The function f(x)=x^3+8x^2+x-42 has zeros located at -7, 2, -3. Verify the zeros of f(x) and explain how you verify them. Describe the behavior of the function
Answers
Step-by-step explanation
Given that the function:
\(f(x)=x^3+8x^2+x-42\)The function has zeros located at -7, 2, -3
First, let check f(2) = 0
\(\begin{gathered} 2^3+8(2)+2-42=0 \\ \\ 8+16+2-42=0 \\ \\ 42-42=0 \end{gathered}\)Therefore, f(2) has a zero, that is (x - 2) is a factor of the polynomial function..
So, divide the given function by (x-2) to get the quadratic function.
\(\frac{x^3+8x^2+x-42}{x-2}=x^2+10x+21\)Now, solve the quadratic function.
\(\begin{gathered} x^2+10x+21=0 \\ \\ x^2+7x+3x+21=0 \\ \\ x(x+7)+3(x+7)=0 \\ \\ x+7=0\text{ }and\text{ }x+3=0 \\ \\ x=-7\text{ }or-3 \end{gathered}\)From the explanation above, it shows that -7, 2, and -3 are the roots (zeros) of the given polynomial function.
Thus, the behavior of the function can be described by using the degree and the leading coefficient.
The leading degree is 3 and the leading coefficient is 1.
So since the leading degree is odd (3), the end of the function will point in the opposite direction.
And since the leading coefficient is positive (+1), the graph rises to the right.
Hence, the behavior of the function falls to the left and rises to the right.
Related Questions
Can someone help me with this pleasee
Answers
Answer:
its D
Step-by-step explanation:
good luck
Answer:
5155.07142857
Step-by-step explanation:
diameter/2 = radius
81/2 = radius
40.5 = radius
Area = π r^2
Area = 22/7 *40.5^2
Area = 5155.07142857
Use SSS, SAS, ASA, AAS, or Not Enough Information to identify the postulate or theorem that immediately confirms the congruence for each pair of triangles. Justify your answer.
Answers
Answer:
e) SAS
f) Not enough information
Step-by-step explanation:
e) Sas because there is an angle in between two sides and for that angle is opposite angles
f) Not enough information because SSA is not a theorem
I NEED HILP PLS HOW IS THIS THE ANSWER....
Answers
Answer:
The answer is correct, here's why:
Step-by-step explanation:
Dr. Silva's tank holds 15\(\frac{7}{8}\) gallons of gas.
She added 11.55 gallons to her tank to fill it up.
This means she must have had 5\(\frac{13}{40}\) gallons to start with because 5\(\frac{7}{8}\) - 11.55 = 5\(\frac{13}{40}\)
According to the journal Chemical Engineering, an important property of a fiber is its water absorbency. A random sample of 20 pieces of cotton fiber was taken and the absorbency on each piece was measured. The following are the absorbency values:
18.71, 21.41, 20.72, 21.81, 19.29, 22.43, 20.17,
23.71, 19.44, 20.50, 18.92, 20.33, 23.00, 22.85,
19.25, 21.77, 22.11, 19.77, 18.04, 21.12,
Required:
a. Calculate the sample mean and median for the above sample values.
b. Compute the 10% trimmed mean.
c. Do a dot plot of the absorbency data.
d. Using only the values of the mean, median, and trimmed mean, do you have evidence of outliers in the data?
Answers
Answer:
Step-by-step explanation:
a )
sample mean = sum total of given data / no of data
= 415.35 / 20 = 20.76
To calculate the median we arrange the data in ascending order and take the average of 10 th and 11 th term .
= 20.50 + 20.72 / 2
= 20.61
b ) To calculate the 10% trimmed mean , we neglect the largest 10% and smallest 10 % data and then calculate the mean . Here we neglect the first two smallest and last two greatest
(18.92 + 19.25 ..... + 22.43 + 22.85) / 16
= 20.74
c )
We can easily plot the data on number line from 17 to 24
d )
Maximum value of data set = 23.71 and minimum value is 18.04
mean is 20.76 , median is 20.61 and trimmed mean is 20.74
They are between maximum and minimum values of given data . Hence there is no outliers .
A wire is 71cm long . you wish to cut it into two pieces. One piece is bent into shape of triangle with legs of equal length .The piece is to be bent into shape of circle .
