Answers
Answer: The maximum value is -3.75
Note: -3.75 = -15/4
=============================================================
Explanation:
The given quadratic is in the form y = ax^2 + bx + c, where,
a = -1b = 1c = -4We'll plug the values of 'a' and b into the formula below
h = -b/(2a)
h = -1/(2(-1))
h = 1/2
h = 0.5
This represents the x coordinate of the vertex. Recall the vertex is (h,k).
Plug this x value into the function to find its corresponding y coordinate
y = -x^2 + x - 4
y = -(0.5)^2 + 0.5 - 4
y = -3.75
The vertex is located at (0.5, -3.75)
Since a < 0, this means the parabola opens downward and that the vertex is the highest point on the parabola. Therefore, the largest y can get is y = -3.75 which we consider the maximum.
The graph visually helps confirm this (see image attachment).
Side note: -3.75 = -15/4
-------------------
Here's another way we can find the vertex (h,k). We'll complete the square to get the function into vertex form
y = -x^2 + x - 4
y + 4 = -x^2 + x
y + 4 = -(x^2 - x)
y + 4 = -(x^2 - x + 0)
y + 4 = -(x^2 - x + 0.25 - 0.25) .... see note below
y + 4 = -(x^2 - x + 0.25) -(-0.25)
y + 4 = -(x^2 - x + 0.25) + 0.25
y + 4 = -(x - 0.5)^2 + 0.25
y = -(x - 0.5)^2 + 0.25 - 4
y = -(x - 0.5)^2 - 3.75
This is in the form y = a(x-h)^2 + k where (h,k) = (0.5, -3.75).
Note: The x coefficient is -1 which cuts in half to -0.5, then that squares to 0.25
Related Questions
Cooper invested $3,100 in an account paying an interest rate of 2%
compounded quarterly. Robert invested $3,100 in an account paying an
interest rate of 3 % compounded continuously.After 12 years, how much
more money would Robert have in his account than Cooper, to the nearest
dollar?
Answers
Answer:
Robert will have $481 more in his account than Cooper.
Step-by-step explanation:
Compound interest:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
Continuous compounding:
Similar to compound interest:
[tex]A(t) = P(1 + r)^t[/tex]
Cooper:
Cooper invested $3,100 in an account paying an interest rate of 2% compounded quarterly. This means that [tex]P = 3100, r = 0.02, n = 4[/tex]
After 12 years is A(12). So
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A(12) = 3100(1 + \frac{0.02}{4})^{4*12}[/tex]
[tex]A(12) = 3938.5[/tex]
Cooper will have $3938.5 in his account.
Robert:
Robert invested $3,100 in an account paying an interest rate of 3 % compounded continuously. So [tex]P = 3100, r = 0.03[/tex].
After 12 years.
[tex]A(t) = P(1 + r)^t[/tex]
[tex]A(12) = 3100(1 + 0.03)^{12}[/tex]
[tex]A(12) = 4419.9[/tex]
Robert will have $4419.9 in his account.
How much more money would Robert have in his account than Cooper, to the nearest dollar?
4419.9 - 3938.5 = 481.4
To the nearest dollar, Robert will have $481 more in his account than Cooper.
Find the missing side. Round to the nearest tenth
Answers
Answer:
x = 12.5
Step-by-step explanation:
From the diagram,
Applying
tanФ = Opposite/Adjacent...................... Equation 1
From the diagram,
Given: Opposite = 16, Adjacent = x, Ф = 52°
Substitute these values into equation 1
tan52° = 16/x
make x the subject of the equation
x = 16/tan52°
x = 16/1.27994
x = 12.5.
if the digit in one’s place of a number is 2 then the last digit of its cube will be?
Answers
Answer:
Thus , if the digit in one's place of a number is 2, then the last digit of its cube will be unit digit of . Since the last digit of cube of 2 is 8. Hence, if the digit in one's place of a number is 2, then the last digit of its cube will be 8
Step-by-step explanation:
The difference between an observational study and an experiment is that
Answers
Answer:
An observational study is a study based on data while as an experiment, your actually using that data and carrying out different procedures with it.
Answer:
in an observational study, the researchers do not control treatment, and in an experiment, they do (B)
Step-by-step explanation:
15-2X = -45 how do I show My work for this?
