Use the graph of the function h below to find the following.All values at which h has a local minimum
All local minimum values of h
If there is more than one answer, separate them with commas.
Answers
Local minimums of a function are points where the function changes from decreasing to increasing. They are found at the x-coordinates where this change occurs, and their specific values are the y-coordinates of these points.
Explanation:A local minimum of a function is a point where the function has lower values than at all nearby points. To find these points on a graph, look for the locations where the function goes from decreasing to increasing. These are the x-values at which the function has a local minimum. To find the actual minimum values, find the y-coordinates of these points. For example, suppose function h has local minimums at x = -2 and x = 3. The y-coordinates of these points, say, y = -5 and y = 0, respectively, would be the local minimum values of h.
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Related Questions
Which equation shows y=−1/2x+4 in standard form?
A. 2x+y=8
B. x+2y=8
C. x+2y=-8
D. 2x-y=8
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Answer: B. x+2y=8
Explanation:
The original equation is:
[tex]y=-\frac{1}{2}x+4[/tex]
The problem asks us to convert the equation in the standard form, so in the form
[tex]ax+by=c[/tex]
with a,b and c being integers.
In order to do that, first of all let's bring on the same side both x and y:
[tex]y+\frac{1}{2}x=4[/tex]
Now we want the coefficient in front of x to be an integer, so let's multiply each term by 2, and we get
[tex]2y+x=8[/tex]
and this corresponds to option B.
The equation that represents y = -1/2x + 4 in standard form is 2x + y = 8.
The equation that shows y = -1/2x + 4 in standard form is 2x + y = 8.
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whats the inverse function of f(x)=3x-1
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Suppose that we have a system consisting of two interconnected tanks, each containing a brine solution. Tank A contains
x(t) pounds of salt in 200 gallons of brine, and tank B contains
y(t) pounds of salt in 300 gallons of brine. The mixture in each tank is kept uniform by constant stirring. When t = 0, brine is pumped from tank A to tank B at 20 gallons/minute and from tank B to tank A at 20 gallons/minute. Find the amount of salt in each tank at time t if x(0) = 10 and y(0) = 40.
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The pump is just mixing the water among the 2 tanks continuously. So eventually the concentration in each tank will be the same as concentration of both tanks put together.
Total gallons = 500, Total Salt = 50
Concentration = 50/500 = 1/10
If tank A has this concentration , then salt = 20
For tank B the salt amount is then 30.
This gives us 2 points, an initial amount and a finishing amount as t -> infinity.
To find functions for x(t) and y(t) , we need to look at the rate of change.
[tex]Rate = R_{in} - R_{out} [/tex]
For tank A, 20/300 or 1/15 of tank B salt is coming in. While 20/200 or 1/10 of its own salt is leaving.
For tank B its just the other way around.
This will give a system of 2 differential equations:
[tex]\frac{dx}{dt} = \frac{y}{15} - \frac{x}{10}[/tex]
[tex]\frac{dy}{dt} = \frac{x}{10} - \frac{y}{15}[/tex]
From this we can say:
[tex]\frac{dy}{dt} = -\frac{dx}{dt}[/tex]
[tex]y = -x+C[/tex]
Plug this in for y in the dx/dt equation:
[tex]\frac{dx}{dt} = \frac{-x+C}{15} -\frac{x}{10} = -\frac{x+C}{6} [/tex]
Solving this differential equation gives:
[tex] \int \frac{dx}{x+C} = \int -\frac{dt}{6} [/tex]
[tex]\ln (x+C) = -\frac{t}{6} +k[/tex]
[tex]x = k e^{-t/6} +C[/tex]
The dy/dt equation is solved exactly the same way, so you have:
[tex]y = k e^{-t/6} +C[/tex]
All thats left is to apply initial and final conditions to get constants.
The final solution is:
[tex]x(t) = -10e^{-t/6}+20[/tex]
[tex]y(t) = 10e^{-t/6}+30[/tex]
You have been hired as an efficiency expert for Math Nerds Inc. The company wants to cut costs and increase profits by increasing the number of math problems their employees can solve in a day. Your job is to help the Math Nerds employees solve math problems more quickly. Show the Math Nerds employees how to rework each problem below using a polynomial identity. (x2+y2)2=(x2-y2)2+(2xy)2
Show the Math Nerds employees how much time you save on each problem by using the polynomial identity to simplify.
1) ( x+2 ) 2 (x+2) 2 = (x+y) 2 =x 2 +2xy+ y 2
2) ( x−3 ) 3 (x−3) 3 = (x−y) 3 =x 3 −3 x 2 y+3x y 2 − y 3
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(x+2)2
without writing (x+2)(x+2)=x2+2x+2x+4=x2+4x+4 instead say y=2 and use the identity to get
x2+2×2x+2^2=x2+4x+4
For every problem-solving activity it's crucial that no less than five alternatives be considered.