Answers
To solve this problem, we need to find the lengths of the two pieces when the wire is cut into two parts. Let's denote the length of each leg of the triangle as\(\(x\).\)
The perimeter of the triangle is the sum of the lengths of its three sides. Since the two legs are equal in length, the perimeter can be expressed as \(\(2x + x = 3x\).\)
The length of the wire is given as 71 cm, so we have the equation \(\(3x = 71\).\)
Solving for\(\(x\),\) we divide both sides of the equation by 3:
\(\(x = \frac{71}{3}\).\)
Now that we know the length of each leg of the triangle, we can proceed to the next part of the problem.
The circumference of a circle is given by the formula \(\(C = 2\pi r\)\), where\(\(C\)\)is the circumference and r is the radius. In this case, the wire of length xis bent into the shape of a circle, so we can set the circumference equal to x and solve for the radius r:
\(\(x = 2\pi r\).\)
Substituting the value of x we found earlier, we have:
\(\(\frac{71}{3} = 2\pi r\).\)
Solving for r, we divide both sides of the equation by \(\(2\pi\):\)
\(\(r = \frac{71}{6\pi}\).\)
Therefore, the two pieces of wire will have lengths\(\(\frac{71}{3}\)\)cm and the radius of the circle will be\(\(\frac{71}{6\pi}\)\) cm.
In summary, when the 71 cm wire is cut into two pieces, one piece will have a length o\(\(\frac{71}{3}\)\)cm, which can be bent into the shape of an equilateral triangle with legs of equal length, and the other piece can be bent into the shape of a circle with a radius of \(\(\frac{71}{6\pi}\)\) cm.
For more such questions on triangle.
https://brainly.com/question/17335144
#SPJ8
Plz guys help me to find the area of this rectangle.
Answers
Answer:
20pq unit²
Step-by-step explanation:
area= length×breadth
area= 4pq×5pq= 20pq unit ²
hope it helps!
Answer:
length*breadthe understand
simplify so that your answer contains only positive exponents
Answers
Answer:
Step-by-step explanation:
\(\frac{3x^4}{(\frac{1}{x^2})^2} \\= 3x^8\)
Answer:
\(3x^{8}\)
Step-by-step explanation:
\((x^{-2})^{2}\) is equal to \(x^{-4}\). Whenever an x has a negative exponent, it means that you can put it to the other side, whether it be from denominator to numerator or numerator to denominator. In this case, because it is in the bottom it goes from denominator to numerator. You will end up with something like \(3x^{4} x^{4}\) but you can add the X's and end up with the answer.
Suppose that sin(a) = 4/6 and cos(b) =1/5 define in the first quadrant, determine cos(a-b). (round to 4 decimal places)
Answers
The value of the cosine of the angle of (a - b) will be 0.80.
What is trigonometry?Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
It is a function that repeats itself in a particular time interval.
Suppose that sin(a) = 4/6 and cos(b) = 1/5.
Then the value of 'a' is given as,
sin(a) = 4/6
sin(a) = 2/3
a = 41.81°
Then the value of 'b' is given as,
cos(b) = 1/5
b = 78.46°
Then the value of the cosine of the angle of (a - b) will be given as,
⇒ cos(41.81° - 78.46°)
⇒ cos(-36.65°)
⇒ cos 36.65°
⇒ 0.80
The value of the cosine of the angle of (a - b) will be 0.80.
More about the trigonometry link is given below.
https://brainly.com/question/22698523
#SPJ1
Sera had the number 548.She adds one to the tens and two to the units. What number would Sera end up with??
Answers
The number she'd have is:
560Explanation:
First, let's see which number is in the tens place and which number is in the ones place (the units place).
In the number 548, the place value of 5 is hundreds, the place value of 4 is tens, and the place value of 8 is ones (or units).
So if Sera adds two to the units, she'll have 10. But, since we can't write the number as 5410 (that would be a totally different number), we just write 0 in the units place, and shift 1 to the tens place, which gives us :
550
That's not all, since we also add 1 to the tens:
560
Hence, Sera ends up with 560.Find the indicated area under the standard normal curve.
The total area to the left of z= - 1.18 and to the right of z= 1.18 under the standard normal curve is ___.
