Segment AB is on the line y − 9 = −4(x + 1), and segment CD is on the line y − 6 = one fourth(x − 3). Which statement proves the relationship of segments AB and CD?
Answer: To prove the relationship between segments AB and CD, we need to determine if they are parallel, perpendicular, or neither.
First, let's find the slope of line AB:
y − 9 = −4(x + 1)
y − 9 = −4x − 4
y = −4x + 5
So the slope of line AB is -4.
Now let's find the slope of line CD:
y − 6 = one fourth(x − 3)
y − 6 = (1/4)x − (3/4)
y = (1/4)x + (21/4)
So the slope of line CD is 1/4.
Since the slopes of the two lines are not equal and not negative reciprocals, they are neither parallel nor perpendicular. Therefore, we cannot determine the relationship between segments AB and CD based on the given information.
Step-by-step explanation:
Write a formula you can use to find the sum of the measurements of a interior angels of a polygon.Use it to find the sum of the measures of the interior angel of a polygon with 11 sides.
The sum of the measures of the interior angles of an 11-sided polygon is 1620 degrees.
The formula to find the sum of the measures of the interior angles of a polygon is:
Sum of interior angles = (n - 2) × 180 degrees
Where n: number of sides of the polygon.
Using this formula, we can find the sum of the measures of the interior angles of a polygon with 11 sides:
Sum of interior angles = (11 - 2) × 180 degrees
Sum of interior angles = 9 × 180 degrees
Sum of interior angles = 1620 degrees
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There are 10 observations arranged in ascending order As given below 45, 47,50,x,x+2,60,62,63. The median of this observations is 53 find the value of x also find the mean and the mode of the data
Answer:
Below in bold.
Step-by-step explanation:
The median will be the average of the 2 middle numbers
so it is:
(x + x + 2)/2 and this equal 53,
(2x + 2)/2 = 53
x + 1 = 53
x = 52.
So, the list is
45, 47, 50, 52, 54, 60, 62, 63
Mean = (45 + 47+ 50+ 52 +54+ 60+ 62+ 63)/ 8
= 54.125
There is no Mode.
Quadrilateral RSTU has vertices at T(1,11), S(9,12), T(13,5) and U(2,-2).
Show that RS is congruent to ST.
Given that RSTU is a quadrilateral with perpendicular diagonals and two adjacent, congruent sides, why isn't RSTU a rhombus?
Hence the product of the slope of RT and SU is -1, so the lines are perpendicular
RS=ST, Hence RS, and ST are congruent to each other, which is why it is a rhombus.
A particular type of rhombus is a parallelogram. In a rhombus, the opposing sides and angles are parallel and equal. The diagonals of a rhombus meet at right angles to form its shape, and it also has equal-length sides on each side. Another name for the rhombus is a diamond or rhombus. The plural of a rhombus is a rhombus or rhombuses.
Quadrilateral RSTU has vertices at T(1,11), S(9,12), T(13,5) and U(2,-2).
The slope RT is k[tex]=-\frac{1}{2}[/tex] and the slope SU is [tex]l=2[/tex]
[tex]kl=-1\\\\RS=\sqrt{8^2+1}=\sqrt65\\and ST=\sqrt(65)\\\\[/tex]
RS=ST ,
hence RS is congurent to ST
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A particular American football player threw 8486 passes and 5956 of them were caught, so his success rate is 0.702. Describe a procedure for using computer software to simulate his next pass. The outcome should be an indication of one of two results: (1) The pass is caught; (2) the pass is not caught.
Therefore , the solution of the given problem of probability comes out to be a random result will be produced with a success probability equal to the specified success rate of 0.702.
What is probability?Finding the likelihood that a claim is true or that a specific event will occur is the primary objective of the branch of mathematics known as parameter estimation. Any number between range 0 but rather 1, where 1 is usually used to symbolise certainty and 0 is typically used to represent possibility, may be utilized to represent chance. A probability diagram shows the chance that a specific event will occur. .
