Answer:
[tex]Vertex = (\frac{1}{2},\frac{7}{4})[/tex]
Step-by-step explanation:
Given
[tex]f(x) = x^2 - x +2[/tex]
Required
The vertex
We have:
[tex]f(x) = x^2 - x +2[/tex]
First, we express the equation as:
[tex]f(x) = a(x - h)^2 +k[/tex]
Where
[tex]Vertex = (h,k)[/tex]
So, we have:
[tex]f(x) = x^2 - x +2[/tex]
--------------------------------------------
Take the coefficient of x: -1
Divide by 2: (-1/2)
Square: (-1/2)^2
Add and subtract this to the equation
--------------------------------------------
[tex]f(x) = x^2 - x +2[/tex]
[tex]f(x) = x^2 - x + (-\frac{1}{2})^2+2 -(-\frac{1}{2})^2[/tex]
[tex]f(x) = x^2 - x + \frac{1}{4}+2 -\frac{1}{4}[/tex]
Expand
[tex]f(x) = x^2 - \frac{1}{2}x- \frac{1}{2}x + \frac{1}{4}+2 -\frac{1}{4}[/tex]
Factorize
[tex]f(x) = x(x - \frac{1}{2})- \frac{1}{2}(x - \frac{1}{2})+2 -\frac{1}{4}[/tex]
Factor out x - 1/2
[tex]f(x) = (x - \frac{1}{2})(x - \frac{1}{2})+2 -\frac{1}{4}[/tex]
[tex]f(x) = (x - \frac{1}{2})^2+2 -\frac{1}{4}[/tex]
[tex]f(x) = (x - \frac{1}{2})^2+ \frac{8 -1 }{4}[/tex]
[tex]f(x) = (x - \frac{1}{2})^2+ \frac{7}{4}[/tex]
Compare to: [tex]f(x) = a(x - h)^2 +k[/tex]
[tex]h = \frac{1}{2}[/tex]
[tex]k = \frac{7}{4}[/tex]
Hence:
[tex]Vertex = (\frac{1}{2},\frac{7}{4})[/tex]
Question: Marsha wants to determine the vertex of the quadratic function f(x) = x2 – x + 2. What is the function’s vertex?
Answer: A or 1/2 , 7/4
Step-by-step explanation:
did it on an assignment on EDGE
Which statement must be true?
A. X
B. X=y
C. x >y
D. No relationship between x and y can be determined from the information given,
ILL GIVE BRAINLIEST
Answer:
A
Step-by-step explanation:
The statement true about the triangles is x < y
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the first triangle be ΔABC
Let the second triangle be ΔDEF
And , the measure of ∠ABC = x°
The measure of ∠DEF = y°
The measure of side AC = 15 units
The measure of side DF = 20 units
For a triangle , the longest side in a triangle is always opposite the largest angle, and the shortest side is opposite the smallest angle
Hence , the angle ∠DEF > ∠ABC of the triangle ( x < y )
To learn more about triangles click :
https://brainly.com/question/16739377
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what is -9.25 as a faction
Answer:
-37 / 4
Step-by-step explanation:
Use OZ with VWXY
What is XY ?
A 30
B. 35
C. 40
D. 50
Answer:
Step-by-step explanation:
Chords having equal measures are equidistant from the center of the circle.
Since, VW = XY
Therefore, ZP = ZR = 15 units
A perpendicular line drawn from the center of a circle to the chord is the bisector of the chord.
VR = WR = 20 units
By applying Pythagoras theorem in ΔZRV,
ZV² = ZR² + VR²
ZV² = (15)² + (20)²
ZV = √(225 + 400)
ZV = √625
ZV = 25 units
Therefore, measure of radius ZV = 25 units.
VW = XY [Given]
Therefore, XY = 2(20)
= 40 units
The question is in the photo, that answer is not correct. At least I do not know if it is.
Answer:
Step-by-step explanation:
To get the solution lying in the shaded region,
Justify the equation with the given options,
Option (1)
[tex]\frac{x^2}{16}+\frac{y^2}{4}\leq 1[/tex]
For (1, 1),
[tex]\frac{1^2}{16}+\frac{1^2}{4}\leq 1[/tex]
[tex]\frac{1}{16}+\frac{1}{4}\leq 1[/tex]
[tex]\frac{1+4}{16}\leq 1[/tex]
[tex]\frac{5}{16}\leq 1[/tex]
True.
Therefore, point (1, 1) justifies the equation.
Option (2)
For (4, 1),
[tex]\frac{x^2}{16}+\frac{y^2}{4}\leq 1[/tex]
[tex]\frac{4^2}{16}+\frac{1^2}{4}\leq 1[/tex]
[tex]1+\frac{1}{4}\leq 1[/tex]
[tex]1\frac{1}{4}\leq 1[/tex]
False.
Therefore, point (4, 1) doesn't justify the equation.
Option (3)
For (-1, 2),
[tex]\frac{x^2}{16}+\frac{y^2}{4}\leq 1[/tex]
[tex]\frac{(-1)^2}{16}+\frac{(2)^2}{4}\leq 1[/tex]
[tex]\frac{1}{16}+1\leq 1[/tex]
[tex]1\frac{1}{16}\leq 1[/tex]
False.
Therefore, point (-1, 2) doesn't justify the equation.
Option (4)
For (2, -2),
[tex]\frac{x^2}{16}+\frac{y^2}{4}\leq 1[/tex]
[tex]\frac{2^2}{16}+\frac{(-2)^2}{4}\leq 1[/tex]
[tex]\frac{1}{4}+1\leq 1[/tex]
[tex]1\frac{1}{4}\leq 1[/tex]
False.
Therefore, point (2, -2) doesn't justify the equation.
Option (1) will be the answer.
Given that A, O & B lie on a straight line segment, evaluate
x
.
Answer:
Step-by-step explanation:
It is the same way:
we know that
if A , O and B lie on a straight line segment
then
∡AOY+∡YOZ+∡ZOB=180°
so
3x+x+x=180-----> 5x=180--------> x=180/5--------> x=36°
the answer is
x=36°
please mark me as brainliest
The plant-breeding department at a major university developed a new hybrid boysenberry plant called Stumptown Berry. Based on research data, the claim is made that from the time shoots are planted 90 days on average are required to obtain the first berry. A corporation that is interested in marketing the product tests 60 shoots by planting them and recording the number of days before each plant produces its first berry. The sample mean is 92.3 days. The corporation wants to know if the mean number of days is different from the 90 days claimed. What are the correct hypotheses?
a) H0:μ≠90
H1:μ=90
b) H0:μ=90
H1:μ≠90
c) H0:μ=92.3
H1:μ≠92.3
d) H0:p=92.3%
H1:p≠92.3%
e) H0:p=90%
H1:p≠90%
Answer:
b) H0:μ=90, H1:μ≠90
Step-by-step explanation:
The corporation wants to know if the mean number of days is different from the 90 days claimed.
This means that at the null hypothesis, we test if the mean number is the claimed value of 90, and so:
[tex]H_0: \mu = 90[/tex]
The corporations wants to know if the mean number is different, and thus, at the alternate hypothesis, we test if the mean number is different from 90, that is:
[tex]H_1: \mu \neq 90[/tex]
This means that the correct answer is given by option b.
9 weeks 2 days = ?
days?
Answer:
9weeks 2days = (9 × 7) + 2 = 63 +2=65 days
Step-by-step explanation:
Answer:
65 days
Step-by-step explanation: 7 days in a week so times that by 9 because its 9 weeks and that is 63 and add 2 more days
-3x+15y=-30
-4x+5y=5
Answer:
(-5,-3)
Step-by-step explanation:
The answer is (-5,-3)
A rabbit hops 8 meters in one second. After 7 seconds, the rabbit has hopped 20 meters. What is the rabbit's average rate of change? A. 1/2 B. 2 C. 5 D. 20
Answer:
Average Rate of change = 2
Step-by-step explanation:
Given - A rabbit hops 8 meters in one second. After 7 seconds, the rabbit has hopped 20 meters.
To find - What is the rabbit's average rate of change?
Formula used -
Average rate of change of a function f(x) in an interval [a, b] is [tex]\frac{f(b) - f(a)}{b - a}[/tex]
Proof -
Given that,
In 1 second - Rabbit hoops 8 meters
In 7 seconds - Rabbit hoops 20 meters
So,
Average Rate of change = [tex]\frac{20 - 8}{7 - 1}[/tex]
= [tex]\frac{12}{6}[/tex]
= 2
⇒Average Rate of change = 2
Which expression is equivalent to 1/3b - 7
Answer:
The answer Is 1/3(b-21)
Step-by-step explanation:
i am requesting help on this asap
What number do the blocks represent?
Write your answer as a decimal.
Please help me due today
Answer:
x = 88
Step-by-step explanation:
Becuase this is a quadrilateral, the opposite angles total 180 degrees. So, the opposite of x is 92. That would mean that x + 92 = 180. We subtract 92 from both non-variable sides to get the x by itself. 180 - 92 = 88. 92 - 92 = 0. this leaves us with X = 88
hope this helps
OLEASE HELP
Which number produces a rational number when added to 1/2
A. 5.38516480...
Β. π
c. √ 10
D. 0.22
Answer:
i donot know appp lado app
The top rail of a boat is 4 ft out of the water. If the water rises 3 ft, how far out of
the water is the top rail of the boat?
Answer:
the correct answer is 1ft
Step-by-step explanation:
4ft-3ft
=1ft
What additional piece of information
would prove ALMK = ANMK by
Side-Angle-Side?
Answer:
MK bisects <LKN
Step-by-step explanation:
We can already say two sets of sides are equal; LK = NK because it is given and MK = MK because of reflexive property. In order to use Side-Angle-Side, we need to prove the angles between the sides are congruent. This means <LKM and <NKM. The only option that would help is with the is the lat option, MK bisects <LKN because, then we could say <LKM and NKM are congruent because MK would be an angle bisector. This is exactly what we want, so the answer is MK bisects <LKN.
what is the answer (x + 3)2 – 5 = 0
x= -1/2 is the answer to your question. Mark as brainliest!!!!
find the area of the figure
area: units2
Answer:
Area of the figure = 25 square units
Step-by-step explanation:
Area of the given figure = Area of ΔCDE + Area of rectangle BCEI + Area of ΔABH + Area of GIF
Area of ΔCDE = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= [tex]\frac{1}{2}(CE)(DK)[/tex]
= [tex]\frac{1}{2}(8)(4)[/tex]
= 16 units²
Area of rectangle BCEI = Length × Width
= CE × EI
= 8 × 1
= 8 units²
Area of ΔABH = Area of ΔGIF = [tex]\frac{1}{2}(1)(1)[/tex]
= [tex]\frac{1}{2}[/tex] units²
Area of the complete figure = 16 + 8 + [tex]\frac{1}{2}[/tex] + [tex]\frac{1}{2}[/tex]
= 25 units²
please help me. f(x) = In(x)^6 find f'(x)
Answer:
f'(x) = 6/x
Step-by-step explanation:
1. Use logarithm rules to move the power to the front so ln(x)^6 becomes 6 ln(x).
2. Differentiate ln(x) which is always 1/x
3. multiply 1/x by the 6
6/x
ABCD is a parallelogram. Find x and the length of CD.
Answer:
3×+9=5x-5
-2×=-14
×=7...thenCD=3(7)+9=30
4x + 6 = 30
What is the solution to the equation?
A. X= 4
B. X= 9
C. X = 6
D. X = 24
Nee
Answer:
x<-4
Step-by-step explanation:
Pleaseeeeeeeeee helppppp
Polygons Determine the measure of one through 12
Answer:
And there are twelve angles... So, the measure of the interior angle of a regular dodecagon is 150 degrees.
Step-by-step explanation:
Which number is an integer?
Answer:
0
Step-by-step explanation:
0 is an integer.
plz mark as brainliest
cheryl wants to buy a bicycle that costs 160$. if she saves 12$ each week, what is the fewest number of weeks she must save in order to buy the bicycle?
please show the answer choices
Answer:
14 weeks.
Step-by-step explanation:
160/12= 13.8
13 weeks earns her $158
14 weeks earns her $160. So the fewest number of weeks she needs is 14.
Which expressions are equivalent to 4d+6+2d?
Choose all answers that apply.
2(3d+3)
6(d+6)
(3d+3) + (3d+3)
i know number 3 is right
Answer:
(3d+3) + (3d+3)
Step-by-step explanation:
Please help me! It isn’t hard im just not sure how to do it .
Answer:
a. Semester 1: 86.8, Semester 2: 87
b. Semester 1: 5.7, Semester 2: 6.3
c. Semester 1 because the standard deviation of the first semester was lower than of the second. This shows that his scores were closer to the mean and therefore he was more consistent.
Step-by-step explanation: Find the mean by taking the sum of the values for each semester and divide that sum by the number of values to find the average. Do this for both semesters. Now, find the absolute value of the difference between the mean and each value of the corresponding data set. Square each if those differences and sum them up. Now divide that sum by the number of data values and take the square root. This number is your standard deviation. You will use the standard deviations to make the comparison for part c. I hope this makes sense and helps!!!!
What is the volume of this triangular pyramid?
5 yd
3 yd
3 yd
Answer:
45
Step-by-step explanation:
volume=length x width x height
5x3x3=45
PLS PLS PLS HELP I WILL MARK BRAINLIEST :)))
Answer:
28.3
Step-by-step explanation:
the formula for area is πr²
where π is 3.14
r is 3
area= 3.14 x 3²
area= 3.14 x 9
area= 28.28 approximately 28.3
What is the y-intercept of this equation?
5x + 4y = 8
Answer:
2
Step-by-step explanation:
5x + 4y = 8
5*0 + 4y = 8
y = 8/4
y=2