Find the coordinates of the vertex of the following parabola using graphing technology. Write your answer as an (x, y) point.
y= -x^2-10x-22
Answers
Answer:
vertex: (-5, 3)
Step-by-step explanation:
Besides providing the graph of the given quadratic equation, I will also demonstrate the algebraic method of solving for the vertex of a parabola.
Method 1: Algebraic SolutionGiven the quadratic equation, y = -x² - 10x - 22, where:
a = -1, b = -10, and c = -22.
Find the x-coordinate of the vertex:In order to find the vertex of the given equation, use the following formula to find the x-coordinate of the vertex: [tex]x = \frac{-b}{2a}[/tex].
[tex]x = \frac{-b}{2a}[/tex]
[tex]x = \frac{-(-10)}{2(-1)}[/tex]
[tex]x = \frac{10}{-2}[/tex]
x = -5
The x-coordinate of the vertex is: x = 5.
Find the y-coordinate of the vertex:Next, substitute the value of the x-coordinate into the given quadratic equation to find its corresponding y-coordinate:
y = -x² - 10x - 22
y = -(-5)² - 10(-5) - 22
y = -25 + 50 - 22
y = 3
Therefore, the vertex of the given parabola is: (-5, 3), where it is the maximum point.
One of the attachments is the screenshot of the graphed quadratic equation (using Desmos), where it shows the vertex as the maximum point.
Method 2: Graphing CalculatorIf you have a graphing calculator (such as the Texas Instruments graphing calculator):
Press Y=Then, simply enter the given quadratic equation, -x² - 10x - 22.Next, press 2ND ⇒ Quit. Press the GRAPH button. Press 2ND ⇒ TRACE Select option 4: maximumIt will ask for the "Left Bound?": move the cursor as close to the maximum point as possiblePress ENTER. Next, it will ask for the "RightBound?" Repeat the same process as in step #7. Press ENTER.It will ask for "Guess?" ⇒ press ENTER, and it will provide the same coordinates for the vertex, (-5, 3).Please let me know if you have any questions or concerns regarding this post.
Related Questions
Complete the sentences to make true statements
6 is 100 times ____.
0.06 is 10 times ____.
60 is 1/100 of ____.
Answers
Answer:
6 is 100 times 0.06
0.06 is 10 times 0.006
60 is 1/100 of 6,000
Step-by-step explanation:
Since 6/100 is equal to 0.06, we can say that 6 is the result of multiplying 0.06 by one hundred (0.06 x 100 = 6).
On the other hand, since 0.06 / 10 is equal to 0.006, it is correct to say that 0.006 x 10 is equal to 0.06 (0.006 x 10 = 0.06).
Finally, 60 is one hundredth of 6000, since multiplying 60 x 100 the result is 6,000 (6,000 / 100 = 60).
hope this really helped!!
mark me brainliest :D
The complete sentences are:
6 is 100 times 0.06 .
0.06 is 10 times 0.006.
60 is 1/100 of 6,000.
"6 is 100 times greater than 0.06":
This means that if you multiply 0.06 by 100, you get 6.
So, 6 is indeed 100 times larger than 0.06.
"0.06 is 10 times greater than 0.006":
In this case, if you multiply 0.006 by 10, you get 0.06.
Thus, 0.06 is 10 times larger than 0.006.
"60 is 1/100 of 6,000":
This means that if you divide 6,000 by 100, you get 60.
So, 60 is a hundredth (1/100) of 6,000.
Hence, 6 is 100 times 0.06
0.06 is 10 times 0.006
60 is 1/100 of 6,000
To learn more on Number system click:
https://brainly.com/question/1763119
#SPJ3
PLEASE HELP.
Directions: find x so that L || M. state the converse used
Answers
Answer:
8. x=6; supplementary consecutive interior angles
10. x = 4; no applicable theorem
Step-by-step explanation:
8.The marked angles are "consecutive interior" angles. When their sum is 180°, the lines l and m will be parallel.
(7x -15) +(24x +9) = 180
31x = 186
x = 6
Consecutive interior angles being supplementary will make the lines parallel.