Here,
Here is a potential Python method for modelling the subsequent pass:
Python: import the random package.
import arbitrary
0.702 is the desired performance rate:
makefile
success rate for copying is 0.702
The random.random() function can be used to produce a random integer between 0 and 1:
random.random rand num ()
Simulate the pass being caught if the random number is less than or equivalent to the success rate. If not, pretend that the throw was not caught:
python
output if rand num = success rate ("The pass is caught.")
if not: output ("The pass is not caught.")
Every time this process is executed, a random result will be produced with a success probability equal to the specified success rate of 0.702.
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simply 1 1/3 + 3 2/3
Answer:
5
Step-by-step explanation:
First, we can add the whole numbers together.
1 + 3 = 4
Next, we know that the denominators (base/bottom of fraction) of the fractions are the same, meaning we simply add the numerators (top of fraction).
1/3 + 2/3 = 3/3
3/3 is equal to 1.
Now, we add the 4 from above to this 1 to get our answer, 5.
Feel free to comment down if this doesn't make sense, and I can explain it in a different way.
3. Meghan earns money babysitting. She charges $5 an hour before
8 P.M. and $8 an hour after 8 P.M. She earned $26 for her last
babysitting job. Between what hours did Meghan babysit?
Answer:
Let's call the number of hours before 8 P.M. that Meghan babysat "x", and the number of hours after 8 P.M. "y". We can set up two equations based on the information given:
5x + 8y = 26 (this is the total amount she earned)
x + y = total number of hours she babysat
We can solve for one of the variables in terms of the other and substitute it into the first equation:
y = total number of hours - x
5x + 8(total number of hours - x) = 26
5x + 8total number of hours - 8x = 26
3x = 26 - 8total number of hours
x = (26 - 8total number of hours)/3
Now we can try different values for the total number of hours she babysat to see if we get a whole number for x:
If she babysat for 1 hour, x = (26 - 8)/3 = 6, which is not a whole number.
If she babysat for 2 hours, x = (26 - 16)/3 = 3, which is a whole number.
If she babysat for 3 hours, x = (26 - 24)/3 = 0.67, which is not a whole number.
So we know she babysat for 2 hours before 8 P.M. and 1 hour after 8 P.M.:
5(2) + 8(1) = 18
2 + 1 = 3 total hours babysat
Therefore, Meghan babysat between 6 P.M. and 9 P.M.
Step-by-step explanation:
The straight line depreciation equation for a luxury car is y = −3,400x + 85,000.
a. What is the original price of the car?
b. How much value does the car lose per year?
c. How many years will it take for the car to totally depreciate?
The original price of the car is 85,000. b. The car loses 3,400 in value per year. c. The car will totally depreciate after 25 years. This is because 85,000 divided by 3,400 equals 25.
What is value?Value in math is the result of a mathematical operation or equation. It is a number or quantity assigned to a mathematical expression. Value can also refer to the worth of an object or activity, such as the value of a specific type of currency or the value of a certain action. Value can refer to the magnitude of a number or a quantity relative to other numbers or quantities, such as the value of a particular number on a scale.
a. The original price of the car can be calculated by setting x=0 in the equation, which gives 85,000. This means that the original price of the car is 85,000.
b. The value of the car decreases by 3,400 per year. This is calculated by looking at the coefficient of x in the equation, which is −3,400. This means that for every year that passes, the value of the car decreases by 3,400.
c. The car will take 25 years to totally depreciate. This is calculated by setting the equation equal to 0 and solving for x. The equation 0 = −3,400x + 85,000 can be rearranged to x = 25. This means that the car will take 25 years to totally depreciate.
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I need help solving these!
The simplification of the following equations will be:[tex]4\sqrt{3}\ \ 6\sqrt{2}\ \ 20\sqrt{3}\ \ 5\sqrt{5}\ \ 50\sqrt{3}\ \ 24\sqrt{2}\ \ 20\sqrt{7}\ \ 6\sqrt{15}\ \ 40\ \ 21\sqrt{2}\ \ 10\sqrt{11907}[/tex].
