Answer:
the vertex of a quadratic equation:
a*x^2 + b*x + c = y
Is located at:
x = -b/2a.
In this case, x = -2
Then:
-b/2a = -2.
And we also have that:
a*(-2)^2 + b*-2 + c = 3
Then we have two equations:
-b/2a = -2
a*(-2)^2 + b*-2 + c = 3
We have only 2 equations and 3 variables, so we can just give the variable c different values and we will find different quadratic equations that are not equivalent.
Let's begin with c = 0, our equations are:
-b/2a = -2
a*(-2)^2 + b*-2 + 0 = 3
In the first equation we can isolate b and get:
b = 4*a
Now we can replace this in the other equation and solve this for a.
a*4 + 4*a*-2 = 3
-4*a = 3
a = -3/4
then:
b = 4*a = 4*-3/4 = -3
The first quadratic equation is:
(-3/4)*x^2 - 3*x = y.
Now, to find the second let's use a different value of c.
c = 1
b = 4*a
a*(-2)^2 + b*-2 + 1 = 3
Let's solve in the same way as before:
a*4 + (4*a)*-2 + 1 = 3
-4*a = 2
a = 2/-4 = -1/2
b = 4*-1/2 = -2.
Then our equation is:
(-1/2)*x^2 - 2*x + 1 = y
For the last equation, let's use c = 2.
then our equations are:
b = 4*a
a*(-2)^2 + b*-2 + 2 = 3
Same as before, replace the first equation in the second.
a*4 + (4*a)*-2 + 2 = 3
-4*a + 2 = 3
-4*a = 1
a = -1/4
Then:
b = 4*(-1/4) = -1
Our third equation is:
(-1/4)*x^2 - 1*x + 2 = y
Now, below you can see all of them graphed.
Where red is the first one, blue the second and green the third one. (and as you can see, all of them share the vertex (-2,3) )
In the diagram below, m/AGF = 62° and m/DGB = 32°. Find m/CGE.
Step
1
2
try
Angle
m/AGF = 62°
m/DGB = 32°
m/
B
D.
O
Select a Reason
32°
G
62°
Reason
Given
Given
A
Step-by-step explanation:
per the laws of intersecting lines the angles on one side of any of the lines must be the same as the angles on the other side of that line - just left-right mirrored.
for that reason, CGE = DGF.
also to remember : the sum of all angles around a point on one side of a line is always 180° (because they represent a half-circle with that point being the center). in other words, these angles are supplementary (together 180°).
therefore,
180 = 62 + 32 + DGF
DGF = CGE = 180 - 62 - 32 = 86°
what are some issues you must consider when choosing the appropriate number of treatment conditions for your experiment? what does it mean to have conditions that are proportional to each other?
When selecting the appropriate number of treatment conditions, it is essential to consider factors such as resources, research complexity, and confounding variables.
Having conditions that are proportional to each other means that the level or intensity of each condition varies in direct proportion to the others, such that if one condition is increased or decreased, the others are also adjusted in a corresponding manner.
When choosing the appropriate number of treatment conditions for an experiment, there are several issues to consider. One of these is the ability to distinguish differences between treatment conditions.
A suitable number of treatment conditions for an experiment should be able to identify important differences between them. If there are too few treatment conditions, differences may not be identified, while if there are too many treatment conditions, resources may be wasted, making it difficult to obtain meaningful results.Another factor to consider is the need for replicability. The more treatment conditions that are used, the more difficult it is to replicate the experiment. A suitable number of treatment conditions should allow for replicability, meaning that the experiment can be repeated with similar results.To have proportional treatment conditions means that the levels of the independent variable (the treatment) are proportionate. This means that the differences between the levels of the independent variable are proportional to each other. This is important because it ensures that the treatment conditions are balanced and that the results obtained are valid. If the levels of the independent variable are not proportional, it can be difficult to interpret the results and draw conclusions.Having conditions that are proportional to each other means that the differences between treatment conditions are consistent across all levels of the independent variable. In other words, if the independent variable increases by a certain amount, the difference between the treatment conditions remains constant. This can be important for ensuring that the treatment effects are interpretable and generalizable to other populations.
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Jaylen's soccer practice started at 8:50 A.M. on Saturday morning. The team practiced dribbling for 20 minutes and practiced shooting for 20 minutes. Then they played a scrimmage game for 50 minutes before practice ended. What time was it when Jaylen's soccer practice ended?
Include A.M. or P.M. in your answer (for example, 11:58 A.M.).
Answer:
it is 10:00 a.m very simple
Answer:
The answer is 10:20 AM
Step-by-step explanation:
First off, add 20 to 8:50. Get 9:10. Add 20 more, get 9:30. Add 50, and get 10:20.
APML - ATAQ. Solve for x and QR
HELP ASAP!!!!! PLZZZZZ
Answer:
x = 7
Step-by-step explanation:
(7x-9)(2x+2) = 35/14
98x - 126 = 70x + 70
28x = 196
x = 7
Find the area of the shaded Sector
A. 8pi
B. 6pi
C. 16pi
D. 4pi
Answer:
4pi
Step-by-step expla
because its pi is the circumference so its times 4
Solve for x
will give brainliest and 5.0 star
Answer:
x = 10
Step-by-step explanation:
1. Because this is a right angle (an angle with 90°), 54 + 3x + 6 = 90.
2. (Solving equation above)
Step 1: Simplify both sides of the equation.
\((3x)+(54+6)=90\) \(3x + 60 = 90\)Step 2: Subtract 60 from both sides.
\(3x + 60 - 60 = 90 - 60\) \(3x = 30\)Step 3: Divide both sides by 3.
\(\frac{3x}{3} =\frac{30}{3}\) \(x = 10\)Step 4: Check if solution is correct.
\(54 + 3(10)+6=90\) \(54+30+6=90\) \(84+6=90\) \(90=90\)Therefore, x = 10.
Of the range, the interquartile range, and the variance, the interquartile range is least influenced by an outlying value in the data set.
Is that true or false? please explane
The statement "the interquartile range is least influenced by an outlying value in the data set" is true.
The range is simply the difference between the maximum and minimum values in a data set.
The variance is a measure of the spread of a data set, and is calculated by finding the average of the squared differences between each data point and the mean of the data set.
The interquartile range, on the other hand, is a measure of the spread of the middle 50% of the data set. It is calculated by finding the difference between the upper quartile and the lower quartile.
Because the interquartile range only takes into account the middle 50% of the data, it is less influenced by outliers than the range and variance. This is because outliers can greatly impact the range and variance, but have little effect on the interquartile range.
In conclusion, the interquartile range is a more robust measure of spread for a data set, as it is less influenced by outliers.
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PLEASE HELP BEEN STUCK ON THIS
Answer: infinitely many solutions
Step-by-step explanation:
The system is only 1 line. So it must be that there are 2 equations that are actually the same so they intersect infinitely many times.
A new health drink has 140% of the recommended daily allowance (RDA) for a certain vitamin. The RDA for this vitamin is 40mg. How many milligrams of the vitamin are in the drink?
The drink contains 56mg of the vitamin while RDA is only 40mg.
What is milligram?The SI unit of mass, the kilogramme, is 1000,000,000 times larger than the milligramme (mg), which is a unit of mass. Using a lowercase m and lowercase g, a milligramme is abbreviated as mg.
There are 1000 milligrammes in a gramme, hence the use of the prefix milli to denote the thousandth.
There are 10-6 kilogrammes in a milligramme. When describing drug doses, milligrammes are frequently used.
We have to count 140% of the RDA to find the how much vitamins its contains.
Here, RDA = 40mg
140% × 40
140/100 × 40
1.4 × 40
56mg
Thus, the drink contains 56mg of the vitamin while RDA is only 40mg.
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In a state's Pick 3 lottery game, you pay $1.23 to select a sequence of three digits (from 0 to 9), such as 199. If you select the same sequence of three digits that are drawn, you win and collect $320.68.
a. How many different selections are possible?
b. What is the probability of winning? (Type an integer or a decimal.)
c. If you win, what is your net profit? (Type an integer or a decimal.)
d. Find the expected value. (Round to the nearest hundredth as needed.)
a. There are 720 different selections possible in the Pick 3 lottery game.
b. The probability of winning is approximately 0.14%.
c. If you win, your net profit would be $319.45.
d. Therefore, the expected value is -$0.21, which means that on average, you can expect to lose $0.21 per ticket.
a. In a Pick 3 lottery game, there are 10 digits (0-9) and you are selecting a sequence of three digits. Therefore, the total number of different selections possible can be calculated using the formula for permutations, which is:
10P₃ = 10!/7! = 10 x 9 x 8 = 720
b. The probability of winning is the number of winning outcomes divided by the total number of possible outcomes. Since there is only one winning sequence of three digits, the probability of winning is:
1/720 = 0.0014
c. If you win, your net profit would be the prize amount ($320.68) minus the cost of the ticket ($1.23), which is:
$320.68 - $1.23 = $319.45
d. The expected value is the sum of the products of each outcome and its probability. In this case, the expected value can be calculated as:
(1/720) x ($320.68) + (719/720) x (-$1.23) = -$0.21
This negative expected value indicates that the lottery is not a good investment as the cost of playing exceeds the expected payout.
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Write this number in standard form: eight thousand seventy-two and eighty-four thousandths.
Answer:
8,072.084
Step-by-step explanation:
what is the GCF sum of 6+18
Answer:
GCF = 6; sum = 6(1 +3)
Step-by-step explanation:
You want the greatest common factor of 6 and 18.
GCFThe greatest common factor is the largest factor common to both numbers. Here, we can factor the numbers as ...
6 = 6·1
18 = 6·3
The factor 6 is common to both numbers. (Other numbers, such as 1, 2, and 3 are also common factors, but 6 is the largest.)
The GCF is 6.
In terms of the GCF, the sum can be written ...
6 +18 = 6(1 +3)
__
Additional comment
If the smaller number is not a factor of the larger, then the next value to check is the difference between the larger and smaller.
Euclid's algorithm tells you the remainder from division of the larger by the smaller will be zero when the divisor is the GCF. Otherwise, the remainder can be used to replace the larger number for trying again.
Here, 18/6 = 3 r 0, so 6 is the GCF.
Solve:3m-2(m-3)=1 please help
Answer:
\(3m - 2(m - 3) = 1 \\ 3m - 2m - 6 = 1 \\ m - 6 = 1 \\ m = 1 + 6 \\ m = 7\)
PLEASE MARK ME BRAINLIESTAnswer:
m = -5
Step-by-step explanation:
3m-2(m-3)=1
Distribute
3m -2m +6 = 1
Combine like terms
m+6 =1
Subtract 6 from each side
m+6-6 =1-6
m = -5
University Data
Receiving
Not Receiving
Total
Financial Aid
Financial Aid
Undergraduates
4222
3898
8120
Graduates
1879
731
2610
Total
6101
4629
10730
If a student is selected at random, what is the
probability that the student is a graduate
(rounded to the nearest percent)? [ ? ]%
Answer:
\( \) \( \) \( \) \( \)
find the expression for g(x)
Hello,
\(f(x) = 4 {x}^{2} - 9\)
\(g(x) = 4 {x}^{2} - 9 + 8 = 4 {x}^{2} - 1\)
Sarah is 13 years older than Mike. The sum of their ages is 37. How old is Sarah and how old is Mike? Enter your answer as on ordered pair (x,y).
Answer:
(24,13)
Step-by-step explanation:
24 is Sarah's age.
13 is Mike's age.
System:
\(\left \{24+13=37\)
I hope this helped!
4. In the Janet's neighborhood, 65% of
households have a landline phone. If there are 80
households in the neighborhood, then how many
have a landline phone?
Answer:
52
Step-by-step explanation:
i just looked up 65% of 80
Which expression is represented on this number line?
Answer:
where's the number line??
11 POINTS
What are the coordinates of T’, the image of point T(2, 4) translated 2 units to the right and 3 units down? T(2, 4) ⇒ T' ( , )
Answer:
(4,1)
Step-by-step explanation:
Answer:
The answer is (4,1)
Step-by-step explanation:
I can confirm cause I took the test :)
f(x) = x - 2
Find f(3)
train leaves in 12 minutes and you are 1 mile from the station. you can walk 4 mph and run at 8 mph. how much time can you afford to walk before you must being to run in order to catch the train
Answer:
i think its 8
Step-by-step explanation:
answer this for me also right answer gets a heart
answer:
3x^3=4x
step-by-step explanation:
hope that helps!
Find 6x + y when x = 6 and y = 4
we have the following:
\(6x+y\)replacing, y =4 and x = 6
\(6\cdot6+4=36+4=40\)the answer is 40
Which expression results from using the Distributive Property of Multiplication over Addition to simplify
4.7(-8.9+2.6)?
a. 4.7(11.5)
b. 4.7(-8.9) + 2.6
c. 4.7(-8.9)+4.7(2.6)
d. 4.7(-6.3)
If (u, v) = 3 and (v, w)2, what is the value of (v,w, + 3u)? Select one: a.02 b.There is no way to tell. c.11 d.7 e.9
Given that (u, v) = 3 and (v, w) = 2.To find the value of (v, w, + 3u), let's substitute the given values.
(v, w, + 3u) = (2, ?, + 3(3))(v, w, + 3u) = (2, ?, 9)(u, v) = 3, and (v, w) = 2∴ The value of (v, w, + 3u) = (2, ?, 9)Option E, 9 is the correct answer.Considering that (u, v) = 3 and (v, w) = 2.Substituting the provided numbers will allow us to determine the value of (v, w, + 3u).(v, w, + 3u) = (2, ?, + 3(3))(v, w, + 3u) = (2, ?, 9)(V, W) = 2, and (U, V) = 3. (V, W, + 3U) has the value (2,?, 9)The right response is option E, number 9.
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The value of expression (v, w, + 3u) is 11, so correct option is C.
Given that (u, v) = 3 and (v, w) = 2.
To find: The value of (v, w, + 3u)
This formula shows how multiplication distributes over addition. It means that when you multiply a number by the sum of two other numbers, it is the same as multiplying the number individually by each of the two numbers and then adding the products together.
We have to apply the formula of distributivity of multiplication over addition:
(a + b) c = ac + bc
We know that 3u = u + u + u,
so substituting in (v, w, + 3u),
we get(v, w, + 3u) = (v, w) + (u + u + u)
Now, substituting the given values of (u, v) = 3 and (v, w) = 2
in the above equation(v, w, + 3u) = (2) + (3 + 3 + 3) = 2 + 9 = 11
Therefore, the value of (v, w, + 3u) is 11.
Hence, the correct option is (c) 11.
NOTE: We should always remember the formula of distributivity of multiplication over addition: (a + b) c = ac + bc.
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Eating Together. In December of 2001, 38% of adults with children under the age of 18 reported
that their family ate dinner together seven nights a week. In a recent poll, 403 of 1122 adults
with children under the age of 18 reported that their family ate dinner together seven nights a
week. Has the proportion of families with children under the age of 18 who age dinner together
seven nights a week decreased? To answer this question, conduct a hypothesis test using the
a = 0. 05 level of significance. Round values for the sample proportion and p-value to three
decimal places
Fewer families with kids under 18 now have dinner together seven nights a week
Given,
Let p represent the percentage of households with kids under 18 that have supper together every night.
So, Null Hypothesis, : p 38% (meaning that more or the same number of families with children under the age of 18 now have dinner together seven nights a week.)
Alternate Hypothesis, : p < 38% {means that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has decreased}
The test statistics that will be used here is One-sample z-test for proportions;
T.S. = ~ N(0,1)
Where,
p = sample proportion of families = 403/1122 = 0.36
n = sample of adults with children under the age of 18 = 1122
So,
The test statistics = -1.32
The value of z-statistics is -1.32.
Also, the P-value of the test statistics is given by;
P-value = P(Z < -1.32) = 1 - P(Z 1.32)
= 1 - 0.9066 = 0.0934
We have enough data to reject our null hypothesis since the test statistics will fall in the rejection region because the P-value for our test statistics is less than the level of significance, which in this case is 0.0934 < 0.10.
As a result, we draw the conclusion that fewer families with children under the age of 18 now have supper together seven nights a week.
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Mairead jogs 2,700 feet, while Paula jogs 0.5 mile. Who jogs farther, and by how many feet?
Please help, I have to be done with this in 2 days so if anybody could help it would be very nice.
Answer:
Paula jogs more by 0.1113636 miles or 600 feet.
Step-by-step explanation:
formula for feet to miles; 5280 / f.
2700 / 5280 = 0.5113636363636
0.113636363636 x 5280 = 600 feet.
Factor the expression
Answer:
(2x+1)(x−2)(2x−5)
Step-by-step explanation:
(3x−6)(4x2−1)−(2x−4)(4x2+4x+1)
4x3−16x2+11x+10
=(2x+1)(x−2)(2x−5)
Solve for X please help
Answer:
x=−5.675726
Step-by-step explanation:
madison estimated that there were 918 jelly beans in a jar. the actual number of jelly beans was 850. what was the percent error of masdion estimate
The percent error of masdion estimate is 8%.
As we know that some degree of error is often associated with measurements. Percent error is used to determine how close the value is to the accepted answer.
We know,
\(\frac{Error}{actual value} = \frac{Percent}{100}\) equation 1
Total number of jelly beans in a jar estimated by madison = 918
The actual number of jelly beans = 850
Error = Estimated jelly beans - Actual number of jelly beans
Error = 918 - 850
Error = 68
Substitute value of error and actual value in equation 1 , we will get
( 68 / 850 ) = ( percent error / 100 )
0.08 × 100 = percent error
percent error = 8 %
Thus, 8% was the percent error of masdion estimate.
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