1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Makovka662 [10]
3 years ago
10

Please help find the formulas for these!! ASAP!!!

Mathematics
1 answer:
Ilya [14]3 years ago
6 0

Answer:

a)\ f(x)=\left\{\begin{array}{cccc}-x+2&for&x\in(0,\ 2]&/0

b)\ f(x)=\left\{\begin{array}{cccc}-3x-3&for&x\in(-1,\ 0]&/-1

Step-by-step explanation:

These are graphs of piecewise functions.

Each part is a graph of the linear function.

The slope-intercept form of an equation of a line:

y=mx+b

<em>m</em><em> - slope</em>

<em>b</em><em> - y-intercept → (0, b)</em>

The formula of a slope:

m=\dfrac{y_2-y_1}{x_2-x_1}

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

<h2>a)</h2>

Part 1:

Points (0, 2) → <em>b = 2</em>, and (2, 0).

Calculate the slope:

m=\dfrac{0-2}{2-0}=\dfrac{-2}{2}=-1

Put the value of <em>m</em> and <em>b</em> to the equation of a line:

(1)\ y=-1x+2=-x+2

Part 2:

Points (2, 1) and (5, 0).

Calculate the slope:

m=\dfrac{0-1}{5-2}=\dfrac{-1}{3}=-\dfrac{1}{3}

Put the value of the slope and the coordinates of the point (5, 0) to the equation of a line:

0=-\dfrac{1}{3}(5)+b

0=-\dfrac{5}{3}+b         <em>add 5/3 to both sides</em>

\dfrac{5}{3}=b

Therefore we have:

y=-\dfrac{1}{3}x+\dfrac{5}{3}

The domain of the function is (0, 2] and (2, 5].

Formula of the piecewise function:

f(x)=\left\{\begin{array}{cccc}-x+2&for&x\in(0,\ 2]&/0

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

<h2>b)</h2>

We solve the same as in a) in Part 1

Part 1:

(-1, 0), (0, -3) → <em>b = -3</em>

m=\dfrac{-3-0}{0-(-1)}=\dfrac{-3}{1}=-3

y=-3x-3

Part 2:

(0, 3) → <em>b = 3</em>, (2, -1)

m=\dfrac{-1-3}{2-0}=\dfrac{-4}{2}=-2

y=-2x+3

Domain: (-1, 0] and (0, 2].

f(x)=\left\{\begin{array}{cccc}-3x-3&for&x\in(-1,\ 0]&/-1

You might be interested in
Two more than 16 times a number is the same as 21 less than the product of -7 and the number
slava [35]

Answer:

  • -1

Step-by-step explanation:

<u>Let the number be x, and we have equation:</u>

  • 16x + 2 = -7x - 21
  • 16x + 7x = - 21 - 2
  • 23x = - 23
  • x = -1

The number is -1

7 0
2 years ago
Read 2 more answers
Will give brainliest answer
andrew-mc [135]

Answer:

A ≈ 12.57

Step-by-step explanation:

You have to take the formula: A = πr^2

1) Plug in what you know: A = π•2^2

2) π = 3.14 and 2^2 = 4

3) Multiply to get: 12.56637

4) Round

A ≈ 12.57

3 0
3 years ago
How do I identify the congruent triangles in each figure
Virty [35]
Congruent triangles have the exact same three sides and the exact same angles. They are identical. So if you look at your triangles carefully, they are congruent. :)
5 0
3 years ago
Which equation demonstrates the distributive property? A) 2 (5 + 7) = 2 (7 + 5) Eliminate B) 2 (5 + 7) = 2 × 5 + 2 × 7 C) (2 × 5
Gemiola [76]

B) 2 (5 + 7) = 2 × 5 + 2 × 7

Distributing the two multiples the five and seven and adds there them together.

7 0
2 years ago
Read 2 more answers
G(x) = x2 – 2 (a) Identify the parent function f.​
Temka [501]

Answer:g(x) is flipped and 2 times as steep and shifted left 5

Step-by-step explanation:

6 0
3 years ago
Other questions:
  • LCD of 1/5 and 9/10?
    12·1 answer
  • This question is a fair question: “Which do you think is the most common age group of people who like pop music?” true or false
    13·1 answer
  • Calculate the mean and variance of the sample data set provided below. show and explain your steps. round to the nearest tenth.
    14·1 answer
  • Determine whether the number could be the probability of an event. Explain your reasoning. -0.25
    6·1 answer
  • What is the answer if you factor completely
    12·1 answer
  • On a road trip,drove at a speed of 60 miles per hour for the first two hours. She then increased her speed by 25%. How fast was
    7·2 answers
  • Michael jogs 3,520 yards every day. What is the distance in miles that he will jog in 10 days? (1 mile = 1,760 yards)
    10·2 answers
  • Tickets for a concert cost $10 each if you order them online, but you must pay a service charge of $8 per order. The tickets cos
    9·1 answer
  • Can someone help and explain this to me?
    5·1 answer
  • Find the value of each variable. Give exact answers.
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!