We want to find out if (x+6) is a factor of the polynomial
[tex]9x^3+57x^2+21x+24[/tex]In order to find this, we can use the factor theorem.
If we have a polynomial f(x) and want to find if (x-a) is a factor of this polynomial, we plug in x = a into the function and if we get 0, (x-a) is a factor(!)
Now, let's plug in:
x = -6 into the polynomial and see if we get a 0 or not.
Steps shown below:
[tex]\begin{gathered} 9x^3+57x^2+21x+24 \\ 9(-6)^3+57(-6)^2+21(-6)+24 \\ =-1944+2052-126+24 \\ =6 \end{gathered}[/tex]AnswerSince it doesn't produce a 0, (x + 6 ) is not a factor of the polynomial given.
see image for question
The angle of rotation = 19.35°
Explanations:The diameter of the ferris wheel = 225 feet
Radius, r = diameter/2
r = 225/2
r = 112.5 feet
The passenger travels 38 feet when the wheel stops
This is the arc length
Arc length = 38 feet
Using the formula for the length of an arc
[tex]\text{Arc length = }\frac{\theta}{360}\times2\text{ }\pi\text{ r}[/tex][tex]\begin{gathered} 38\text{ = }\frac{\theta}{360}\times2\times\frac{22}{7}\times112.5 \\ \theta\text{ = }\frac{38\times360\times7}{2\times22\times112.5} \\ \theta\text{ = }\frac{95760}{4950} \\ \theta\text{ = }19.35^0 \end{gathered}[/tex]The angle of rotation = 19.35°
Male and females high school students reported how many hours they worked each week in summer jobs . The data represented in the following box plots
Answer:
The correct answer is c.
Step-by-step explanation:
Boys:
Range from 0 to 15 hours worked.
The third quartile, which is shown by the line in the box, is of 10 hours.
Females:
More bunched together, ranging from 15 to 20 hours worked, with a median, shown by a line on the middle of the box, of 17.5.
However, the line for females begins at around 1 hour, far from the median, which means that there is a significant outlier at the low end for females.
The correct answer is c.
About 13 out of 20 homes have a personalcomputer. On a street with 60 homes, howmany would you expect to have a personalcomputer?
Answer:
On a street with 60 homes, the number of homes expected to have a personal computer is;
[tex]39\text{ }[/tex]Expected
Given that;
About 13 out of 20 homes have a personal computer.
It means that;
[tex]\frac{13}{20}\text{ PC/home}[/tex]Out of 60 homes, the expected number of homes with PC is;
[tex]\begin{gathered} n=\frac{13}{20}\times60 \\ n=39 \end{gathered}[/tex]Therefore, On a street with 60 homes, the number of homes expected to have a personal computer is;
[tex]39\text{ }[/tex]Find the domain and range of the relation Choose the correct domain below. a.) all real numbers b.) x=3c.) all real numbers except 3d.) none of the above Choose the correct range below a.) y=3b.)all real numbers except 3c.) all real numbers d.)none of the above
As this is a vertical line, its domain is just one point, x=3. And it's range is all the real numbers
John makes 15 goals for every 25 shots he attempts. How many
goals can you expect John to miss if he shoots 75 shots in a
season?
Answer:
45 goals
Step-by-step explanation:
g = # of goals
s = # of shots
15g = 25s
45g = 75s
25 x 3 = 75
15 x 3 = 45
Answer:
30 missed shoots expected================
Ratio of goals per shoots:
g : s = 15 : 25If the number of shoots is 75, then number of goals is proportional:
g : 75 = 15 : 25g = 75 × 15 : 25g = 45Number of missed shoots:
75 - 45 = 30Jenny has a deck of 52 alphabet cards (26 uppercase and 26 lower case). Jenny selects one card.What is the probability that she selects a vowel?
We know that we have five vowels in the alphabet. Since the deck has uppercase and lower case cards this means that it has a total of 10 vowels.
The probability is given by the quotient between the number of favorable outcomes and the number of total outcomes; then in this case we have:
[tex]P=\frac{10}{52}=\frac{5}{26}[/tex]Therefore the probability of selecting a vowel is 5/26
Find the area of the rectangle if the length is y + 4 inches and the width is y - 5 inches. Enter your answer as a polynomial in terms of variable y and in standard form, ay2 + by + c.
