The roots of the cubic function:
f(x)= x³ + 3x² - x - 3
are x = 1, x= -1, x = -3
How to find the roots of the function?We want to find the roots of the function:
f(x)= x³ + 3x² - x - 3
We know that x = 1 is a root, because f(1) = 0.
Then we can write that function as:
(x - 1)*(x - a)*(x - b)
Where a and b are the other two roots, then we need to solve:
x³ + 3x² - x - 3 = (x - 1)*(x - a)*(x - b)
Expanding the right side, we will get:
x³ + 3x² - x - 3 = x³ + (-a - b - 1)x² + (a + b + ab)x + (-ab)
Comparing like terms, we can see that:
(-a - b - 1) = 3
(a + b + ab) = -1
(-ab) = -3
The third equation gives:
ab = 3
Replacing that in the second one we get:
a + b + 3 = -1
a + b = - 1 - 3 = -4
a + b = -4
a = -4 - b
Replacing that in the relation above:
ab = 3
(-4 - b)*b = 3
-4b - b² = 3
b² + 4b + 3 = 0
The zeros of that function are:
[tex]b = \frac{-4 \pm \sqrt{4^2 -4*3*1} }{2*1} \\\\b = \frac{-4 \pm 2}{2}[/tex]
Then if b is the value when we take the positive sign:
b = (-4 + 2)/2 = -1
the value of a is:
a = -4 - b = -4 + 1 = -3
These are the other two roots.
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SOMEBODY PLEASE PLEASE HELP ME
ILL GIVE YOU 5 STARS, BRAINLIEST AND GIVE A HEART PLEASE HELP
(Please answer the questions and )
Part A ;
For Bus:
mean = 17.5
median = 15
mode= 15 and 16
Range= 17
For walking:
mean = 20.5
median = 20.5
mode= 20 and 21
Range= 3
How to calculate the various variables given above?For Bus
To calculate the mean:
= 16+14+15+14+31+15/6
= 105/6
= 17.5
To calculate the median;
= 14,14,15,15,16,31
= 15+15/2 = 15
To calculate the range:
= 31-14 = 17
For walking;
To calculate the mean:
= 19+20+20+21+21+22/6
= 123/6
= 20.5 mins
To calculate the median
= 20+21/2
= 20.5
To calculate the mode:
=20 and 21
To calculate the range:
= 22-19
= 3
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Can someone please answer and provide an explanation for these problems?
The slope of each line is given as follows:
58) -2.
59) 1.
60) -2/3.
61) 2.
How to define a linear function?The slope-intercept equation for a linear function is presented as follows:
y = mx + b
The parameters of the definition of the linear function are given as follows:
m is the slope.b is the intercept.When two lines are parallel, they have the same slope, which are the cases for itens 58 and 59, as the slope is given by the multiplier of x.
When two lines are perpendicular, we have that the multiplication of the slopes of the line is of -1, hence the slope for item 60 is given as follows:
3m/2 = -1
3m = -2
m = -2/3.
For item 61, the slope is given as follows:
-m/2 = -1
m = 2.
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Sneha went to a shopkeeper to purchase sugar.The dishonest shopkeeper uses a weight of 990 g for measuring 1 kg . If Sneha bought 5/2 kg of sugar, find the amount of sugar she actually got.
Sneha actually got 2475 g of sugar instead of 2500 g.
We have,
If the shopkeeper uses a weight of 990 g for measuring 1 kg, it means that he is using a weight that is 10 g less than the actual weight of 1 kg.
So, the actual weight of 1 kg is 1000 g.
Now,
If Sneha bought 5/2 kg of sugar, she should have received:
= (5/2) x 1000 g
= 2500 g
But since the shopkeeper uses a weight of 990 g for measuring 1 kg, the weight of 5/2 kg would be:
= (5/2) x 990 g
= 2475 g
Thus,
Sneha actually got 2475 g of sugar instead of 2500 g.
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer:
The correct answer:
(B) reduction
What is the median of the following set of numbers? 35, 33, 36, 34, 33, 33, 32, 38, 35
A.35
B. 34
C.33
D.36
Median of the set is 34, as it is the middle value of the ordered set (32, 33, 33, 33, 34, 35, 35, 36, 38).
To find the middle of a bunch of numbers, the initial step is to organize the numbers all together from least to most prominent. For this situation, the arranged set is: 32, 33, 33, 33, 34, 35, 35, 36, 38.
The middle is the center number in the arranged set. On the off chance that there is an odd number of values, the middle is the center worth. On the off chance that there is a considerably number of values, the middle is the normal of the two center qualities.
