Answer:
There were 333 seniors in 1990
153 seniors had jobs in 2010.
Step-by-step explanation:
Let the number of high school seniors in 1990 = x
75% of x had jobs in 1990
In 2010 there were 50 more seniors. That is, the number of seniors is x+50.
40% of (x+50) had jobs in 2010.
Total number of jobs in both years = 403.
\[0.75 * x + 0.4 * (x + 50) = 403\]
\[0.75 * x + 0.4 * x + 20 = 403\]
=> \[1.15 * x = 403 - 20\]
=> \[1.15 * x = 383\]
=> \[x = 383/1.15\]
=> \[x = 333\]
Number of seniors having job in 2010 = 0.4 * (333 + 50) = 0.4 * 383 = 153.2 = 153(approx)
24 Attitudes toward alcohol At a party there are 30 students over age 21 and 20 students under age 21. You choose at random 3 of those over 21 and separately choose at random 2 of those under 21 to interview about attitudes toward alcohol. You have given every student at the party the same chance to be interviewed.
Answer:
From the solution we come to know that every student in a party contain 10% chance of being chosen . And it is not SRS because student have been grouped into over 21 and under 21
Step-by-step explanation:
This question asks about sampling methods in statistics to determine attitudes toward alcohol at a party.
Explanation:This question is about sampling methods in statistics. The goal is to determine the attitudes toward alcohol of students at a party. To achieve this, the party attendees are divided into two groups: those over 21 and those under 21. Then, a random sample of 3 students over 21 and a random sample of 2 students under 21 are chosen to be interviewed. This method ensures that each student at the party has an equal chance of being interviewed and provides a representative sample of the party's attendees.
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Franks electric bill for the month of March was $85.78. The electric company charged a flat monthly fee of $20.00 for service plus $0.14 per kilowatt-hour of electricity used. Approximately how many kilowatt-hours of electricity did frank use in March?
Answer:
I got 469.8 kilowatt-hours. I got this by taking the total of Frank's bill, which was $85.78, and subtracting the flat monthly fee of $20.00. I did this because I need to find out the number of kilowatt-hours Frank used. Then, I divided $65.78 by $0.14 since that is the price per kilowatt-hour and got about 469.8 kilowatt-hours used by Frank.
The power utilised by frank in the month of march is 470 kilowatts - per hour.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Franks's electric bill for the month of March was $85.78. The electric company charged a flat monthly fee of $20.00 for service plus $0.14 per kilowatt-hour of electricity used.
The equation will be written as,
B = 20 + 0.14K
85.78 = 20 + 0.14k
k = ( 80.78 - 20 ) / 0.14
K = 65.78 / 0.14
K = 470 Kilowatt-hour
Therefore, the power utilised by frank in the month of march is 470 kilowatts - per hour.
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Serious answers only. Do not answer if you dont know please!How does the graph of the circle described by x^2 + (y-7)^2 = 49 change when its equation is changed to (x +5)^2 + (y-4)^2 =64. Select each correct answer. The circles radious increases, The circle moves up, The circle moves left, The circles radious decreases, The circle moves down, The circle movea right.
Answer:
The circles radious increases The circles moves left The circles moves downStep-by-step explanation:
The equation of a circle can be written as [tex](x-a)^2+(y-b)^2=r^2[/tex], where "r" is the radious, and (a,b) are the coordenates in the axis x and b respectively.Then, in the first circle the coordenates are (0,7), which means that the circle will be center there, and the radious is 7 ([tex]\sqrt{49}[/tex]).The second circle have different coordenates: (-5,4), which means that the circle has moved left (from 0 to -7 in the x axis) and down (from 7 to 4 in the y axis). Additionally, its radious has increased from 7 ([tex]\sqrt{49}[/tex], from 8 ([tex]\sqrt{64}[/tex]).See the attached figure please.Then, the correct answers are:The circles radious increases (from r=7 to r=8)The circles moves left (from x=0 to x=-5)The circles moves down (from y=7 to y=4)What property is shown in step 8?
D??
I think, because its in brackets, you multiply? not too sure though!