What are prime factors?Prime factorization is the process of transforming a number into a prime product. A prime number simply has the number itself and the number itself as its two components. The prime numbers, for instance, are 2, 3, 5, 7, 11, 13, and 19. Any integer can be expressed as the sum of prime integers thanks to prime factorization.
[tex]$\sqrt{48} = \sqrt{16 \cdot 3} = \sqrt{16} \cdot \sqrt{3} = 4 \sqrt{3}$[/tex]
[tex]$\sqrt{72} = \sqrt{36 \cdot 2} = \sqrt{36} \cdot \sqrt{2} = 6 \sqrt{2}$[/tex]
[tex]$\sqrt{1200} = \sqrt{400 \cdot 3} = \sqrt{400} \cdot \sqrt{3} = 20 \sqrt{3}$[/tex]
[tex]$\sqrt{125} = \sqrt{25 \cdot 5} = \sqrt{25} \cdot \sqrt{5} = 5 \sqrt{5}$[/tex]
[tex]$\sqrt{98}$[/tex] 98 already has the simplest root form, since it does not have a perfect square factor.
[tex]$\sqrt{7500} = \sqrt{25 \cdot 300} = \sqrt{25} \cdot \sqrt{300} = 5 \sqrt{300} = 5 \sqrt{100 \cdot 3} = 5 \cdot 10 \sqrt{3} = 50 \sqrt{3}$[/tex]
[tex]$6 \sqrt{32} = 6 \sqrt{16 \cdot 2} = 6 \sqrt{16} \cdot \sqrt{2} = 6 \cdot 4 \sqrt{2} = 24 \sqrt{2}$[/tex]
[tex]$10 \sqrt{28} = 10 \sqrt{4 \cdot 7} = 10 \sqrt{4} \cdot \sqrt{7} = 20 \sqrt{7}$[/tex]
[tex]$3 \sqrt{60} = 3 \sqrt{4 \cdot 15} = 3 \sqrt{4} \cdot \sqrt{15} = 6 \sqrt{15}$[/tex]
[tex]$5 \sqrt{64} = 5 \cdot 8 = 40$[/tex]
[tex]$7 \sqrt{18} = 7 \sqrt{9 \cdot 2} = 7 \sqrt{9} \cdot \sqrt{2} = 21 \sqrt{2}$[/tex]
[tex]$\sqrt{1190700} = \sqrt{100 \cdot 11907} = \sqrt{100} \cdot \sqrt{11907} = 10 \sqrt{11907}$[/tex]
So the above are the prime factors of the given equation. Among them, the square root is not exact.
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Suppose you are a district manager of a health management organization (HMO) that is monitoring the office of a local doctor or nurse in general family practice. This morning the office you are monitoring has eight office visits on the schedule. What is the probability that
(a) at least half the patients are under 15 years old? First, explain how this can be modeled as a binomial distribution with 8 trials, where success is visitor age is under 15 years old and the probability of success is .
(b) from 2 to 5 patients are 65 years old or older (include 2 and 5 )?
(c) from 2 to 5 patients are 45 years old or older (include 2 and 5 )? Hint: Success is 45 or older. Use the table to compute the probability of success on a single trial.
(d) all the patients are under 25 years of age?
(e) all the patients are 15 years old or older?
(a) The probability that at least half the patients are under 15 years old is 0.01562.
(b) The probability that from 2 to 5 patients are 65 years old or older is, 0.92179.
(c) The probability that from 2 to 5 patients are 45 years old or older is, 0.9216.
(d) The probability that all the patients are under 25 years of age is 0.00065.
(e) The probability that all the patients are 15 years old or older is 0.16777.
(a) We can model this situation as a binomial distribution with 8 trials, where success is a visitor age being under 15 years old and the probability of success is unknown.
To find the probability that at least half the patients are under 15 years old, we can use the binomial cumulative distribution function.