We have the following:
We have that the area of a rectangle is the following
[tex]\begin{gathered} A=l\cdot w \\ \text{In this case:} \\ l=y+4 \\ w=y-5 \end{gathered}[/tex]replacing:
[tex]\begin{gathered} A=(y+4)(y-5)=y^2-5y+4y-20 \\ A=y^2-y-20 \end{gathered}[/tex]5 Three pipes are connected to a water tank. One of the pipes can fill the tank in 30 minutes. The second pipe can fill it in 20 minutes. The third pipe can fill the tank in 40 minutes. How long will it take to fill the tank if all three pipes are opened together? If the slowest pipe is shut off after 3 minutes and the fastest pipe is shut off 3 minutes later, how long will it take the remaining open pipe to finish filling the tank?
Let's call the total volume of the tank as V. The rate each pipe fills the tank is given by the total volume of the tank divided by the amount of time it takes to fill the tank. Let's call the rate of the first pipe as r1, the rate of the second pipe as r2 and the rate of the third pipe as r3.
[tex]\begin{gathered} r_1=\frac{V}{30} \\ r_2=\frac{V}{20} \\ r_3=\frac{V}{40} \end{gathered}[/tex]The product between the rate and the time that has passed will give to us the fraction of the tank that has been filled. When we open the three pipes at once, we sum their rates. When the tank is filled, the product between the rate and the time passed must give the total volume of the tank, therefore, we have the following equation:
[tex]\begin{gathered} (\frac{V}{30}+\frac{V}{20}+\frac{V}{40})t=V \\ \frac{13V}{120}t=V \\ \frac{13}{120}t=1 \\ t=\frac{120}{13} \\ t=9.23076923077... \\ t\approx9.23 \end{gathered}[/tex]It will take approximately 9.23 minutes to fill the tank if all pipes are opened together.
When the three pipes are opened, the fraction that has been filled(let's call it as x) is given by:
[tex]\begin{gathered} (\frac{1}{30}+\frac{1}{20}+\frac{1}{40})\cdot3=x \\ x=\frac{13}{40} \end{gathered}[/tex]Then, the slowest pipe(the third pipe) is closed, then, after 3 more minutes we're going to fill an extra y amount of water, given by:
[tex]\begin{gathered} (\frac{1}{30}+\frac{1}{20})\cdot3=y \\ \frac{1}{10}+\frac{3}{20}=y \\ \frac{5}{20}=y \\ y=\frac{1}{4} \end{gathered}[/tex]Then, after a time t with the first pipe open, we're going to fill the tank(remember that it has been filled already by the amounts x and y, therefore, we must subtract it from the total volume).
[tex]\begin{gathered} \frac{1}{30}\cdot t=1-\frac{13}{40}-\frac{1}{4} \\ \frac{t}{30}=\frac{27}{40}-\frac{10}{40} \\ t=30\cdot\frac{17}{40} \\ t=12.75 \end{gathered}[/tex]If the slowest pipe is shut off after 3 minutes and the fastest pipe is shut off 3 minutes later, it will take 12.75 minutes for the remaining open pipe to finish filling the tank.
In the diagram below, quadrilateral ABCD is inscribed in circle P.What is m< DCB?
ANSWER
A) 70º
EXPLANATION
In quadrilaterals inscribed in a circle, opposite angles are supplementary - their measures add up 180º. Therefore:
[tex]\begin{gathered} m\angle DAB+m\angle DCB=180º \\ 110º+m\angle DCB=180º \\ m\angle DCB=180º-110º \\ m\angle DCB=70º \end{gathered}[/tex]Write 5e slopes as a fraction or improper fraction using a slash
Given:
Given a graph of the function.
[tex]\begin{gathered} (x1,y1)=(0,3) \\ (x2,y2)=(-5,0) \end{gathered}[/tex]Required:
To find the slope.
Explanation:
The slope is
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ \\ =\frac{0-3}{-5-0} \\ \\ =\frac{-3}{-5} \\ \\ =\frac{3}{5} \end{gathered}[/tex]The y-intercept is at (0,3).
Final Answer:
The slope is : 3/5.
y-intercept : (0,3)
Given sinx= 5/13 andπ/2 < x < π find the exact value of tan 2x
Given sin(x)=5/13
First, lets find cos(x).