For this situation, there are nine qualities in the set, which is an odd number. The center worth is the fifth worth, which is 34. Thusly, the middle of the set is B. 34.
To confirm, we can count four qualities before 34 and four qualities after 34 in the arranged set. Since there are an equivalent number of values when the middle, we can infer that 34 is for sure the middle.
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Given that A={1,2,3,4,5} list the elements of the following sets. i.{x2:x€A} ii.{ :x€A} iii.{2x :x€A} iv.{4x+1:x€A}
Answer:no idea
Step-by-step explanation:
Compare:
58,565 ____ 58,566
Answer:
58,565 < 58,566
Step-by-step explanation:
You have to determine which number is greater. I usually start comparing from the farthest left digit (In this case, the ten thousands place.) and work my way up
hope this helped :)
Can someone please help me find the domain and range thank you all so much for the help
The domain and the range of the graph are Domain = [-10, -8] and Range = [-10, -1]
Calculating the domain and range of the graphFrom the question, we have the following parameters that can be used in our computation:
The graph
The above graph can be represented as a list of ordered pairs
The rule of a graph is that
The domain is the x valuesThe range is the f(x) valuesUsing the above as a guide, we have the following:
Domain = [-10, -8]
Range = [-10, -1]
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Which statement about the location of √7 on the number line is true?
A= It is located at the number 7 on the number line.
B= It is located at the number 3.5 on the number line.
C= It is located between the numbers 2 and 3 on the number line.
D=It is located between the numbers 4 and 9 on the number line
Given f(x) = x^2 what is the range of g(x) = f(x+2)-5
The range of the function g(x) = f(x+2)-5 is:
R = [0, ∞)
What is the range of g(x) = f(x+2)-5?For a function y = f(x), we define the range as the set of possible outputs of the function.
Here we want to find the range of:
g(x) = f(x+2)-5
Where f(x) = x²
Replacing f(x) in the rule for g, we will get the composition:
g(x) = (x + 2)² - 5
The first part can only be a positive number or 0, then the minimum of the range is -5
And then the function only grows, then the range of g(x) is:
R = [0, ∞)
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here is my algebra 13 homework screenshot. can somebody please help me! QUICK
The function which has a range of real numbers is f(x) = -x + 2
Range is the set of the values that the function obtains this set is the values that the function obtains when we put an x value in the function.
In f(x) = -x + 2 when we put any value of x we get real number so the function range is ( -∞ , ∞ )
In g(x) = -x² when we put any value of x we get all negative number function range is (-∞ , 0]
In h(x) = [tex]2^{x}[/tex] + 1 when we put any value of x we get all positive number so the function range is (1 , ∞)
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Please help with pictures below.
The proportion is solved and the variables are a/b = c/d
Given data ,
Let the proportion be represented as A
Now , the value of A is
a / b = c / d
On simplifying the equation , we get
( a + b ) / b = ( c + d ) / d
On dividing the numerator of the fraction by the denominator , we get
( a / b ) + ( b / b ) = ( c / d ) + ( d / d )
On further simplification , we get
( a / b ) + 1 = ( c / d ) + 1
Subtracting 1 on both sides , we get
( a / b ) = ( c / d )
Hence , the proportion is ( a / b ) = ( c / d )
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What the meaning of statement this?
The statement Y = {u: (z X)uez) = U{z: zEX}=UX, means that the set Y is the union of all the sets z that are elements of X. In other words, Y is the set of all elements that are in at least one of the sets in X.
How to explain the statementThe statement can be broken down into two parts:
The first part, Y = {u: (z X)uez), says that Y is the set of all elements u such that u is an element of at least one set z that is an element of X.
The second part, U{z: zEX}=UX, says that the union of all the sets z that are elements of X is equal to the set UX.
The two parts of the statement can be combined to say that Y is the union of all the sets z that are elements of X.
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A spinner has three sections. The table shows the results of spinning the arrow on the spinner 80 times.
What is the experimental probability of the arrow stopping over Section 1?
A} 1/28
B} 7/20
C} 7/13
D} 4/5
Answer:
B} 7/20
Step-by-step explanation:
total: 80
section 1: 28
p(section 1) = 28/80 = 7/20
Please help I need this for my final to pass and graduate ☹️
Another representation of (1, 1/4 π) in which r> 0, 2π < θ < 4π is (1, 3/4 π)
Understanding Bi-polar CoordinateIn Bi-polar Coordinates, the point (1, 1/4 π) can be represented in polar coordinates as (r, θ).
