x³ + 2x² - 9x - 18 is the polynomial function of least degree with integral coefficients that had the zeros -3 , 3 , -2.
Given, the zeros of a polynomial be,
-3 , 3 and -2
As, the polynomial has 3 zeros then the degree of the polynomial is also be , 3.
Let the polynomial be,
p(x) = (x - (-3))(x - 3)(x - (-2))
p(x) = (x + 3)(x - 3)(x + 2)
On multiplying the factors, we get
p(x) = (x² - 3²)(x + 2)
p(x) = (x² - 9)(x + 2)
p(x) = (x³ - 9x + 2x² - 18)
p(x) = x³ + 2x² - 9x - 18
So, x³ + 2x² - 9x - 18 is the polynomial function of least degree with integral coefficients that had the zeros -3 , 3 , -2.
Hence, x³ + 2x² - 9x - 18 is the polynomial function of least degree with integral coefficients that had the zeros -3 , 3 , -2.
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In a mid-size company, the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell-shaped and has a mean of 44 and a standard deviation of 4. Using the empirical rule, what is the approximate percentage of daily phone calls numbering between 36 and 52?
The empirical rule is an approximation that can be used sometimes if we have data in a normal distribution. If we know the mean and standard deviation, we can use the rule to approximate the percentage of the data that is 1, 2, and 3 standard deviations from the mean. The rules is:
In this case, the mean is 44. The receptionist who answered less than 44 phone calls are to the left of the mean, and to the right are the ones who answered more. Since we want to know the percentage of phone calls numbering between 36 and 52, we know that:
[tex]\begin{gathered} 44+4=48 \\ . \\ 48+4=52 \end{gathered}[/tex][tex]\begin{gathered} 44-4=40 \\ . \\ 40-4=36 \end{gathered}[/tex]Thus, the lower bound is two standard deviations from the mean, and the upper bond is also 2 standard deviations from the mean.
Using the chart above, we can see that this corresponds to approximately 95% of the data.
The answer is approximately 95% of the data is numbering between 36 and 52
During a snowstorm, Grayson tracked the amount of snow on the ground. When the storm began, there were 4 inches of snow on the ground. For the first 3 hours of the storm, snow fell at a constant rate of 1 inch per hour. The storm then stopped for 5 hours and then started again at a constant rate of 3 inches per hour for the next 2 hours. As soon as the storm stopped again, the sun came out and melted the snow for the next 2 hours at a constant rate of 4 inches per hour. Make a graph showing the inches of snow on the ground over time using the data that Grayson collected.
We can plot all that happened in the next graph:
This is the graph showing the inches of the snow on the ground over time using the data that Grayson collected.
Given:• AJKL is an equilateral triangle.• N is the midpoint of JK.• JL 24.What is the length of NL?L24JKNO 12O 8V3O 12V2O 1213
Answer:
12√3
Explanation:
First, we know that JL = 24.
Then, the triangle JKL is equilateral. It means that all the sides are equal, so JK is also equal to 24.
Finally, N is the midpoint of segment JK, so it divides the segment JK into two equal parts. Therefore, JN = 12.
Now, we have a right triangle JLN, where JL = 24 and JN = 12.
Then, we can use the Pythagorean theorem to find the third side of the triangle, so NL is equal to:
[tex]\begin{gathered} NL=\sqrt[]{(JL)^2-(JN)^2} \\ NL=\sqrt[]{24^2-12^2} \end{gathered}[/tex]Because JL is the hypotenuse of the triangle and JN and NL are the legs.