It is known that:
[tex]\begin{gathered} \sin ^2(x)+\cos ^2(x)=1 \\ (\frac{5}{13})^2+\cos ^2(x)=1 \\ \cos ^2(x)=1-\frac{25}{169} \\ \cos ^2(x)=\frac{169-25}{169}=\frac{144}{169} \\ \cos (x)=\pm\sqrt[]{\frac{144}{169}}\text{ = }\frac{\sqrt[]{144}}{\sqrt[]{169}} \\ \cos (x)=\pm\frac{12}{13} \end{gathered}[/tex]Since π/2 < x < π, we are in 2nd quadrant. Then, cos(x) is negative.
[tex]\cos (x)=-\frac{12}{13}[/tex]Since we know the values for sin and cos, we can find tan(x):
[tex]\begin{gathered} \tan (x)=\frac{\sin(x)}{\cos(x)} \\ \tan (x)=\frac{\frac{5}{13}}{-\frac{12}{13}} \\ \tan (x)==-\frac{5}{12} \end{gathered}[/tex]Now, lets work with the expression tan(2x)
It is known that:
[tex]\tan (2x)=\frac{2\tan(x)}{1-\tan^2(x)}[/tex]
Since we know tan(x), we can substitute in the expression above and find the value of tan(2x):
[tex]\begin{gathered} \tan (2x)=\frac{2\tan(x)}{1-\tan^2(x)} \\ \tan (2x)=\frac{2\cdot(-\frac{5}{12}_{})}{1-(-\frac{5}{12})^2} \\ \tan (2x)=\frac{-\frac{10}{12}}{1-\frac{25}{144}}=\frac{-\frac{10}{12}}{\frac{144-25}{144}}=\frac{-\frac{10}{12}}{\frac{119}{144}}=-\frac{10}{12}\cdot\frac{144}{119} \\ \tan (2x)=-\frac{120}{119} \end{gathered}[/tex]Answer: -120/119
Question 9 of 10What is the length of AB?O A. 3B. 6O c. 9O D. 12
Answer:
Step-by-step explanation:
c. it is the answer
it's a graph, I need help with the first one to understand how to do the rest. Please draw it clearly and understandably.
1) In this inequality 3x ≥ 9 we have to find a set of values for x.
3x ≥ 9 Divide both sides by 3
x ≥3
2) We can express this set of solutions in the number line as well. Since is greater than or equal to we'll use a closed dot. To include this 3.
3) Hence the graph above represents that every value greater than and the 3 satisfies the restraint x ≥3.
Which of the following measurements is greatest? O 6 yards O All of the measurements above are equal. O 19 feet O 187 inches
To answer this questions we have to remember the following rules
1 ft = 12 in
1 yd = 3 ft
Then we have to convert all our measurements to the same units, so we can compare them.
6 yd = 18 f
solve the equation: y+2.4=15.6
Use the properties of equalities to solve the given equation:
[tex]y+2.4=15.6[/tex]Substract 2.4 from both sides of the equation:
[tex]\begin{gathered} y+2.4-2.4=15.6-2.4 \\ \Rightarrow y=13.2 \end{gathered}[/tex]Therefore, the solution to the equation is:
[tex]y=13.2[/tex]Question Joan invested $1,420 at the start of the year and found she had $1,621.40 at the end of the year. What is the annual effective yield of her investment? Input your answer as a percentage rounded to two decimal.
Money invested = $1420
Final money = $1621.4
Effective yield = [ 1 + i/n]^n - 1
i = nominal rate let's consider 10%
n = number of payments 12 payments because it is in a year
Effective yield = [1 + 0.1/12]^12 - 1
= [ 1 + 0.00833]^12 - 1
= [1.0083]^12 - 1
= 1.1 - 1
Effective yield = 0.10 %
I need help with this question... the correct answer choice
Since the polygon shown is a regular one, a rotation will carry it onto for every angle that makes a vertex to the place of another vertex.
So, we can fisrt figure the angle we need to rotate to get a vertex onto the next one, that is, we want to find the following angle:
We know tha the polygon is regular, so this angles is the same as the angles between the other consecutive vertexes. Since we have 5 vertexes, this angle is 1/5 of the role 360°. So, this angles is:
[tex]\frac{360\degree}{5}=72\degree[/tex]That means that a rotation of 72° will always endup in the same figure.
This also means that a rotation of any multiple of 72° will also end up in the same figure.
Thus, we just have to check which alternative is a multiple of 72°.
- 60° isn't a multiple, because it is lower.
- 108° also isn't because the 2*72 = 144, which is higher than 108°.
- 540° isn't, because 7*72 = 504 and 576, which passed through 540°
- 216° is a multiple because 3*72 = 216 exactly.
This means that if we rotate the figure by 210° it will end up in the same figure.
So, the correct alternative is the last one: 216°.
It is known that the lengths of trout (centimetres) in dams in North America is Normally distributed with a standard deviation of 5 cm. For monitoring purposes, a sample of 15 trout were captured, measured and released. The sample gave a mean of 50 cm and a standard deviation of 2 cm.The 99% confidence interval for the population average length of trout isSelect one:a.(49.3 ; 50.2)b.(49.2 ; 50.9)c.(46.7 ; 53.3)d.(47.8 ; 52.3)e.(46.2 ; 53.8)
The average length of the trout in the area with a 99% confidence interval is between 46.7 cm and 53.3 cm.
The distribution used should be t distribution as the sample standard deviation is to be used.
We need to build the 99% confidence interval for the population mean . The following information is provided:
Sample Mean = 50
Sample Standard Deviation = 2 cm
Sample Size = 15
The confidence interval for the trout population is computed as shown below:
[tex]\Pr \left({\bar {X}}-{\frac {cS}{\sqrt {n}}}\leq \mu \leq {\bar {X}}+{\frac {cS}{\sqrt {n}}}\right)=0.99\,[/tex]
now we will substitute the values in the equation of the CI.
[tex]{\bar {X}}-{\frac {2.7}{\sqrt {15}}}\leq \mu \leq {\bar {X}}+{\frac {2.7}{\sqrt {15}}}=0.99\,[/tex]
now solving for the confidence interval we get : 47.8 ; 52.3
Lower limit = 50 - 3.307 = 46.69 ≈ 46.7
upper limit = 50 + 3.307 = 53.307 ≈ 53.3
Hence the average length of the trout in the area is between 46.7 cm and 53.3 cm.
To learn more about confidence interval visit:
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Can I get help with my math homework I’m struggling with ? 3
Step 1:
The slope intercept form formula is
y = mx + c
m = slope
c = intercept on the y-axis
Final answer
Slope Intercept
Step
Ton graph the function, find both x=intercept and y-intercept
[tex]\begin{gathered} \text{From y = }\frac{3}{2}x\text{ + 1} \\ y-\text{intercept c = 1} \\ \text{Make x subject of the formula} \\ 3x\text{ = 2y - 2} \\ x\text{ = }\frac{2}{3}y\text{ - }\frac{2}{3} \\ x-\text{intercept c = -}\frac{2}{3} \end{gathered}[/tex]Next plot the graph.
2. Given that the indicated lines in figure 10.30(a) are parallel, determine the unknown angles without actually measuring them. Explain your reasoning briefly.
The opposie angles are equal
c is opposite to a, so
[tex]c=a=34^o[/tex]The angle p is opposite to that of n, so
[tex]p=118^o[/tex]The total angle of rotation in a line is 180°. so,
[tex]o=180-118=62[/tex]This o is the oppsite to m, and hence m=o.
similarly,
[tex]d=180-34=146[/tex]And hence, b=d=146
1. Drag the fractions in order from least to greatest value L
Given the fractions 3/4 and 5/16
In order to determine which is less or greater, we need to first express them in percentage as shown;
3/4 = 3/4*100%
3/4 = 3*25 = 75%
5/16 = 5/16 * 100
5/16 = 500/16 = 31.25%
Since 75% is greater than 31.25% hence;
3/4 is greater than 5/16 and the sign that will be in the box will be the greater than sign i.e 3/4>5/16
Strategy: I compared the fraction to the bench mark of >
Find the sum: - 5/8 + 1/3
Answer:
-7/24
Explanation:
Given the expression:
[tex]-\frac{5}{8}+\frac{1}{3}[/tex]Step 1: Find the lowest common multiple of the denominators.
The L.C.M. of 8 and 3 = 24
Step 2: Use the LCM to combine the fractions.
[tex]=\frac{-5(3)+1(8)}{24}[/tex]Step 3: Simplify:
[tex]\begin{gathered} =\frac{-15+8}{24} \\ =-\frac{7}{24} \end{gathered}[/tex]The result of the sum is -7/24.
define the imaginary unit, i
An imaginary unit, i is a solution to the quadratic equation:
[tex]\text{ x}^2\text{ + 1 = 0}[/tex]Or to simply say,
[tex]i\text{ = }\sqrt[]{-1}[/tex]It can
A sofa regularly sells for $600. The sale price is $504.00. Find the percent decrease of the sale price from the regular price
STEP - BY - STEP EXPLANATION
What to find?
Percentage decreaase.
Given:
Original price = $600
new price = $504
Step 1
Recall the formula for percentage decrease.
[tex]\text{ \% decrease=}\frac{decrease}{original\text{ price}}\times100\text{ \%}[/tex]Step 2
Determine the value for the dcerease.
[tex]Decrease=new\text{ price - original price}[/tex][tex]Decrease=504-600=-96[/tex]Step 3
Substitute into the formula and simplify.
[tex]\text{ \% decrease=-}\frac{96}{600}\times100\text{ \%}[/tex][tex]=-16\text{ \%}[/tex]ANSWER
Percent decrease = 16% decrease
can two rays be put together to form a line
ANSWER:
Only in the case that the rays are opposite.
STEP-BY-STEP EXPLANATION:
We have that a ray is part of a line that has an end point and continues infinitely in a single direction.
Therefore, a pair of opposite rays are two rays that have the same end point and extend in opposite directions. So together a pair of opposing rays always form a straight line.
Graphically a ray and a line are like this:
Answer: if the rays are opposite they will always form a straight line but if the are not opposite they will not form a line
Step-by-step explanation:
Help me solve for equation 6x+3=33
Given:
[tex]6x+3=33[/tex]is given.
Required:
We need to solve this equation.
Explanation:
Here an equation given as
[tex]6x+3=33[/tex]now add both side negative 3 and we get
[tex]\begin{gathered} 6x+3-3=33-3 \\ 6x=30 \end{gathered}[/tex]now multiply both side with inverse 6
[tex]\begin{gathered} \frac{1}{6}*6x=30*\frac{1}{6} \\ x=5 \end{gathered}[/tex]Final answer:
Solution of given equation is
[tex]x=5[/tex]
Help me with this math problem plsWrite the formula for g(x) in terms of f(x)
Given:
Given a graph of f(x) and g(x).
Required:
To write the formula for g(x) in terms of f(x).
Explanation:
The graph of g(x) is 5 units left and 1 units up gfrom the graph of f(x).
Therefore the function g(x) is
[tex]g(x)=f(x+5)+1[/tex]Final Answer:
[tex]g(x)=f(x+5)+1[/tex]20 4/5 whats the decimal number
20 4/5
it means 20 integers and 4/5
4/5 = 0.8
so the number 20 4/5 is equal to 20.8
answer: 20.8
20 7/8 is 20 integers and 7/8
7/8 = 0.875
so 20 7/8 is equal to 20.875
Give the domain of definition of the function and find the asymptotes to the following function y = arctan 1/x - x
we have the function
[tex]y=arctan(\frac{1}{x}-x)[/tex]using a graphing tool
see the attached figure below
The domain is all real numbers except for x=0
The range is the interval (-pi/2, pi/2)
there are horizontal asymptotes at
y=pi/2 and y=-pi/2
The strength of a beam varies inversely with the square of its length. If a 10-foot beam can support 500 pounds how many pounds can a 13 foot beam support? Round the answer to the nearest pound.
The beam varies inversely with the square of it's length. Let's call S the strength and L the length.
Then we can write:
[tex]S=\frac{k}{L^2}[/tex]For a constant k.
Then, we know that if L = 10ft then S = 500 pounds
We write:
[tex]\begin{gathered} 500=\frac{k}{(10)^2} \\ \end{gathered}[/tex]And solve for k:
[tex]k=500\cdot10^2=500\cdot100=50,000[/tex]Then the inverse relation equation is:
[tex]S=\frac{50,000}{L^2}[/tex]Then, for L = 13ft, the strength is:
[tex]S=\frac{50,000}{13^2}=\frac{50,000}{169}=295.857[/tex]To the nearest pound, a beam of 13ft can support 296 pounds.