Assume that the probability of success (visitor age under 15) is 0.5,
The probability of at least half of the patients being under 15 is,
⇒ P(X ≥ 4) = 1 - P(X < 4) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3))
= 1 - (0.03125 + 0.21875 + 0.42188 + 0.3125)
= 0.01562
Therefore,
The probability that at least half the patients are under 15 years old is 0.01562.
(b) To find the probability that from 2 to 5 patients are 65 years old or older,
First find the probability of each individual case and then add them up. The probability of success (visitor age being 65 or older) on a single trial is unknown.
Assume it is 0.2. Then,
⇒ P(X = 2) = 0.29376 P(X = 3)
= 0.32496 P(X = 4)
= 0.21499 P(X = 5)
= 0.08808
Therefore, the probability that from 2 to 5 patients are 65 years old or older is,
⇒ P(2 ≤ X ≤ 5) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)
= 0.29376 + 0.32496 + 0.21499 + 0.08808
= 0.92179
(c) To find the probability that from 2 to 5 patients are 45 years old or older,
We need to use a different probability of success for each individual case, depending on the age of the patients scheduled for the day.
Assume that the probability of success (visitor age being 45 or older) is 0.6. Then,
⇒ P(X = 2) = 0.2304 P(X = 3)
= 0.3456 P(X = 4)
= 0.2592 P(X = 5)
= 0.0864
Therefore, the probability that from 2 to 5 patients are 45 years old or older is,
⇒ P(2 ≤ X ≤ 5) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)
= 0.2304 + 0.3456 + 0.2592 + 0.0864
= 0.9216
(d) To find the probability that all the patients are under 25 years of age, we can assume that the probability of success (visitor age under 25) is unknown.
Assume it is 0.3. Then,
⇒ P(X = 8) = [tex]0.3^8[/tex]
= 0.00065
Therefore, the probability that all the patients are under 25 years of age 0.00065.
(e) To find the probability that all the patients are 15 years old or older, we can assume that the probability of success (visitor age being 15 or older) is unknown.
Assume it is 0.8. Then,
⇒ P(X = 8) = [tex]0.8^8[/tex]
= 0.16777
Therefore, the probability that all the patients are 15 years old or older is approximately 0.16777.
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there is a mound of g pounds of gravel in a quarry. throughout the day, 300 pounds of gravel is added to the mound. two orders of 600 pounds are sold and the gravel is removed from the mound. at the end of the day, the mound has 1400 pounds of gravel.
solve for g.
Answer:
2000 pounds
Step-by-step explanation:
Let's start with the initial amount of gravel in the mound, which is g pounds.
After 300 pounds are added, the total amount of gravel in the mound becomes:
g + 300
Then, two orders of 600 pounds are sold and removed from the mound. So, the total amount of gravel in the mound after these two orders are sold becomes:
g + 300 - 2(600) = g + 300 - 1200 = g - 900
Finally, we know that at the end of the day, the mound has 1400 pounds of gravel. So, we can set up an equation:
g - 900 + 300 = 1400
Simplifying this equation, we get:
g - 600 = 1400
Adding 600 to both sides, we get:
g = 2000
Therefore, the initial amount of gravel in the mound was 2000 pounds.
Answer:
2000 pounds
Step-by-step explanation:
sorry it took a while;)
What 3-dimensional shape is formed by this net? PLS HELP
Answer:
A triangular prism.
Step-by-step explanation:
Answer: Triangular prism
Step-by-step explanation:
A triangular prism is a three dimensional shape, consisting of two triangular and three rectangular faces. Based on the image provided, and the description of a triangular prism, we can deduct this three dimensional shape is a triangular prism.
I. The distribution is skewed left
II. The interquartile range is 6
III. The median is 22
Identify the true statement or statements.
The statement that is true about the boxplot is option (E) I, III, and IV
I. It is a left skewed distribution which has outliers.
True. The boxplot is skewed to the left, as the median line is closer to the bottom whisker than to the top whisker. Additionally, there are circles (outliers) on the left-hand side of the plot.
II. It is a symmetrical distribution which has outliers.
False. The plot is not symmetrical because the median line is not in the middle of the box.