__
10.The sum of the remote interior angles of a triangle is equal to the exterior angle:
28x = 48 +16x
12x = 48
x = 4
The above relation holds regardless of whether line l is parallel to line m. There is no applicable theorem or converse.
_____
Additional comment
Adding the marking shown in the attachment would make the converse of the alternate interior angles theorem applicable to problem 10.
find the degree of the polynomial 5ab^3-7a^5c^2-5
Answers
Answer:
7
Step-by-step explanation:
as -7a^5c^2 term has two cofficient a and b and each have power.by adding power of one term we get 7
Please view the image above for the question ^^
Answers
Answer:
2
Step-by-step explanation:
After reflecting ABC over the y-axis and translating that image down, ABC will map onto DEF.
Answer:
(2)
Step-by-step explanation:
If you reflect ABC across the y axis it would look like DEF but above the x axis; translate it down and you get DEF.
If u=log(x3+y3+z3-3xyz)show that d2u/dx2+d2u/dy2+d2u/dz2=-3/(X+y+z)^2
Answers
X+y=6 x-y=-2 solve by elimination
Answers
Step-by-step explanation:
x + y = 6
+ x - y = -2
------------------
2x + 0 = 4
x = 2
2 + y = 6
y = 4
7.
"iş, oluş, durum bildiren köklere fiil kökü denir. Fill
kökleri -mek / -mak mastar eki ile anlamlı şekilde
söylenir."
Açıklamaya göre verilen sözcüklerden hangisi-
nin kökü fiil değildir?
A) evim
B) seçim
C) giyim
D) verim
Answers
Answer:
ABWJRIRISBDBDBHSHS
Step-by-step explanation:
Hatdog HWHWHWHSHSHSQIWIW
Ivan was the 31st person in line. His position in line was just behind 5/9 of the total number of people in line. How many people were in line? HELP PLEASE WILL MARK BRAINLIEST
Answers
31=1-(5/9)x
30=-(5/9)x
x=54
The answer is 54 people.
hope this helps :)
Find the 20 th term of the given sequence 2, 5, 8, 11,..
Answers
Answer:
14,17, 20
Step-by-step explanation:
Kindly see the picture I have solved it as required
let f be the function given by f(x)=sin x + e^-x +3x. which of the following statements is true for y=f(x).
Answers
Applying derivatives, it is found that the correct options are:
A. [tex]y^{\prime\prime}(x) = -\sin{x} + e^{-x}[/tex]
D. [tex]y - y^{\prime\prime\prime\prime}(x) = 3x[/tex]
The function given is:
[tex]f(x) = \sin{x} + e^{-x} + 3x[/tex]
It's first four derivatives are:
[tex]y^{\prime}(x) = \cos{x} - e^{-x} + 3[/tex]
[tex]y^{\prime\prime}(x) = -\sin{x} + e^{-x}[/tex]
Hence, option A is correct.
[tex]y^{\prime\prime\prime}(x) = -cos{x} - e^{-x}[/tex]
[tex]y^{\prime\prime\prime}(x) \neq y^{\prime}(x)[/tex], hence, option B is incorrect.
[tex]y^{\prime\prime\prime\prime}(x) = sin{x} + e^{-x}[/tex]
It is not the multiplication of the first and of the third derivative, hence option C is incorrect.
[tex]y - y^{\prime\prime\prime\prime}(x) = 3x[/tex]
[tex]\sin{x} + e^{-x} + 3x - \sin{x} - e^{-x} = 3x[/tex]
[tex]3x = 3x[/tex]
Hence, option D is correct.
A similar problem is given at https://brainly.com/question/17042788
6+7+8+...+(n+5) find the sum.
Answers
Answer:
n + 26
Step-by-step explanation:
first you have to simplify
6 + 7 +8 + n + 5
then combine the like terms
6 + 7 + 8 + n + 5
(n) + ( 6 + 7 + 8 + 5)
= n + 26
hope this helps
If F=(-3)
Find: F(x)=4x^2-5
Answers:
-41
31
29
None of the Above
Answers
Answer:
31
Step-by-step explanation:
as we put the value of X in the function it gives 3
what is a degree 3 polynomial with integer coefficients with zeros 3, -4, 5
Answers
Evaluate.
