Given the function h(x) =1/3 |x-6| +4, evaluate the function when x = - 3, - 2, and 0

H(-3) =
H(-2)=
H(0)=

Answers

Answer 1

|x| = x for x ≥ 0

examples:

|3| = 3; |0.56| = 0.56; |102| = 102

|x| = -x for x < 0

examples:

|-3| = -(-3) = 3; |-0.56| = -(-0.56) = 0.56; |-102| = 102

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

Use PEMDAS:

P Parentheses first

E Exponents (ie Powers and Square Roots, etc.)

MD Multiplication and Division (left-to-right)

AS Addition and Subtraction (left-to-right)

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

[tex]h(x)=\dfrac{1}{3}|x-6|+4[/tex]

Put the values of x to the equation of the function h(x):

[tex]x=-3\to h(-3)=\dfrac{1}{3}|-3-6|+4=\dfrac{1}{3}|-9|+4=\dfrac{1}{3}(9)+4=3+4=7\\\\x=-2\to h(-2)=\dfrac{1}{3}|-2-6|+4=\dfrac{1}{3}|-8|+4=\dfrac{1}{3}(8)+4=\dfrac{8}{3}+\dfrac{12}{3}=\dfrac{20}{3}\\\\x=0\to h(0)=\dfrac{1}{3}|0-6|+4=\dfrac{1}{3}|-6|+4=\dfrac{1}{3}(6)+4=2+4=6[/tex]



Related Questions

A store is offering a 20% discount on all sales over $50.if you purchase a shirt and a pair of jeans for $62.50,what is the amount of the discount you would receive

Answers

Answer:

50 dollars

Step-by-step explanation:

If you have a 20% discount,that means you pay for 80% of your items. So to find percent you make 80 percent 0.8 and then multiply by 62.50.

Answer:

$10

Step-by-step explanation:

You would multiply $62.50 by 20% or .2 to find the discount which is $10. If you need to find the sale price you would subtract $62.50 - $10 = $52.50.

Your discount amount is $10

Your Sale Price is $52.50

how to find plato algebra 1 answers

Answers

Final answer:

To find Plato's Algebra 1 answers, it's important to understand the principles of algebra, apply them to solve problems, and practice regularly. Seek help from tutors, textbooks, and online resources, and strive to understand the process, not just find the answers.

Explanation:

Finding answers to Plato's Algebra involves understanding the concepts and principles of Algebra, applying these to solve problems, and continuously practising. Consider seeking help from your teacher, using textbooks, online resources, and practicing more problems. Whatever resources you use, it's crucial to check your answers with a credible source. Remember, the goal is not only to find the answers but to understand how to solve different algebraic problems.

In Algebra 1, you will come across different topics such as equations, inequalities, functions, and graphing. Each topic requires understanding the fundamental concepts and practising the exercises.

For example, if you're solving a linear equation, it's important to know that what you do on one side of the = sign has to be done on the other side to maintain balance. With lots of practice, Algebra 1 will become easier to grasp.

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A wood stove burns 4 logs in 2 hours how many logs burn in 9 hours ?

Answers

Answer:

18 logs.

Step-by-step explanation:

Since a stove burns 4 logs per 2 hours, then the stove will burn 2 logs in one hour. There fore in 9 hours the stove will burn 2*9 which is 18 logs.

4:2= 2 logs per hour

2*9=18 logs per 9 hours.


Answer:

16

Step-by-step explanation:

16 Because 2 divided by 8 equals 4 then 4x4 equal 16

What is the equation in the point-slope form of the line that passes through the point (-1,-4) and has a slope of -3?

Answers

Answer:

y=mx+b;  y=-3x+-4

Step-by-step explanation:

Substitute the slope, and the y-intercept in place of m and b

Answer: [tex] (y+4)=-3(x+1)[/tex]

Step-by-step explanation:

We know that the equation a line in point-slope form having slope m and passing through point (a,b) is given by :-

[tex](y-b)=m(x-a)[/tex]

Then , the equation a line in point-slope form having slope '-3' and passing through point (-1,-4) is given by :-

[tex](y-(-4))=-3(x-(-1))\\\\\Righarrow\ (y+4)=-3(x+1)[/tex]

Hello I need someone to help me with basic science Pls help will do anything!

Answers

Answer:

What you need???