III. The interquartile range is less than 1.
True. The box covers the range from the first quartile (Q1) to the third quartile (Q3), and the length of the box is less than 1.
IV. Approximately 75% of the observations have a GPA of less than 3.
True. The top of the box represents the 75th percentile, which is approximately 3.
Therefore, the correct option is (E) I, III, and IV
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The given question is incomplete, the complete question is:
Which statement is true about the boxplot below?
I. It is a left skewed distribution which has outliers.
II. It is a symmetrical distribution which has outliers.
III. The interquartile range is less than 1.
IV. Approximately 75% of the observations have a GPA of less than 3.
(A) I only
(B) II only
(C) II and III
(D) III and IV only
(E) I, III, and IV
7 Maryam is trying to expand and simplify (n - 2)²
Here is her working.
A
(n-2)² = (n − 2)(n-2)
= n²-2n - 2n-4
= n²-4n-4
Maryam's answer is wrong.
(a) Find Maryam's mistake.
I should be
Answer[tex]n^{2} -4n+4[/tex]
Step-by-step explanation:
had to keep the minus than add a plus sign
Suppose X is an exponential random variable with mean μ , i.e.,
X∼μExpo(1). Invert appropriate UMP tests of H0 :μ=μ0 to find (a) a 90% confidence interval for μ of the form [∗,[infinity]); (b) a 90% confidence interval for μ of the form [0,∗]
The answer of the given question based on the exponential random variable with mean i.e. [tex]\mu o \leq \bar x + \frac{z \alpha \sigma}{\sqrt{n} }[/tex].
What is Null hypothesis?The null hypothesis is statement or assumption about population parameter that is tested for its validity using statistical methods. It is statement of no effect, no difference, or no relationship between the variables of interest,
(a) To test the null hypothesis [tex]H$ o: \mu =\mu o[/tex], we can use a one-sided test with rejection region R = [tex]\bar x \geq \mu o + \frac{z \alpha \sigma}{\sqrt{n} }[/tex], is the critical value from the Standard Normal distribution that corresponds to a significance level of α = 0.10 (since we want a 90% confidence interval). If the observed sample mean falls in the rejection region R, we reject the null hypothesis and conclude that the true mean μ is greater than μ0 with 90% confidence.
To find the confidence interval of the form [∗,[infinity]), we can solve the inequality [tex]\bar x \geq \mu o + \frac{z \alpha \sigma}{\sqrt{n} }[/tex] for [tex]\mu[/tex] which gives:
[tex]\mu o \leq \bar x - \frac{z \alpha \sigma}{\sqrt{n} }[/tex]
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I do not understand this question, please help
To simplify 3(w+11) /6w, we can first simplify the numerator by distributing the 3:
3(w+11) = 3w + 33
Now we have:
(3w + 33) / 6w
We can further simplify by factoring out a 3 from the numerator:
3(w + 11) = 3 * 1(w + 11)
So we have:
(3 * 1(w + 11)) / 6w
The 3's cancel out, leaving:
(w + 11) / 2w
Therefore, the fully simplified expression is (w + 11) / 2w.
At Downtown Dogs, 10 of the last 15 customers wanted mustard on their hot dogs. What is the experimental probability that the next customer will want mustard?
The experimental probability that the next customer will want mustard on their hot dog is 2/3.
The ratio of the number of times an event has occurred to the total number of trials or observations is the experimental probability that the event will occur.
We are told that 10 out of the previous 15 customers at Downtown Dogs requested mustard on their hot dogs in this instance. Hence, the following is the experimental likelihood that a client will request mustard on their hot dog:
Number of consumers who requested mustard divided by the total number of customers is the experimental probability.
10/15 is the experimental probability.
By dividing the numerator and denominator of the fraction by 5, we may simplify it to:
2/3 is the experimental probability.
The experimental likelihood that the following consumer will request mustard on their hot dog is therefore 2/3.
