Answer:
[tex]\left(\dfrac{1}{4},\dfrac{49}{8}\right)[/tex]
Step-by-step explanation:
Turning points (stationary points) occur when the gradient of a graph is zero.
To find when the gradient of the graph is zero, differentiate the function, set it zero, then solve for x.
Given function:
[tex]f(x)=-2x^2+x+6[/tex]
Differentiate:
[tex]\implies f'(x)=(2)(-2)x^{2-1}+(1)x^{1-1}+6(0)[/tex]
[tex]\implies f'(x)=-4x+1[/tex]
Set the differentiated function to zero and solve for x:
[tex]\implies f'(x)=0[/tex]
[tex]\implies -4x+1=0[/tex]
[tex]\implies 4x=1[/tex]
[tex]\implies x=\dfrac{1}{4}[/tex]
To find the y-coordinate, input the found value of y into the given function:
[tex]\implies f\left(\dfrac{1}{4}\right)=-2\left(\dfrac{1}{4}\right)^2+\left(\dfrac{1}{4}\right)+6[/tex]
[tex]\implies f\left(\dfrac{1}{4}\right)=\dfrac{49}{8}[/tex]
Therefore, the turning point of the function is:
[tex]\left(\dfrac{1}{4},\dfrac{49}{8}\right)[/tex]
answers
f=1/4=49/8
Step-by-step explanation:
identify the coefficients
a=-2, b=1
substitute the coefficient into the expression
x= -1/((2x(-2))
then solve it out the equation
x=1/4
evaluate the function x =1/4
f(x) =-2x²+x+6(1/4)
f=1/4=49/8
POINTS!!! Answer both 3 and 4 PLEASE
Answer:
yes not function because 1 is repeated
Can someone please answer this, ill give you brainliest Would be very appreciated.
Explanation:
f(x) = (x-4)(x+2)
1) For x-intercept, y will be 0
(x-4)(x+2) = 0(x-4) =0, (x+2) = 0x = 4, x = -2x-intercept: (4, 0), (-2, 0)
2) For vertex: x = -b/2a where ax² + bx + c
Quadratic function:
(x-4)(x+2)x² +2x-4x -8x² -2x -8vertex:
x = -(-2)/2(1)x = 1y: (x-4)(x+2) = (1-4)(1+2) = -9
ordered pair of vertex: (1, -9)
3) For y-intercept, x will be 0
(x-4)(x+2)(0-4)(0+2)-8y-intercept: (0, -8)
Answer:
(4, 0) and (-2, 0)(1, -9)(0, -8)Step-by-step explanation:
Q1 : Finding x-intercepts
Take f(x) to be 0, because the intercepts lie on the x-axis0 = (x - 4)(x + 2)x = 4 and x = -2The x-intercepts are : (4, 0) and (-2, 0)Q2
Coordinates of vertex are : (h, k)Expand the polynomialx² - 2x - 8h = -b/2a = 2/2 = 1k = -D/4aD = b² - 4ac = 4 - 4(1)(-8) = 4 + 32 = 36k = -36/4 = -9The vertex is : (1, -9)Q3
Take x = 0y = 0² - 2(0) - 8y = -8y-intercept is : (0, -8)Bob is throwing a party. He has 22 pints of soda. At the end of the party, there are 8
pints of soda.
How many cups of soda were drank during the party?
Answer:
14
Step-by-step explanation:
If Bob has 22 pints, and one glass is one pint, the 22-8 = 14
Answer:
14
Step-by-step explanation:
you would subtract 8 pints of soda left from the total pints which is 22 to get 14 pints used during the party
22-8=14
How many different trains can you make of length three?
Using the combination formula, and supposing that you have n parts, it is found that the number of trains you can make is of:
[tex]N = C_{n,3} = \frac{n!}{3!(n - 3)!} = \frac{n!}{6(n-3)!}[/tex]
The order in which the parts are taken is not important, hence the combination formula is used to solve this question.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, 3 parts are taken from a set of n, hence the total number of trains is given by:
[tex]N = C_{n,3} = \frac{n!}{3!(n - 3)!} = \frac{n!}{6(n-3)!}[/tex]
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Please simplify this!
Answer:
May be the answer is 5 . I don't think it's the answer .