The monthly output P of a light bulb factory is given by the formula P = 450LK, where L is the amount invested in labor and K the amount invested in equipment (in thousands of dollars). If the company needs to produce 4,000 units per month, how should the investment be divided among labor and equipment to minimize the cost of production? The cost of production is L + K. (Round your answers to the nearest cent.)investment in labor _______ $investment in equipment ________$
Answer:
C(p) = 4,96 (in thousands of dollars)
l = 2980 $ invest in labor
k = 2980 $ invest in equipment
Step-by-step explanation:
Information we have:
Monthly output P = 450*l*k ⇒ k = P/450*l
But the production need to be 4000
Then k = 4000/450*l
Cost of production = l * k (in thousands of dollars)
C(l) = l + 4000/450*l
Taking derivatives (both members of the equation)
C´(l) = 1 - 400 /45*l² ⇒ C´(l) = 0 ⇒ 1 - 400/45l² = 0
45*l² - 400 = 0 ⇒ l² = 400/45
l = 2.98 (in thousands of dollars)
l = 2980 $ And
k = 400/45*l ⇒ k 400/45*2.98
k = 2.98 (in thousands of dollars)
C(p) = l + k
C(p) = 2980 + 2980
C(p) = 5960 $
If 40% of a number is 32, what is 25% of that number?
Answer:
I think that the answer is 24
Answer:
The number is 80. 25% of that number is = 20.
Step-by-step explanation:
A warehouse employs 21 workers on first shift, 15 workers on second shift, and 13 workers on third shift. Eight workers are chosen at random to be interviewed about the work environment. Find the probability of choosing exactly two second shift workers and two third shift workers.
Answer: Our required probability is 0.11.
Step-by-step explanation:
Since we have given that
Number of workers in first shift = 21
Number of workers in second shift = 15
Number of workers in third shift = 13
We need to find the probability of choosing exactly two second shift workers and two third shift workers.
So, it becomes,
[tex]\dfrac{^{15}C_2\times ^{13}C_2\times ^{21}C_4}{^{49}C_8}\\\\=0.11[/tex]
Hence, our required probability is 0.11.
The probability question asks to determine the chance of choosing two second shift and two third shift workers from a warehouse workforce. Combinations are used to calculate the number of ways to select the workers, and the probability is found by dividing the desired combination by the total number of ways to choose eight workers.
Explanation:The question involves calculating the probability of choosing a specific combination of warehouse workers from different shifts for interviews. There are a total of 49 workers (21 first shift, 15 second shift, and 13 third shift). To find the probability of choosing exactly two second shift workers and two third shift workers, we need to consider the total number of ways to choose eight workers and the number of ways to choose two workers from each of the specified shifts.
The probability of selecting exactly two second shift workers is calculated as the combination of 2 from 15, and the probability of selecting exactly two third shift workers is the combination of 2 from 13. Since we're choosing 8 workers in total, we also have to choose the remaining 4 workers from the first shift, which can be done in combinations of 4 from 21. The probability is then calculated by dividing these combinations by the total number of ways 8 workers can be chosen from all 49 workers.
To calculate the combinations, we use the combination formula C(n, k) = n! / (k!(n-k)!). Then the overall probability is a fraction where the numerator is the product of the combinations for each selection and the denominator is the combination of 8 from 49.
A stockbroker trades shares she does not own with an obligation of later repayment, and in the hope that the price of traded shares will fall. She then repays share debt with shares purchased at a lower price and pockets the spread between initial share price and repayment price. This attempt to profit from a falling stock price is known as ___________.
Answer:
short selling
Step-by-step explanation:
Short-selling is a process when a shareholder buys shares and sold them instantly and expecting that he or she will be able to have them at cheaper price later on .After then seller transfer them to lender from where he/she borrow the stock and after keep the difference as a income.
Short selling is a simple idea in which a shareholder borrow a stock, sells the stock to other person, then again buys that stock to give it back to a lender. Short sellers believe that the stock they have sell is going to fall in value
A hovercraft takes off from a platform. Its height (in meters), xxx seconds after takeoff, is modeled by h(x)=-(x-11)(x+3)h(x)=−(x−11)(x+3)h, left parenthesis, x, right parenthesis, equals, minus, left parenthesis, x, minus, 11, right parenthesis, left parenthesis, x, plus, 3, right parenthesis How many seconds after takeoff will the hovercraft land on the ground?
Answer:
After 11 seconds the hovercraft will land on ground
Step-by-step explanation:
Given function that shows the height of a hovercraft,
[tex]h(x) = -(x-11)(x+3)[/tex]
Where,
x = number of second.
When the hovercraft land the ground,
[tex]h(x) = 0[/tex]
[tex]-(x-11)(x+3)=0[/tex]
[tex]\implies (x-11)(x+3)=0[/tex]
By zero product property,
x - 11 = 0 or x + 3 = 0
⇒ x = 11 or x = -3 ( not possible ),
Hence, after 11 seconds the hovercraft will land on ground.
at the time I am writing this the other answer only has a 3.2 rating, but I can vouch that the answer is still correct: 11 seconds !
A potato chip manufacturer has found that in the past the standard deviation of bag weight has been 0.2 ounce. They want to test whether the standard deviation has changed. What is the null hypothesis?
Answer:
Null Hypothesis: [tex]\sigma=0.2[/tex]
Alternative hypothesis: [tex]\sigma \neq 0.2[/tex] (Changes on the deviation)
Step-by-step explanation:
s represent the sample standard deviation
[tex]\sigma[/tex] represent the population standard deviation (variable of interest)
[tex]\sigma_o =0.2[/tex] represent the value that we want to test
n represent the sample size
A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".
The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".
The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".
Based on this the system of hypothesis should be:
Null Hypothesis: [tex]\sigma=0.2[/tex]
Alternative hypothesis: [tex]\sigma \neq 0.2[/tex] (Changes on the deviation)
In order to test these system of hypothesis we need to select a significance level [tex]\alpha[/tex], then we need to calculate an statistic given by this formula.
[tex]\chi^2 =\frac{(n-1)s^2}{\sigma^2_o}[/tex]
Then we need to calculate the degrees of freedom for the statistic on this case
[tex]df=n-1[/tex]
And after this we need to calculate the pvalue based on the significance, the alternative hypothesis and the statistic calculated.
If the [tex]p_v <\alpha[/tex] we reject the null hypothesis
If the [tex]p_v >\alpha[/tex] we FAIL reject the null hypothesis
A bag of M&Ms was randomly selected from the grocery store shelf, and the color counts were:
Brown 22
Red 22
Yellow 22
Orange 12
Green 15
Blue 15
Find the 95% confidence interval for the proportion of yellow M&Ms in that bag
Answer: 95% confidence interval for the proportion of yellow is (0.125,0.275).
Step-by-step explanation:
Since we have given that
n = 22+22+22+12+15+15=108
x = yellow = 22
So, [tex]\hat{p}=\dfrac{22}{108}=0.20[/tex]
We need to find the 95% confidence interval.
So, z = 1.96
So, Interval would be
[tex]\hat{p}\pm z\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\\\\=0.20\pm 1.96\times \sqrt{\dfrac{0.2\times 0.8}{108}}\\\\=0.20\pm 0.075\\\\=(0.20-0.075, 0.20+0.075)\\\\=(0.125, 0.275)[/tex]
Hence, 95% confidence interval for the proportion of yellow is (0.125,0.275).
Based on counting the number of galaxies in a small patch of the sky and multiplying by the number of such patches needed to cover the entire sky, the total number of galaxies in the observable universe is estimated to be approximately
A) 100 million.
B) 100 billion.
C) 1 billion.
D) 1 trillion.
E) 10 billion.
Answer:
100 billion
Step-by-step explanation:
Some astronauts reveals that there are 100 billion galaxies in the universe.
Is it possible for two numbers to have a difference of 6
Answer:
yes
Step-by-step explanation:
For example, 8 and 2.
8 - 2 = 6.
6 is the difference
The radius of a circle is increased from 8.008.00 to 8.038.03 m. Estimate the resulting change in area, and then express the estimate as a percentage of the circle's original area. The estimated change in area is nothing msquared2.
Answer:
Step-by-step explanation:
The area of a circle is expressed as
Area = πr^2
Where r = radius of the circle
π = constant = 3.14
The radius of a circle is increased from 8.00800 to 8.03803 m. This means that the original radius of the circle is 8.00800 and the new radius of the circle is 8.03803
Area of original circle =
3.14 × 8.00800^2 = 201.36212096
Area of new circle =
3.14 × 8.03803^2 = 202.87516852203
Increase in area = 202.87516852203 - 201.36212096
= 1.51304756203
Expressing the change as a percentage, it becomes
1.51304756203/201.36212096 ×100
Percentage change = 0.75 %
An exam consists of 47 multiple-choice questions. Each question has a choice of five answers, only one of which is correct. For each correct answer, a candidate gets 1 mark, and no penalty is applied for getting an incorrect answer. A particular candidate answers each question purely by guess-work. Using Normal approximation to Binomial distribution with continuity correction, what is the estimated probability this student obtains a score greater than or equal to 10?
Calculate the mean and standard deviation for the binomial distribution, adjust for continuity correction, find the z-score, and use the standard normal distribution to estimate the probability of scoring at least 10 correct out of 47 purely guessed multiple-choice questions.
Explanation:To estimate the probability of a student guessing and scoring at least 10 correct answers out of 47 multiple-choice questions using normal approximation to binomial distribution, we start by finding the mean ( extmu) and standard deviation ( extsigma) of the binomial distribution. Since each question has five options, the probability of guessing a question correctly (p) is 1/5, and the probability of guessing incorrectly (q) is 4/5.
The expected number of correct answers (mean) is extmu = np = 47(1/5) = 9.4, and the variance ( extsigma^2) is npq = 47(1/5)(4/5) = 7.52. So, the standard deviation is extsigma = extsqrt{7.52}.
To apply the continuity correction, we adjust the score of 10 down by 0.5, giving us a z-score. The z-score is calculated by (X - extmu)/ extsigma, where X is the adjusted score. Finally, we use the standard normal distribution to find the probability associated with this z-score, which will yield the likelihood of the student scoring at least 10 correct answers.
Jayne stopped to get gas before going on a road trip. The tank already had 4 gallons of gas in it. Write an equation relates the total amount of gasoline in the tank
Answer: y = x + 4
Step-by-step explanation:
Let "y" be the total number of gallons in the tank, and let "x" be the total number of unfilled gasoline.
Since we already have an initial "4 gallons" in the tank, the total capacity of the tank will be "x + 4".
Answer:
A y=4+x
Step-by-step explanation:
Trixie has 3/4 packages on marigold seeds he plants 1/6 of those seeds in this garden and divides the rest equally into 10 fraction packages of seed is planted in each flower pot
Answer:
[tex]\frac{7}{120}[/tex] of seed planted in each flower pot.
Step-by-step explanation:
Given:
Total number of marigold seeds packages Trixie have= ¾
Number of seeds Trixie planted in the garden= 1/6
Number of fraction into which Trixie dived the remaining seed =10
To Find:
Fraction of seed planted in each flower pot=?
Solution:
Seed left after planting 1/6 of seeds in the garden = [tex]\frac{3}{4}-\frac{1}{6}[/tex]
=>[tex]\frac{18-4}{24}[/tex]
=>[tex]\frac{14}{24}[/tex]
=>[tex]\frac{7}{12}[/tex]
Now Trixie divides these remaining seeds into 10 parts
=>[tex]\frac{\frac{7}{12} }{10}[/tex]
=>[tex]\frac{7}{12}\times\frac{1}{10}[/tex]
=>[tex]\frac{7}{120}[/tex]
Please Help
What is the solution for x in the equation?
9 − 10x = 2x + 1 − 8x
Answer:
x=2
Step-by-step explanation:
9-10x=2x+1-8x
9-10x=1-6x
8=4x
x=2
Combine like terms in the equation 9 − 10x = 2x + 1 − 8x to simplify it to 9 − 10x = −6x + 1. Rearranging the equation to -4x = -8 and dividing by -4, we find that x = 2.
Explanation:The solution for x in the equation 9 − 10x = 2x + 1 − 8x can be found by first combining like terms on both sides of the equation.
On both the left and right side, the terms involving x are −10x and 2x − 8x respectively. After combining, the equation simplifies to 9 − 10x = −6x + 1.
Then, we can solve for x by shifting terms around. Getting all x-terms on one side and constant terms on the other side, we get -10x + 6x = 1 - 9. This simplifies to -4x = -8.
Finally, dividing the equation by -4 which is the coefficient of x, we obtain the solution x = 2.
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Consider the following problem: A farmer with 850 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the four pens?
Answer:
18,062.5 square feet
Step-by-step explanation:
The largest area will be obtained when half the fence is used in each of the orthogonal directions. That is, the pen will have two parallel sides that total 425 feet, and 5 parallel sides and partitions that total 425 feet.
The long sides are 212.5 feet, and the short sides are 85 feet, so the overall area is ...
(212.5 ft)(85 ft) = 18,062.5 ft²
__
Working Out
Suppose the long side is length x. Then the lengths of the 2 ends and 3 dividers are ...
short side = (850 -2x)/5
Then the overall area is the product of long side and short side:
A = x(850 -2x)/5 = (2/5)(x)(425 -x)
This equation is that of a parabola that opens downward. Its vertex (maximum) is at the value of x halfway between the zeros of 0 and 425. That is, area is a maximum when x=212.5.
That maximum area is ...
A = (2/5)(212.5)(425 -212.5) = 18,062.5 . . . square feet
v11.1% complete This is a Single Choice Question; skip ahead to question content A B C D E Confirm The label on a ceiling lighting fixture warns you to use a lightbulb of 60 watts or less. The voltage to the lightbulb is 120 volts. An intern calculated how much amperage a bulb of the maximum allowed wattage will draw. You are checking her work, shown below. If there is an error, what is the first step that has an error, and why is it an error? Step 1 volts × amps = watts write down formula Step 2 120 × ? = 60 fill in what is known Step 3 It looks like 0.5 will work 120 × 0.5 = 60 check Step 4 amps = 0.5 Step 1, because the formula should be amps = watts ÷ volts. Step 2, because the question mark should be by itself on the right side of the equation. Step 3, because you can’t just guess at a solution. Step 4, because the answer in the previous step was 60. There is no error. Report Content Errors © 2019 by ACT, Inc. All rights reserved. Terms of UsePrivacy PolicyContact Support
Answer:
There is no error
Step-by-step explanation:
While it is not necessary to guess an answer, because the answer can be calculated using the properties of equality, guessing is a legitimate solution method actually taught in (some) schools these days.*
The equation is properly written, data properly filled in, and the solution properly verified. There is no error.
_____
* What doesn't seem to be taught in US schools are methods of refining an incorrect guess. These are actually well-developed, and are legitimate ways to get to a good answer.
Final answer:
The correct formula to find the current is I = P ÷ V, which gives 0.5 amps for a 60W lightbulb at 120V. The error in the calculation is in Step 1 where the formula was not rearranged to solve for current.
Explanation:
The calculation for determining the current drawn by a 60-watt (W) lightbulb with a voltage supply of 120 volts (V) requires use of the power formula, which relates power (P), voltage (V), and current (I): P = V × I, where P stands for power in watts, V for voltage in volts, and I for current in amperes (amps).
In this scenario, the correct step to find the amperage of the bulb would be to rearrange the power formula to solve for current (I): I = P ÷ V. By inserting the known values, we get I = 60 W ÷ 120 V, which simplifies to I = 0.5 amps.
The error in the intern's calculation is in Step 1, as the formula written should be amps = watts ÷ volts, not volts × amps = watts as it needs to be rearranged to solve for the unknown current.
find the quotient following this pattern
image attached
Answer:
x⁵ +x⁴ +x³ +x² +x +1
Step-by-step explanation:
Your expression matches the pattern with n=6, so fill in that value of n in the quotient the pattern shows:
[tex]\dfrac{x^6-1}{x-1}=x^5+x^4+x^3+x^2+x+1[/tex]
At a restaurant you order a lunch that costs $6.50 and a beverage that costs $1.50.You leave a 20% tip and the sales tax is 7%.What is the cost of the meal
Answer:8.45
Step-by-step explanation:
$12,400 is invested, part at 6% and the rest at 5%. If the interest earned from the amount invested at 6% exceeds the interest earned from the amount invested at 5% by $577.00, how much is invested at each rate? (Round to two decimal places if necessary.) Define variables x and y and set up a system of two linear equations that represents the information given in the problem.
Answer: $10881.81 is invested at 6% and $1518.18 is invested at 5%.
Step-by-step explanation:
Since we have given that
Amount invested = $12400
Rate of interest for first part = 6%
Rate of interest for second part = 5%
Let the amount invested for 6% be 'x'.
Let the amount invested for 5% be 'y'
According to question, we get that
[tex]0.06x-0.05y=577\\\\x+y=12400\\\\\implies x=12400-y[/tex]
So, it becomes,
[tex]0.06(12400-y)-0.05y=577\\\\744-0.06y-0.05y=577\\\\-0.11y=577-744\\\\-0.11y=-167\\\\y=\dfrac{167}{0.11}\\\\y=1518.18[/tex]
x=12400-y=12400-1518.18=$10881.81
Hence, $10881.81 is invested at 6% and $1518.18 is invested at 5%.
The value of a car is 18,500. It loses 10.3% of its value every year. Find the approximate monthly decrease in value. Round your answer to the nearest tenth
Final answer:
The value of a car worth $18,500 that loses 10.3% annually decreases by approximately $158.8 per month.
Explanation:
To find the approximate monthly decrease in value of a car worth $18,500 that loses 10.3% of its value every year, we first calculate the annual decrease and then divide by 12 to get the monthly decrease.
The annual decrease is calculated as 10.3% of $18,500, which is:
0.103 imes $18,500 = $1,905.50 per year.
To find the monthly decrease, we divide the annual decrease by 12:
$1,905.50 \/ 12 \\approx $158.79 per month.
Therefore, the car's value decreases approximately $158.8 per month.
Geoffrey has 30 problems to do for math homework he finished 60 percent of them before play practice how many problems did Geoffrey finish before play practice
Answer:
18 answers
Step-by-step explanation:
1) 30 of 60%
2)30*.6
3)18
check:
18/30=0.6
0.6=60%
Step-by-step explanation:
30=100%
? =60
=18 problems
You are given a choice of taking the simple interest on $10,000 invested for 2 years at a rate of 3% or the interest on $100,000 invested for 2 years at an interest rate of 3% compounded daily (use the Banker's rule ).
Which investment earns the greater amount of interest?
Give the difference between the amounts of interest earned by the two investments.
Answer:
Compount interest earns more. Difference between 2 interest is $92 445.39
Step-by-step explanation:
Simple Interest:
[tex]I = \frac{prt}{100} [/tex]
p = $10000
r = 3%
t = 2years
I = (10000×3×2)/100
= $600
Total amount = $10 600
Compound Interest:
[tex]A = p( {1 + \frac{r}{100}) }^{n} [/tex]
p = $100000
r = 3/730 (daily)
t = 730 (2yrs)
A = 100000[1+(3/73000)]^730
= $103 045.39 (2d.p)
Difference = $103045.39 -
$10600
= $92 445.39
(Correct me if i am wrong)
A rectangular parking lot has a perimeter of 384 meters. The length of the parking lot is 36 meters less than the width. Find the length and the width.
Answer:
The length and width of the parking lot is 78 meters and 114 meters respectively.
Step-by-step explanation:
Given;
Perimeter of the parking lot = [tex]384\ m[/tex]
Solution,
Let the width of the parking lot be x.
Then, according to question length = (x-36).
The perimeter of a rectangle is sum of all the sides of rectangle. Which is given by an expression;
[tex]perimeter=2\times(length+width)[/tex]
Now substituting the values, we get;
[tex]384=2\times(x-36+x)\\\frac{384}{2}=(2x-36)\\192=2x-36\\192+36=2x\\2x=228\\x=\frac{228}{2}= 114[/tex]
Width = [tex]114\ m[/tex]
Length = [tex]x-36=114-36=78\ m[/tex]
Hence the length and width of the parking lot is 78 meters and 114 meters respectively.
Please help me!! Due today
Answer:
Step-by-step explanation:
y = (-1/4)x - 4 has a y-intercept of (0, -4). Place a dark dot at (0, -4).
Now we use the info from the slope, -1/4:
Starting with your pencil point on the dot (0, -4), move the pencil point 4 units to the right and then 1 unit down. You will now be at (4, -5). Place a dark dot there.
Then draw a straight, solid line through (0, -4) and (4, -5).
Write a quadratic function in vertex form whose graph has the vertex (-2,-4 ) and passes through the point (-1,-6)
Answer:
[tex]y = (-2)(x + 2)^2 - 4[/tex].
Step-by-step explanation:
The vertex form of a quadratic function is in the form
[tex]y = a (x - h)^2 + k[/tex],
where
[tex]a[/tex] is a coefficient that needs to be found, and [tex](h, k)[/tex] is the vertex of this function.In this question, the vertex of this quadratic function is at the point [tex](-2, -4)[/tex]. In other words, [tex]h = (-2)[/tex] and [tex]k = (-4)[/tex]. Substitute these value into the general equation:
[tex]y = a (x - (-2))^2 +(- 4)[/tex].
Simplify to obtain:
[tex]y = a (x + 2)^2 - 4[/tex].
The only missing piece here is the coefficient [tex]a[/tex]. That's likely why the problem gave [tex](-1, -6)[/tex], yet another point on this quadratic function. If this function indeed contains the point [tex](-1, -6)[/tex], [tex]y[/tex] should be equal to [tex](-6)[/tex] when [tex]x = (-1)[/tex]. That is:
[tex]-6 = a(-1 + 2)^2 -4[/tex].
Solve this equation for [tex]a[/tex]:
[tex]a = -6 - (-4) = -2[/tex].
Hence the equation of the quadratic function in its vertex form:
[tex]y = (-2)(x + 2)^2 - 4[/tex].
The quadratic function in vertex form that the student is looking for is f(x) = -2(x+2)² - 4. We obtained this by substituting the given vertex (-2, -4) and the point (-1, -6) into the general form of a vertex form quadratic function.
Explanation:The question is asking us to find the equation of a quadratic function, also known as a second-order polynomial, in vertex form. The vertex form of a quadratic function can be written as f(x) = a(x-h)² + k, where (h, k) is the vertex and 'a' is a non-zero number.
The vertex is given as (-2, -4). Therefore, h = -2 and k = -4. The equation becomes f(x) = a(x+2)² - 4. We also know that the graph passes through the point (-1, -6), which we can substitute into the equation to get: -6 = a(-1 + 2)² - 4. We solve this equation for 'a', and find that a = -2. Therefore, the quadratic function in vertex form is f(x) = -2(x+2)² - 4.
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The Quadratic Formula 7:Solving Quadratic Equations
laro
The Quadratic Formula
Text
Guided Practice
Use the quadratic formula to solve the equation. If necessary, round answers to the nearest hundredth.
8x2-3x - 7=0
A. 1.12, -0.74
B. 1.14,-0.77
C. -1.14,0.77
Answer:
B. 1.14, -0.77
Step-by-step explanation:
As you know the quadratic formula gives you the solution to
ax² + bx + c = 0
as ...
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Here, we have a=8, b=-3, c=-7, so the formula tells us the solution is ...
[tex]x=\dfrac{-(-3)\pm\sqrt{(-3)^2-4(8)(-7)}}{2(8)}=\dfrac{3\pm\sqrt{233}}{16}\\\\x\approx \{-0.7665,1.1415\} \qquad\text{matches choice B}[/tex]
Answer:
1.14, –0.77
Step-by-step explanation:
I got it right in grandpoint.