Answers
Answer:15-2x=-45
15-2=13
13=-45
Step-by-step explanation:
I hope that helps you!
Answer:
x = 30
Step-by-step explanation:
15 - 2x = -45
+ 2x to both sides
15 = 2x - 45
+ 45 to both sides
60 = 2x
divide both sides by two
x = 30
At 7 p.m the temperature was 15 F in the next 2 hours, the temperature fell 15F
Select all true statement based on the the above information.
A. The temperature was 30 F at 9 pm
B.The temperature was 0 F at 9 pm
C. The change in temperature from 7 PM to 9 PM is represented by -15
D. The change in temperature from 7 PM to 9 PM is represented by 15.
E. The expression 15+( -15) represents the temperature change
F. The expression 15+15 represents the temperature change
Answers
Answer:
The answer is 0
Step-by-step explanation:
Because if the tempurature was 15 and it dropped 15 = 0°
Factor this trinomial. Your answer should consist of two binomials.
n^2-11n +28
Answers
Answer:
(n-4)(n-7)
Step-by-step explanation:
hopefully that helps
Give an example of tangents in the real world that have not been presented in this lesson.
Explain how you know the tangent and the radius in your example are perpendicular.
This is in relation to tangent lines and not cosine, sine, etc!
My example is attached via photo!
Answers
Answer:
Hey! Sorry im too late lol but here-
Step-by-step explanation:
Example of tangent in the real world-
When a stone gets tied at one end of a string & the other end is rotated, then the stone will form a circle.
How you know the tangent and radius are perpendicular:
The radius is formed vertically and is completely straight, while the tangent is completely straight but horizontal. You can draw a right triangle angle between the radius and tangent line by adding a third line, and a right angle is 90 degrees. So, this forms a perpendicular line.
Hope this helped :))
Part A: The path of the ball in relation to the curved path of the thrower
Part A: The path the ball takes is perpendicular to the hand, bat or feet at the point of last contact
Reason for the selection:
Part A
A real world example of tangents is the direction of a ball immediately it is released and the circular path of the motion, that provides the force input that is given to the ball to cause it to move in the required direction
The tangent is the path the ball takes immediately it is moving without contact to the bat, hand or feet that causes it to move
The circular path is the motion of the hand, leg, bat or feet that makes before the ball is released
The radius is the hand, leg, or bat that rotates in a circular path, so as to move the ball
Part B
How the radius is perpendicular to the tangent
The radius, such as the leg kicking a ball is perpendicular to the tangent of the which is the path of the ball because a kick to send the ball into air, the orientation of leg at the point the ball leaves is perpendicular to the angle of elevation with which the ball is launched
Learn more about tangents here:
https://brainly.com/question/16300584
Figure abc is a triangle with a base of 22 inches if abc is dilated by a scale factor of 0.5 what will be the base of the figure
Answers
Answer:
11
Step-by-step explanation:
Scale factor 0.5 means 1/2
so multiply base length with scale factor
22×0.5 = 11
Vector V has components of (6,9) determine the angle in degrees that vector vee makes with the X axis
Answers
Given :
Vector V has components of (6,9).
To Find :
The angle in degrees that vector V makes with the x-axis.
Solution :
The x-component of vector is, x = 6 units.
The y-component of vector is, y = 9 units.
So, the angle the vector makes from the horizon is :
[tex]\theta = tan^{-1}{\dfrac{y}{x}}\\\\\theta = tan^{-1}{\dfrac{9}{6}}\\\\\theta = 56.31^o[/tex]
Hence, this is the required solution.
Find the volume of cylinder
Answers
Answer:
1539.4 rounded
Step-by-step explanation:
Have a great day
Given
A ∆GHJ with k
GH
L on GI
are K and L the midpoints of GH and GJ respectively?
is KL || HJ?
is HJ = 2KL?
Answers
Answer:
Is there diagram for this?
The following list shows three factors that can either increase or decrease the probability of a Type II error. The sample size is increased. The significance level is increased. The standard error is increased. Which factors alone will cause the probability of a Type II error to increase?
Answers
Answer:
Standard Error is increased.