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i need help asap thanks
Answer:
im sure this isnt much help but i used desmos and i got the answer 0.5 w
Step-by-step explanation:
heres what i did on the calculator. i did what the screen shows it shows an adjacent(4) and the opposite(2) so therefor i did the obvious evaluation and thought oppostie over adjacent which is tangent formula by the way. so then i did tan(2/4) and got 0.008726867791 and then did what a video that i watched to refresh myself on this topic. so the video said that after that your supposed to do tan-1(0.00872687791) and then i got 0.5... not sure if that makes sense. i typed alot so ill just link the video for you to watch.
https://youtu.be/Rbxb6DOjarI
3x+15+2x+20=180
solve for x
FOR 200 POINTSSSSSS
This figure consists of a rectangle and a quarter circle.
What is the perimeter of this figure?
Use 3.14 for π .
Enter your answer as a decimal in the box.
__ cm
the perimeter of the figure is approximately 48.56 cm.
What are the definitions of perimeter and its unit?The perimeter of a shape in geometry refers to its whole boundaries. The lengths of a shape's edges and sides are added to find its perimeter.
from the question:
The lengths of all the figure's sides must be added up in order to determine their perimeter.
The rectangle has two sides that are 10 cm long and two that are 8 cm long, making its perimeter:
P_rect = 2(10 cm) + 2(8 cm) = 36 cm
Since it shares a side with the rectangle, the quarter circle has a radius of 8 cm and an arc length that is one-fourth of the circle's diameter, which is:
L_circle = (1/4)(2πr) = (1/4)(2π)(8 cm) = 4π cm
Therefore, the perimeter of the figure is:
P = P_rect + L_circle = 36 cm + 4π cm ≈ 48.56 cm
The figure's perimeter, when rounded to two decimal places, is roughly 48.56 cm.
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Which research scenario would most likely be biased against non-voters? Select all that apply.
1. a convenience sample collected at a political rally used to determine candidate preferences
2. a volunteer sample collected at a political rally used to determine candidate preferences
3. a simple random sample of all non-voters used to determine why they don’t vote
4. a simple random sample of all eligible voters, some of whom didn’t have time to vote
5. a volunteer sample collected at large department store to determine who they voted for
Research scenariο wοuld mοst likely be biased against nοn-vοters are :
a cοnvenience sample cοllected at a pοlitical rally used tο determine candidate preferences.a vοlunteer sample cοllected at a pοlitical rally used tο determine candidate preferences.a vοlunteer sample cοllected at large department stοre tο determine whο they vοted fοr.What is Bias?Bias in research refers tο a systematic deviatiοn frοm the truth in the results οf a study, usually due tο factοrs that affect the sampling, measurement, οr analysis οf data. A research scenariο is biased against nοn-vοters if it systematically under-represents οr misrepresents the views, οpiniοns, οr behaviοrs οf peοple whο dοn't vοte in the sample οr pοpulatiοn under study.
In the given οptiοns, the scenariοs that are biased against nοn-vοters are:
a cοnvenience sample cοllected at a pοlitical rally used tο determine candidate preferences: A cοnvenience sample is a nοn-randοm sample that is cοmpοsed οf individuals whο are easily accessible οr available. A cοnvenience sample cοllected at a pοlitical rally is biased against nοn-vοters because it is likely tο οver-represent peοple whο are pοlitically active, mοtivated, and engaged, and under-represent peοple whο are apathetic, disengaged, οr unable tο attend the rally, including nοn-vοters.a vοlunteer sample cοllected at a pοlitical rally used tο determine candidate preferences: A vοlunteer sample is a nοn-randοm sample that is cοmpοsed οf individuals whο self-select οr vοlunteer tο participate in the study. A vοlunteer sample cοllected at a pοlitical rally is biased against nοn-vοters because it is likely tο οver-represent peοple whο are pοlitically active, mοtivated, and engaged, and under-represent peοple whο are apathetic, disengaged, οr unable tο attend the rally, including nοn-vοters.a vοlunteer sample cοllected at large department stοre tο determine whο they vοted fοr: This scenariο is biased against nοn-vοters fοr similar reasοns as the previοus twο scenariοs. A vοlunteer sample cοllected at a large department stοre is likely tο οver-represent peοple whο are willing tο participate in surveys, and under-represent peοple whο are nοt interested, busy, οr unable tο participate, including nοn-vοters.Therefοre, research scenariο wοuld mοst likely be biased against nοn-vοters are :
a cοnvenience sample cοllected at a pοlitical rally used tο determine candidate preferences.a vοlunteer sample cοllected at a pοlitical rally used tο determine candidate preferences.a vοlunteer sample cοllected at large department stοre tο determine whο they vοted fοr.To know more about bias visit :
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List the values for a , b , and c from the quadratic above x^2+3x-4=0
1, 3, -4
Step-by-step explanation:Second-degree functions are known as quadratics.