Answers
Answer:
0.1190
Step-by-step explanation:
If z = -1.18, the total area to the left under the standard normal curve is taken from the z-distribution table attached;
P(z < - 1.18) = 0.1190
Also, to the right of z = 1.18, we have;
P(z > 1.18) = 1 - P(z < 1.18)
From the second image attached from z-table, we have;
P(z > 1.18) = 1 - 0.8810
P(z > 1.18) = 0.1190
Thus, the total area to the left of z= - 1.18 and to the right of z= 1.18 under the standard normal curve is 0.1190
A wire costs $3 / meter. How much will 10 km of wire cost?
Answers
Answer:
\({\green{\boxed{\boxed{\red{300000}}}}}\)Step-by-step explanation:
10 Km = 10 × 1000 = 10000 m
3 × 10000 = $30000
Let's Learn#AyoBelajarIf two standard, six-sided die were rolled and the numbers that turned up on each were added together, which of the following would be the probability their sum would be equal to 4?
Answers
Answer:
3/36 or 8.333
Step-by-step explanation:
the way you get it is write all the possibilities and that how you get 3/36
Pls help i don’t know how to do this
Answers
Using the altitude or leg rule, we have:
x ≈ 42.7
y = 40
z ≈ 53.4
How to Apply the Altitude or Leg Rule?The leg rule is given as:
hypotenuse/leg = leg/part.
The altitude rule is:
left/altitude = altitude/right
To find the value of x, apply the altitude rule:
left = x
right = 24
altitude = 32
Substitute:
x/32 = 32/24
Cross multiply:
24x = 32²
24x = 1,024
x ≈ 42.7
To find y, apply the leg rule:
leg = y
part = 24
hypotenuse = x + 24 = 42.7 + 24 = 66.7
Substitute:
66.7/y = y/24
y² = 1,600.8
y = √1x00.8
y = 40
To find z, apply the leg rule:
leg = z
part = x = 42.7
Hypotenuse = 66.7
Substitute:
66.7/z = z/42.7
z² = 2,848.09
z = √2,848.09
z ≈ 53.4
Learn more about the leg or altitude rule on:
https://brainly.com/question/26257841
#SPJ1
x-intercept of 3 and y-intercept of 8
How do you write a lunar equation given this information and how do you write the equation in slope form
Answers
Answer:
y = -8/3x + 8
Step-by-step explanation:
Step 1: Identify which values we have and need to find in the slope-intercept form:
The general equation of the slope-intercept form of a line is given by:
y = mx + b, where
(x, y) is any point,m is the slope,and b is the y-intercept.Since we're told that the y-intercept is 8, this is our b value in the slope-intercept form.
Step 2: Find m, the slope of the line:
Since the x-intercept is 3, the entire coordinates of the x-intercept are (3, 0)Thus, we can find m, the slope of the line by plugging in (3, 0) for (x, y) and 8 for b:
0 = m(3) + 8
0 = 3m + 8
-8 = 3m
-8/3 = m
Thus, the slope is -8/3.
Therefore, the the equation of the line in slope-intercept form whose x-intercept is 3 and whose y-intercept is 8 is y = -8/3x + 8.
Optional Step 3: Check the validity of the answer:
We know that the entire coordinates of the x-intercept are (3, 0) and the entire coordinates of the y-intercept are (0, 8).Thus, we can check that we've found the correct equation in slope-intercept form by plugging in (3, 0) and (0, 8) for (x, y), -8/3 for m, and 8 for b and seeing if we get the same answer on both sides of the equation when simplifying:
Plugging in (3, 0) for (x, y) along with -8/3 for m and 8 for b:
0 = -8/3(3) + 8
0 = -24/3 + 8
0 = -8 = 8
0 = 0
Plugging in (0, 8) for (x, y) along with -8/3 for m and 8 for b;
8 = -8/3(0) + 8
8 = 0 + 8
8 = 8
Thus, the equation we've found is correct as it contains the points (3, 0) and (0, 8), which are the x and y intercepts.
write each info entire radical √48
Answers
The value of the radical √48 is 4√3.
Radical is a symbol (√) that denotes square roots and nth roots. The number inside the symbol is called Radicand and the expression containing the radical or a square root is called a Radical expression.