Step-by-step explanation:
Type 2 error is failure to reject a false null hypothesis. This is a 'false negative' result of hypothesis testing, represented by beta 'β'.
Power of test is 1 - β, which shows probability of accurately stating a null hypothesis false, when it is actually false.
Increased sample size increases the power of test accuracy, hence reduces type 2 error. Increased level of significance implies higher probability of rejecting a true null hypothesis, ie type 1 (false positive) error. So, it decreases type 2 error.
Standard Error increase implies lower level of t statistic , ie = (x - u) / (s / √ n) Lower the t value, higher is the probability of not rejecting null hypothesis, which implies higher chance of type 2 error.
Type II error is 1 - power of the test. The factor that can alone make the type II error to increase is: Option C: The standard error is increased.
What is Type I and Type II error?
Firstly the whole story starts from hypotheses. The null hypothesis is tried to reject and we try to accept the alternate hypothesis.
The type 1 error occurs if we get false positive conclusion (false positive means we accuse null hypothesis being wrong when it was actually correct).The type 2 error occurs if we get false negative conclusion (false negative means we accept null hypothesis when it was actually false). It is 1 - statistical power of the test. Thus, increasing power of the test decreases this error.How are the type I error and type II error are related to level of significance?The probability of committing the type I error is called the significance level of the hypothesis test.
And the more we increase the level of significance, the less area the test statistic gets to fall in, and its chances of falling in region outside level of significance increases, which makes us to reject the null hypothesis more probable, thus, decreasing its chance of tagging as negative, not mattering if true or false.
Thus, increasing level of significance increases the type I error but decreases the type II error.
If it is increases, the likely area for test statistic falling increases, thus, increasing probability of tagging the null hypothesis tagging to be true, so increasing result of test being declared negative, thus, increasing type II error.
How is type II error and sample size related?Increasing sample size increases statistical power, thus, decreasing the type II error.
Thus, for the given case, as the sampling size is increased, the type II error will decrease, as the significance level is increased, the type II error will decrease, and as the standard error is increased, the type II error will increase with it.
Thus, out of the given factors, only the last factor (increasing the standard error) makes the type II error to get increased.
Thus, the factor that can alone make the type II error to increase is: Option C: The standard error is increased.
Learn more about type II error here:
https://brainly.com/question/26067196
what is the volume of the rectangular prism? will give brainliest
Answers
Answer:
30
Step-by-step explanation:
Well if it is 2 blocks wide, you just count the cubes, but if you cant see the blocks behind, then just and the block you see with 2.
my guess
Brainlest? please?
Find the length of the missing side.
14.5 m
7.3 m
X
Answers
Answer:
x= 12.528
*rounded is 12.53 or 12.5
Step-by-step explanation:
7.3 ^2 + x^2 = 14.5^2
53.29 + x^2 = 210.25
-53.29 -53.29
x^2= 156.96
x= 12.528
elementary math! please help Mark brainlist
Answers
Answer: 1 minute and 43 seconds faster
Step-by-step explanation:
Answer:
1 minute and 43 seconds faster
Step-by-step explanation:
Trent grew 12 plants with 4 seed packets. With 5 seed packets.
how many plants can he grow?
Answers
The results of a survey of 38 students and the foreign language they are studying are shown in the two-way frequency table. Language Gender Chinese French Spanish Total Girl 4 7 10 21 Boy 1 1 15 17 Total 5 8 25 38 What fraction of the surveyed students are taking Chinese? of the surveyed students are taking Chinese.
Answers
Answer:
5/38
Step-by-step explanation:
A fraction is a quantity that is not a whole number. In maths, a fraction usually has a numerator and a denominator.
The numerator is the number above. While the denominator is the number below
an example of a fraction = [tex]\frac{4}{5}[/tex]
4 is the numerator while 5 is the denominator
fraction of the surveyed students are taking Chinese = total number of students surveyed / total number of students surveyed
5/38
50 POINTS!!!!
Analyze the graph of the cube root function shown
on the right to determine the transformations of the
parent function. Then, determine the values of a, h,
and k in the general equation.
y = a3x - h + k
h =
k=
Answers
Answer:
Let's solve for h.
y=a3x−h+k
Step 1: Flip the equation.
a3x−h+k=y
Step 2: Add -a^3x to both sides.
a3x−h+k+−a3x=y+−a3x
−h+k=−a3x+y
Step 3: Add -k to both sides.