Step-by-step explanation:


Answer:

I will be willing to help

Step-by-step explanation:

1. tell me what ur questions are

2. i will answer them

3. U use the answers for ur personal use

4. U thank me

5. Hope I can help


How do you solve:

3(a+2)=2(a-7) and 9(t-1)=6(t+2)-t

Answers

Answer:

t=3

Step-by-step explanation:

Simplifying

5 + -1(t + 3) = -1 + 2(t + -3)   Reorder the terms:

5 + -1(3 + t) = -1 + 2(t + -3)

5 + (3 * -1 + t * -1) = -1 + 2(t + -3)

5 + (-3 + -1t) = -1 + 2(t + -3)

Combine like terms: 5 + -3 = 2

2 + -1t = -1 + 2(t + -3)

Reorder the terms:

2 + -1t = -1 + 2(-3 + t)

2 + -1t = -1 + (-3 * 2 + t * 2)

2 + -1t = -1 + (-6 + 2t)

Combine like terms: -1 + -6 = -7

2 + -1t = -7 + 2t

Solving

2 + -1t = -7 + 2t

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '-2t' to each side of the equation.

2 + -1t + -2t = -7 + 2t + -2t

Combine like terms: -1t + -2t = -3t

2 + -3t = -7 + 2t + -2t

Combine like terms: 2t + -2t = 0

2 + -3t = -7 + 0

2 + -3t = -7

Add '-2' to each side of the equation.

2 + -2 + -3t = -7 + -2

Combine like terms: 2 + -2 = 0

0 + -3t = -7 + -2

-3t = -7 + -2

Combine like terms: -7 + -2 = -9

-3t = -9

Divide each side by '-3'.

t = 3

Simplifying

t = 3

There are many many steps ,but the answer is t=3

Vector u has its initial Point at (15,22) and it’s terminal point at (5,-4)

Answers

Final answer:

The position vector of vector u is (-10, -26). The magnitude of vector u is sqrt(776). The direction of vector u is 68.2 degrees.

Explanation:

The position vector of vector u can be found by subtracting the initial point from the terminal point. So, the position vector of u is (5-15, -4-22) = (-10, -26).

The magnitude of vector u can be found using the distance formula, which calculates the length of a vector. The formula is: magnitude = sqrt(x^2 + y^2), where x and y are the components of the vector. So, for vector u, the magnitude is: sqrt((-10)^2 + (-26)^2) = sqrt(100 + 676) = sqrt(776).

The direction of vector u can be found using trigonometry. The direction angle (theta) is given by tan(theta) = y/x. So, for vector u, the direction angle is: tan(theta) = (-26)/(-10) = 2.6. Converting to degrees, theta = arctan(2.6) = 68.2 degrees.

Please help how to answer this

Answers

Answer:

1563.2

Step-by-step explanation:

The value of 3 in 156.32 is 0.3

The value of 3 in 1563.2 is 3

So 0.3 × 10 = 3

How much cash did the person who filled out this deposit slip receive? a. $849.25 b. $715.56 c. $7,621.53 d. $721.50

Answers

Well what’s the equation

Answer: its D $721.50



50-u>48


u>?

please help too lazy

Answers

[tex]50-u>48\qquad\text{subtract 50 from both sides}\\\\-u>-2\qquad\text{change the signs}\\\\u<2[/tex]

which expression is equivalent to 0.4 x 8.7
A: (4x87) x (1/100 x 1/10)
B: (4x87) x (100 x 10)
C: (4x87) x (1/100 x 1/100)
D: (4 x 87) x (1/10 x 1/10)

Answers

Answer: D: (4 x 87) x (1/10 x 1/10)

Note that
a2 + b2 = c2.


To work under a car, a mechanic drives it up steel ramps like the ones shown below. Find the length of each side of the ramp.
a = ft
b = ft
c = ft

Answers


[tex](x + 1)^{2} + {x}^{2} = (x + 2)^{2} \\ x ^{2} + 2x + {1}^{2} + {x}^{2} = {x}^{2} + 4x + {2}^{2} \\ 2 {x}^{2} + 2x + 1 = {x}^{2} + 4x + 4 \\ {x}^{2} - 2x - 3 = 0[/tex]
Solve quadratic equation:
x= 3 or x=-1 (rejected.because length cannot be negative)

The ratio of the number of model cars that Jim owns to the number of model cars Terrence owns is 4 : 3. Terrence owns 36 models cars. How many model cars does Jim own?

Answers

Jim-4
Terrence-3

Terrence has 36
12×3=36

so let's multiply 4 by 12 also and that is 48

so, therefore jim has 48 model cars

A triangle with side lengths of 11, 13, and 15 is a scalene triangle. True False

Answers

Answer:

True

Hope it helps!!


The answer is true

Hopes this helps

Can someone help me?

Answers

Answer:

y=1/3x+8

Step-by-step explanation:

you can use the formula y=mx+b

y=1/3x-1

10=1/3*6+b

10=2+b

b=8

y=1/3x+8


A 52% video game is advertised for 20% off. If sales tax is 6%,how much will the video game cost

Answers

Answer:

Equation: 52+(52•.20) that is the first part for your answer you should get 10.4 or $10.40. Then you would take 52-10.4=41.60 then keeping that number in mind you do 41.60• .06 and get, rounded, 2.50. Then you would add 41.60+2.50 and get $44.10 as your answer . I hope I could help

Step-by-step explanation:

Solve x2 − 7x = −13.

