Figure ABCDE has vertices A(-2, 3), B(2, 3), C(5,-2), D(0, -4), and E(-2,-2). Plot the points on your own coordinate grid and connect the points in alphabetical order. Decompose Figure ABCDE into rectangles and triangles. Part A: How many triangles and rectangles did you make? (1 point) Part B: Use Figure ABCDE created on your coordinate grid to find the lengths, in units, of Sides AB and AE. (4 points) Part C: What is the area of Figure ABCDE? Show your work. (5 points)
Answers
9514 1404 393
Answer:
A: 1 rectangle and 2 triangles (or 1 trapezoid and 1 triangle)
B: AB = 4; AE = 5
C: area = 34.5 square units
Step-by-step explanation:
Part AThe figure can be decomposed into a right trapezoid and a triangle. The right trapezoid can be decomposed into a rectangle and a triangle.
easiest decomposition: 1 right trapezoid and 1 triangle
decomposition per instructions: 1 rectangle and 2 triangles.
__
Part BAB is a horizontal line, so its length is the difference of the x-coordinates of B and A: 2 -(-2) = 4.
AE is a vertical line, so its length is the difference of the y-coordinates of A and E: 3 -(-2) = 5.
AB = 4, AE = 5
__
Part CThe area of the trapezoid is given by ...
A = 1/2(b1 +b2)h
The figure shows the base lengths to be 4 and 7, and the height to be 5. The trapezoid's area is ...
A = 1/2(4+7)(5) = 27.5 . . . . square units
The area of triangle CDE is given by the formula ...
A = 1/2bh
The figure shows the base length to be 7 and the height to be 2 units. The triangle area is ...
A = 1/2(7)(2) = 7 . . . . square units
The total area of figure ABCDE is 27.5 +7 = 34.5 square units.
Answer:
Answer:
A: 1 rectangle and 2 triangles (or 1 trapezoid and 1 triangle)
B: AB = 4; AE = 5
C: area = 34.5 square units
Step-by-step explanation:
Part A
The figure can be decomposed into a right trapezoid and a triangle. The right trapezoid can be decomposed into a rectangle and a triangle.
easiest decomposition: 1 right trapezoid and 1 triangle
decomposition per instructions: 1 rectangle and 2 triangles.
__
Part B
AB is a horizontal line, so its length is the difference of the x-coordinates of B and A: 2 -(-2) = 4.
AE is a vertical line, so its length is the difference of the y-coordinates of A and E: 3 -(-2) = 5.
AB = 4, AE = 5
__
Part C
The area of the trapezoid is given by ...
A = 1/2(b1 +b2)h
The figure shows the base lengths to be 4 and 7, and the height to be 5. The trapezoid's area is ...
A = 1/2(4+7)(5) = 27.5 . . . . square units
The area of triangle CDE is given by the formula ...
A = 1/2bh
The figure shows the base length to be 7 and the height to be 2 units. The triangle area is ...
A = 1/2(7)(2) = 7 . . . . square units
The total area of figure ABCDE is 27.5 +7 = 34.5 square units.
Step-by-step explanation:
trust meh
Related Questions
Solve for x in the equation x squared + 2 x + 1 = 17.
Answers
Step-by-step explanation:
quadratic formula
-b+-√b^2
2a
-2+-√2^2-4×1×-16
2×1
-2+-√68
2
either
x= 3.125
or
x= -5.125
Help me wit this rq…………..
Answers
Let W be part of the solid sphere of radius 4, centered at the origin, that lies above the plane z = 2. Set up an integral in cylindrical coordinates to find the volume of the region. Do NOT actually integrate.
Answers
Answer:
V = ∫∫∫rdrdθdz integrating from z = 2 to z = 4, r = 0 to √(16 - z²) and θ = 0 to 2π
Step-by-step explanation:
Since we have the radius of the sphere R = 4, we have R² = r² + z² where r = radius of cylinder in z-plane and z = height² of cylinder.
