Consider the functions:


f(x) = x2


g(x) = (x + 1)2 – 2


h(x) = (x + 3)2 + 4


Which statement describes the relationship between the minimums of the functions?


a The minimum of h(x) is farther left and up than the minimum of f(x) and g(x).

b The minimum of g(x) is in the fourth quadrant. The minimum of h(x) is in the first quadrant.

c The minimum of g(x) is farther right and down than the minimum of f(x) and h(x).

d The minimum of g(x) is in the second quadrant. The minimum of h(x) is in the first quadrant.

Answers

Answer 1

Answer:

a The minimum of h(x) is farther left and up than the minimum of f(x) and g(x)

Step-by-step explanation:

To know the relation between the minima of the functions you calculate the minima by using the derivative:

[tex]f'(x)=2x\\\\g'(x)=2(x+1)\\\\h'(x)=2(x+3)[/tex]

to find the values of x you equal the derivative of the function to zero:

[tex]f'(x)=0;\ x=0;\\\\g'(x)=0; \ x=-1;\\\\h'(x)=0;\ x=-3;[/tex]

by evaluating this values of x you obtain the coordinates of the minima:

[tex]f(0)=0\\\\g(-1)=-2\\\\h(-3)=4[/tex]

hence, the coordinates will be:

f -> (0,0)

g -> (-1,-2)

h -> (-3,4)

hence, the relation is:

a The minimum of h(x) is farther left and up than the minimum of f(x) and g(x).


Related Questions

Bobby is helping buy meats, for grilling, for the school picnic. He bought 10 pounds of sausage at $1.69 per pound, 100 pounds of hamburgers at $1.99 pound, 1,000 pounds of hot dogs at $2.09 per pound, and 100 pounds of chicken at $3.69 per pound. Which of the items he bought cost the most?

Answers

Answer:

It would be the chicken.

Step-by-step explanation:

10×1.69= $16.90

100×1.99= $199.00

1000×2.09= $2090.00

100×3.69= $3691.00

what is the value of X?

Answers

Answer:

x = 1

Step-by-step explanation:

Triangle ABC is congruent to Angle DEF

13x - 12 = 7x - 6

6x = 6

x = 1

Answer:

x = 1

Step-by-step explanation:

These are congruent triangles

The single line is the same length in ABC as the single line in DEF

The double line is the same length in ABC as the double line in DEF

13x-12 is the same length as 7x-6

13x-12 = 7x-6

Subtract 7x from each side

13x-12 -7x =7x-6 -7x

6x-12 =-6

Add 12 to each side

6x-12+12 = -6+12

6x = 6

Divide each side by 6

6x/6 = 6/6

x = 6/6

x = 1

Can you guys help please I’ll give brainliest

Answers

Answer:

The admission fee for the movies is 1.7$ per group.K amount of people buy popcorn,which is 3 dollars each.You end up spending 18.2$.How much people did you bring in your group?

Step-by-step explanation:

Using the sum of the angle measures of a triangle,
m

Answers

Answer:

a = 2.18 units

Step-by-step explanation:

[tex] \sin \: 33 \degree = \frac{a}{4} \\ 0.544639035 = \frac{a}{4} \\ a = 4 \times 0.544639035 \\ a = 2.17855614 \\ a = 2.18 \: units[/tex]

The sum of the angles in a triangle is always 180 degrees. This fundamental concept helps in calculating unknown angles in triangles.

Triangle Angle Sum Theorem: The sum of the angles in a triangle is always equal to 180 degrees.

Explanation: In any triangle, the three interior angles add up to 180 degrees. This theorem is fundamental in geometry and can be used to solve for unknown angles in triangles.

Example: If two angles in a triangle are 30 degrees and 60 degrees, the third angle can be found by subtracting the sum of the given angles from 180, which gives 90 degrees.

1 point
1.
The slide at the playground has a height of 6 feet. The base
of the slide measured on the ground is 8 feet. What is the
length of the slide?

Answers

Answer:

The length of the slide is 10 feet.