Where r is the distance from the origin to the point and θ is the angle between the positive x-axis and the line segment connecting the origin to the point.
a. For r> 0, 2π < θ < 4π
Add 2π to the original angle of 1/4 π:
(r, θ+2π) = (1, 1/4 π + 2π)
= (1, 9/4 π)
b. For r < 0, 0 < θ < 2π,
Add π and reflect the original point across the origin:
(r, θ+π) = (-1, 1/4 π + π)
= (-1, 5/4 π)
c. For r> 0, -2π < θ < 0,
Subtract 2π from the original angle of 1/4 π:
(r, θ-2π) = (1, 1/4 π - 2π)
= (1, -7/4 π)
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A random number from 1 to 5 is selected 50 times. The number 1 is selected 13 times, 2 is s elected 8 times, 3 is selected 14 times, 4 is selected 6 times, and 5 is selected 9 times. What (äbä 2) *?is the relative frequency of selecting a 2
The relative frequency of selecting the number 2 is 0.16 or 16%.
Relative Frequency is a proportion or percentage which is calculated with the help of given frequency.
To calculate the relative frequency of selecting the number 2, you need to divide the number of times 2 was selected by the total number of selections. In this case, 2 was selected 8 times out of a total of 50 selections.
Relative frequency of selecting 2 = (Number of times 2 was selected) / (Total number of selections)
= 8 / 50
= 0.16
Therefore, the relative frequency of selecting the number 2 is 0.16 or 16%.
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Question 5
TABLE 4 below shows the distribution of revenue among the different spheres of
government in South Africa from the 2017/2018 to 2021/2022 financial year. Some values
have been omitted.
TABLE 4: Distribution of Revenue among the different government spheres for
the financial years 2017/2018 to 2021/2022.
R(billion)
2019/20
546.1
471,4
Government
BHOJDIN
National
Provincial
Local
TOTAL
2017/18
453.4
410.6
**
2018/19
490,00
439,5
87.6
1 017,1
98.3
1:15.8
2020/21
557,5
500,4
103.3
1 161.2
2021/22
1 240.5
(adapted from DBE 2014 MLQP)
Use the table above to answer questions that follows
When the revenue of the local government sector was compared to the provincial sec
2017/18, it was found to be 20, 12% of the provincial sector.
Calculate
the missing value E, the total revenue for the period 2017/18.
ont sector always receives a larger share than t
The missing value E, the total revenue for the period 2017/18, is approximately 82.61 billion.
How to calculate the valueLocal government sector's revenue in 2017/18 (L): Missing value (to be calculated)
Provincial sector's revenue in 2017/18 (P): 410.6 (billion)
According to the information provided, L is 20.12% of P. Mathematically, we can write this as:
L = 20.12/100 * P
Substituting the known value of P, we get:
L = 20.12/100 * 410.6
L ≈ 82.61 (rounded to two decimal places)
Therefore, the missing value E, the total revenue for the period 2017/18, is approximately 82.61 billion.
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Given f(x)=4x^2 - 1 and g (x) = 2x- 1 , find each function
1. ( f+g )( x )
2. ( fg ) ( x )
3. ( f^n ) ( x )
The values of the composite functions are
(1) (f + g)(x) = 4x² + 2x - 2
(2) (fg)(x) = 8x³ - 4x² - 2x + 1
(3) (fⁿ)(x) = (4x² - 1)ⁿ
How to evaluate the composite functionsFrom the question, we have the following functions that can be used in our computation:
f(x) = 4x² - 1
g(x) = 2x - 1
Using the above as a guide, we have the following:
(f + g)(x) = f(x) + g(x)
(f + g)(x) = 4x² - 1 + 2x - 1
Evaluate the like terms
(f + g)(x) = 4x² + 2x - 2
(fg)(x) = f(x) * g(x)
(fg)(x) = (4x² - 1) * (2x - 1)
Evaluate the products
(fg)(x) = 8x³ - 4x² - 2x + 1
(fⁿ)(x) = (f(x))ⁿ
So, we have
(fⁿ)(x) = (4x² - 1)ⁿ
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in a bag if marbles 1/2 are blue 1/6 are green 1/12 are yellow you pick a marble with out looking what color marble are you most likely going to choose
Answer: Blue
Step-by-step explanation:
Half of the entire freaking bag is blue,it states it in the question.If there is so many,unless by pure blind luck you will get that.
I hope it helps!
find the area of a triangle whose base is 8 inches and whose height is 12 in.