2 1/4 + 2/5 / (-1/2)-1/4
Enter your answer as a mixed number in simplest form in the box.
Answers
Answer:
[tex]1\frac{1}{5}[/tex]
Step-by-step explanation:
2 1/4 + 2/5 / (-1/2)-1/4
order of operation states you do division before subtraction or addition
2 1/4 -4/5 -1/4....divide 2/5 by -1/2
2 - 4/5.................combine like terms
6/5........................subtract
1 1/5.......................simplify
The graph below represents the function f(x) and the translated function g(x).
AVA
2x
/g(x)
a
If f(x) = x, which of the following functions could be an algebraic representation of g(x)?
Answers
-7(8) What is it please help me I need help help help help
Answers
Consider the following data to determine whether there is a significant difference between the values of Group 1 and Group 2. Let the significance level be 5%. Group 1: 15, 17, 26, 11, 18, 21, 13, 29 Group 2: 23, 14, 24, 13, 22, 23, 18, 21 What rank will be given to the value 15
Answers
Using the t-distribution, it is found that since the p-value of the test is 0.72 > 0.05, there is not significant difference between the values of each group.
At the null hypothesis, we test if the groups have the same values, that is, the subtraction of their means is 0:
[tex]H_0: \mu_2 - \mu_1 = 0[/tex]
At the alternative hypothesis, we test if the groups have different values, that is, the subtraction of their means is different of 0:
[tex]H_1: \mu_2 - \mu_1 \neq 0[/tex]
First, we have to find the mean and the standard deviation for both samples, hence, using a calculator:
[tex]\mu_1 = 18.75, \sigma_1 = 6.2507, \mu_2 = 19.75, \sigma_2 = 4.2678[/tex]
The standard errors are:
[tex]s_1 = \frac{\sigma_1}{\sqrt{n_1}} = \frac{6.2507}{\sqrt{8}} = 2.21[/tex]
[tex]s_2 = \frac{\sigma_2}{\sqrt{n_2}} = \frac{4.2678}{\sqrt{8}} = 1.5089[/tex]
For the distribution of differences, we have that:
[tex]\overline{x} = \mu_2 - \mu_1 = 19.75 - 18.75 = 1[/tex]
[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{2.21^2 + 1.5089^2} = 2.676[/tex]
We have the standard deviation for the samples, hence, the t-distribution is used. The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{s}[/tex]
In which [tex]\mu[/tex] is the value tested at the null hypothesis, which is 0 for this problem. Hence, the value of the test statistic is:
[tex]t = \frac{\overline{x} - \mu}{s}[/tex]
[tex]t = \frac{1 - 0}{2.676}[/tex]
[tex]t = 0.37[/tex]
To find the p-value, we have a two-tailed test, as we test if the means are different from a value, with t = 0.37 and 8 + 8 - 2 = 14 df.
Using a t-distribution calculator, this p-value is of 0.72.
Since the p-value of the test is 0.72 > 0.05, there is not significant difference between the values of each group.
A similar problem is given at https://brainly.com/question/15682365
Help!!!!! I will give out brainiest to best answer!!!
Answers
Answer:
see below
Step-by-step explanation:
a = 4
b = -2
c = -8
d = -11
Answer:
a=4, b=-2, c=-8, and d=-11
Step-by-step explanation:
its pretty easy
Please Help me Solve this question
Answers
Answer:
Step-by-step explanation:
Correct Answer: C
We can rely on the guess and check method to easily solve this problem. Let’s first pick arbitrary values of x and y to eliminate some answer choices.
Let’s consider the case where |x| and let x = 3 and y = -10.
Because x/y = -3/10 < 1, answer choice A is incorrect.
Because |x|2 = (3)2 = 9 and |-10| = 10, we have that |x|2 < y, so answer choice B is also incorrect.
Because x2 + 1= (3)2 + 1 = 10 and y2 + 1 = (10)2 + 1 = 101, we have that x2 + 1 < y2 + 1, so answer choice D is also incorrect.
Now, let’s consider the case where |x|>|y| and let x = 3 and y = -2.
Then, x-2 = 1/x2 = 1/9 and y-2 = 1/y2 = 1/4. This means that x-2 < y-2 , so answer choice E is also incorrect.