Step-by-step explanation:

To find the length of the slide you have to use the formula:

a^2 + b^2 = c^2 (^2 means squared)

In this case:

a= 6 and b=8 c= unknown

6 squared (6 times 6) is 36

8 squared (8 times 8) is 64

Add these two numbers to get:

36+64=100

6^2+8^2=100

However, the length of the slide in not 100 feet. In order to find the correct length you must find the square root of 100. Which is 10.

What number times itself equals 100? 10.

The length of the slide in 10 feet.

Solve for b. 9000-b=-11,000+b

Answers

Answer:

b=10,000

Step-by-step explanation:

[tex]9,000-b=-11,000+b[/tex]

Regroup terms

[tex]9,000-b=b-11,000[/tex]

Add b to both sides

[tex]9,000-b+b=b+b-11,000\\9,000=2b-11,000[/tex]

Add 11,000 to both sides

[tex]9,000+11,000=2b-11,000+11,000\\9,000+11,000=2b[/tex]

Simplify by adding

[tex]20,000=2b[/tex]

Divide both sides by 2

[tex]\frac{20,000}{2}=\frac{2b}{2}\\ \\10,000=b[/tex]

Switch sides

[tex]b=10,000[/tex]

Done.

Answer:

b=10000

Step-by-step explanation:

add b on both sides

9000=-11000+2b

add -11000 on both sides

20000=2b

divide by 2 on both sides

b=10000

Graph the polygon with vertices at P (–4, 8),
Q (0, 8), R (4, –2), and S (–8, 3).

What is the name of this polygon?
Heptagon
Hexagon
Quadrilateral
Triangle

Answers

Answer:

Quadrilateral

Step-by-step explanation:

When Theresa walks at a pace of 88 steps per minute, it takes her 90 minutes to walk the trail. If she alters her pace to 33 steps per minute, how long will it take her to walk the trail?

Answers

Answer: 33 minutes

Step-by-step explanation:

Hi to answer this question we have to write a proportion

Speed rate = 88 step per minute

Time = 90 minutes

So, the proportion is 88 step/min / 90 minutes

For 33 steps per minutes = 33 / x minutes

88/90 = 33/x

solving for x:

x= 33/ (88/90)

x = 33.75 = 33 minutes.

Feel free to ask for more if needed or if you did not understand something.

You are designing a circular path surrounding a circular pond. The pond has a diameter of 90 feet. The path is 15 feet wide. (the outer edge of the path is 15 feet from the edge of the pond.) What is the area in square-feet of the path?

Answers

Answer:

The area of the path is 11,304 square feet.

Step-by-step explanation:

Please see the attached files for details

The expression equivalent to sin 3x+ sin xis
The expression equivalent to sin 3x sin xis

Answers

Answer:

jvjfufjgjgkggjchvkvkf

I need help figuring which of the answers are it I need to pick 3 please help

Answers

a , b & c ?
lmk if i’m wrong tho

How many solutions does 5-2x=3+x-4-3x have?

Answers

Answer:

no solutions

Step-by-step explanation:

A linear equation having same variable term on both RHS and LHS is not defined. The number of solutions for the equation 5 - 2x = 3 + x - 4 - 3x is zero.

What is a Linear equation?

A linear equation is can be defined as a equation that has its degree as one.

To find the solution of n unknown quantities n number of equations with n number of variables are required.

The given equation is as below,

5 - 2x = 3 + x - 4 - 3x

It can be simplified as,

5 - 2x = 7 - 2x

Since both LHS and RHS contain the same variable term 2x which can be cancelled out so that there will be no variables.

Thus, the given equation has no solutions.

Hence, the number of solutions for the given equation is zero.

To know more about linear equation click on,

brainly.com/question/11897796

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Select the two statements that are true about the equation y-5= 12(x - 4).

Answers

Answer:

I know one answer is "The slope of the line is 12" Not sure about the other answer though

Step-by-step explanation:

sorry

Answer:

The two answers are the slope is 12 and one point on the line is (4,5)

Step-by-step explanation:

[x = -4y] [3x + 2y = 20] *

Answers

Hi there! Hopefully this helps!

