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
77julia77 [94]
3 years ago
5

Use the area of the rectangle to find the area of the triangle

Mathematics
1 answer:
bezimeni [28]3 years ago
3 0

Answer:

The area of the Triangle is 1/2 the area of the Rectangle

The answer is D.

Step-by-step explanation:

Ignore the area of the rectangle for the moment, just so you can get the answer.

Area Triangle = 1/2 * b * h

Area Triangle = 1/2 * 8 * 4

Area Triangle = 1/2 32

Area Triangle = 16 square feet.

The area of the rectangle = L * W

L = 8

W = 4

Area of the rectangle = 8*4 = 32

You might be interested in
15 The unit cost per pound for green beans is represented by the
Reptile [31]

Answer:

mbnmbnmbnmbnmbnm

Step-by-step explanation:

bnmbnmbnmbnm

3 0
3 years ago
Read 2 more answers
Pls help me with my math
givi [52]

Answer:

The definition for the given piecewise-defined function is:   \boxed{\displaystyle\sf\ Option\:D:\:\: f(x) = \begin{cases}\displaystyle\sf\ x + 2 & \sf\:{if\:\:x \leq -1} \\\displaystyle\sf\ 2x + 4 & \sf\:{if\:\:x > -1}\end{cases}}.

Step-by-step explanation:

<h3>General Concepts:</h3>
  • Piecewise-defined functions.
  • Interval notations.

<h3>What is a piecewise-defined function?</h3>

A piecewise-defined function represents specific rules over different intervals of the domain.  

<h3>Symbols used in expressing interval notations:</h3>

Open interval: This means that the endpoint is <em>not</em> included in the interval.

We can use the following symbols to indicate the <u>exclusion</u> of endpoints in the interval:

  • Left or right parenthesis, "(  )" (or both).
  • Greater than (>) or less than (<) symbols.
  • Open dot "\circ" is another way of expressing the exclusion of an endpoint in the graph of a piecewise-defined function.

Closed interval: This implies the inclusion of endpoints in the interval.

We can use the following symbols to indicate the <u>inclusion</u> of endpoints in the interval:

  • Open- or closed brackets (or both), "[  ]."
  • Greater than or equal to (≥) or less than or equal to (≤) symbols.
  • Closed circle or dot, "•" is another way of expressing the <em>inclusion</em> of the endpoint in the graph of a piecewise-defined function.  

<h2>Determine the appropriate function rule that defines different parts of the domain.  </h2>

The best way to determine which piecewise-defined function represents the graph is by observing the <u>endpoints</u> and <u>orientation</u> of both partial lines.

  • Open circle on (-1, 2):  The graph shows that one of the partial lines has an <em>excluded</em> endpoint of (-1, 2) extending towards the <u>right</u>. This implies that its domain values are defined when x > -1.
  • Closed circle on (-1, 1): The graph shows that one of the partial lines has an <em>included</em> endpoint of (-1, 1) extended towards the <u>left</u>. Hence,  its domain values are defined when x ≤ -1.

Based on our observations from the previous step, we can infer that x > -1 or x ≤ -1 apply to piecewise-defined functions A or D. However, only one of those two options represent the graph.

<h2>Solution:</h2><h3>a) Test option A:</h3>

    \boxed{\displaystyle\sf Option\:A)\:\:\:f(x) = \begin{cases}\displaystyle\sf\ 2x + 2 & \sf\:{if\:\:x \leq -1} \\\displaystyle\sf\ x + 4 & \sf\:{if\:\:x > -1}\end{cases}}

<h3>Piece 1: If x ≤ -1, then it is defined by f(x) = 2x + 2. </h3>

We must choose a domain value that falls within the interval of x ≤ -1 whose output is included is included in the graph of the partial line with a <u>closed dot</u>.

Substitute x = -2 into f(x) = 2x + 2:  

  • f(x) = 2x + 2
  • f(-2) = 2(-2) + 2
  • f(-2) = -4 + 2
  • f(-2) = -2  ⇒  <em>False statement</em>.

⇒ The output value of f(-2) = -2 is <u>not</u> included in the graph of the partial line whose endpoint is at (-1, 1).

<h3>Piece 2: If x > -1, then it is defined by f(x) = x + 4. </h3>

We must choose a domain value that falls within the interval of x > -1 whose output is included in the graph of the partial line with an <u>open dot</u>.

Substitute x = 0 into  f(x) = x + 4:

  • f(x) = x + 4
  • f(0) = (0) + 4
  • f(0) = 4  ⇒  <em>True statement</em>.

⇒ The output value of f(0) = 4 <u>is</u> included in the graph of the partial line whose endpoint is at (-1, 2).

Conclusion for Option A:

Option A is not the correct piecewise-defined function because one of the pieces, f(x) = 2x + 2, does not specify the interval (-∞, -1].

<h3>b) Test option D:</h3>

    \boxed{\displaystyle\sf Option\:D)\:\:\:f(x) = \begin{cases}\displaystyle\sf\ x + 2 & \sf\:{if\:\:x \leq -1} \\\displaystyle\sf\ 2x + 4 & \sf\:{if\:\:x > -1}\end{cases}}

<h3>Piece 1:  If x ≤ -1, then it is defined by f(x) = x + 2. </h3>

We must choose a domain value that falls within the interval of x ≤ -1 whose output is included is included in the graph of the partial line with a <u>closed dot</u>.

Substitute x = -2 into f(x) = x + 2:

  • f(x) = x + 2
  • f(-2) = (-2) + 2
  • f(-2) = 0  ⇒  <em>True statement</em>.

⇒ The output value of f(-2) = 0 <u>is</u> included the graph of the partial line whose endpoint is at (-1, 1).

<h3>Piece 2: If x > -1, then it is defined by f(x) = 2x + 4.</h3>

We must choose a domain value that falls within the interval of x > -1 whose output is included is included in the graph of the partial line with an <u>open dot</u>.

Substitute x = 0 into f(x) = 2x + 4:

  • f(x) = 2x + 4
  • f(0) = 2(0) + 4
  • f(0) = 0 + 4 = 0  ⇒  <em>True statement</em>.

⇒ The output value of f(0) = 4 <u>is</u> included in the graph of the partial line whose endpoint is at (-1, 2).  

<h2>Final Answer: </h2>

We can infer that the piecewise-defined function that represents the graph is:

\boxed{\displaystyle\sf\ Option\:D:\:\: f(x) = \begin{cases}\displaystyle\sf\ x + 2 & \sf\:{if\:\:x \leq -1} \\\displaystyle\sf\ 2x + 4 & \sf\:{if\:\:x > -1}\end{cases}}.

________________________________________

Learn more about piecewise-defined functions here:

brainly.com/question/26145479

8 0
2 years ago
If you were given the following statements write your conclusion <br> if you are given :
prohojiy [21]

Answer:

ab and cd intersect at E because they are vertically opposite angles they always intersect at a point

6 0
2 years ago
1. Kim's age is twice that of her sister. When you add Kim's age to her sister's age, you get 36. How old is each sister? (a) Wr
Jlenok [28]
A)
Kim's age=k
Sister's age=s
k=2s
k+s=36
b)
k=2s
k+s=36
k=36-s
2s=36-s
3s=36
s=12
12*2=24
Kim is 24 and her sister is 12

Hope this helps :)

6 0
3 years ago
Read 2 more answers
You have 12 shirts and plan to wear a different one each day from Monday
JulsSmile [24]
It should be 95,040. On the first day, you have 12 choices. On the second, eleven, and so on, until day 5. 12x11x10x9x8.
6 0
3 years ago
Read 2 more answers
Other questions:
  • Find the center, vertices, and foci of the ellipse with equation 2x2 + 9y2 = 18.
    11·1 answer
  • 9 times (30+7=(9 times _)+(9 times 7)<br><img src="https://tex.z-dn.net/?f=9%20%5Ctimes%20%2830%20%2B%207%29%20%3D%20%289%20%5Ct
    13·2 answers
  • At grace’s job,15% of the time she has to answer the phone. Write this percent as a decimal.
    12·1 answer
  • How to find the mean of <br><br> A)4,5,7,5,6,3
    5·2 answers
  • Please who can help me?
    14·1 answer
  • Luis has a cooler filled with cans of soda. For every 5 cans of coke, there are 3 cans of sprite. If there are 25 cans of coke ,
    8·1 answer
  • Let ∠D be an acute angle such that cosD=0.33. Use a calculator to approximate the measure of ∠D to the nearest tenth of a degree
    8·2 answers
  • Write the ratio 2/3/5 in simplest form​
    6·2 answers
  • Given: AM = 8, AB = 5x +1 and M is the midpoint of AB, find x and AB<br> X=<br> AB=
    9·1 answer
  • -31+(-42)=<br> 38+(-43)=
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!