Find the area of a sector of a circle with a radius of 6 and angle of the sector is 40 degrees
Answer:
12.56 units²Step-by-step explanation:
Area of sector :
πr² x θ/360π(6)² x 40/36036π x 1/93.14 x 412.56 units²PLSSS HELP IF YOU TURLY KNOW THISS
Alice’s backyard is a rectangular piece of property that is twice as long as it is wide. the total area of her yard is 1,000 m2. what is the approximate width of her backyard? a = lw 11.2 m 15.8 m 22.4 m 44.8 m
Interior and Exterior Triangle Angles (0/5)
Please full explanation
I will mark brainlist to whoever answers first
Answer:
∠R = 69Step-by-step explanation:
Angle sum propertySum of all angles of triangle = 180
5x - 11 + 3x - 3 + 3x + 18 = 180
5x + 3x + 3x -11 - 3 + 18 = 180
Combine like terms
11x + 4 = 180
11x = 180 - 4
11x = 176
x = 176/11
x = 16
∠R = 5x - 11
= 5*16 - 11
= 80 - 11
= 69
Apply angle sum property
5x-11+3x-3+3x+18=18011x+4=18011x=176x=16m<R
5(16)-1180-1169°#57 will give brainliest to the best answer. please explain
Answer:
(x+y)(z+1)
Step-by-step explanation:
trust me .......
Answer:
(x+y) (z+1)
Step-by-step explanation:
xz + x + yz + y
- group the first two terms and the last two terms.
(xz + x ) + yz + y
- factor out the greatest common factor (GCF) from each group.
x (z + 1) + y (z + 1)
- factor the polynomial by factoring out the greatest common factor, z + 1.
(x+y) (z+1)
Someone help please.its really important
Answer: Angle Y is 90 degrees, angle X is 35.
Answer:x=35 and y=35
Step-by-step explanation:
Angle on straight line =180
so 180/2=90
90-55=35
and x and y opposite angle so are eqaul
*ANSWER*
What is the value of x?
x =6
Answer;
10
Step-by-step explanation:
from the question we observed that the shape is a right angled triangle.
and according to Pythagoras theorem, In a right angled triangle the square of the hypothenus is equal to the square of the sum of the other two side
hypothenus = 10
10^2= 8^ + X^2
100= 64 +X^2
X^2 = 100-64
X^2 = 36
X = √36
X= 6
Find the equation of a line parallel to -x + y = -5 that passes through the point
(-6,-8).
Oy=x-5
O-x+y=-2
Submit Answer
Oy=-x-2
O-z-y=14
Answer:
O -x+y=-2
Step-by-step explanation:
-x + y = -5
⇔ y = x - 5
a line parallel to y = x - 5 must have the same slope as the line y = x - 5
Then
The equation of the parallel line is of the form : y = x + p
Finding p :
the point (-6,-8) lies on the parallel line means :
-8 = -6 + p
Then
p = -8 + 6 = -2
Finally :
y = x - 2 ⇔ -x + y = -2
2 1/6 - (-8/3) + (-4 7/9) what does it eqaul i cant figure it out
Answer:
- 95/18
Step-by-step explanation:
1st you have to convert the mixed number to an improper fraction so 2 ×6 = 12 +1 = 13 and that together equals 13/6 same goes for the next take away the parentheses 13/6 - 8/3 - 4 7/9
then you have to do the same thing with the 1st fraction convert it 4 × 9 = 36 + 7 = 43 that equals together 43/9
lastly you have to calculate the difference 13/6 - 8/3 - 43/9 and that equals negative 95/18
by the way the 95 isnt a negative the fraction itself is
Problem 4.2
A textbook has 428 numbered pages, starting with 1.
A textbook has 428 numbered pages, starting with 1.
You are equally likely to stop on any of the pages if you flip through the book randomly.
What is the probability that you turn to an even-numbered page?
Answer:
50%
half of the numbers are even
Step-by-step explanation:
Segment side a e is 7 inches and side a h is 7 startroot 3 endroot inches. what is the length of side e h? round to the nearest tenth. a cube. the top face has points a, b, d, c. the bottom face has points e, f, h, g. 7.0 inches 9.9 inches 12.1 inches 14.0 inches
The length of the side eh can be found using Pythagoras theorem. Therefore, EH = 9.9 inches
How to use Pythagoras theorem?Pythagoras theorem can be used to find eh.
Therefore,
c²= a² + b²
where
c = hypotenuse sidea and b are the other two legs.Therefore,
AE = 7 inches
AH = 7√3 inches
Therefore,
EH² = ( 7√3 )² - 7²
EH² = 147 - 49
EH = √98
EH = 9.89949493661
EH = 9.9 inches
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Answer: ITS BBBBBBBBBBBBBBBBBBBBB
Step-by-step explanation:
Simplify the expression.
-81 ÷ (-9)
Please help
Answer:
-81/-9
both minus will be cut so
81/9
9
Step-by-step explanation:
the answer is 9
The half-life of a radioactive kind of praseodymium is 17 minutes. If you start with 56 grams of it, how much will be left after 34 minutes?
grams
Answer:
14 gm
Step-by-step explanation:
34 minutes is TWO half lives 1/2 * 1/2 = 1/4 will be left
1/4 * 56 = 14 gm
Solve the following literal equation for y 16=2y-4x
Answer:
y=2x+8
Step-by-step explanation:
Move 4x to other side and divide everything by 2
Prove the following tan^2 A/(tan A -1 )+ cot A/(1 - tan A)=1 +sec A cosec A
In Image, Question is No.4 (vi)
See below for the proof of the trigonometry identity [tex]\frac{\tan^2(A)}{\tan(A) - 1} + \frac{\cot(A)}{1 - \tan(A)} =1 + \sec(A)\csc(A)[/tex]
How to prove the trigonometry identity?The trigonometry equation is given as:
[tex]\frac{\tan^2(A)}{\tan(A) - 1} + \frac{\cot(A)}{1 - \tan(A)} =1 + \sec(A)\csc(A)[/tex]
Rewrite the equation as:
[tex]\frac{\tan^2(A) }{\tan(A) - 1} - \frac{\cot(A)}{ \tan(A) - 1} =1 + \sec(A)\csc(A)[/tex]
Take LCM
[tex]\frac{\tan^2(A) - \cot(A)}{ \tan(A) - 1} =1 + \sec(A)\csc(A)[/tex]
Express cot(A) as 1/tan(A)
[tex]\frac{\tan^2(A) - \frac{1}{\tan(A)}}{ \tan(A) - 1} =1 + \sec(A)\csc(A)[/tex]
Take LCM
[tex]\frac{\tan^3(A) - 1}{\tan(A)(\tan(A) - 1)} =1 + \sec(A)\csc(A)[/tex]
Apply the difference of two cubes on the numerator
[tex]\frac{(\tan(A) - 1)(\tan^2(A) + \tan(A) + 1)}{\tan(A)(\tan(A) - 1)} =1 + \sec(A)\csc(A)[/tex]
Cancel out the common factors
[tex]\frac{\tan^2(A) + \tan(A) + 1}{\tan(A)} =1 + \sec(A)\csc(A)[/tex]
Rewrite as:
[tex]\frac{\tan(A) + \tan^2(A) + 1}{\tan(A)} =1 + \sec(A)\csc(A)[/tex]
Split the fraction
[tex]1 + \frac{\tan^2(A) + 1}{\tan(A)} =1 + \sec(A)\csc(A)[/tex]
Express [tex]\tan^2(A) + 1[/tex] as [tex]\sec^2(A)[/tex]
[tex]1 + \frac{sec^2(A)}{\tan(A)} =1 + \sec(A)\csc(A)[/tex]
Divide [tex]\sec^2(A)[/tex] by [tex]\tan(A)[/tex]
[tex]1 + \frac{1}{\sin(A)\cos(A)} = 1 + \sec(A)\csc(A)[/tex]
Take the inverse of sin and cosine
[tex]1 + \sec(A)\csc(A) = 1 + \sec(A)\csc(A)[/tex]
Both sides of the equation are the same.
Hence, the trigonometry identity [tex]\frac{\tan^2(A)}{\tan(A) - 1} + \frac{\cot(A)}{1 - \tan(A)} =1 + \sec(A)\csc(A)[/tex] has been proved
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Would somebody be willing to help me please! I really need to pass this lesson!!
Answer:
x= -2 y= 36 (-2. 36)
x = -1 y = 6 (-1, 6)
x = 1 y = [tex]\frac{1}{6}[/tex] (1, [tex]\frac{1}{6}[/tex])
Step-by-step explanation:
Our function is [tex]y = (\frac{1}{6})^x[/tex]
all we need to do is fill in our x (given in the table) to solve for y
[tex]y = (\frac{1}{6})^{-2}[/tex]
[tex]y = 36[/tex]
[tex]y = (\frac{1}{6})^{-1}[/tex]
[tex]y = 6[/tex]
[tex]y = (\frac{1}{6})^1 = \frac{1}{6}[/tex]
Solve for y y/8 = 4
Answer:
32
Step-by-step explanation:
Multiply both sides by 8.
y/8 = 4
y/8 × 8 = 4 × 8
y = 32
Please, please help. Unit test is due. (K12 User)
△ACB is bisected by CP←→. m∠PCB=65° and PB=11 ft.
What is the approximate area of each half of △ACB ?
28 ft²
56 ft²
67 ft²
143 ft²
The approximate area of each half of △ACB is 28 square feet
Area of a triangleThe formula for calculating the area of a triangle is expressed as:
A = 0.5absintheta
Given the following
PB =11ft
<PCB = 65degrees
Using the SOH CAH TOA identity
tan<PCB = 11/CP
CP = 11/tan65
CP = 5.13 ft
Determine the required area
Area = 0.5(11)(5.13)sin90
Area = 5.5 * 5.13
Area . = 28 square ft
Hence the approximate area of each half of △ACB is 28 square feet
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Elias was given a lock for his school locker. The lock contains numbers between
O and 59 (60 different numbers). If 3 numbers are used to unlock the lock, and
the numbers can't repeat, how many codes can his lock have?
Answer:
34,220
Step-by-step explanation:
Because order doesn't matter, but the numbers can't be repeated, we need to find the number of combinations where 3 individual numbers can be chosen out of 60 possible numbers using the binomial coefficient:
[tex]\binom{n}{k}=\frac{n!}{k!(n-k)!}\\ \\\binom{60}{3}=\frac{60!}{3!(60-3)!}\\\\\binom{60}{3}=\frac{60!}{3!(57)!}\\\\\binom{60}{3}=\frac{60*59*58}{3*2*1}\\ \\\binom{60}{3}=34220[/tex]
Thus, Elias can make 34,220 unique 3-number codes given 60 different numbers.
Combine the like terms to create an equivalent expression.
2q+2+92
Answer:
2q + 94
Step-by-step explanation:
2q + 2 + 92 ← collect like terms
= 2q + (2 + 92)
= 2q + 94
Answer:
2q + 94Step-by-step explanation:
2q + 2 + 92
Reorder and group
2q + (2 + 92)
Caculate
2q + 94
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For what values of x is x2-36=5x true? -9 and -4 -4 and 9 4 and -9 9 and 4.
Answer: -4 and 9
Step-by-step explanation:
a shoe company needs to create a shoe box...
Answer:
Step-by-step explanation:
21/7=3
5*3=15 width
3*3=9 height
Evaluate
6x+4y-z. X:4,y:-2,z:3
Step-by-step explanation:
x = 4
y = -2
z = 3
= 6x + 4y - z
= 6.4 + 4.-2 - 3
= 24 - 8 - 3
= 13
On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 0. it crosses the y-axis at (0, 4). what is the initial value of the exponential function shown on the graph? 0 1 2 4
Answer:
its 4
Step-by-step explanation:
trust me bro im a geinus
The initial value of the exponential function shown on the graph should be 4.
What is an exponential function?The exponential function represents a dependency relationship. In this type of mathematical operation there is a variable in the exponent and the real number in the base.
In this case, the exponential function is:
F(X)=Y
Knowing that the given points correspond to X=0 and Y= 4, when placing in the formula of the function, one finds:
F(0)=4
F(4)=0
So, the initial value of the exponential function shown on the graph should be 4.
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Janet and Bill leave their home at the same time, Janet has 60 miles to travel and drives at 40 mph. Bill has 80 miles to travel and also drives at 40 mph.
a) How long does Janet's journey take?
b) How much longer does Bill spend driving than Janet?
Answer:
Question 1 = 1 hour 30 minutes
Question 2 = he spent 30 more minutes driving
Step-by-step explanation:
time = distance ÷ speed
Answer:
Below in bold.
Step-by-step explanation:
Speed = distance / time.
a) Janet's journey:
40 = 60 / t
4ot = 60
t = 60/40 = 1 1/2 hours.
Janet's journey takes 1 1/2 hours.
b) Bills journey:
40 = 80/t
t = 80/40 = 2 hours.
Bill travels for 1/2 hour more than Janet.