-----------------------------------------------------------------------------------------------------------

Answer to solving for y: y = -2.

Answer for simplifying the expression: -12y - 4.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

We are given that x = -4y and that the equation is 3x + 2y = 20.

We need to evaluate.

3x + 2y = 20

||

\/

3(-4y) + 2y = 20.

To solve for y, y = -2.

||

\/

3(-4y) + 2(-2) = -12y - 4.

Answer:

y= -2 x=8

Step-by-step explanation:

3 (-4y)+2y=20

-12y+2y=20

-10y=20

y= -2

x= -4 (-2)

x=8

Solve these equations

|x+8|=−2

Answers

Answer:

no solution

Step-by-step explanation:

lets isolate the absolute value first:

so

|x|-8+8=-2-8

|x|=-10

since absolute value cannot be less than -10, there is no solution.

Hope this helps!

The equation |x+8|=−2 has no solution because the absolute value of a number cannot be negative.

The equation |x+8|=−2 does not have a solution because the absolute value of a number is always non-negative, and it cannot equal a negative number. The absolute value represents the distance from zero on the number line, and distance cannot be negative. Thus, the equation |x+8|=−2 is inconsistent because it implies that a non-negative quantity (the absolute value) is equal to a negative number (−2), which is not possible.

When solving equations involving absolute values such as |x| = a, if 'a' is positive, then the solutions are x = a or x = -a, because both distances a and -a from zero have the same absolute value. However, if 'a' is negative, the equation has no solution, as the absolute value cannot take on negative values. If you encounter an absolute value equation set to a negative number, you can immediately conclude that there are no solutions.

PLEASE HELP ME!
What is the Area?
A.
176 in.2

B.
88 in.2

C.
64 in.2

D.
30 in.2

Answers

it’s B.
Because formula of triangle is
1/2 x base x height
The height is 8inches and base is 22 inches.
so 1/2 x 8 x 22 = 88:)

Answer:

88

Step-by-step explanation:

You multiply the base times height which is 22 times 8 and divide it by 2.

(08.05)Some students reported how many textbooks they have. The dot plot shows the data collected:
Students' Textbooks
2 3 4 5 6
Number of Textbooks
What do the dots above the number 6 indicate?
A•There are exactly 6 students with 4 textbooks
B•There are exactly 4 students with 6 textbooks
C•There are exactly 6 students with less than 4 textbooks
D•There are exactly 4 students with less than 6 textbooks
(PLEASE NO GUESSING)
:)​

Answers

Answer:

There are exactly 4 students with 6 textbooks.

Hope this helps! :)

Answer:

B

Step-by-step explanation:

The dots on the lines indicate how many students have that specific number of textbooks.

The mark at 6 on the number line indicates 6 textbooks. The dots above it indicate how many students have 6 textbooks. Since there are 4 dots, we know that 4 students have 6 textbooks.

Thus, the answer is B.

Hope this helps!

Which of the following is equivalent to 180 centimeters?
Choose 1 answer:
0.18 meter
1.8 meters
18 meters
18,000 meters
180,000 meters
HELP ME OUT ASAP !!! PLEASEEEEE

Answers

The answer is 1.8 meters

Answer:

1.8 meters there are 100 cm in every meter.

Step-by-step explanation:

By combining with the name of the unit the prefixes deka, hecto, and kilo meaning, respectively, 10, 100, and 1000, and deci, centi, and milli, meaning, respectively, one-tenth, one-hundredth, and one-thousandth

Based on what you have learned about Malala’s viewpoints and setting, why is a blog a good way for Malala to speak up? Write two to four sentences explaining your answer.

Answers

Malala can express her opinion and share with others around the world. She can also be in control with her website/blog. I hope this helps! I think more info would’ve helped!

Sample Response: Malala lived in the Swat Valley, which was taken over by the Taliban. Using a blog was a good way for her to let people all over the world know that she disagreed with the Taliban's view of girls' education. Even though she lived in a small and faraway city, the blog gave her a huge audience that she could reach at the click of a button.

on the first day of every month Katie gets 450 phones she repairs 10 phones every day how many phones does she have left to repair at the end of the 11 day of the month​

Answers

Answer:

340 phones

Step-by-step explanation:

Make an expression

She repairs 10 phones each day, d.