True
False
Answers
Problem-solving activity includes
1.Understanding the problem,that is nature of the problem, then Completely define in your own way.
2. Determining why this problem has accrued,
3. Identifying the ways to solve the problem,
4. Prioritizing the given alternatives that is ways and then arranging the alternatives for a solution,
5. Then applying the best solution or arrangement for the given problem.
There are two ways considered for problem-solving activity
(1). Trial and Error (2) Reduction in steps
It totally depends on the kind of problem , which you are solving. There may be Less than five alternatives ,equal to five alternatives or more than five alternatives to solve the problem.
Option B: False
Solve the equation for the letter L: A=LW
Answers
Answer:
[tex]L=A/W[/tex]
Step-by-step explanation:
we have
[tex]A=LW[/tex]
Solve for L means -------> isolate the variable L
so
Divide by [tex]W[/tex] both sides
[tex]A/W=LW/W[/tex]
Simplify
[tex]L=A/W[/tex]
Jake earns $7.50 per hour working at a local car wash. The function, ƒ(x) = 7.50x, relates the amount Jake earns to the number of hours he works. Write the inverse of this relation
Answers
where x is the number of hours that Jake works.
f ( x ) = y
y = 7.50 x
x = y / 7.50
Answer:
The inverse is:
y = x / 7.50
For this case we have the following function:
[tex] f(x) = 7.50x
[/tex]
An equivalent way to write this function is:
[tex] y = 7.50x
[/tex]
From here, we clear the value of x.
We have then:
[tex] x = \frac{y}{7.50}
[/tex]
Returning the variables we have that the inverse of the function is:
[tex] f (x) ^ - 1 =\frac{x}{7.50}
[/tex]
Answer:
the inverse of this relation is:
[tex] f (x) ^ - 1 =\frac{x}{7.50}
[/tex]
Each month, the census bureau mails survey forms to 250,000 U.S. households asking questions about the people living in the household and about things such as motor vehicles and housing costs. Telephone calls are made to households that don't return the form. In one month, responses were obtained from 240,000 of the households contacted. The population of interest is A.the 240,000 households contacted. B.the 250,000 households contacted. C.only U.S. households with phones. D.all U.S. households.
Answers
Because the 240,000 responses are from them. Furthermore, with the given information you do not know how many of those responses came due to the frist contact (by mail) or due to the phone call made to the houses that didn't return the form when received the mail.
if x=y and y=2 then 3x=
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try urself and tell me the result
____ two points are collinear.
A. Any
B. Sometimes
C. No
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for 2 answer is Any.
What is 1.2 divided by 9?
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Trylon Eager took out an $85,000, 20-year term policy at age 40. The premium per $1,000 was $5.00. He will be 60 years old this year. The premium per $1,000 will be $5.90. The percent increase to the nearest whole number is ____%. (Enter only the number.)
Answers
Hey guys I have 2 short Q! Ill mark as brainliest whoevr helps me ^~^ ThankU x3 (IMAGE is Below for both Qs!)
What is the length of leg y of the right triangle?
A right triangle with hypotenuse 37 and legs 35 and y
A) 2
B) 8
C) 12
D) 35
#2: Which of the following shows the length of the third side, in inches, of the triangle below?
A right triangle is shown. One side of the triangle is labeled as 25 inches. The height of the triangle is labeled as 15 inches.
A) 20 inches
B) Square root of 850 inches
C) Square root of 10 inches
D) 40 inches
Answers
35^2 + y^2 = 37^2
y^2 = 37^2 - 35^2
y^2 = 1369 - 1225
y^2 = 144...take sqrt of both sides, eliminating the ^2
y = sqrt 144
y = 12 <===
a^2 + b^2 = c^2
15^2 + b^2 = 25^2
b^2 = 25^2 - 15^2
b^2 = 625 - 225
b^2 = 400
b = sqrt 400
b = 20 <===
ALGEBRA 1 help please!! Urgent
Answers
9/10x + y = 5/3...multiply entire equation by common denominator 30
27x + 30y = 50 <==
Given 9801 = 3x3x3x3x11x11 , find √9801 (square root i think) ...?
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Is the root of 9801
Use trigonometric substitution to write the algebraic expression as a trigonometric function of θ, where 0 < θ <π/2.
√(100) - 4x^(2), x = 5cos(θ)
Answers
case 1
perhaps it is √(100)² - 4x^(2), x = 5cos(θ)
because if so, √(100)²=100
√(100)² - 4x^(2) = 100- 100cos²(θ) = 100( 1 - cos²(θ))= 100sin²(θ), and
0 < θ <π/2.
case2
if it is true that √(100) - 4x^(2), the possible equality is √(100) - 100cos²(θ)
What is the length of a picture frame whose width is 3 inches and whose proportions are the same as a 9-inch wide by 15-inch long picture frame?
Answers
Proportion is 3:5
So if width is 3 then the length shud be 5
5 inches
Does 1/3 divided by 4 equal 1/12
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PLEASE HELP!