So, r = √(R² - z²)
r = √(4² - z²)
r = √(16 - z²)
Since the region is above the plane z = 2, we integrate z from z = 2 to z = R = 4
Our volume integral in cylindrical coordinates is thus
V = ∫∫∫rdrdθdz integrating from z = 2 to z = 4, r = 0 to √(16 - z²) and θ = 0 to 2π
Answer:
[tex]\displaystyle V = \int\limits^{2 \pi}_{0} \int\limits^{2\sqrt{3}}_{0} \int\limits^{\sqrt{16 - r^2}}_2 {r} \, dz \, dr \, d\theta[/tex]
General Formulas and Concepts:
Multivariable Calculus
Cylindrical Coordinate Conversions:
[tex]\displaystyle x = r \cos \theta[/tex][tex]\displaystyle y = r \sin \theta[/tex][tex]\displaystyle z = z[/tex][tex]\displaystyle r^2 = x^2 + y^2[/tex][tex]\displaystyle \tan \theta = \frac{y}{x}[/tex]Volume Formula [Cylindrical Coordinates]:
[tex]\displaystyle V = \iiint_T \, dV \rightarrow V = \iiint_T {r} \, dz \, dr \, d\theta[/tex]
Step-by-step explanation:
Step 1: Define
Identify given.
Solid sphere w/ radius 4 centered at (0, 0, 0) → x² + y² + z² = 4²
Plane z = 2
Step 2: Find Volume Pt. 1
Find bounds of z.
[Sphere] Substitute in plane z:[tex]\displaystyle x^2 + y^2 + 2^2 = 4^2[/tex]Substitute in cylindrical conversions:
[tex]\displaystyle (r \cos \theta)^2 + (r \sin \theta)^2 + 2^2 = 4^2[/tex]Simplify:
[tex]\displaystyle r^2 + 4 = 16[/tex]Solve for r:
[tex]\displaystyle r = 2\sqrt{3}[/tex]
∴ 0 ≤ r ≤ 2√3
Step 2: Find Volume Pt. 2
[Sphere] Substitute in plane z:[tex]\displaystyle x^2 + y^2 + 4 = 16[/tex]Isolate variables:
[tex]\displaystyle x^2 + y^2 = 12[/tex][Unit Circle] Graph [See 2nd Attachment]
∴ 0 ≤ θ ≤ 2π
Step 3: Find Volume Pt. 3
[Sphere] Substitute in cylindrical conversions:[tex]\displaystyle (r \cos \theta)^2 + (r \sin \theta)^2 + z^2 = 4^2[/tex]Simplify:
[tex]\displaystyle r^2 + z^2 = 4^2[/tex]Solve for z:
[tex]\displaystyle z = \sqrt{16 - r^2}[/tex]
∴ 2 ≤ z ≤ √(16 - r²)
Step 4: Find Volume Pt. 4
Substitute in variables [Volume Formula - Cylindrical Coordinates]:[tex]\displaystyle V = \int\limits^{2 \pi}_{0} \int\limits^{2\sqrt{3}}_{0} \int\limits^{\sqrt{16 - r^2}}_2 {r} \, dz \, dr \, d\theta[/tex]
∴ the volume of the region is found with the integral above.
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Learn more about multivariable calculus: https://brainly.com/question/17203772
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Topic: Multivariable Calculus
Unit: Triple Integral Applications
What is the solution to flog4(x+8) - 427
Answers
Answer:
4270
Step-by-step explanation:
so I already classified it as a square but I need to solve for x and y please help
Answers
Could you show the options we can choose from?
Answer:
x = 2
y = 1
Step-by-step explanation:
Compare one of the dimensions with the same variable with another.
5x - 4 = 3x
5(2) - 4 = 3(2)
10 - 4 = 6
6 = 6
Statement: True
2y + 4 = 5y + 1
2(1) + 4 = 5(1) + 1
2 + 4 = 5 + 1
6 = 6
Answers: x = 2 y = 1
Will mark Brainlest help please (find the value of x or theta) step by step
Answers
Answer:
Step-by-step explanation:
BC=[tex]\sqrt{5^2+5^2}[/tex]
x =[tex]\sqrt{50}[/tex]
x = 5[tex]\sqrt{2}[/tex]
tan theta= 5/5
theta= tan^-1 (5/5)
=45°
Step-by-step explanation:
BC=\sqrt{5^2+5^2}52+52
x =\sqrt{50}50
x = 5\sqrt{2}2
tan theta= 5/5
theta= tan^-1 (5/5)
=45°
Is this quadratic? If so what form is it?
Answers
Answer:
Yes. Factored form.
Step-by-step explanation:
Answer:
yes, and it's in intercept form
Step-by-step explanation:
Hi there!