Here, we are given the radical √48
To find the value of the radical, we will factorize 48
i.e., 48 = 2×2×2×2×3
= 16×3
Now, the square root of 48, that is, √48
= \(\sqrt{16\cdot3}\) =\(\sqrt{16} \cdot \sqrt{3}\)
We know 16 is a perfect square of 4, that is, the square root of 16= 4
⇒√16=4
Using this, we have √48= 4√3
The correct answer is 4√3.
Learn more about radicals here:
https://brainly.com/question/12739054
#SPJ1
Player A led baseball league in runs battled in for the 2007 regular season. Player B, who came in second had 14 fewer runs batted in for the 2007 regular season. Together these two players brought home 236 runs during the 2007 regular season. How many runs batted in did player A and player B account for ?
Answers
Given:
Player B, who came in second had 14 fewer runs batted in for the 2007 regular season.
Together these two players brought home 236 runs during the 2007 regular season.
Let the player A and player B scored runs be x and y respectively.
x=y+14 ... (1)
x+y=236 .... (2)
Substitute equation (1) in (2)
\(y+14+y=236\)\(2y=222\)\(y=111\)\(x=111+14\)\(x=125\)Player A runs battled in for the 2007 regular season is 125.
Player B runs battled in for the 2007 regular season is 111.
Pilar and her sister Marisol live near the beach. Pilar has 80 seashells in her collection when Marisol started collecting seashells. Marisol started with zero seashells in her collection.
● Pilar adds 10 seashelles to her collection each week for x weeks.
● Marisol adds 20 seashells to her collection each week for x weeks. Please write and solve the equation that represents the situation when the number of seashells in Marisol's collection is the same as the number of seashells in Pilar's collection. Please make sure to show every step in solving this equation. THANK YOU FOR YOUR TIME.
Answers
Answer:
x=8
Step-by-step explanation:
80+10x=20x
-10x -10x
80=10x
80/10=x
8=x
Suppose there is a simple index of two stocks, stock A and stock B. Stock A opens on Monday with 5000 shares at $2.75 per share. Stock B opens on Monday with 3000 shares at $4.30 per share. Stock A opens on Tuesday at $3.10 per share, and stock B opens on Tuesday at $4.85 per share. Both stocks have the same number of shares that they opened with on Monday. What is the rate of change of this simple index over 1 day?
Answers
The rate of change of the simple index over one day is approximately 12.78%.
To calculate the rate of change of the simple index over one day, we need to determine the percent change in the total value of the index between Monday's opening and Tuesday's opening.
On Monday, Stock A has 5000 shares at $2.75 per share, so its total value is:
Total value of Stock A on Monday = 5000 * $2.75 = $13,750
Similarly, on Monday, Stock B has 3000 shares at $4.30 per share, so its total value is:
Total value of Stock B on Monday = 3000 * $4.30 = $12,900
The total value of the index on Monday is the sum of the values of Stock A and Stock B:
Total value of the index on Monday = $13,750 + $12,900 = $26,650
On Tuesday, Stock A opens at $3.10 per share, and Stock B opens at $4.85 per share. Both stocks still have the same number of shares as on Monday.
The total value of Stock A on Tuesday is:
Total value of Stock A on Tuesday = 5000 * $3.10 = $15,500
The total value of Stock B on Tuesday is:
Total value of Stock B on Tuesday = 3000 * $4.85 = $14,550
The total value of the index on Tuesday is the sum of the values of Stock A and Stock B:
Total value of the index on Tuesday = $15,500 + $14,550 = $30,050
To calculate the percent change in the index, we use the formula:
Percent Change = ((New Value - Old Value) / Old Value) * 100
Percent Change = (($30,050 - $26,650) / $26,650) * 100 ≈ 12.78%
For more such question on index. visit :
https://brainly.com/question/15361818
#SPJ8
Real Estate Agent:
A woman bought 4 lots for $48,000 each. She then subdivided
them into a total of 7 lots that sold for $33,000 each. What was
her percent of profit? I
Savings and Loan Counselor:
A customer wishes to borrow $30,000, make monthly payments
of interest only, and pay the full amount of the principal at the
end of the term. If the interest rate is 12% annually, what are the
monthly payments for a five-year term?