The initial amount of people that are sick with the flu is 36 and growing at a rate of 8% every day.
How many people will be sick with the flu in 11 days?
Round to the nearest whole number.
Answers
Answer: 84
Step-by-step explanation:
36 Counts as day 0
Day 1 : 36 x 1.08 = 38.88
Day 2 : 38.88 x 1.08 = 41.9904
Day 3 : 41.9904 x 1.08 = 45.349632
Day 4 : 45.349632 x 1.08 = 48.97760256
Day 5 : 48.97760256 x 1.08 = 52.8958107648
Day 6 : 52.8958107648 x 1.08 = 57.127475625984
Day 7 : 57.127475625984 x 1.08 = 61.69767367606272
Day 8 : 61.69767367606272 x 1.08 = 66.6334875701477376
Day 9 : 66.6334875701477376 x 1.08 = 71.964166575759556608
Day 10 : 71.964166575759556608 x 1.08 = 77.72129990182032113664
Day 11: 77.72129990182032113664 x 1.08 = 83.9390038939659468275712
83.9390038939659468275712 rounded to the nearest whole number is 84.
Based on the number of people who were initially sick and the rate of increase, the number who will be sick in 11 days is 84 people.
To find the number who will be sick in 11 days use the future value formula:
= Initial people x ( 1 +rate) ^ number of days
Solving will give:
= 36 x ( 1 + 8%) ¹¹
= 83.9
= 84 people
In conclusion, 84 people will be sick.
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The sum of nine times a number and fifteen is less than or equal to the sum of twenty-four and ten times the number
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q plus 12 minus 2=????
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plz help asap!!!! the perimeter of a rectangle is 200 cm. what is the length of the rectangle if the width is y cm?
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the length is 80
minimize Q=x^2+2y^2, where x+y=3
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To minimize the function Q=x^2+2y^2, substitute x=3-y and expand the expression. Use the vertex formula to find the minimum value of Q. The minimum value is 13.5 when x=1.5 and y=1.5.
Explanation:To minimize the function Q=x^2+2y^2, where x+y=3, we can substitute x=3-y into the function to get Q=(3-y)^2+2y^2. Expanding this expression gives Q=9-6y+y^2+2y^2. Combining like terms, we have Q=3y^2-6y+9.
To find the minimum value of Q, we can use the vertex formula. The x-coordinate of the vertex of the parabola represented by Q=a(x-h)^2+k is x=-h. In our case, h=-(-3)/2=1.5. Substituting this value of x into the equation Q=3y^2-6y+9 gives Q=3(1.5)^2-6(1.5)+9=13.5-9+9=13.5.
Therefore, the minimum value of Q is 13.5 when x=1.5 and y=1.5.
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At the bank, brent exchanges $50 in bills for 50 one-dollar coins. the total mass of the coins is 405 grams. estimate the mass of 1 one- dollar coins
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What is the gratest common factor of 84 and 108?
Answers
108: 1,2,3,4,6,9,12,18,27,36,54,108
Therefore, your G.C.F. is: 12
The distance between two cities is one hundred miles, and a woman drives from one city to the other at a rate of fifty mph. At what rate must she return if the total travel time is three hours and forty minutes?
Answers
v1= 50mph
d1=100 m
t1=?
t=d/v=100/50=2h
that's meat that she will take 2hours during the first travel
and total travel time = 3h
she wants to take only 1 h in her second travel
v2=?
d2=100 m
t2= 1h
v2= d2 *t2 =100mph
#
well in her first travel (when she goes to the anther city)
v1= 50mph
d1=100 m
t1=?
t=d/v=100/50=2h
that's meat that she will take 2hours during the first travel
and total travel time = 3h
she wants to take only 1 h in her second travel
v2=?
d2=100 m
t2= 1h
v2= d2 *t2 =100mph
total travel time is 3 hours and 40 minutes so i belive the correct answer is 60mph
Which of these transformations are isometries? The diagrams are not drawn to scale.
Answers
First and second we flipped horizontaly while last one we flipped both verticaly and horizontaly but sides and angles remained the same.
Answer:
the answer is D. I, II, and III
Step-by-step explanation:
What's the answer I don't know it
Answers
What is the period of y = 5 cos x?
What is the period of y= cos 5x
Answers
first case, B = 1
Second case, B = 2
so period of 5*cos x is 2pi/1 = 2pi
period of cos 5x is 2pi/5
hope this help
A high school chorus has $1000 in its school account at the beginning of the year. They are putting on a fall concert to raise money for a trip later in the year. At the concert last year they sold tickets for $10 each. If they sell tickets at the same price the total amount in the chorus account can be represented by the linear function T = 10x + 1000. If they increase the ticket price to $15, how many tickets will they have to sell to have a total of $4000 in the account?
A) 100 tickets
B) 150 tickets
C) 200 tickets
D) 250 tickets