−h+k+−k=−a3x+y+−k
−h=−a3x−k+y
Step 4: Divide both sides by -1.
−h
−1
=
−a3x−k+y
−1
h=a3x+k−y
Answer:
h=a3x+k−y
Let's solve for k.
y=a3x−h+k
Step 1: Flip the equation.
a3x−h+k=y
Step 2: Add -a^3x to both sides.
a3x−h+k+−a3x=y+−a3x
−h+k=−a3x+y
Step 3: Add h to both sides.
−h+k+h=−a3x+y+h
k=−a^3x+h+y
Answer:
k=−a^3x+h+y
Step-by-step explanation:
The required values are h = 1 and k = 4 the given cube root function.
What is the cube root function?The cube root function is a function that takes the cube root of its input. The formula for the cube root function is:
f(x) = ∛x
The graph is given in the question, as shown.
To find the symmetric center of the cube root function, we need to find the point on the function that is equidistant from the two opposite sides of the function graph.
Since the given cube root function is an odd function, it is symmetric about the point (1, 4).
So, the symmetric center of the cube root function is the point (1, 4).
Thus, h = 1 and k = 4
Therefore, the required values are h = 1 and k = 4 the given cube root function.
Learn more about the cube root function here:
https://brainly.com/question/29082141
#SPJ2
The complete question would be as:
Heather had 20 stickers. She bought 27 stickers from a store in the mall and got 6 stickers for her birthday. Then Heather gave 4 of the stickers to her sister and used 11 to decorate a greeting card. How many stickers does Heather have left?
Answers
Answer:
38 stickers
Step-by-step explanation:
20+27=47
47+6=53
53-4=49
49-11=38
20+27+6-(4+11)=38 stickers
The hypotenuse of a right triangle will be a diameter of the triangle. True or false?
Answers
Solve for h.
h − 999 = –341
Answers
Answer:
Step-by-step explanation:
=> h=-341+999
=> h= 658
Make me the brainliest pls :))
Kelly purchased 9 planters for a total of $63. She wants purchase another 20 planters at the same unit price.
How much will 20 planters cost?
Answers
140 :D
Explanation
PLEASE HELP!Write the standard form of equation with p=sqrt3, 0=150°
Answers
Answer:
I heard it's not b
Step-by-step explanation:
was A the correct answer?
A pound of chocolate costs 8 dollars. Kala buys p pounds. Write an equation to represent the total cost c that Kala pays.
Answers
Answer:
8p=c
Step-by-step explanation:
For questions like this, it isn't asking for a numerical answer or anything complicated. It's mainly just using common sense and figuring out what you would do if you had actual numbers instead of variables. You would multiply the amount of pounds (p) by the cost per pound of $8, and that would be your answer (c). I hope I could help.
The whole number between -1 and 1, with the symbol 0. Show’s that there is no amount:
Answers
Answer:
The number between -1 and 1 is 0 ( zero)
Choose the best answer to complete the sentence.
If a point lies on the angle bisector of an angle, then it is
[Select)
from the two sides of the angle.
B
Answers
Answer:
Equidistant
Step-by-step explanation:
When we have a point lying on the angle bisector, it stands at an equal distance from the two sides of the angle
The purpose of the angle bisector is to divide the angle into two different equal parts
So, for a point to lie on this, it means it of the same distance from the two points of the angle
9 gal and 1 pt - 2pt
Answers
please complete the question so we can help you out!! :)
Directions: Use the information given to write the equation of the circle in standard form.
16. center:(-10,-4), point on circle: (4, -2) 17. center: (-9, -3), point on circle: (-11, 2) 18. center: (5.-7), point on circle: (-3,-1)
19. center: (8,2), point on circle: (14,-1) WO
Answers
Answer:
subject?
Step-by-step explanation:
Are the two triangles similar? Explain your answer.
Answers
Answer:
Yeah they similar
Step-by-step explanation:
Answer:
Yes.
Step-by-step explanation:
These triangles are both obtuse with a 102 degree angle, 30 degree angle, and a 48 degree angle. (180 - 48 = 30.)