Quadratic Functions
Quadratic functions are second-degree. This means that the highest exponent of any term is 2. When graphed, quadratic functions form parabolas, which look like U-shape.
To find the a, b, and c values of a quadratic, the function must be set equal to zero and in standard form. Remember that standard form is when the terms are written in descending order of degree (exponent). This equation given is already set equal to zero and in standard form.
Standard Form
When in standard form, quadratics are written like ax^2+bx+c. The coefficients go in alphabetic order.
The a-value is always the coefficient of x^2The b-value is always the coefficient of xThe c-value is always the constantThis means that for the given equation: a = 1, b = 3, c = -4. These values can be used in different ways, mainly the quadratic equation.
2 Let y = 3x 2 − 4x + 2. Write y in the form a(x + b) 2 + c
The required form of a(x + b)² + c to rewrite the given expression y = 3x² − 4x + 2 is given by y = 3(x - (2/3))² + 4/3.
Expression is equal to,
y = 3x² − 4x + 2
Required form to express 'y' is equal to,
a(x + b)² + c
Complete the square by adding and subtracting the square of half the coefficient of the x-term we get,
y = 3x² - 4x + 2
⇒ y = 3(x² - (4/3)x) + 2
⇒ y = 3(x² - 2(2/3)x) + 2
⇒ y = 3(x² - (4/3)x + (2/3)² - (2/3)²) + 2
⇒ y = 3(x - (2/3))² - 3(2/3)² + 2
Simplify the constant terms we have,
⇒ y = 3(x - (2/3))² - 2/3 + 2
⇒ y = 3(x - (2/3))² + 4/3
Therefore, the expression y = 3x² − 4x + 2 written in the form a(x + b)² + c is equal to y = 3(x - (2/3))² + 4/3.
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The above question is incomplete, the complete question is :
Let the expression y = 3x² − 4x + 2. Write expression y in the form
a(x + b)² + c.
4.02 Lesson check ! (6)
The value 8 is the common difference of the given sequence.
Determining the common difference of a sequenceA sequence is a list of objects where repeats are allowed and the order is important. It includes members, much like a set. The length of the sequence is measured by the total number of elements.
Given the sequence below
12, 20, 28, 36...
The nth term of an arithmetic sequence is given as Tn = a + (n-1)d
The common difference is the difference between the preceding and the succeeding term.
First term = 12
Second term = 20
Common difference = 20 -12 = 28 - 20
Common difference = 8
Hence the common difference of the sequence is 8
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State whether the angle is an angle of elevation or an angle of depression.
The angles are classified as follows
angle 1 angle of elevation
angle 2 angle of depression
angle 3 angle of elevation
angle 4 angle of depression
What is angle of elevation?The angle of elevation is the angle between the horizontal plane and the line of sight or upward direction to an object or point that is above the observer. It is usually measured from the observer's eye to the object or point of interest, and is expressed in degrees or radians.
The angle of elevation is commonly used in trigonometry to solve problems involving right triangles and heights of objects.
The angle of depression is the angle between the horizontal plane and the line of sight or downward direction to an object or point that is below the observer. It is measured from the observer's eye to the object or point of interest, and is also expressed in degrees or radians.
