If for example, you were given y = 2(x-3)^2 + 5, then the vertex is (3,5)
As another example, the equation y = 7(x+1)^2 + 10 has the vertex (-1,10)
The general vertex form is y = a(x-h)^2 + k with the vertex (h,k)
Answer:
(-h,k)
Step-by-step explanation:
vertex form:
y＝a(x-h)^2+k
switch sign of h and you get the x
keep sign of k and you get y
ex- 3(x-5)+7
vertex＝（5,7）
When draining her hot tub, the height of the water in Brittany’s hot tub decreases at a rate of 2 inches per minute. After 9 minutes there are 11 inches of water in the tub. Assume that the height is decreasing at a constant rate.
a. Write an equation for the height of water left in the tub (h) as a function of the number of the minutes (t) that have elapsed.
b. What values of the domain, t, make sense? Why?
c. What values of the range, h, make sense? Why?
Step-by-step explanation:
a.
Let's give the starting amount of water as s. Every minute, 2 inches of water are lost, meaning that given the starting amount, s, we subtract 2 inches from s every minute, so s - 2 every minute = height of water left, so s - 2t (t representing minutes) = h
To figure out s, we simply plug our known value -- 9 minutes in and 11 inches left. s - 2(9) = 11, s-18=11, s= 29
29 - 2t = h
b. We know that we cannot have negative minutes, so the minimum amount of time that makes sense is 0. To figure out the maximum, we stop counting how much time has occurred when there is no water left, so we have to figure out when h = 0
29-2t = h = 0
t=14.5
Therefore, anything between 0 and 14.5 minutes makes sense
c. Anything between 0 and 29 makes sense because the height of water cannot be negative and we cannot get higher than the starting amount
WILL GIVE BRAINLIEST
4
3
2x + 4
x+7
Answer:
x = 8
Step-by-step explanation:
[tex]\frac{x+7}{3} =\frac{2x+4}{4}[/tex]
do cross multiplication
[tex]3(2x+4) = 4(x+7)\\6x + 12 = 4x + 28\\6x - 4x = 12 - 16\\2x = 16\\x = 16/2\\x = 8[/tex]
(05.01 MC) choose the systems of equations which matches the following graph
Answer:
a
Step-by-step explanation:
x+2y=-10
-x -x
2y=-10-x
y=(1/2)x-5
This is one of the lines and reduces the options to a or c.
3x-y=12
-3x -3x
-y=12-3x
y=3x-12
This is the line with the positive slope and since both lines match, the answer is a.
What’s the value of X????
seven more than the quotient of a number and 2 is equal to 3 equation
Answer:
Step-by-step explanation:
seven more than the quotient of a number and 2 is 10
7+n/2=10 n=6 check 7+3=10 ok
Need help quick! Will give brainliest
Assume that Y is normally distributed with mean μ and standard deviation σ. After observing a value of Y, a mathematician will construct a rectangle with length L = |Y|and width W = 3 |Y|. Let A denote the area of the resulting rectangle. What is E(A)?
A driver works 40 hours a week for the first two months on the job. How much more per week does the driver make after 28 days?
Answer:
is there something missing in this question. i cant understand
Step-by-step explanation:
please tell me if there is more to this
12(5x+10x^2)=480+60x
(^ = exponents)(show work)
x=−2 is the aswer to this problem i was wrong before
Given the equation Y-4=3/4(x+8) in point-slope form, identify the equation of the same line in standard form
Answer:
3x-4y=-40
Step-by-step explanation:
Hi there!
We're given the equation of the line, y-4=3/4(x+8) in point-slope form (y-[tex]y_{1}[/tex]=m(x-[tex]x_{1}[/tex]), where ([tex]x_{1}[/tex],[tex]y_{1}[/tex]) is a point and m is the slope)
We need to convert y-4=3/4(x+8) into standard form (ax+by=c, where a, b, and c are integer coefficients; a CANNOT be 0, and CANNOT be negative).
So we need to get y-4=3/4(x+8) out of point-slope form
We can do this by converting the equation into slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept
to do this, we need to isolate y by itself in the equation
first, do the distributive property and distribute 3/4 on the right side
y-4=3/4x+6
add 4 to both sides
y=3/4x+10
now the equation is in slope-intercept form, but remember, we want it in standard form
x and y are on the same side in standard form, so let's subtract 3/4 x from both sides
-3/4x+y=10
however we aren't done; in standard form, the coefficients need to be integers (whole numbers), and a (the coefficient in front of x) CANNOT be negative
so let's multiply both sides by -4 to clear the fraction and change the sign of a
-4(-3/4x+y)=-4(10)
do the distributive property
3x-4y=-40
Hope this helps! :)
NEED HELP ASAP!!! please!!
Is the graph of the function shown in the graph below one-to-one? why?
The midterm grades for two high school algebra classes are provided in the tables below. For convenience, the data have been ordered.
Class 1: 72 73 74 75 76 79 82 83 84 86 91
92 93 93 94 95 97 97 98 98
Class 2: 59 65 68 69 72 73 78 80 82 82
83 83 85 88 88 89 94 96 97 98
A. Sketch parallel boxplots for the two classes.
B. Which class has the better overall performance? Justify your answer.
C. The teacher for the two classes calculates a 90% confidence interval for the difference in mean midterm grades between Class #1 and Class #2. The confidence interval is (0.09299, 11.413). Assume that confidence interval conditions are met. Based on the confidence interval, do you think there is a difference in the population mean midterm grades for the two classes? Explain.
Answer:
Following are the responses to the given question:
Step-by-step explanation:
For point a:
In R-Studio, we first insert the data set,
Please notice that perhaps the blue colored lines are input and the green lines are R-Studio results.
[tex]Class \ 1 = c(72,73,74,75,76,79,82,83,84,86,91,92,93,93,94,95,95,97,98,98)\\\\Class\ 2 = c(59,65,68,68,69,72,73,78,80,82,82,83,83,85,88,88,89,94,96,97,98)[/tex]
We will get the smallest observation, first, mid, third, and largest quartile for both classes and use a summary of 5 numbers,
[tex]\to five\ num(Class\ 1) \\\\\[1\] \ 72.0 77.5 88.5 94.5 98.0 \\\\\to five\ num(Class\ 2) \\\\\[1\]\ 59 72 82 88 98[/tex]
The table can be defined as follows:
[tex]Class\ 1\ \ \ \ \ \ \ \ \ \ \ \ Class\ 2 \\[/tex]
[tex]Smallest \ value\ \ \ \ \ \ \ 72\ \ \ \ \ \ \ 59\\First \ quartile \ Q1\ \ \ \ \ \ \ 77.5\ \ \ \ \ \ \ 72\\Median\ Q2 \ \ \ \ \ \ \ 88.5\ \ \ \ \ \ \ 82\\Third \ quartile \ Q3 \ \ \ \ \ \ \ 94.5\ \ \ \ \ \ \ 88\\Largest \ value \ \ \ \ \ \ \ 98\ \ \ \ \ \ \ 98\\[/tex]
The parallel boxplots in R-Studio as,
[tex]\text{boxplot(Class1, Class2, xlab = "Class", ylab = "midterm grades", main = "Boxplots")}[/tex]Please find the graph file.
For point b:
Its performance overall of Class 1 is better, while the median of class 1 is greater than class 2, as well as the value (grades) of class 1, is less dispersed in relation to class 2.
For point c:
The stated 90 percent confidence interval for a significant difference is (0.09299, 11.413) Users now calculate the difference among Class 1 and Class 2 plan presented of mean value as:
[tex]mean \ (Class \ 1) \\\\\[1\]\ 86.5\\\\mean\ (Class\ 2)\\\\[/tex]
[tex]\[ 1 \] \ 80.80952\\\\Difference = 86.5 - 80.80952 = 5.69048[/tex]
Its discrepancy among two estimations is between confidence interval of 90 percent (0.09299, 11.413). Its mean population of grades of two classes therefore differs significantly.
Actividad N°2: Marque la alternativa correcta en la siguiente pregunta.
Sea una función tal que () = 7 − 3 cuyo dominio es el conjunto () =
{−1, 0, 1, 2, 3}, entonces el () es:
5 PUNTOS
A) () = {−2, 1, 4, 7, 10}
B) () = {−1, 0, 1, 2, 3}
C) () = {4, 7, 10, 13, 16}
D) () = {1, 2, 3, 4, 5}
E) () = {−16, −13, −10, −7, −4}
Answer:
Hola busco amigos
Perdí mi otra cuenta
Ayúdame y te ayudo con tus tareas
¿ si?
Step-by-step explanation:
Assume X is normally distributed with a mean of 5 and a standard deviation of 2. Determine the value for x that solves each of the following.
a. P(X > x) = 0.5
b. P(X > x) = 0.95
c. P(x < X < 9) = 0.2
d. P(3 < X < x) = 0.95
e. P(-x < X - 5 < x) =0.99
Answer:
U = 5
S = 4
1.) P(X>x) = 0.5
Prob = 1-0.5 = 0.5
We have z = 0, that is the z score with the probability of 0.5
X = u + z(s)
= 5+0*4
= 5
2.) 1-0.95 = 0.05
Z score having this probability
Z = -1.64
X = 5-1.64*4
= 5-6.56
= -1.56
3.) P(z<1.0) - p(X<x) = 0.2
0.841345-0.2 = .641345
We find the z score given this probability
Z= 0.36
X = 5+0.36*4
= 5+1.44
= 6.44
4.) P(X<x)-P(Z<-.5)
0.95 = p(X<x)-0.308538
p(X<x) = 0.308538 + 0.95
= 1.258538
There is no x value here, given that the probability is more than 1.
5. 1-0.99/2 = 0.005
We get the z score value
= -2.58
U - 5 = 5-5 = 0
-x = 0-2.58(4)
X = 10.32
this distance-time graph represents a journey made by Jo
a) At 10 minutes the line is at y - 1, which means she reached 1 km in 10 minutes.
b) The last 30 minutes would be 30 minutes to 60 minutes.
at 30 minutes she was at 0km at 60 minutes she was at 4 km, so in 30 minutes she traveled 4 km. 30 minutes is a half hour, so multiply distance by 2: 4 x 2 = 8, she was traveling at 8 km per hour.
The following data represent the number of loaves of bread, in thousands, which were sold by various grocery stores in the month of June. Construct a dot plot for the given data.
4, 8, 11, 10, 10, 4, 5, 13,
6, 13, 8, 14, 8, 1, 10, 9
Select any value to see the controls for increasing or decreasing the frequency.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Answer:
Following are the solution to these question:
Step-by-step explanation:
The frequency of the data value will be the same in dot plots for the number of dots. The frequency table is following:
[tex]X \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Frequency \\\\1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1\\\\2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0\\\\3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0\\\\4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2\\\\5\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1\\\\6\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1\\\\7\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0\\\\8\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3\\\\9\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1\\\\10\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3\\\\11\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1\\\\[/tex]
[tex]12\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0\\\\13\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2\\\\14\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1\\\\[/tex]
Why is it useful to factor out the GCF first when factoring?
Answer:
Because it makes factoring easier because the coefficient are smaller requiring less step
NO LINKS NO FILES. Write the next two integers: -48, -24, -12, _, _
Answer:
-6,-3
hope this helps
have a good day :)
Step-by-step explanation:
An angle measures 104° more than the measure of its supplementary angle. What is the measure of each angle?
___° and ___°
thank you <3 best answer will get brainliest.
Mark Brainliest please
Answer:
38 degrees
Step-by-step explanation:
Let the angle be x
Supplement:: 180-x
Equation:
x = 180-x + 104
2x = 284
x = 142 degrees
therefore , 180-x = 180-142= 38 degrees
Which pair of expressions below are equivalent?
a. 7(2n) and 9
b. 3n + 5n and 15n
c. 4(2n-6) and 8n - 24
d. 7(2n) and 72n
Answer:
The answer is C
Hope this helped!
Balu had a collection of coins1/2 of the coins were from Asian countries,1/3
of them from European countries and the remaining 36 from America.
How many coins were from ASIAN countries?
A)18
B)30
C)108
D)216 step by step explanation please
Step-by-step explanation:
[tex] \frac{1}{2} = asian \\ \frac{1}{3} = european \\ 36 = american \\ \frac{1}{2} + \frac{1}{3} = \frac{3 + 2}{6} = \frac{5}{6} \\ \frac{6}{6} - \frac{5}{6} = \frac{1}{6} = 36 \\ \frac{1}{6} = 36 \: so \\ \frac{6}{6} =6 \times 36 = 216 \\ \frac{1}{2} \times 216 = asian \\ \frac{1}{2} \times 216 = 108asian \\ please \: mark \: brainliest[/tex]
There are total 108 coins belonging to Asian countries.
What is equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, Balu had a collection of coins 1/2 of the coins were from Asian countries, 1/3 of them from European countries and the remaining 36 from America.
Let the total number of coins be x,
Establishing the equation, we get,
x/3+x/2+36 = x
Multiplying the equation by 6, we get,
2x+3x+216 = 6x
6x-5x = 216
x = 216
Therefore, the total numbers of coins are 216,
Since, there are 1/2 of total coins are Asian coins,
Therefore, number of Asian coins = 216 / 2 = 108
Hence, There are total 108 coins belonging to Asian countries.
For more references on equations, click;
https://brainly.com/question/29657983
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170 lbs to kg round to nearest tenth
Three airlines serve a small town in Ohio. Airline A has 48% of all scheduled flights, airline B has 26% and airline C has the remaining 26%. Their on-time rates are 81%, 61%, and 40%, respectively. A flight just left on-time. What is the probability that it was a flight of airline A?
Answer:
0.5969 = 59.69% probability that it was a flight of airline A
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Left on time.
Event B: From airline A.
Probability of a flight leaving on time:
81% of 48%(airline A).
61% of 26%(airline B)
40% of 26%(airline C). So
[tex]P(A) = 0.81*0.48 + 0.61*0.26 + 0.40*0.26 = 0.6514[/tex]
Probability of leaving on time and being from airline A:
81% of 48%. So
[tex]P(A \cap B) = 0.81*0.48 = 0.3888[/tex]
What is the probability that it was a flight of airline A?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.3888}{0.6514} = 0.5969[/tex]
0.5969 = 59.69% probability that it was a flight of airline A
What’s the answer?!!
Answer:
6x+10mm=p is the answer
brainlest plz
What is the gradient of the blue line
Answer:
Up 2 to the right 1
Step-by-step explanation:
that would be i think
Laura, David, and Carlos served a total of 115 orders Monday at the school cafeteria. David served 3 times as many orders as Carlos. Laura served 10 more orders than Carlos. How many orders did they each serve?
Answer:
Step-by-step explanation: ts 6 11 19 56
Laura, David, and Carlos served a total of 115 orders
David served 3 times as many orders as Carlos. David = 3x
Laura served 10 more orders than Carlos. let Carlos = x
How many orders did they each serve? Laura = x + 10
Carlos + David + Laura = 115
x + 3x + x+10 = 115
5x + 10 = 115
5x = 115 - 10
5x = 105
x = 21 Carlos
63 Davide
31 Laura
add then up 115 Total
ABCD is a quadrilateral such that the measures of three of its interior angles are given as B=122 degrees, C= 75 degrees, D= 51 degrees, find m=A
please help me with explanation
Answer:
angle A is 112 degree.
Step-by-step explanation:
quadilateral have 4 angles .
sum of the interior angles of a quadilateral is 360 degree
Here,
angle A = be x
angle B = 122
angle C = 75
angle D = 51
Now,
angle A + angle B + angle C + angle D =360 degree
x + 122 + 75 + 51 = 360
x + 248 = 360
x = 360 - 248
x = 112
A children's inflatable pool takes 17 minutes to fill with an electric air pump. It takes 53 minutes to let the air out of the pool. If the pool's vale is accidentally left open, how long will ot take to fill the pool?
Answer:
less than 17 minutes
Step-by-step explanation:
Classify each angle of the degrees
Answer:
acute
right angle or obtuse
obtuse
Step-by-step explanation:
those are the answers
pls help me out in this assignment PLSSSSS anyone plss
Answer:
what number?
number three or number two