Answers
Step-by-step explanation:
A.
Cost of 4 lots for $48,000= 48000*4
=$192,000
Sales made from all 7 lots = 33000*7
= $213,000
Profit =213,000-192,000
Profit =$39,000
Percent profit =(39000/192000) *100
=0.20*100
=20%
B.
Total interest formula=
Principal Loan Amount x Interest Rate x Time
Interest =30000x0.12x5
Interest = $18,000
Monthly payments for 5 years
= 18000/12*5
=18000/60
=$300
Question Below.
Answers: 250|253|254|255|307|433|434|435|507|.
First to answer this question the quickest is rewarded branliest + 100 points
Answers
Answer:
Minimum--> 250
Q1--> 255
Q2--> (Median): 307
Q3--> 433
Maximum-->507
Step-by-step explanation:
To find the five-number summary of this data set, we need to determine the minimum value, maximum value, and three quartiles (Q1, Q2, Q3) which divide the data into four equal parts.
First, we need to sort the data set in ascending order:
{ 250, 253, 255, 267, 307, 425, 433, 435, 507 }
Minimum: 250
Maximum: 507
To find the quartiles, we need to find the median of the entire data set (Q2) and then the medians of the two halves of the data set, which will give us Q1 and Q3.
Q2 (Median): The median of the entire data set can be found by averaging the two middle numbers.
Q1: The median of the lower half of the data set is 255, which is the middle value of { 250, 253, 255, 267, 307 }. Therefore, Q1 = 255.
Q3: The median of the upper half of the data set is 433, which is the middle value of { 425, 433, 435, 507 }. Therefore, Q3 = 433.
Can someone help me with this, please?
Answers
π√π÷√π is an irrational number. So option (a) is required answer.
What is irrational number?A real number that cannot be stated as a ratio of integers is said to be irrational; an example of this is the number 2. Any irrational number, such as p/q, where p and q are integers, q, cannot be expressed as a ratio. Once more, an irrational number's decimal expansion is neither ending nor recurrent.
Examples of irrational number: √3, ∛2, π
π is an irrational because it is neither ending nor recurrent.
Solving each part of options, we get
π√π÷√π = π
√25 = 5
√π÷π = 1
2√2 ÷ √2 = 2
As most of the option give rational number only one option gives irrational number which is π
We get π from option (a)
So, option (a) is correct option.
Learn more about irrational number here:
https://brainly.com/question/43641
#SPJ1
Please help I have no clue on what to do I will give you guys multiple points if you are able to help.
Answers
Based on the information, we can infer that the graph would be a curve like the one shown in the attached image.
How to graph this information?First of all, to graph the information about the body temperature of children, we must consult on the internet or other sources what is the body temperature of children. Below is the information:
The average body temperature is 98.6 F (37 C). But normal body temperature can range between 97 F (36.1 C) and 99 F (37.2 C) or more.According to the above, the graph should present a higher frequency at a temperature of 98.6, so the highest point on the graph would be at that temperature. On the other hand, the other temperatures would decrease because they are less frequent among children.
Learn more about body temperature in: https://brainly.com/question/18883752
#SPJ1
If the function y=sin(x) is transformed to y = sin(2x), how does the graph change?
It is stretched vertically.
It is compressed vertically.
It is stretched horizontally.
It is compressed horizontally..
Answers
Step-by-step explanation:
The transformation y = sin(2x) affects the graph of y = sin(x) by compressing it horizontally.
The function y = sin(2x) has a coefficient of 2 in front of the x variable. This means that for every x value in the original function, the transformed function will have half the x value.
To see the effect of this transformation, let's compare the graphs of y = sin(x) and y = sin(2x) by plotting some points:
For y = sin(x):
x = 0, y = 0
x = π/2, y = 1
x = π, y = 0
x = 3π/2, y = -1
x = 2π, y = 0
For y = sin(2x):
x = 0, y = 0
x = π/2, y = 0
x = π, y = 0
x = 3π/2, y = 0
x = 2π, y = 0
As you can see, the y-values of the transformed function remain the same as the original function at every x-value, while the x-values of the transformed function are compressed by a factor of 2. This means that the graph of y = sin(2x) appears narrower or more "squeezed" horizontally compared to y = sin(x).