Each day she repairs 10 phones, it is 10 phones off the total number (450) she has to repair, so we can subtract 10d from 450.

450-10d

We want to find how many she has left after 11 days, so we can substitute 11 in for d

450-10(11)

Multiply

450-110

340

She will still have 340 phones left to repair

Final answer:

Katie would have repaired 110 phones by the end of the 11th day. She started with 450 phones, so after subtracting the number of repaired phones, she has 340 phones left to repair.

Explanation:

To determine the number of phones Katie has left to repair at the end of the 11th day, we need to calculate how many phones she has repaired so far. Since Katie repairs 10 phones every day, after 11 days, she will have repaired 10 phones/day * 11 days = 110 phones.

Katie starts with 450 phones at the beginning of the month. So, to find out how many are left un-repaired, you subtract the number of phones she has repaired from the starting amount.

Therefore, 450 phones - 110 phones = 340 phones are left to repair at the end of the 11th day.

Learn more about Simple Subtraction here:

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Express 15 seconds as a fraction of 2 hours

Answers

It’s 1/4 hope it helps:))
Final answer:

To express 15 seconds as a fraction of 2 hours, first convert 2 hours to seconds, which is 7200 seconds. The fraction is thus 15 / 7200, and simplified, it is 1/480.

Explanation:

To express 15 seconds as a fraction of 2 hours, we need to convert both quantities to the same unit.

There are 60 seconds in a minute and 60 minutes in an hour, so 2 hours is equivalent to 2 × 60 × 60 = 7200 seconds.

The fraction representing 15 seconds out of 2 hours is therefore 15 / 7200.

Simplifying this fraction, we divide numerator and denominator by the greatest common divisor (15), which gives us 1 / 480. Thus, 15 seconds is 1/480 of 2 hours.

Now let's review some additional units of time:

15 minutes + 60 minutes = 75 minutes,10 minutes + 20 minutes = 30 minutes,15 seconds + 45 seconds = 60 seconds or 1 minute.

For conversion, 1 hour is equal to 60 minutes, so if we have 100 minutes, we can represent it as 1 hour 40 minutes. Similarly, the sum of 1 hour 55 minutes and 45 minutes is 2 hours 40 minutes.

It's important to remember to start your subtractions by subtracting seconds from seconds and minutes from minutes, borrowing from the larger units when necessary.


Write a number in the blank space so that the equation will have an infinite number of solutions

The answer is 3x + 5 = 3x - ______ has infinitely many solutions- type a number only

Answers

Answer: 5

Step-by-step explanation:

3x + 5=3x - 5

Final answer:

To achieve an infinite number of solutions in the equation '3x + 5 = 3x - ______', the blank should be filled with the number 5, making both sides of the equation identical and true for all values of x.

Explanation:

To make an equation have an infinite number of solutions, both sides of the equation must be identical. Looking at the equation 3x + 5 = 3x - ______, we want to find the number that would make the statement an identity.

The only way for this equation to have infinite solutions is if the variable terms (3x) are equal and the constant terms are also equal. Hence, the blank must be filled with the number 5, making the equation 3x + 5 = 3x + 5, which is true for all values of x.

estimate 54.57 + 47.870 by first rounding each number to the nearest whole number

Answers

Step-by-step explanation:

Rounding to the nearest whole so 54. 57 will be 55 and 47.870 will be 48 so

55 + 48 = 103

What is the recursive rule for the sequence:

11, 22, 44, 88...

Answers

Answer:

The recursive rule for the sequence is

[tex]a_n= 2a_{n-1}[/tex] ,

where n is positive integer.

Step-by-step explanation:

Given sequence is

11,22,44,88........

Here the first term of the sequence is = 11

Second term of the sequence is = 22

Third term of the sequence is = 44

Fourth term of the sequence is = 88.

............