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Select all the trinomials that have (3x+2) as a factor. 6x^(2)+19x+10 6x^(2)-x-2 6x^(2)+7x-3 6x^(2)-5x-6 12x^(2)-x-6
The trinomials that have (3x+2) as a factor are [tex]x^{2} 6x^2+19x+10, 6x^2-x-2\sqrt{x} \\\\[/tex] , [tex]6x^2+7x-3, 6x^2-5x-6 and 12x^2-x-6.[/tex]
A trinomial is a polynomial with three terms. Each trinomial can be written in the form ax^2+bx+c, where a, b and c are constants, and x is a variable. If a trinomial has (3x+2) as a factor, then it can be written in the form (3x+2)(ax+b). By multiplying out this expression, we can obtain the trinomial ax^2+bx+c.
To find the trinomials that have (3x+2) as a factor, we need to solve the equation ax^2+bx+c = (3x+2)(ax+b). This can be done by equating coefficients of the same powers of x. For example, equating the coefficients of x^2 gives us the equation a = 3a. Since a cannot equal both 3a and 0, we must have a = 0. Similarly, equating the coefficients of x gives us the equation b = 3b+2a, so b = -2a. Finally, equating the constants gives us the equation c = 3b+2a, so c = 2a.
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an electrician needs 2/5 rolls of electrical wire in each room in a house. How many rooms can he wire with 2 rolls of wire?
Answer:
The number of rooms he can wire with 3/4 of a roll of wire is 1/4.
What are proportions?
Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.
Given that, an electrician needs 3 rolls of electrical wire to wire each room in a house.
Let the number of rooms he can wire with 3/4 of a roll of wire be x.
Now, the proportion is
3/1 = 3/4/x
3x=3/4
x=1/4
The diameter of a circle is 24 cm. Find its area to the nearest whole number.
The area of the circle given a diameter of 24 inches is 452 square centimeters
Calculatng the area of a circle.To calculate the area of a circle with a diameter of 24cm, we first need to find the radius.
The radius is half the diameter, so it would be 12cm.
Once we have the radius, we can use the formula for the area of a circle, which is A = πr².
Substituting the value of the radius into the formula gives us:
A = π(12)² = 144π
Evaluate
A = 452cm²
Hence, the area of the circle is 144π square centimeters or 452cm²
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A group of penguins swam 4/5 mile in 1/3 hour. How many miles did the penguins swim in one hour?
A group of penguins swam 4/5 mile in 1/3 hour, [tex]\frac{4*3}{5}=\frac{12}{5}[/tex] miles did the penguins swim in one hour.
A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.
We frequently employ these fundamental mathematical operations in our daily lives: +, -,, and. We employ mathematical operations for every situation when we must determine the annual budget or distribute things equitably to a lot of people.
[tex]\frac{4}{5}[/tex] miles swim in [tex]\frac{1}{3}[/tex] hour
swim in one hour = [tex]\frac{4*3}{5}=\frac{12}{5}[/tex] mile
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(09.02 MC)
A quadrilateral PQRS is inscribed in a circle, as shown below:
A quadrilateral PQRS is inscribed in a circle. The measure of angle PQR is 85 degrees.
What is the measure of arc PQR? (1 point)
Accοrding tο the given infοrmatiοn the measure οf arc PQR is 170 degrees.
What is quadrilateral ?A quadrilateral is a fοur-sided pοlygοn, which is a twο-dimensiοnal geοmetric figure with straight sides. Quadrilaterals can have a variety οf shapes, sizes, and angles, but they all have fοur sides and fοur vertices (cοrners).
Since the quadrilateral PQRS is inscribed in a circle, we knοw that angle PQR is an inscribed angle οf arc PR. By the Inscribed Angle Theοrem, the measure οf an inscribed angle is equal tο half the measure οf its intercepted arc. Therefοre, the measure οf arc PQR is twice the measure οf angle PQR, which is:
2 * 85 = 170 degrees.
Therefοre, accοrding tο the given infοrmatiοn the measure οf arc PQR is 170 degrees.
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