We are asked about the probability that the student preferred morning classes given he or she is a freshman.
Total number of freshmen = 44 (in table)
Number of freshmen students who preferred morning classes = 19 (in table)
∴ The probability that the student preferred morning classes given he or she is a freshman = number of freshmen students who preferred morning classes/total number of freshmen = 19/44 ≈ 0.432
∴ The probability that the student preferred morning classes given he or she is a freshman is 0.432. Option D. is the right choice.
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4
Find the distance between A (3, 4) and B (15, 13).
Answer:
15
Step-by-step explanation:
use distance formula
HELP ME PLSS ASAP
2. (03.01 LC)
Given that g(x) = 4x + 6, find the value of x that makes g(x) = 14. (5 points)
-50
-5
2
8

Can someone help me on this question? I’ll give brainliest if you answer soon!!!
Answer:
1 number angle represent an angle vertical to <UXR
Jordan types at a constant rate of 40 words per minute. The number of words typed, y, is a function of the number of minutes spent typing, x
Part A
Which equation models this situation?
(PLEASE HELP!)
Answer: A
Step-by-step explanation:
[tex]\mathrm{In \ 1 \min}. $\rightarrow40$ words \\$\Rightarrow$ Let number of words typed $=y$\\\& number of time spent typing $=x$\\$\Rightarrow$ (A) $40 x=y$\\\\ \mbox{$\therefore y=40 x$}[/tex]
A tree in Austin's backyard is 5.22 meters tall. If the tree grows 0.6 meters each month, for how many months has the tree been growing?
Answer:
6.525 or 6.53
Step-by-step explanation:
Marta ha comprado 5 paquetes de 12 lápices cada uno y le han costado24 €. Cual es el precio de cada lapiz?
Respuesta:
5 paquetes x 12 lapices= 24€
60 lapices=24€
1 lapiz= 0.4€
¿Cuál es el precio de cada lápiz?
El precio de cada lápiz es 0.4€
Si quiere tener 100 lápices, ¿Cuánto le costará?
0.4 X 100=40€
Le costará 40€
How are mass and volume related on this graph?
As the mass decreases the volume increases
There is no relation
As the volume increases the mass decreases
As the mass increases, the volume also increases
The mass increases, the volume also increases.
What is proportionality?A graph is a line straight or curved that shows relation between two quantities out of which one varies as a result of change in other.
A graph is a line straight or curved that shows relation between two quantities out of which one varies as a result of change in other. To make it clear let us consider we have two variables x and y where, y=2x. The variable that is made to alter or change is called the independent variable.
As, from the graph we can see that the the volume represented by x axis and the mass represented by y axis show a direct relation.
As, the volume increases horizontally then the mass increases vertically.
let us take the coordinate (5, 25), (10, 50), (20, 100)
from the above coordinate we can see that the coordinate for both x and y axis increases.
Hence, mass increases, the volume also increases.
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Stephanie needs to buy birthday gifts for her family. She wants to stick to a budget of . $150.She buys a board game for her brother that costs,$49.50 a book for her sister that costs,$19.99 and a toy for her dog that costs.$15.00 She needs to buy a gift for her spouse, but she cannot decide between a watch that costs.$75.00 and a pair of shoes that costs. $59.99
Part A: How much has Stephanie spent on gifts so far?
Part B: How much does Stephanie have left to spend on gifts?
Part C: Which gift should Stephanie buy? Justify your answer.
Answer:
A. 84.50
B. She has 65.5$ left
C. Shoes
Step-by-step explanation:
A. If you add them it is 84.5
B. subtract 150 by 84.5 it is 65.5
C. Shoes because they are within the budget