(a) 96in.²
(b) 10in ²
(c) 20in.²
(d) 48in.²
Answer:
48in.²
Step-by-step explanation:
The formula for the area of a triangle is 1/2 x b x h
Since the b = 8 and the h = 12, substitute 8 and 12 for b and h.
1/2 x 8 x 12
4 x 12
48in.²
Answer:
d
Step-by-step explanation:
area= ½ × b × h
= ½ × 8 × 12
= ½ × 96
= ⁹⁶/²
= 48in²
FInd the measure of the arc using the picture provided , please and thanks
The measure of arc angle QTP is 204 degrees.
How to find arc angle?When a tangent and a secant intersect outside a circle then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.
Therefore, let's find the measure of arc angle QTP as follows:
90 = 0.5(x - 68)
90 = 0.5x - 34
0.5x = 124
x = 124 / 0.5
x = 248 degrees
Where
x = arc angle TSQ
Therefore,
arc QP = 44 degrees
Therefore,
arc QTP = 248 - 44
arc QTP = 204 degrees
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The figure below is a net for a cube. 3.9 ft What is the surface area of the cube, in square feet?
Answer:91.26ft squared
Teena uses 1/4 cup of oil for a cake. How many cakes can she make if she has 6 cups of oil?
Answer:
24 cakes.
Step-by-step explanation:
6 cups of oil divided by 1/4 cup oil per cake = 24 cakes
6/(1/4) = 24
or 6/(0.25) = 24
She can make 24 cakes with 6 cups of oil.
What is one-way ANOVA?
Discuss and explain how the five steps of hypothesis testing are used in one-way ANOVA.
One-way ANOVA utilizes the five steps of hypothesis testing to determine if there are significant differences among the means of three or more groups.
One-way ANOVA, or analysis of variance, is a statistical test used to compare the means of three or more groups to determine if there are significant differences among them. It helps in determining whether the variations between the group means are due to random chance or if they are statistically significant.
The five steps of hypothesis testing are commonly used in one-way ANOVA to analyze and draw conclusions from the data. These steps are as follows:
1. Formulating the null and alternative hypotheses: In one-way ANOVA, the null hypothesis (H0) states that there are no significant differences between the group means, while the alternative hypothesis (Ha) states that at least one group mean differs significantly from the others.
2. Choosing a significance level: The significance level, denoted as α, represents the threshold below which the null hypothesis is rejected. Commonly used values for α are 0.05 or 0.01, indicating a 5% or 1% chance, respectively, of rejecting the null hypothesis incorrectly.
3. Computing the test statistic: In one-way ANOVA, the test statistic is the F-statistic, which compares the between-group variation to the within-group variation. It measures the ratio of the mean square between (MSB) to the mean square within (MSW).
4. Determining the critical value: The critical value is derived from the F-distribution table and depends on the significance level and the degrees of freedom associated with the numerator and denominator of the F-statistic.
5. Making a decision: If the calculated F-value is greater than the critical value, the null hypothesis is rejected, and it can be concluded that there are significant differences between at least two group means. Conversely, if the calculated F-value is smaller than the critical value, the null hypothesis is not rejected, indicating that there is no significant difference between the group means.
If the null hypothesis is rejected, post-hoc tests can be conducted to determine which specific group means differ significantly from each other.
one-way ANOVA utilizes the five steps of hypothesis testing to determine if there are significant differences among the means of three or more groups.
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how many triangles?(urgent)
There are 75 triangles that can be formed using these 9 vertices.
Here we have,
We have 9 vertices arranged in a pattern where 5 vertices are above and 4 vertices are below in a parallel direction.
And we want to know how many triangles can be formed using these vertices.
In order to this,
Count the number of ways to choose 3 vertices from the 9 vertices.
This can be done using the combination formula, which is:
[tex]^{9}C_{3}[/tex] = 9! / (3! * (9-3)!)
= 84.
Since,
A degenerate triangle is one where all three vertices lie on the same line. To count the number of degenerate triangles,
We need to count how many ways we can choose 3 vertices that lie on the same line.
There are 5 lines with 3 points each (the 5 lines with the upper vertices). So the number of degenerate triangles is:
5 [tex]^{3}C_{3}[/tex] + 4 [tex]^{3}C_{3}[/tex] = 9.
Subtract the number of degenerate triangles from the total number of triangles to get the number of non-degenerate triangles.
Therefore, the number of non-degenerate triangles is:
84 - 9 = 75.
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MA.7.DP.1.4
A group of friends has been given $800 to host a party. They must decide how much money
will be spent on food, drinks, paper products, music and decorations.