This means that answer choice C is correct. We can manipulate the inequality to see why this is true: (x/3 – 5) > (y/3 – 5)
We add 5 to both sides: x/3 > y/3
We multiply both sides by 3: x > y.
We know this is true since we are given that x > 1 > -1 > y, which simplifies to x > y.
Keith’s Florists has 15 delivery trucks, used mainly to deliver flowers and flower arrangements
in the Greenville, South Carolina, area. Of these 15 trucks, 6 have brake problems. A sample
of 5 trucks is randomly selected.
a. What is the probability that 2 of those tested have defective brakes? (5 marks)
b. Is this a discrete or continuous distribution? Explain.
Answers
Answer:
= 0.419
Step-by-step explanation:
in pic
(Hope this helps can I please have brainlist (crown)☺️)
Aldo earns 51 dollars a week working at the bookstore he makes one dollar more for each book that he sells . the amount , A (in dollars )that Aldo earns a week of he sales b books is given by the following function
A(b)=51+b
Answers
Answer:
False.
Step-by-step explanation:
A x b does not equal to A + b. Addition and mutiplication is different.
They estimate that their current fridge (older) which they got for free cost them $19 a month in electricity charges to operate
Answers
Answer:
That's an expensive a ss refrigerator It's time to choose an energy star refrigerator that's only going to cost them about $2.90 per month. in about 32 months paying $19 a month they would have paid for an energy star refrigerator. if they keep that same refrigerator they would be buying a brand new refrigerator every 32 months. spending the 600 dollars now for a new refrigerator would save them $16.10 per month. The savings would pay for that same refrigerator in about 38 months.
The length of the
hypotenuse of a right-
angled triangle is 7.8 cm,
correct to 1 decimal place.
One of the shorter side
lengths is 2.1 cm, correct
to 1 decimal place. Estimate
the length of the remaining
side, rounding your answer
to 1 decimal place.
Answers
Answer:
7.5 cm
Step-by-step explanation:
Since it's a right triangle, apply pythegorean theorem
Let the missing side be x
[tex] {7.8}^{2} = 2.1 { }^{2} + x {}^{2} [/tex]
[tex]60.84 = 4.41 + {x}^{2} [/tex]
[tex] {x}^{2} = 60.84 - 4.41[/tex]
[tex] {x}^{2} = 56.43[/tex]
[tex] \sqrt{ {x}^{2} } = \sqrt{56.43} [/tex]
[tex]x = 7.5[/tex]
Therefore, the length of the missing side is 7.5 cm
what is the area of the rectangle below?
Answers
Answer:
B. 120sq. unitsStep-by-step explanation:
The area A of a rectangle is given by the formula, A=lw , where l is the length and w is the width.
so
8 * 15 = 120sq. units
what is the measure of angle x
Answers
Answer:
180
Step-by-step explanation:
Find the value of X in triangles by subtracting known angle measurements from 180 degrees. Since the value of all angles within a triangle must equal 180 degrees, if you know at least two angles, you can subtract them from 180 to find the missing third angle.
6d + 20b ≤ 150
Solve for D and B
The help is highly appreciated and the best answer will get brainliest
thank you
Answers
Answer:
solving for b is b ≤ 15/2 - 3d/10
solving for d is d ≤ 25 - 10b/3
Write the equation of the line in fully simplified slope-intercept form.
Answers
Answer:
Where is the problem?
Step-by-step explanation:
5 lb 6 oz = __________ oz
Explain yourself
Answers
Answer:
86 oz
Step-by-step explanation:
1 lb = 16 oz
5 lb * 16 oz = 80 oz
80 oz + 6 oz = 86 oz
1/8 of a pumpkin pie has 379 calories. How many calories
are in the whole pie?
Answers
Answer:
379*8
Step-by-step explanation:
1. 300*8=2400
2.70*8 = 560
3. 9*8=72
3032
What's 9 + 10?
Whoever gets it right get's the crown!
Answers
Answer:
jokes aside it is 19
Step-by-step explanation:
but if it is jokes then 21
Answer:
Step-by-step explanation:
the answer would be 21