Answer the questions below about the quadratic function.g(x) = -x + 6x-8Does the function have a minimum or maximum value?MinimumMaximumWhere does the minimum or maximum value occur?X =.What is the function's minimum or maximum value?
Answers
#A
The function given to us is a quadratic equation of the form:
\(g(x)=-x^2+6x-8\)We are asked to figure out whether or not the function has a minimum or maximum value.
Generally, the equation of the form:
\(y=ax^2+bx+c\)has a graph that looks like this:
While functions of the form:
\(y=-ax^2+bx+c\)have graphs that look like this:
Since the function given to us is similar to this second function because of the negative coefficient of x-squared, we know that the function given has a maximum value.
Hence, the answer to the first question is:
"The graph has a Maximum value"
#B
The next part of the question asks us where this maximum value occurs.
In order to solve this, we must follow a couple of steps:
1. We differentiate the function to find the equation of the slope of the function.
2. We equate the slope function to zero because at the maximum value, the graph stops changing i.e. the slope becomes zero.
3. We find x from the slope function equated to zero in step 2. This is the value of x for which the original equation has its maximum value.
4. Substitute the value of x into the original equation to find the value of y. This value of y would be the maximum value.
Now, let us use the following steps to solve.
1. We differentiate the function to find the equation of the slope of the function.:
\(\begin{gathered} g(x)=-x^2+6x-8 \\ \text{differentiating the function} \\ g^{\prime}(x)=-2x+6 \end{gathered}\)The above function g'(x) is the slope function of the quadratic equation.
2. We equate the slope function to zero because at the maximum value, the graph stops changing i.e. the slope becomes zero.
\(\begin{gathered} g^{\prime}(x)=-2x+6 \\ \text{equate g'(x) to zero to find maximum value} \\ -2x+6=0 \end{gathered}\)3. We find x from the slope function equated to zero in step 2. This is the value of x for which the original equation has its maximum value.
\(\begin{gathered} -2x+6=0 \\ \text{subtract 6 from both sides} \\ -2x=-6 \\ \text{divide both sides by -2} \\ -\frac{2x}{-2}=-\frac{6}{-2} \\ \\ \therefore x=3 \end{gathered}\)Now, to find the maximum value, at x = 3
4. Substitute the value of x into the original equation to find the value of y. This value of y would be the maximum value.
\(\begin{gathered} y=-x^2+6x-8 \\ \text{put x = 3} \\ y=-3^2+6(3)-8 \\ y=-9+18-8 \\ \\ \therefore y=1\text{ (Maximum value)} \end{gathered}\)Therefore, the maximum value is: y = 1
Related Questions
PLEASE HELP
5|12-r|>15
Answers
Step-by-step explanation:
5.|12 - r| > 15
|12 - r| > 15/5
|12 - r| > 3
12 - r < -3 or 12 - r > 3
-r < -3 - 12 or -r > 3 - 12
-r < -15 or -r > -9
r > 15 or r < 9
Solve for x.
Can anyone help me please?
Answers
Answer:
The answer is 1
Step-by-step explanation:
3-4= -1
-1+x= 1
Armelia wants to paint three walls in her family room, wwo walls are 26 feet long by 9 feet wide. The other wall is 18 feet Hong by 9 feet wide. Each gallon of paint covers about 250 square feet. How many gallons of paint should Amella buy to paint the walls?
Answers
Answer: Wall 1 & 2 : 26 ft by 9 ft
Wall 3 : 18 ft by 9 ft
Area 1 : 26 ft x 9 ft = 234 ft²
Area 2 : 26 ft x 9 ft = 234 ft²
Area 3 : 18 ft x 9 ft = 162 ft²
Total Area : 234 ft² + 234 ft² + 162 ft² = 630 ft²
1 Gallon = 250 ft²
630 ft² ÷ 250 ft² per gallon = 2.52 gallons
△BCD is a right triangle. The length of the hypotenuse is 19 centimeters. The length of one of the legs is 13 centimeters.
What is the length of the other leg?
Answers
The length of the other leg of the right triangle is 13.9 cm.
How to find the side of a right triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees. The side of the right triangle can be named according to it angle position as hypotenuse side, adjacent side and opposite side.
Therefore, let's find the other leg of a right triangle with hypotenuse as 19 cm and one leg as 13 cm using Pythagoras's theorem as follows:
c² = a² + b²
where
c = hypotenusea and b are the other legsTherefore,
b = √19² - 13²
b = √361 - 169
b = √192
b = 13.8564064606
Therefore,
length of the other leg = 13.9 cm
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There are four rational numbers which are listed smallest to largest, A, B, C, and D. If the numbers are 5/3 7/15 6/10 and 25/5 , identify which is A, which is B, which is C, and which is D. brainly
Answers
The rational numbers are given as follows:
A = 7/15.B = 6/10.C = 5/3.D = 25/5.How to order the rational numbers?To order the rational numbers, we must convert the fractions to decimal, dividing the numerator of the fraction by the denominator.
The conversion of each number is given as follows:
5/3 = 1.67.7/15 = 0.47.6/10 = 0.6.25/5 = 5.Hence they are ordered as follows:
7/15, 6/10, 5/3, 25/5.
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Need help again with maths homework
Answers
Answer:
10
Step-by-step explanation:
Answer:
The answer for this problems are:
1) a= 2
2) a= b-3, b= 3+a
Thanks
For a potential investment of $5,000, a portfolio has an EMV of $1,000 and a standard deviation of $100. What is the rate of return?
Answers
Answer:
The value is \(R = 20\%\)
Step-by-step explanation:
From the question we are told that
The potential investment is \(i = \$ 5000\)
The EMV of the portfolio is \(EMV = \$ 1000\)
The standard deviation is \(\sigma = \$ 100\)
Generally the rate of return is mathematically represented as
\(R = \frac{EMV}{i} * 100\)
=> \(R = \frac{1000}{5000} * 100\)
=> \(R = 20\%\)
what is the ratio of 1:2:4 multiply by 70
Answers
Answer:
0.125 is the answer (I don't know step by step)
PLEASE HELP WILL GIVE BRAINLIST
Answers
Answer:
3^6
Step-by-step explanation:
Answer:
answer is c 3⁶
Step-by-step explanation:
its 3 multiplied by itself 6 times
Ben plots a point on the coordinate plane below. One of the coordinates of the point is positive, and one is negative. In which quadrants could Ben plot the point?
Answers
Answer:
Me personally id say quadrant 4
Step-by-step explanation:
Find the value of p.
-25 = -4p + 19
Answers
4p= 19+25
2. Add 19 and 25
4p= 44
3. Divide by 4
p= 11
Answer:
9.75
Step-by-step explanation:
-25 = -4p + 19
-25 - 19 = -4p
-39 ÷ -4 = p
9.75 = p
Compare the best estimate for 1.789/178 and 0.05. Which is less?
Answers
Answer:
The smaller number in 0.01
Step-by-step explanation:
To find this answer, just take the fraction and find the quotient of both numbers.
1.789/178 = 0.01005056179
Now take the quotient and compare it to 0.05.
Is 0.01 larger or 0.05 - the answer is 0.01.
based on his past record, luke, an archer for a college archery team, has a probability of 0.90 of hitting the inner ring of the target with a shot of the arrow. assume that in one practice luke will attempt 5 shots of the arrow and that each shot is independent from the others. let the random variable x represent the number of times he hits the inner ring of the target in 5 attempts. the probability distribution of x is given in the table. P(X) 0 000001 0,00045 0.00810 0.07290 03280S 0.59049
What is the probability that the number of times Luke will hit the inner ring of the target out of the 5 attempts is less than the mean of X?
(A) 0.40951
(B) 0.50000
(C) 0.59049
(D) 0.91854
(E) 0.99144
Answers
The probability that Luke will touch the target's inner ring fewer times than the mean of X out of five attempts is 0.40951.
What is probability ?Probability refers to possibility.
A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.
Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.
According to our question-
P(target) equals 0.90
Let the random variable X stand in for the number of times the arrow is fired at the target's ring.
The probability distribution of X is
x: 0 1 2 3 4 5
P(x): 0.00001 0.00045 0.00810 0.07290 0.32805 0.59049
Hence, The probability that Luke will touch the target's inner ring fewer times than the mean of X out of five attempts is 0.40951.
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Assume that the matrices below are partitioned conformably for block multiplication. Compute the product shown Find the product, recalling that I is the identity matrix
Answers
The product is calculated by multiplying each row of matrix A by each column of matrix B and summing the results.The result of the operation is the matrix AB = [9 6; 5 4].
Matrix multiplication is defined as the process of multiplying two matrices together to form a third matrix. The product of two matrices A and B is denoted as AB. To calculate the product, each entry in the resulting matrix is calculated by multiplying each row of matrix A by each column of matrix B and summing the results. In other words, the entry in row i and column j of the product matrix AB is the sum of the products of elements in row i of matrix A and column j of matrix B.In the example given, the product of matrices A and B is AB. The product is calculated by multiplying each row of matrix A by each column of matrix B and summing the results. For example, the first entry in the product matrix, AB, is calculated as (1*2 + 0*3 + 0*4) + (0*2 + 1*3 + 0*4) + (0*2 + 0*3 + 1*4) = 2 + 3 + 4 = 9. The remaining entries are calculated in the same way. The result of the operation is the matrix AB = [9 6; 5 4].
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Solve
11× +9-7
8s- 11s+ 6s
Answers
Answer:
i dont know if this the answer for the first on x=1.45454545455 and the other on is 3s
Step-by-step explanation:
according to census the total number of male and female was 88,51,84,692, if number of male was 45,40,34,570what was the number of number of female population
Answers
According to census the total number of male and female was 88,51,84,692, if number of male was 45,40,34,570 the number of female population is 43,11,50,122.
To find the wide variety of girl population, we will subtract the quantity of male population from the full population.
Total population = 88,51,84,692
Number of male = 45,40,34,570
Number of female = Total population - Number of male
= 88,51,84,692 - 45,40,34,570
= 43,11,50,122
Therefore, the number of female population is 43,11,50,122.
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An angle whose measure is -302° is in standard position. In which quadrant does the terminal side of the angle fall?
- Quadrant I
- Quadrant II
- Quadrant III
- Quadrant IV
Answers
Answer: its quad 1
Step-by-step explanation:
Zero(s) where the graph touches, but does not cross the -axis for f(x)=(x+3)(x+2)(x-1)
Answers
The zero where the graph of f(x) touches but does not cross the x-axis is \(x = -2.\)
What is the function?To find the zeros of the function f(x)=(x+3)(x+2)(x-1) where the graph touches but does not cross the x-axis, we need to look for the point. where the function changes sign from positive to zero, without actually crossing the x-axis.
The function f(x) will touch but not cross the x-axis at the zeros where the multiplicity is even, which means that the factor (x-a) occurs in the factorization with an even exponent. Therefore, we need to find the roots of the function and determine their multiplicities.
To find the roots of the function, we set f(x) equal to zero:
\(f(x) = (x+3)(x+2)(x-1) = 0\)
This equation has three roots, which are -3, -2, and 1. We can see that all three roots have multiplicity 1, because each factor appears only once in the factorization.
Now we need to check the multiplicity of each root by looking at the sign of the function near each root. We will use the first derivative test to determine the sign of the function.
\(f'(x) = 3x^2 + 8x - 6\)
The critical points are the roots of the derivative, which are approximately -2.12 and 0.94. We can see that f'(x) is negative for x < -2.12, positive for -2.12 < x < 0.94, and negative again for x > 0.94.
Therefore, we can conclude that:
At x = -3, f(x) changes sign from negative to positive, so the graph of f(x) crosses the x-axis at x = -3.
At x = -2, f(x) changes sign from positive to zero, so the graph of f(x) touches but does not cross the x-axis at x = -2.
At x = 1, f(x) changes sign from negative to positive, so the graph of f(x) crosses the x-axis at x = 1.
Therefore, the zero where the graph of f(x) touches but does not cross the x-axis is \(x = -2\) .
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A woodworker builds a box as a present for her daughter. The box has a length of 2x + 2, a width of 3x, and a
height of 4x-2 Find the surface area and volume of the box in terms of x.
help me please
Answers
Answer:
Step-by-step explanation:
Length, L = 2x + 2
Width, W = 3x
Height, H = 4x - 2
\(Surface\ Area = 2 (LW + WH + HL)\\\\\)
\(= 2 ( (2x +2)(3x) + (3x)(4x -2) + (4x - 2)(2x + 2))\\\\=2(6x ^2 + 6x + 12x^2 - 6x + 8x^2 + 8x - 4x - 4)\\\\=2(26x^2 +4x -4) \ square \ units\)
\(Volume = L \times W \times H\)
\(= (2x+2)(3x)(4x-2)\\\\=(6x^2 + 6x)(4x-2)\\\\=24x^3 -12x^2 + 24x^2 - 12x\\\\=24x^3 +12x^2 -12x \ cubic \ units\)
2015-{2015÷5(x-5)÷5}=2014
Answers
Answer:
x=80.8
Step-by-step explanation:
follow BODMAS
2015-(2015÷5(x-5)÷5)=2014
2015-(2015÷5x-25÷5)=2014
2015-(405/x-5)=2014
2015-(405-5x)=2014
2015-405+5x=2014
1610+5x=2014
5x=2014-1610
(5x=404)1/5
x=80.8
A mans basic wage for a 40 hour week is 160 . He is paid 5 per hour for overtime .If he fors for 6.5 hours overtime in a certain week , his wages for that week is
Answers
Answer: $192.50
Step-by-step explanation:
wages for 40 hrs + wages for overtime work
$160.00 + 6hrs × $5.00 + $2.50 (1/2 hrs)
$192.50
Credit: anjalijalan3126
A restaurant mixes homemade barbecue sauce with their smoked pulled pork using a ratio of two cups of sauce for every four pounds of shredded pulled pork. Write two rates to represent this relationship.
Answers
The two rates that can be used to represent this relationship are:
2 cups : 4 pounds, and 1 cup : 2 poundsWhat is a ratio?A ratio is a comparison between two numbers that can be separated with (:) sign or can be represented as a fraction. This comparison deals with the same units.
However,
A rate of a ratio deals with the comparison between different units.From the parameters given:
The ratio rates occur between the homemade barbecue and smoked pulled porkFor every 2 cups of barbecue sauce, 4 pounds of pulled pork is used.
Therefore, we can conclude that the two rates that can be used to represent this relationship are:
2 cups : 4 pounds, and 1 cup : 2 poundsLearn more about ratio here:
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Express 602.16 dam in decimeters
Answers
The expression of 602.16 dam in decimeters can be written as 60216 decimeter.
How can the expression of 602.16 dam be converted to decimeters?The concept that will be used in the calculation is conversion. to perform this conversion, it is important to note that 1 Decimeter (dm) is equal to 0.01 dekameter (dam).
Then, if 1dm = 0.01 dam
Xdm = 602.16 dam
Where x is the value in decimeter.
Then we can cross multiply as :
X= (602.16 dam * 1dm)/ 0.01 dam
= 60216 decimeter.
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How many real and complex roots exist for the polynomial
F(x)= x³ +2x² + 4x+8 ?
OA. 2 real roots and 1 complex root
OB. 1 real root and 2 complex roots
C. 3 real roots and 0 complex roots
D. 0 real roots and 3 complex roots
Answers
The roots of the function F(x) = x³ + 2x² + 4x + 8 are given as follows:
B. 1 real root and 2 complex roots.
How to identify the zeros of the function?The function in this problem is defined as follows:
F(x) = x³ + 2x² + 4x + 8.
The function is of the third degree, hence the total number of zeros of the function is of 3.
From the graph, the function has only one x-intercept, which is given as follows:
x = -2.
Hence the two remaining roots are the complex roots, meaning that option B is the correct option for this problem.
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if the average of 6 numbers is 60, what is their sum?
Answers
Answer:
10
Step-by-step explanation:
The average of a dataset is the mean value of the dataset. It is calculated by dividing the sum of the dataset by the number of items in the dataset. The sum of the 6 numbers is 360.
Given that:
\(Average = 60\)
\(n = 6\) --- the number of data in the dataset
The average of a dataset is represented as:
\(Average = \frac{Sum}{n}\)
Make Sum the subject
\(Sum = Average * n\)
This gives:
\(Sum = 60 * 6\)
\(Sum = 360\)
Hence, the sum of the 6 numbers is 360.
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mark is paid $12.45 and hour at his job.he works a shift of 4 hours and 20minutes. how much does john earn for this shift?
Answers
Answer:
$53.95
Step-by-step explanation:
[Setting up an equation] 12.45x = y
() x is time worked and y is money made
[Plugging-in time worked] 12.45(4 \(\frac{1}{3}\)) = y
[Multiply] 53.95 = y
[Answer] y = $53.95
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
General form of
Y= 1/3x +3 and has an x intercept of 3
Answers
Answer:
Step-by-step explanation:
y
=
1
3
x
−
3
Use the slope-intercept form to find the slope and y-intercept
Slope:
1
3
y-intercept:
(
0
,
−
3
)
Any line can be graphed using two points. Select two
x
values, and plug them into the equation to find the corresponding
y
values.
x
y
0
−
3
3
−
2
Graph the line using the slope and the y-intercept, or the points.
Slope:
1
3
y-intercept:
(
0
,
−
3
)
x
y
0
−
3
3
−
2
image of graph
What is the solution to this system of equations?
8a−4b=20
5a−8b=62
a=
b=
Answers
Answer:
Hello there, I think this is the answer
a = - 2
b = - 9
i need assistance on This Math problem no links or I will report you
Answers
Answer:
B 26 < 30
Step-by-step explanation:
30 is greater than 26, and this is the only statement that is correct.
-2(x + 27) = -34
Well I need a hole lot of help
Answers
Answer: x=-2
Step-by-step explanation: Distribute then add -54 to both sides bam then divide by -2
Answer:
X= -10 | Hope this helped! :')
Steps for answer!
1. Divide both sides by -2.
x+27=-34/-2
2. Two negatives make a positive.
x+27=34/2
3. Simplify 34/2 to 17.
x+27=17
4. Subtract 27 from both sides.
x=17-27
5. Simplify 17-27 to -10.
x=-10
---------------------
Checking answer:
−2(x+27)=−34
1. Let x=−10.
−2×(−10+27)=−34
2. Simplify -10+27 to 17.
−2×17=−34
3. Simplify -2 x 17 to -34.
-34=-34
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