Part A. As a group, develop two options for the friends to choose from regarding how to
spend their money. Decide how much to spend in each area and create a circle
graph for each option to represent your choices.
Part B. Mikel presented the circle graph below with his recommendations on how to
spend the money. How much did he choose to spend on food and drinks? How
much did he choose to spend on music?
Party Spending Proposal
Mail
17%
Paper Products
Answer: $130 money did Brenda and Hazel have all together before buying decorations and snacks.
Here, we have,
You want to know Brenda and Hazel's combined money when the ratio of their remaining balances is 1 : 4 after Brenda spent $58 and Hazel spent $37. They had the same amount to start with.
Setup
Let x represent the total amount the two women started with. Then x/2 is the amount each began with, and their fnal balance ratio is ...
(x/2 -58) : (x/2 -37) = 1 : 4
Solution
Cross-multiplying gives ...
4(x/2 -58) = (x/2 -37)
2x -232 = x/2 -37 . . . . . . eliminate parentheses
3/2x = 195 . . . . . . . . . . . . add 232-x/2
x = (2/3)(195) = 130 . . . . . multiply by 2/3
Brenda and Hazel had $130 altogether before their purchases.
Alternate solution
The difference in their spending is $58 -37 = $21.
This is the same as the difference in their final balances.
That difference is 4-1 = 3 "ratio units", so each of those ratio units is $21/3 = $7.
Their ending total is 1+4 = 5 ratio units, or $35.
The total they started with is $58 +37 +35 = $130.
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complete question:
Brenda and Hazel decide to throw a surprise party for their friend, Aerica. Brenda and Hazel each go to the store with the same amount of money. Brenda spends $58 on decorations, and Hazel spends $37 on snacks. When they leave the store, the ratio of Brenda’s money to Hazel’s money is 1 : 4. How much money did Brenda and Hazel have all together before buying decorations and snacks?
Find the average rate of change of f(x)=x²+2x+1 from x=4 to x=6.
The average rate of change of the function over the interval is 12
Finding the average rate of changeFrom the question, we have the following parameters that can be used in our computation:
f(x) = x² + 2x + 1
The interval is given as
From x = 4 to x = 6
The function is a quadratic function
This means that it does not have a constant average rate of change
So, we have
f(4) = 4² + 2(4) + 1 = 25
f(6) = 6² + 2(6) + 1 = 49
Next, we have
Rate = (49 - 25)/(6 - 4)
Evaluate
Rate = 12
Hence, the rate is 12
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100 Points! Algebra question. Photo attached. Please show as much work as possible. Thank you!
The probability of the digestive tract disease, given a positive test result, is 45%.
A. Two-Way Frequency Table:
Let's create a two-way frequency table to represent the situation:
Test Positive Test Negative Total
Disease Present A B 5,000
Disease Not Present C D 95,000
Total 5,000 95,000 100,000
In this table:
A represents the number of sheep that have the disease and test positive.B represents the number of sheep that have the disease but test negative.C represents the number of sheep that do not have the disease but test positive.D represents the number of sheep that do not have the disease and test negative.B. Probability of Disease Given Positive Test Result:
P(Disease | Positive)
= (P(Positive | Disease) x P(Disease)) / P(Positive)
= 0.94 x 0.05 / P(Positive)
To calculate P(Positive), we can use the law of total probability:
P(Positive) = P(Positive | Disease) x P(Disease) + P(Positive | No Disease) x P(No Disease)
So, P(Positive | No Disease) = 1 - P(Test Negative | No Disease)
= 1 - 0.94 = 0.06
P(No Disease) = 1 - P(Disease) = 1 - 0.05 = 0.95
Now, P(Positive) = (0.94 x 0.05) + (0.06 x 0.95)
= 0.047 + 0.057
= 0.104
Finally, we can calculate P(Disease | Positive):
P(Disease | Positive) = (0.94 x 0.05) / 0.104
= 0.047 / 0.104
≈ 0.452
Therefore, the probability of the digestive tract disease, given a positive test result, is 45%.
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Emilia loves to play the piano but doesn't like practicing the exercises her piano teacher assigns. Emilia knows the exercises will help her play better though, so she tries to motivate herself using her favorite treat — chocolate chip cookies. There is a proportional relationship between the amount of time (in hours) that Emilia practices the piano, x, and how many cookies she gives herself, y.
When Emilia practices for 1 hour, she gives herself 4 cookies. Write the equation for the relationship between x and y.
Answer: Is it x=y(4)? Can someone tell me if that's right?
Step-by-step explanation:
What are the zeros of the function
Answer: i think c
Step-by-step explanation: