Which of the following is the parent function of all absolute value functions?
f(x) = 3x
f(x) = |x|
f(x) = 2|x|
f(x)=x²

Answers

Answer 1
f(x)=|x|

a parent function is the basic function before it has undergone transformations.

Related Questions

Suppose we have a stick of length 1.a) We randomly uniformly choose a point and break the stick into two pieces.Find the expected length of the smaller piece.b) We randomly uniformly choose two points (independently) and break thestick into three pieces. Find the probability that the three resulting piecescan be arranged to form a triangle (i.e. all triangle inequalities are satisfied;i.e no piece is longer than the sum of the other two).

Answers

Answer:

Step-by-step explanation:

1) The smaller sticks will range in length from almost 0 unit up to a maximum of 0.5 unit, with each length equally possible.

Therefore, the average length will be about (0 + 0.5)/2 = 0.25 unit

2)If you assume that each break in the stick is uniformly distributed along the length of the stick and is independent of the location of the other break, then the odds are 25% that you will be able to form a triangle with the 3 pieces.

We'll call the length of the stick 1, so each break can occur at a position in the interval [0,1]. Let x and y represent the two breaks. Then we can look at the area of the region in the square bounded x=0, x=1, y=0, y=1, which represents combinations of x and y, for which we can form a triangle. Since the area of the whole square is 1, the area of the region inside is our probability.

If y>x, then the lengths of the pieces are x, y-x, and 1-y.

The triangle inequality must hold for each combination of edges.

for y>x ...

x+y−x≥1−y

x+1−y≥y−x

y−x+1−y≥x

these simplify to...

for y>x ...

y≥1/2

x+1/2≥y

x≤1/2

If we cut our 1x1 square into two triangles along the line x=y,

then the region in the upper triangle which satisfies the inequalities above forms a smaller triangle which connects the midpoints of the upper triangle.

The lower triangle (x>y), is just a reflection about x=y of the upper triangle, so together, the entire region looks like a bow-tie at a 45 degree angle.

This region takes up 25% of the square, so the probability that you can form a triangle is 25%

For brainliest answer this ASAP


The hypotenuse of a right triangle is 4 meters more than three times the length of the shorter . The length of the longer leg is less than that of the hypotenuse. Find the length of the shorter leg of the triangle .

Answers

Answer:

The hypotenuse of a right triangle is 4m longer than the shorter leg and 2m longer than the longer leg. What are the lengths of the sides?

Just for variety, consider the hypotenuse = h, the short leg h-4 and the long leg h-2.

c^2 = a^2 + b^2; so h^2 = (h-4)^2 + (h-2)^2; h^2 = h^2 - 8h + 16 +h^2 -4h +4;

h^2 -12h +20 = 0 factors to (h - 10)(h - 2) = 0 so h = 2 or h = 10

Since (h - 2) = (2 - 2) = 0 and a triangle cannot have a side of zero length, 10 is the length of the hypotenuse.

h^2 = (h-4)^2 + (h-2); 10^2 = (10-4)^2 + (10-2); (10)^2 = (6)^2 + (8)

The hypotenuse is 10 cm, short leg 6 cm and long leg 8 cm.

I NEEEDDD HELPPP!!! someone please help me outttt

Answers

Answer:

45°

Step-by-step explanation:

Segments GJ and HK intersect at F.

That makes angles JFK and GFH vertical angles and congruent.

An arc has the same measure as its central angle.

m<GFH = 45°

m<JFK = m<GFH

m<JFK = 45°

please please please answer!! will give brainliest and extra points!

Answers

Answer:

a) y = x

b) y = 10

c) x = 3

Step-by-step explanation:

a) the line passes through the points (-5, -5) and (1, 1).

Step 1. Identify the slope

M = slope

M = change in y/change in x

Two points: (-5, -5) & (1, 1)

M = (y2 - y1)/(x2 - x1)

where y2 = 1 y1 = -5 x2 = 1 & x1 = -5

M = (1 - -5)/(1 - -5)

Note: Two negative signs together makes addition!

M = 6/6

M = 1

Step 2. Find the y-intercept

The slope is 1 but then we need a y-intercept. To do this we have to take a look when the first y-intercept happened.

Answer: y-intercept undefined so therefore our final answer is y = x
••••••••••••••••••••••••••••••••••••••••••••••••••
b) the line that passes through (-2, 10) and (3, 10).

If we would’ve graphed this, we can see that they’re in line with the y-axis so there wouldn’t be any slope.

Step 1. Find the slope.

M = slope

M = change in y/change in x

Two points: (-2, 10) & (3, 10)

M = (y2 - y1)/(x2 - x1)

M = (10 - 10)/(3 - -2)

M = 0/5

M = 0

Therefore the slope is 0

Step 2. Find the y-intercept

And the y-intercept is 10 obviously so now our answer would be y = 10
•••••••••••••••••••••••••••••••••••••••••••••••••••
c) the line parallel to the y-axis that passes through the point (3, -7)

Equation of line parallel to y-axis is x = k

(3, -7) lies on our required line

-> k = 3

The equation of the required line is x = 3
••••••••••••••••••••••••••••••••••••••••••••••••••
d) & e)

I don’t know the answer to the rest I’m sorry but at least appreciate these 3 answers that I’m giving you

Have a good day!

-Unluckydoom

20
2, Nine people fit comfortably in a 3 ft. by 3 ft. area. Use this value to
estimate the size of a crowd that is 8 yards deep and 1 mile long.
Determine the Area of the crowd?
A. Area = 3 feet x 3 feet
B. Area = 8 yards v 1 mile = (8 x 3 feet) x (1 x 5280 feet)
C. Area = 24 feet x 1 feet.
D. Area = 8 feet x 5280 feet
.

Answers

Answer:

B

Step-by-step explanation:

8 yards = 3 * 8 = 24 ft^2

1 mile = 5280

3*3 = 9 square feet

9 square feet holds 9 people.

1 square foot holds 1 person

8*3 * 5280 people could stand in an area of 8 yards * 1 mile

Though it's not quite correct, the answer is B

solve for θ.
sin(74) = cos(θ)

1. 6°
2. 74°
3. 36°
4. 16° ​

Answers

Sin74 = Cos16

cause 16 + 74 = 90

Whenever the sum of two angles is equal with 90, the Sin of one is equal with the Cos of the other like :

Sin(30) = Cos(60)

and also

Tan(30) = Cot(60)

Answer:

16

Step-by-step explanation:

sin(74) = cos(x)

sin(x)=cos(90-x)

sin (74) = cos(90-74)

sin 74 = cos( 16)

help me please its confusing

Answers

Answer:

9c^7d^13

Step-by-step explanation:

A matrix having unequal number of rows and columns is called​

Answers

A rectangular matrix :)

PLS HELP ASAP! 20 PTS

evaluate

Answers

Answer:

Step-by-step explanation:

Cos^-1(1/2) = 60

To get from a degree to radian, simply multiply by pi then divide by 180. So the final answer is 1/3pi or approximately 1.0472

I hope this helped! :D

the quotient of a number and -9 is increased by 10 the result is 11 what is the number? ​

Answers

Answer:

so the division of a number and -9 or

x/-9+10=11 or

(x/-9)+10=11

subtract 10 from both sides

x/-9=1

multiply both sides by -9

x=-9

f(x)=−4x
2
+5x
\text{Find }f(6)
Find f(6)

Answers

Answer:

-114

Step-by-step explanation:

f(x) = -4x^2 +5x

Let x = 6

f(6) = -4(6)^2 +5(6)

     = -4(36) +30

     - 144+30

   = -114

A basketball is shot into the air. Its height is represented by the polynomial equation h(t) = –16t2 + 35t + 5, where h is the height of the basketball at t seconds. What's the height of the basketball at 1.5 seconds?
Question 4 options:

20.2 feet


18.8 feet


21.5 feet


16.7 feet

Answers

Answer:

height = 21.5 ft

Step-by-step explanation:

Substitute t = 1.5 into h(t) and evaluate

h(1.5) = - 16(1.5)² + 35(1.5) + 5

        = - 16(2.25) + 52.5 + 5

       = - 36 + 57.5

      = 21.5 ft

Answer:

21.5 feet.

Step-by-step explanation:

Let t = 1.5

[tex]h(1.5)=-16(1.5)^2+35(1.5)+5\\h(1.5)=-36+52.5+5\\h(1.5)=21.5[/tex]

Therefore, at 1.5 seconds, the basketball is 21.5 feet in the air.

Suppose f(x) = x^2. what is the graph of g(x)

Answers

Answer:  g(x) = (1/16)*x^2

========================================================

Explanation:

Plug x = 4 into f(x) to find that f(4) = 16.

The output y = 16 drops to y = 1. We've multiplied by 1/16 to get this to happen.

In other words,

g(x) = (1/16)*f(x)

g(4) = (1/16)*f(4)

g(4) = (1/16)*16

g(4) = 1

So we can say that,

g(x) = (1/16)*f(x)

g(x) = (1/16)*x^2

and furthermore, we can say f(x) has been vertically compressed by a factor of 16.

Find the following measure for this figure.
12
10

Answers

Answer:

13 units

Step-by-step explanation:

Using the right triangle formed by the 2 legs and the slant height s

The legs are 12 and 10 ÷ 2 = 5, with hypotenuse s

Using Pythagoras' identity in the right triangle, then

s² = 12² + 5² = 144 + 25 = 169 ( take the square root of both sides )

s = [tex]\sqrt{169}[/tex] = 13

Hello! I really need some help with this (:

Answers

Answer:

y = 3x + 3

Step-by-step explanation:

As x increases, y increases by 3. Therefore, the slope of the function is 3.

Setting x = 0 will give an output of 3. Therefore, the y-intercept is (0, 3).

Overall, the function rule for the given data set is y = 3x + 3.

Pure mathematicsssss

Answers

Answer:

(i) a = 2

   b = -1

   c = -1

(ii) x= 1

Step-by-step explanation:

Step 1: Factorise

[tex]f(x) = 2(x^{2} -2x+\frac{1}{2})[/tex]  

Step 2: Use the complete square method.

[tex]f(x)=2(x^{2} -2x+(\frac{-2}{2})^{2} + \frac{1}{2} - (\frac{-2}{2})^{2} )[/tex]  

Step 3: Have it to [tex]a(x+b)^{2} +c[/tex]

[tex]f(x)=2((x-1)^{2} -\frac{1}{2} )\\ = 2(x-1)^{2} -1[/tex]

Line of symmetry:  

To find line of symmetry, we use -b/2a formula.

Based from [tex]2x^{2} -4x+1[/tex]:

a=2, b=-4

-b/2a = -(-4)/2(2) = 1

1:4 of 2,500 what is it???

Answers

Answer:

40% of 2500=

100

40

×2500

=1000

Step-by-step explanation:

Write the calculation exactly as you say it:

SEE QUESTION IN IMAGE

Answers

Answer:

20

Find the mean:

(2*1 + 1*2 + 2*3 + 1*4 + 2*5)/(2 + 1 + 2 + 1 + 2) = 3

Find the variance:

[2*(1-3)² + (2 - 3)² + 2*(3 - 3)² + (4 - 3)² + 2*(5 - 3)²]/8 = 18/8 = 9/421

Find the range:

10 - 2 = 8

Find the mean:

(2 + 3 + 4 + 5 + 6 + 6 + 7 + 8 + 9 + 10)/10 = 6

Find the variance:

[(2 - 6)² + (3 - 6)² + (4 - 6)² + (5 - 6)² + 2(6 - 6)² + (7 - 6)² + (8 - 6)² + (9 -6)² + (10 - 6)²]/10 = 6

The difference:

8- 6 = 222

The mean:

(0 + x + 2 + 3x + 6 + 4x + 8)/4 = 8

Find the value of x and the data points:

8x + 16 = 328x = 16x = 2

The points are:

0, 2 + 2 = 4, 3*2 + 6 = 12, 4*2 + 8 = 16

The mean deviation:

(0 - 8 + 4 - 8 + 12 - 8 + 16 - 8)/4 = 0

Note. Mean absolute deviation is different, this is the average of absolute values of mean deviations:

(8 + 4 + 4 + 8)/4 = 6

Helppp!! Summer math Packet!
(+4) +(-7) =

Answers

Answer: -3

Explanation: imagine you owe someone 7 dollars but you don’t have that yet. Later you pay them 4 dollars. Now you need to pay them 3 more dollars.

Step-by-step explanation:

(+4)+(-7)

=4-7

=-3

Hope it will help you..

How many number less than 300 is exactly divisible by 8, 12, 18?​

Answers

Count how many multiples of 8, 12, or 18 there are in the range {1, 2, 3, …, 300}:

⌊300/8⌋ = 37

⌊300/12⌋ = 25

⌊300/18⌋ = 16

(where ⌊n⌋ denotes the floor of n, i.e. the largest integer that is smaller than n; for instance, 300/8 = 37.5, so ⌊300/8⌋ = ⌊37.5⌋ = 37)

Take pairwise LCMs, as well as the LCM of all three numbers:

LCM(8, 12) = LCM(2³, 2²×3) = 2³×3 = 24

LCM(8, 18) = LCM(2³, 2×3²) = 2³×3² = 72

LCM(12, 18) = LCM(2²×3, 2×3²) = 2²×3² = 36

LCM(8, 12, 18) = LCM(2³, 2²×3, 2×3²) = 2³×3² = 72

Count how many multiples there are of each of these LCMs that are less than 300:

⌊300/24⌋ = 12

⌊300/72⌋ = 4

⌊300/36⌋ = 8

Then, using the inclusion/exclusion principle, the number of numbers less than 300 that are exactly divisible by 8, 12, or 18 is

{multiples of 8} + {multiples of 12} + {multiples of 18}

- {multiples of 24} - {multiples of 72} - {multiples of 36}

+ {multiples of 72}

= 37 + 25 + 16 - 12 - 4 - 8 + 4 = 58

You roll a six-sided number cube and flip a coin. What is the probability of rolling a number greater than 1 and flipping heads? Write your answer as a fraction in simplest form.

Answers

Answer:

5/12

Step-by-step explanation:

Number cube:

Numbers greater than 1 → 5 options out of 6

Coin:

Heads → 1 out of 2

Required probability:

P(>1 & H) = 5/6*1/2 = 5/12

Answer: Probability of rolling a number more than one: 5/6

Probability of heads: 1/2

Probability of both: 1/2 + 5/6 = 4/3

Step-by-step explanation:

pls look at the image and solve all.​

Answers

Answer:

Solution of question number 23

Step-by-step explanation:

Given,

5a - 12

= 5 × 12

= 15 - 12

= 3 answer

Find the value of x in each case

Answers

Answer: x=45

Step-by-step explanation:

To solve for x, we first need to understand the figure. We know TV and RS are parallel lines. If we extend TV to the left, we get a straight line parallel to RS. By Alternate Interior Angles, We know ∠R is equivalent to ∠T on the very left. Therefore, we can set it equal to 180° and solve.

x+2x+x=180          [combine like terms]

4x=180                  [divide both sides by 4]

x=45

Now, we know x=45.

Inverse property of addition for real numbers

Answers

Answer:

The answer would be -a

Step-by-step explanation:

In the examples,

5 + (-5) = 0

-1.33 + 1.33 = 0

THat means there will be a negative then a positive, or a positive then a negative.

INVERSE is the key word in this problem.

Please help me with this anyone please and thank you

Answers

Answer:

w∈ {-1/5, -5/3]

If this is what you were looking for...

SOMEONE PLEASE HELP ME ITS URGENT (PICTURE)

Answers

Answer:

Question #1

x and its opposing side are equal in length. One of the sides have no fence.

Set up an equation to find x:

[tex]x+x+10=26\\2x=26-10\\2x=16\\x=8[/tex]

The length of the side marked x is 8.0 m.

Question #2

New length = 10 + 1 = 11 cmNew width = xNew perimeter = old perimeter = 34 cm

Set up an equation to find x

[tex]11+11+x+x=34\\2x=34-22\\2x=12\\x=6[/tex]

The new width is 6 cm.

I don’t understand how taxes and discounts work in math, could someone explain to me?

Answers

Some additional context would be helpful in providing a complete answer. But the basic idea is this:

• Object ABC has a price X set on it.

• Hey, ABC is on sale! Let's say there's a 20% discount. That means 20% of the price X is subtracted from X.

• Boo, there's a 15% sales tax! This means whatever you would pay for ABC, discount included, you will ultimately have to pay an additional 15% of, or 0.15 times, that amount in tax.

Suppose you're looking to buy a T-shirt. The price tag on says it costs $25, but there's a 20% discount and a 15% sales tax.

• The discount has a value of 0.2 ($25) = $5. Subtract this from the original price, and its discounted price is $20.

• The sales tax is applied to this discounted price, and comes out to 0.15 ($20) = $3. This gets added to the discounted price, so you end up paying $23.

what is the angle what it use

Answers

Answer:

Which angle are you talking about please?

add a picture of your question if you can for further help to be offered ! :)

Find the value of f(x) at the given value of x: f(x) = (x -4)(x + 3), x = 3​

Answers

Answer:

-6

Step-by-step explanation:

f(x)= (3- 4)(3+3)

=( -1 )(6)

= -6

The recursive formula for a geometric sequence is: a = 4 an=an-1×3 What is the 3rd term of this sequence?​

Answers

Answer:

36

Step-by-step explanation:

a1 = 4

an=an-1 *3

a2 = a1 *3 = 4*3 = 12

a3 = a2*3 = 12*3 = 36

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