So, solving for NL, we get:
[tex]\begin{gathered} NL=\sqrt[]{576-144} \\ NL=\sqrt[]{432} \\ NL=\sqrt[]{144(3)} \\ NL=\sqrt[]{144}\cdot\sqrt[]{3} \\ NL=12\sqrt[]{3} \end{gathered}[/tex]Therefore, the length of NL is 12√3
Find the missing factor. 8x2 - X - 9 = (x + 1)(
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
8x² - x - 9 = (x + 1) ( ? )
Step 02:
We must find the missing root to solve the exercise.
x1 = - 1
x2 :
a = 8
b = -1
c = -9
[tex]x\text{ = }\frac{-(-1)\pm\sqrt[]{(-1)^2-4\cdot8\cdot(-9)}_{}}{2\cdot8}[/tex][tex]x\text{ = }\frac{1\pm17}{16}[/tex][tex]x\text{ = }\frac{1+17}{16}=\frac{18}{16}=\frac{9}{8}[/tex]x2 = 9 / 8
The answer is:
( x - 9/8)
8x² - x - 9 = (x + 1) ( x - 9/8 )
Given y=0.5x^2, describe the transformation (x,y) --> (x,4y) and sketch the graph of this image
We are given the equation y = 0.5x^2. To describe its transformation from (x, y) to (x, 4y), we can start by first graphing the given equation.
To graph, let's use sample points (x- and y-values):
x y
-2 2
-1 0.5
0 0
1 0.5
2 2
So we have the points (-2, 2), (-1, 0.5), (0, 0), (1, 0.5), and (2, 2) to help us graph the equation.
A transformation of (x, y) --> (x, ay) where a > 1 means a vertical stretch equal to |a|. In this case, because (x, y) is transformed to (x, 4y), the graph stretches vertically by a factor of 4.
To graph, let's use sample points (x- and y-values):
x y
-2 4(2) = 8
-1 4(0.5) = 2
0 4(0) = 0
1 4(0.5) = 2
2 4(2) = 8
The new graph would now look like this:
The area of a triangle is 2312 . Two of the side lengths are 93 and 96 and the included angle is obtuse. Find the measure of the included angle, to the nearest tenth of a degree.
to facilitate the exercise we will draw the triangle
We start using the area
[tex]A=\frac{b\times h}{2}[/tex]where A is the area, b the base and h the height
if we replace A=2312 and b=96 we can calculate the height(h)
[tex]\begin{gathered} 2312=\frac{96\times h}{2} \\ \\ h=\frac{2312\times2}{96} \\ \\ h=\frac{289}{6} \end{gathered}[/tex]now to calculate the measure of the angles we can solve the red triangle
first we find Y using trigonometric ratio of the sine
[tex]\sin (\alpha)=\frac{O}{H}[/tex]where alpha is the reference angle, O the opposite side from the angle and H the hypotenuse of the triangle
using Y like reference angle and replacing
[tex]\sin (y)=\frac{\frac{289}{6}}{93}[/tex]simplify
[tex]\sin (y)=\frac{289}{558}[/tex]and solve for y
[tex]\begin{gathered} y=\sin ^{-1}(\frac{289}{558}) \\ \\ y=31.2 \end{gathered}[/tex]value of angle y is 31.2°
Y and X are complementary because make a right line then if we add both numbers the solution is 180°
[tex]\begin{gathered} y+x=180 \\ 31.2+x=180 \end{gathered}[/tex]and solve for x
[tex]\begin{gathered} x=180-31.2 \\ x=148.8 \end{gathered}[/tex]measure of the included angle is 148.8°
what is the y- intercept in the following equationy=-4x-5
how do you solve for x in the following problem... 4 (x + 3) -2x + 8 = 28
Given the expression
[tex]4(x+3)-2x+8=28[/tex]To solve it for x, the first step is to calculate the term in parentheses, for this you have to apply the distributive property of multiplication.
[tex]\begin{gathered} (4\cdot x)+(4\cdot3)-2x+8=28 \\ 4x+12-2x+8=28 \end{gathered}[/tex]Next order the alike terms toghether and calculate:
[tex]\begin{gathered} 4x-2x+12+8=28 \\ 2x+20=28 \end{gathered}[/tex]Subtract 20 to both sides of the equation:
[tex]\begin{gathered} 2x+20-20=28-20 \\ 2x=8 \end{gathered}[/tex]And finally divide by 2 to reach the value of x:
[tex]\begin{gathered} \frac{2x}{2}=\frac{8}{2} \\ x=4 \end{gathered}[/tex]For this equation x=4
If the figure below were reflected across the waxis, what would be the new coordinates of point A
The coordinates of point A are (-2,3). A reflection across the y-axis is given by:
[tex](x,y)\rightarrow(-x,y)[/tex]Applying this rule to point A we have:
[tex](-2,3)\rightarrow(2,3)[/tex]Therefore, the image of point A is (2,3) and the correct option is B.
11) -3(1 + 6r) = 14 - r
Distributing over parentheses,
[tex]\begin{gathered} -3\cdot1+(-3)\cdot6r=14-r \\ -3-18r=14-r \end{gathered}[/tex]Adding r at both sides,
[tex]\begin{gathered} -3-18r+r=14-r+r \\ -3-17r=14 \end{gathered}[/tex]Adding 3 at both sides,
[tex]\begin{gathered} -3-17r+3=14+3 \\ -17r=17 \end{gathered}[/tex]Dividing by -17 at both sides,
[tex]\begin{gathered} \frac{-17r}{-17}=\frac{17}{-17} \\ r=-1 \end{gathered}[/tex]I need help quick with a math question !
Step-by-step explanation:
A paper is sold for Php60.00, which is 150% of the cost. How much is the store's cost?
The store's cost is php40
Let's call the store Cost = C
This means that this cost is elevated a 150% in order to get the price of php60
In an mathematical expression, this is:
C · 150% = php60
Then, let's convert the percentage to decimal. To do this, we just divide the percentage by 100:
150% ÷ 100 = 1.5
Now we can solve:
[tex]\begin{gathered} C\cdot1.5=60 \\ C=\frac{60}{1.5}=40 \end{gathered}[/tex]Then the store cost is C = php40
Match each solid cone to it’s surface area. Answers are rounded to the nearest square unit
The surface area of a cone is given by the formula below:
[tex]S=\pi r^2+\pi rs[/tex]Where r is the base radius and s is the slant height.
So, calculating the surface area of first cone, we have:
[tex]\begin{gathered} s^2=21^2+6^2\\ \\ s^2=441+36\\ \\ s^2=477\\ \\ s=21.84\\ \\ S=\pi\cdot6^2+\pi\cdot6\cdot21.84\\ \\ S=525 \end{gathered}[/tex]The surface area of the second cone is:
[tex]\begin{gathered} s^2=8^2+12^2\\ \\ s^2=64+144\\ \\ s^2=208\\ \\ s=14.42\\ \\ S=\pi\cdot12^2+\pi\cdot12\cdot14.42\\ \\ S=996 \end{gathered}[/tex]The surface area of the third cone is:
[tex]\begin{gathered} s^2=15^2+8^2\\ \\ s^2=225+64\\ \\ s^2=289\\ \\ s=17\\ \\ S=\pi\cdot8^2+\pi\cdot8\cdot17\\ \\ S=628 \end{gathered}[/tex]And the surface area of the fourth cone is:
[tex]\begin{gathered} s^2=10^2+10^2\\ \\ s^2=100+100\\ \\ s^2=200\\ \\ s=14.14\\ \\ S=\pi\cdot10^2+\pi\cdot10\cdot14.14\\ \\ S=758 \end{gathered}[/tex]3. A coin is tossed 140 times. The probability of getting tails is p = 0.500. Would a result of 55heads out of the 140 trials be considered usual or unusual? Why?Unusual, because the result is less than the maximum usual value.O Usual, because the result is between the minimum and maximum usual values.Unusual, because the result is less than the minimum usual value.Unusual, because the result is more than the maximum usual value
In order to calculate the minimum and maximum usual values, first let's calculate the mean and standard deviation of this distribution:
[tex]\begin{gathered} \mu=n\cdot p=140\cdot0.5=70\\ \\ \sigma=\sqrt{np(1-p)}=\sqrt{140\cdot0.5\cdot0.5}=5.92 \end{gathered}[/tex]Now, calculating the minimum and maximum usual values, we have:
[tex]\begin{gathered} minimum=\mu-2\sigma=70-11.84=58.16\\ \\ maximum=\mu+2\sigma=70+11.84=81.84 \end{gathered}[/tex]Since the given result is 55, it is an unusual reslt, because it is less tahan the minimum usual value.
Correct option: third one.
In the diagram below the larger angle is four times bigger than the smaller angle find the larger angle
Answer:
Given that,
In the diagram below the larger angle is four times bigger than the smaller angle
To find the larger angle.
Let x be smaller angle.
Then we get,
Larger angle is,
[tex]4x[/tex]Larger angle and smaller angle are a linear pair.
Therefore we get,
[tex]x+4x=180[/tex][tex]5x=180[/tex][tex]x=36\degree[/tex]Larger angle is,
[tex]4x=4\times36=144[/tex]The larger angle is 144 degrees.
Cris pays a total of $11 for every 6 Gatoraid bottles. Circle the graph models a relationship with the same unit rate?
The line that describes this relationship goes from (0,0) to the point (6,11),we can draw it like this:
On a map, the scale shown is1 inch : 5 miles. If a park is75 square miles, what is thearea of the park on the map?The park's area issquarelinches on the map.
We have the relationship between inches and miles is:
1 inch to 5 miles.
The park has an actual area of:
[tex]75mi^2[/tex]Now, to make the conversion to inches, we need to consider that 1 inch represent 5 miles. Thus:
[tex]\begin{gathered} 1in=5mi \\ 1in^2=25mi^2 \end{gathered}[/tex]We squared this amounts, if 1 inch is 5 miles, 1 inch squared will be equal to 5 squared which is 25.
Now we divide 75 miles squared by 25, to know how many inches squared will the park represent on the map:
[tex]\frac{75}{25}=3in^2[/tex]Answer: the area of the park on the map will be 3 inches squared.
If the number 659, 983 is rounded to the nearest hundred, how many zeros does the rounded number have?The solution is
We will have the following:
*For 569:
For this number we would round to 600, thus the number of zeros the rounded number would be 2.
*For 983:
For this number, we would round to 1000, thus the number of zeros the rounded number would be 3.
If ABCD is dilated by a factor of 1/2coordinate of d' would be
Suzie has cards in numbers 9-21 in a bag. What is the probability she will pull a card lower than 17?
She has cards that go from 9 to 21.
We assume she has one card with each number that goes from 9 to 21:
9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21.
If we want to calculate the probability she pulls a card lower than 17, we have to count how many cards are lower than 17 and then divide this number by the total amount of cards.
NOTE: each card is a possible event. We will calculate the probability as the quotient between the number of successful events (cards lower than 17) and the total possible events (number of cards available).
We have 17-9 = 8 cards that are lower than 17.
The total number is 22-9 = 13 cards (all the cards lower than 22).
Then, we can calculate the probability as:
[tex]P(C<17)=\frac{8}{13}[/tex]Answer: The probabilty she pull a card lower than 17 is P=8/13
Given ABC shown below. Map ABC using the transformations given below. In each case, start with ABC , graph the image and state the Coodinates of the image's vertices.a) a reflection in the line x = 2 to produce A' B' C'b) a reflection in the line y= 1 to produce A" B"C"
a) A'(8,7), B' (10, -6) and C' (2,-3)
b) A" (-4,-5) B" (-6,8) C" (2,5)
1) Examining the graph, we can locate the following points of ABC
To reflect across line x=2 let's count to the left the same distance from x=2
Pre-image Reflection in the line x=2
A (-4, 7) (x+8, y) A'(8,7)
B (-6,-6) (x+16, y) B' (10, -6)
C (2,-3) (x,y) C' (2,-3) Remains the same since C is on x=2
b) A reflection about the line y=1 similarly we'll count the distances and then write new points over the line y=1.
So the Image of this is going to be
Pre-image Reflection in the line x=2
A (-4, 7) (x, y-12) A" (-4,-5)
B (-6,-6) (x, y) B" (-6, 8)
C (2,-3) (x,y) C' (2,5)
A" (-4,-5)
B" (-6,8)
C" (2,5)
a new car is purchased for 24800. the value of the car depreciates at 12% per year what is the Y intercept of starting value
EXPLANATION
Let's see the facts:
Purchase Price = $24,800
Depretiation = 12%/year
We should apply the formula for exponential decay wich is expressed as:
A = P(1-r)^t
A= value of the car after t years
t= number of years
P = Initial Value
r= rate of decay in decimal form
We have that A=unknown t=? P=24,800 r=0.12
Replacing terms:
A=24,800(1-0.12)^t
Now, the y-intercept is the value obtained when t=0, so substituting this on the equation give us the following result:
A=24,800(1-0.12)^0 = 24,800(0.88)^0= 24,800*1=24,800
The starting value is $24,800
..Sam works 40 hours in one week and is paid $610. How much does Samearn per hour?
Answer:
Sam earns $15.25 per hour.
Explanation:
Sam works 40 hours in one week, and is paid $610
To know how much Sam earns per hour, we divide the amount earned by the number of hours worked.
This is:
[tex]\frac{610}{40}=15.25[/tex]Therefore, Sam earns $15.25 per hour.
For the following line, name the slope and y-intercept. Then write the equation of the line in slope-interceptform.Slope= y - intercept = (0,_ ) Equation: y =
Given:
A line that passes the through the points (4, 0) and (0,-3).
Required:
Slope, y-intercept, and the equation of the given line.
Explanation:
As the line passes through the points (4, 0) and (0,-3), the slope is calculated as,
[tex]\begin{gathered} Slope\text{ = }\frac{y_2-y_1}{x_2-\text{ x}_1} \\ Slope\text{ = }\frac{-3\text{ - 0}}{0\text{ - 4}} \\ Slope\text{ = }\frac{-3\text{ }}{-4} \\ Slope\text{ = }\frac{3}{4} \end{gathered}[/tex]The y-intercept of the given line is the point through which the given line passes on the y-axis which is -3. Therefore the intercept of the given line is -3.
The equation of line in slope point form is given as,
[tex]y\text{ = mx + c}[/tex]Where m is the slope and c is the y-intercept. Therefore the equation of the line is given as,
[tex]y\text{ = }\frac{3}{4}x\text{ - 3}[/tex]Answer:
Thus the required equation of line is
[tex]y\text{ }=\text{ }\frac{3}{4}\text{x{\text{ - 3}}}[/tex]Consider the following measures shown in the diagram with the circle centered at point A. Determine the arc length of CB.
Answer:
[tex]\frac{4}{3}\pi\; cm[/tex]Explanation:
If an arc of a circle radius, r is subtended by a central angle, θ, then:
[tex]\text{Arc Length}=\frac{\theta}{360\degree}\times2\pi r[/tex]In Circle A:
• The central angle, θ = 40 degrees
,• Radius = 6cm
Therefore, the length of arc CB:
[tex]\begin{gathered} =\frac{40}{360}\times2\times6\times\pi \\ =\frac{4}{3}\pi\; cm \end{gathered}[/tex]The correct choice is C.
What is 6 hundred thousand in hundreds
600,000 (Six hundred thousand)
1) If we divide 600,000 by 100 we'll have 6000
So 600,000 is equal to 6000 hundreds.
Yolanda has a rectangular poster that is 16 cm long and 10 cm wide what is the area of the poster in square meters do not round your answer is sure to include the correct unit in your answer
The area of a rectangle can be calculated as the height times the wide.
But be careful, the problem asks it in square meters! So let's use meters instead of centimeters.
Remember that : 1 m = 100 cm ----> 1 cm = 0.01 m
[tex]\begin{gathered} A=b\cdot h \\ \\ A=0.16\cdot0.10 \end{gathered}[/tex]Doing the multiplication
[tex]A=0.016\text{ m}^2[/tex]Therefore the area of the poster is 0.016 square meters
Which expression is equivalent to sin(71(1) cos (72) - cos () sin (77.)?1?O cos (5)O sin (5)COS2012sin
Let:
[tex]\begin{gathered} A=\frac{\pi}{12} \\ B=\frac{7\pi}{12} \end{gathered}[/tex]Using the sine difference identity:
[tex]\begin{gathered} \sin (A)\cos (B)-\cos (A)\sin (B)=\sin (A-B) \\ so\colon \\ \sin (\frac{\pi}{12})\cos (\frac{7\pi}{12})-\cos (\frac{\pi}{12})\sin (\frac{7\pi}{12})=\sin (\frac{\pi}{12}-\frac{7\pi}{12}) \\ \sin (\frac{\pi}{12}-\frac{7\pi}{12})=\sin (-\frac{6\pi}{12}) \\ \sin (-\frac{\pi}{2}) \end{gathered}[/tex]Answer:
[tex]\sin (-\frac{\pi}{2})[/tex]During a coffee house's grand opening.350 out of the first 500 customers who visited ordered only one single item while the rest ordered multiple items. Among the 150 customs who left a tip 60 of them ordered multiple items?
We are given a two-way frequency table with some missing joint frequencies.
The frequencies in the total row and column are called "marginal frequencies"
The frequencies in the other rows and columns are called "joint frequencies"
Let us first find the joint frequency "Single Item and Tip"
[tex]\begin{gathered} x+60=150 \\ x=150-60 \\ x=90 \end{gathered}[/tex]So, the joint frequency "Single Item and Tip" is 90 (option B)
Now, let us find the joint frequency "Single Item and No Tip"
[tex]\begin{gathered} 90+x=360 \\ x=360-90 \\ x=270 \end{gathered}[/tex]So, the joint frequency "Single Item and No Tip" is 270 (option D)
Now first we need to find the marginal frequency as below
[tex]\begin{gathered} 360+x=500 \\ x=500-360 \\ x=140 \end{gathered}[/tex]Finally, now we can find the joint frequency "Multiple Items and No Tip"
[tex]\begin{gathered} 60+x=140 \\ x=140-60 \\ x=80 \end{gathered}[/tex]So, the joint frequency "Multiple Items and No Tip" is 80 (option A)
Therefore, the missing joint frequencies are
Option A
Option B
Option D
Use the graphing tool to determine the true statementsregarding the represented function. Check all that apply.f(x) > 0 over the interval (1,).Of(x) < 0 over the interval [1,0).Of(x) 0 over the interval (-∞, 1].Of(x) > 0 over the interval (-∞, 1).Of(x) > 0 over the interval (-∞o).Intro2010-202
The true statements are,
f(x) > 0 over the interval (1, ∞)
f(x) ≤ 0 over the interval (-∞, 1]
Interval of a function:
If the value of the function f (x) rises as the value of x rises, the function interval is said to be positive. Instead, if the value of the function f (x) drops as the value of x increases, the function interval is said to be negative.
If the endpoints are absent from an interval, it is referred to as being open. It's indicated by ( ). Examples are (1, 2), which denotes larger than 1 and less than 2. Any interval that contains all the limit points is said to be closed. The symbol for it is []. For instance, [2, 5] denotes a value greater or equal to 2 and lower or equal to 5. If one of an open interval's endpoints is present, it is referred to as a half-open interval.
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