A) x equals quantity of negative 7 plus or minus I square root of 6 all over 2
B) x equals quantity of negative 7 plus or minus I square root of 3 all over 2
C) x equals quantity of 7 plus or minus I square root of 6 all over 2
D) x equals quantity of 7 plus or minus I square root of 3 all over 2

Answers

Answer: the actual correct answer is D

Step-by-step explanation: i know the test answers because i am in flvs too

percent of change of $49 to $149

Answers

To find the percentage change, here is what we can do:

difference/original value x 100%

The difference: 149-49 = 100

The original value:149

The percentage change:

100/149 x 100%

=67.11409...%

Therefore the answer is 67.1%(corr. to three significant figures)

Hope it helps!

The percent of change from $49 to $149 is approximately 204.08%.

To calculate the percent of change from $49 to $149, we first find the difference in the two amounts.

The difference between $149 and $49 is $149 - $49 = $100.

Then, we divide the difference by the original amount (in this case, $49) to find the change in terms of the original amount.

This gives us $100 / $49 = 2.0408.

To convert this to a percentage, we multiply by 100. 2.0408 x 100

= 204.08%.

So the percent of change from $49 to $149 is approximately 204.08%.

Solve by elimination. 4x-y=6 3x+2y=21

Answers

Answer:

x=3, y=6

Step-by-step explanation:

4x-y =6

3x+2y = 21

To use elimination we will multiply the first equation by 2

2(4x-y) =6*2

8x -2y =12

We will add this equation to the second equation to eliminate y

8x -2y =12

3x+2y = 21

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

11x = 33

Divide each side by 11

11x/11 = 33/11

x =3

We still need to solve for y

3x+2y = 21

Substituting x=3

3*3+2y = 21

9+2y =21

Subtract 9 from each side

9-9+2y = 21-9

2y = 12

2y/2 = 12/2

y =6



The following function is quadratic.

f(x)=(x+4)(x-6)

What is the value of the positive x-intercept of the graph of the related equation y = (x+4)(x-6)?

Answers

Answer: 6

You replace f(x) or y with 0, and then solve for x

y = (x+4)(x-6)

(x+4)(x-6) = y

(x+4)(x-6) = 0

x+4 = 0 or x-6 = 0 .... zero product property

x = -4 or x = 6

The x intercepts are -4 and 6. In this case, only 6 is the positive x intercept.

side note: The term "root" is another way to say "x-intercept"

Explain how you know that 0.38 is a rational number?

Answers

Answer:

0.38 is a rational number because it can be expressed as fraction, and it isn't a repeating decimal.

Step-by-step explanation:

Repeating decimals aren't rational, and all rational numbers can be expressed as a fraction, or they aren't rational.

It's a rational number because it stops, the decimal is irrational if it continues forever without a pattern


I need help!!!!

Can someone help me

Answers

D.

But to be accurate, this isn't even a function. For it to be a function, that -2 couldn't be without a pair. There should be a 1 on the right side. So, when you do f(x) = -2 + 3 you get 1. This set of numbers (-2, -1, 3 and 5) is called domain, and all elements of the function's domain has to have a pair in the codomain(2, 6, 8, 4). That doesn't happen, as we don't see a 1 there, that could be assigned to the - 2 of the domain.

A baker has 2 2/3 cups of flour for her recipe, but she only has a 1/3 cup scoop. How many scoops will she need for the recipe?

Answers

Answer:

Step-by-step explanation:

8

She will need 8 scoops for the recipe if the baker has 2 2/3 cups of flour for her recipe, but she only has a 1/3 cup scoop.

What is a fraction?

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

We have:

A baker has 2 2/3 cups of flour for her recipe

2 2/3 = 8/3

She only has a 1/3 cup scoop.

Scoops she will need for the recipe = (8/3)/(1/3) = 8

Thus, she will need 8 scoops for the recipe if the baker has 2 2/3 cups of flour for her recipe, but she only has a 1/3 cup scoop.

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Which algebraic rule describes the transformation?

A) (x, y) → (x + 1, y − 3)

B) (x, y) → (x + 3, y − 1)

C) (x, y) → (x − 1, y + 3)

D) (x, y) → (x − 3, y + 1)

Answers

Answer:

It's B.

Step-by-step explanation:

(x, y) ---> (x + 3, y - 1)

Using point X as an example:

(x, y) ---> (x + 3, y - 1)

(0, 0) ---> (0 + 3, 0 -1)

(0, 0) ---> (3, -1)

The algebraic rule that describes the transformations is;

B) (x, y) → (x + 3, y − 1)

What are coordinates?