Second term = 2×first term

Third term = 2 × Second term

Fourth term = 2 × Fourth term

The recursive rule for the sequence is

[tex]a_n= 2a_{n-1}[/tex] ,

where n is positive integer.

THIRD TIME ASKING THIS) A multiple choice question has 6 options. What is the percentage of getting the answer correct ? Can you write the answer as a ratio too?

Answers

Answer:

1:6

Step-by-step explanation:

cause it is

Well if you divide 100 by 6 that would give you about a 16.7% chance that you will get the correct answer.


If it were it be written ratio then only 1 answer is correct so it would be 1:6.

Find the percent of change between the two numbers 2 and 1.42.

Answers

Answer:

29%

Step-by-step explanation:

[tex] \frac{0.58}{2} \times 100 \\ [/tex]

29%

Percent decrease formula: new value - old value / old value

Solve with the given values.

2 - 1.42 / 2

0.58 / 2

0.29

Turn the decimal into a percentage.

0.29 * 100% = 29%

Therefore, there is a 29% decrease.

Best of Luck!



Solve: 2x =

1

8


Step 1: 2x = 8-1

Step 2: 2x = 2-3

Step 3: x = -3

Heather is solving the problem. Determine the step(s) in which Heather made a mistake, if any.


A) Step 1

B) Step 2

C) Step 3

D) There is no mistake

Answers

Answer:D

Step-by-step explanation:

Nam has a bag of 8 chips numbered 1 to 8. He will perform an experiment to model the theoretical probability of pulling a chip with the number 6.

Select from the drop-down menus to correctly complete the sentences.
Nam should pull a chip and replace it after each turn
A. as many times as possible
B. 8 times

, and then divide the number of times 6 occurs by
A. 8
B. the number of trials

. After many trials, the experimental probability will be close to the theoretical probability of
A. 1/8
B. 2/3
C. 1/6
.

Answers

B is the correct answer I believe

Answer:

1. A

2. B

3. A

Step-by-step explanation:

He should conduct the experiment as many times as possible, more the better estimate can be obtained.

Record the no. of 6's and divide the no. of trials to get an estimate of the probability of 6

After many trials, the experimental probability would get closer and closer to the theoretical probability which is 1/8

1. Liza and Marta mow lawns during the summer to earn money. Liza determined that she can earn between $6.00 and $6.25 per hour. Marta estimates that she earns between $7.50 and $8.00 per hour. About how much more money will Marta earn than Liza if they each work 22 hours?
A. $25.01 to $45.00
B. $65.01 to $85.00
C. $45.01 to $65.00
D. $5.00 to $25.00




2. Last month, Belinda worked 160 hours at a rate of $10.00 per hour. If her employer retains 9% of her gross salary, is $1,500 a reasonable estimate of her net salary?
A. Yes, because $1,500 is close to
B. No, because $1,300 is a better estimate.
C. No, because retaining 10% of her salary would leave her with about $1,350.
D. Yes, because her salary will be a bit more than 1600-160=1440

Answers

Answer:

$137.50 for Liza with cents and 132 without any cents. $154 for marta wihtout cents and 165 dollars with cents. First try subtracting 137.50 from 165 and then try 154 subtract 132.

step-by-step explanation:

First you need to multiply 6 x 22 and you get your dollars! Then multiply 22 x 25 to get your cents. Also try to do it without any cents. Convert all your cents to dollars and add to your product. And multiply 7 x 22 to get the amount of dollars for marta and 50 x 22 to get the cents for marta. Also try it without cents like it could be right or wrong. Convert the cents to dollars. Lastly, subtract what marta got in 22 hours and liza got in 22 hours. Pick the closest answer.

Answer:

$25.01 to $45.00

Step-by-step explanation:

im not 100% sure so lmk if im wrong plss

its right i just took the quiz

what is the vertex, axis of symmetry, domain, and range of the graph above in the picture.

Answers

Answer:

1,-4 is the vertex x=1 is the axis of symetry and domain is positive infinity to negative infinity y is any number greater than or equal to -4

Step-by-step explanation:hope this helps god bless please giv brainlyest

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