Therefore, the correct statement is: It is compressed horizontally.
Selling Price = $ 504 and Gain % = 12%
Answers
Answer:
Step-by-step explanation:
sp = 504
gain = 12%
in this case
sp =100%+12%=504
112%=504
1%=504/112 =4.5
100%=450
so cost =$450
Hope im correct, if i am im glad to be of service.
Can someone help me with my math homework?
Please and I will mark brainliest
College for Readiness and High School students
Answers
Answer:
Sure, I can try to help.
Step-by-step explanation:
Answer:
The discrimination is positive
Step-by-step explanation:
The graph shows the parabola with branches go up in positive y-direction. This gives you that a>0.
Since parabola has two x-intercepts, then the equation has two different solutions and the discriminant is greater than 0.
The overhead reach distances of adult females are normally distributed with a mean of 202.5 cm and a standard deviation of 8.6 cm.
a. Find the probability that an individual distance is greater than 211.80 cm.
b. Find the probability that the mean for 20 randomly selected distances is greater than 200.30 cm.
c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?
a. The probability is
(Round to four decimal places as needed.)
Answers
Answer: I am not sure if you're accustomed to using a z-score and table of probabilities or technology, so I will answer using both!
a) Since you're choosing one person from the population, you will use the mean and standard deviation from the population. z= (210.9-197.5)/8.6 = 1.56 Using a table of normal probabilities,
P(x>210.9)= 1-P(z<1.56)= 1- 0.9406=0.0594
Using technology: normalcdf(210.9, 1E99, 197.5, 8.6)=0.0596
b) Since you're calculating the population for a sample to occur, you need to get a mean of the sampling distribution and standard deviation of the sampling distribution.
Meanpop=Meansampling dist.=197.5
St. Devsampling dist.= Stdpopulation/√n = 8.6/√15 = 2.22
Using technology, P(X>196.20)= normalcdf( 196.20, 1E99, 197.5, 2.22) = 0.7209
c) You only have to worry about the sample size in a sampling distribution if you either do not know the shape of the distribution of the population or if the distribution of the population is not normally distributed. Since this population is normally distributed (as stated in the given information), then your sample size does not have to be greater than 30.
Hope this helps! I can solve part b using a z-score if you need me to.
Step-by-step explanation:
Question 15
1 pts
Liam buys a computer for $1800. He takes out a simple interest loan at 8% for this computer for 3
years. He puts no money down. What will be his monthly payments if he plans on paying it off in 3
years? Round to the nearest cent.
Answers
Answer:
$62
Step-by-step explanation:
To start off, we will calculate the end amount he will pay:
A = P(1 + rt)
= 1800(1+3(0.08)
= 1800(1+0.24)
= 1800(1.24)
= 2232
He will have to pay 2232 dollars in 3 years
Since he plans to pay it off with monthly payments throughout the 3 years, we will have that loan divided by the amount of times he will make those monthly payments
3 years = 3 ( 12 months )
= 36 months
He will make 36 monthly payments
2232 / 36 = 62
So, in each monthly payment, he will pay $62.
Feel free to ask me any questions you may have about this problem!
Please help out!! Math question about angles/triangle
Answers
Answer:
Because one pair are vertical angles
Because one pair are each supplementary to equal angles
Step-by-step explanation:
LKO is congurent to LMO
Step-by-step explanation:
angle k =angle m
lk=LM
lo=Lo (common)
mark me brainlist
Simplify the following expression.
Be sure to follow the correct oder of operations.
23.3 + 5.4 x 15.75
Answers
Answer:
108.35
Step-by-step explanation:
Order of Operations: PEMDAS
PEMDAS =
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction.
First, multiply 5.4 with 15.75:
5.4 x 15.75 = 85.05
Next, add:
85.05 + 23.3 = 108.35
108.35 is your answer.
~
Answer:
108.35Step-by-step explanation:
\(23.3+5.4\cdot \:15.75\\\\\mathrm{Multiply\:the\:numbers:}\:5.4\cdot \:15.75=85.05\\=23.3+85.05\\\\\mathrm{Add\:the\:numbers:}\\:23.3+85.05=108.35\)
what is the equivalent fraction of 13%