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

Given, A graph where we can see a Graph of a triangle XYZ that transforms to become x'y'z'.

Since the given graph is transformed not scaled.

Thus, the dimension will be the same and we can justify the means by just Calculating for one point.

For Point x:

Original coordinates os x = (0, 0)

coordinates of the x after transformation = (3, -1)

Thus,

horizontal displacement in X = +3

vertical displacement in X = -1

therefore, (x, y) → (x + 3, y − 1) is the algebraic rule that describes the transformation.

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Genevieve collected pledges of $3.50 for every complete mile she runs in a charity race. Her goal is to raise at least $50.00. Genevieve wrote the inequality 3.5m ≥ 50 to find out how many miles she needs to run.

Genevieve thinks she needs to run at least 14 miles.

But Carla says Genevieve needs to run more miles than that.
Who is correct and why?

A.
Carla is correct because 3.5 × 14 is less than 50.


B.
Genevieve is correct because 3.5 × 14 is about 50.


C.
Carla is correct because 3.5 × 14 is not equal to 50.


D.
Genevieve is correct because 3.5 × 14 is greater than 50.


Answers

Answer:

A.

Carla is correct because 3.5 × 14 is less than 50.

Step-by-step explanation:

3.5m ≥ 50

To determine how many miles she needs to run, divide each side by 3.5

3.5m/3.5  3.5m ≥ 50 50/3.5

m ≥ 14.28571429

She must run more than 14 miles

Carla is correct because 14* 3.5 = 49.  That is less than the 50 she wants to raise.

10.210 ÷ 10 (Long Division Work)

Answers

1.0210 is the answer

hoped this helped

Here is how you solve this problem with long-division. Hopefully it helps!

Bob raked 5% more leaves than Adam raked. Bob raked 357 liters of leaves. How many liters did Adam rake?

Answers

Answer:

Adam raked 340 liters

Step-by-step explanation:

Bob raked more leaves than Adam

5% more means take 100 % and add 5% = 105%

105% as a decimal is 1.05

Bob = 1.05 * Adam

We know Bob raked 357

357 = 1.05 Adam

Divide by 1.05

357/1.05 =1.05/1.05 Adam

340 = Adam


consider the triangle below

Answers

Answer:

[tex]m\angle M=90[/tex]

[tex]m\angle A=63[/tex]

[tex]m\angle N=27[/tex]

[tex]\Delta MAN[/tex] is a right triangle.

Step-by-step explanation:

Since we know that sum of all angles of triangles equals to 180 degrees.

To find the measure of our given angles we will have to find the value of x. The value of x can be found by equating the measure of all angles of our given triangle with 180.

[tex]4x-5+9x-9+10x+10=180[/tex]  

[tex]23x-14+10=180[/tex]  

[tex]23x-4=180[/tex]  

[tex]23x=180+4[/tex]

[tex]23x=184[/tex]  

[tex]x=\frac{184}{23}[/tex]

[tex]x=8[/tex]    

Now let us find measure of each angle by substituting value of x in given expressions.

[tex]m\angle M=10*x+10[/tex]

[tex]m\angle M=10*8+10[/tex]

[tex]m\angle M=80+10[/tex]

[tex]m\angle M=90[/tex]

Therefore, measure of angle M is 90 degrees.

[tex]m\angle A=9*x-9[/tex]

[tex]m\angle A=9*8-9[/tex]

[tex]m\angle A=72-9[/tex]

[tex]m\angle A=63[/tex]

Therefore, measure of angle A is 63 degrees.

[tex]m\angle N=4*x-5[/tex]

[tex]m\angle N=4*8-5[/tex]

[tex]m\angle N=32-5[/tex]

[tex]m\angle N=27[/tex]

Therefore, measure of angle N is 27 degrees.

From the measures of angles we can say that triangle MAN is a right triangle.

Using arithmetic operations, rewrite this polynomial in standard, simplest form. (3x2 + 9x + 6) − (8x2 + 3x − 10) + (2x + 4)(3x − 7)

Answers

Answer:

x∧2+4x-16

Step-by-step explanation:


Answer:x^2+4x-12

Step-by-step explanation: I got it right

Maria is playing a video game. She earns 15 points when she completes level one. Each time she completes a level, she earns twice as many points as the previous level. How many points will Maria earn when she completes level eight?

Answers

Answer:

She will earn 1,920 points.  PLEASE GIVE BRAINLIEST!!!

Step-by-step explanation:

Level 1 : 15 points   x 2 = level 2

Level 2 : 30 points   x 2 = level 3

Level 3: 60 points    x2 = level 4

Level 4:  120 points   x2 = level 5

Level 5:  240 points   x2 = level 6

Level 6:  480 points  x2 = level 7

Level 7:  960 points  x2 = level 8

Level 8:  1,920 points

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