We are given the function f(x)=-2(x-4)(x+3)
A quadratic function is a function that has a degree of 2 (the highest exponent in the function is to the 2nd power)
There are 3 forms to write a quadratic function:
standard form, which is f(x)=ax²+bx+c, where a, b, and c are free coefficients (numbers)
vertex form, which is f(x)=a(x-h)²+k, where a is a free coefficient and (h,k) is the vertex
intercept form, which is f(x)=a(x-[tex]x_{1}[/tex])(x-[tex]x_{2}[/tex]), where a is a free coefficient and [tex]x_{1}[/tex] and [tex]x_{2}[/tex] are the x intercepts
You may notice that f(x)=-2(x-4)(x+3) is actually in intercept form; a is -2 and [tex]x_{1}[/tex] and [tex]x_{2}[/tex] are 4 and -3 respectively (remember: the formula for intercept form has -[tex]x_{1}[/tex] and -[tex]x_{2}[/tex], but the x intercepts are [tex]x_{1}[/tex] and [tex]x_{2}[/tex]. Therefore, the x intercepts should be the opposites of -[tex]x_{1}[/tex] and -[tex]x_{2}[/tex]).
If the formula is in intercept form, it should be quadratic.
However, if you want to be sure it's quadratic, you can expand the function.
f(x)=-2(x-4)(x+3)
first, multiply the binomials together using FOIL
(x-4)(x+3)
x²-x-12
now multiply x²-x-12 by -2
-2(x²-x-12)
do the distributive property
-2x²+2x+24
It's a quadratic function! The value of the highest exponent is 2 :)
Hope this helps!
Factor completely
9 – 25x^2
Pls help i will mark the brainliest!
Answers
Answer:
more
Step-by-step explanation:
The answer is (5x+3)(-5x+3)
Following the car in front of you at a closer distance _____.
A. Gets you to your location faster
B. Doesn’t get you to your location faster
C. Is a safer way to drive
D.saves you some gas
Answers
Step-by-step explanation:
the answer is b, it doesnt get you to your location faster
Answer: Option A will be the correct answer
Step By Step Explanation: Because Main thing is its matching to the sentence
Write 5/9
as an equivalent fraction with a denominator of 18
Answers
Answer:
10/18
Step-by-step explanation:
Multiply both the numerator and denominator by 2
To get an equivalent fraction with a denominator of 18. Means we need to move the denominator of 9 to get to 18.
In order to do so we multiply the bottom by 2. 9x2=18. However because we want an equal fraction, the top needs to be multiples by 2
CAN SOMEONE HELP ME PLS
Answers
solve the literal equation for C. -3x+2c=-3
Answers
Step-by-step explanation:
I'm sorry I can't answer that but I know something so you can answer that. search Chrome quickmath all your problems, equations and more can be solved
Answer:
c = 3/2x + −3/2
Step-by-step explanation:
Let's solve for c
-3x+2c=-3
Step 1: Add 3x to both sides.
2c −3x + 3x = −3 + 3x
2c = 3x −3
Step 2: Divide both sides by 2.
2c = 3x−3
2 2
c = 3/2x + −3/2
Answer:
c = 3/2x + −3/2
Which graph represents an increasing function? (1 point) Four graphs of y against x are shown. The title for the first graph is Graph A, the title for the second graph is Graph B, the title for the third graph is Graph C, and the title for the fourth graph is Graph D. Graph A is a straight line joining the ordered pairs 0, 6 and 3, 0. Graph B is a straight line joining the points 3, 0 and 3, 5. Graph C is a straight line joining the points 0, 3 and 3, 3. Graph D is a straight line joining the points 0, 0 and 3,3.
Graph A
Graph B
Graph C
Graph D
Answers
Answer:
a
Step-by-step explanation:
aàaaaaaaaaaqaaaarsgbfyjvdujcgujhgkud parlo
Answer:
d
Step-by-step explanation:
Please help it’s summer school and i need serious help
Answers
Answer:
B
Step-by-step explanation:
Find the area of the circle shown below if the diameter is 24 inches. Use 3.14 for π. Use the formula π x r^2
A)1,808.64 inches
B) None of these answers
C)37.68 inches
D)452.16 inches
E)150.72 inches
Answers
==============================================================
Explanation:
The diameter is 24 inches, so the radius is half that at r = d/2 = 24/2 = 12 inches.
We'll use this along with the approximation pi = 3.14 to get the area
A = pi*r^2
A = 3.14*12^2
A = 452.16 square inches
Your teacher should have used "square inches" instead of "inches" as the unit.
We can abbreviate the "square inches" into "sq in" or "in^2".
This value is approximate since pi = 3.14 is approximate. Use more decimal digits of pi to find a more accurate value.
The exact area is 144pi
Answer:
D. 452.16 sq inches
Step-by-step explanation:
d = 24 ==> r = 24/2= 12 inches
the area = π×r²
= 3.14 × 12²
= 3.14 × 144
= 452.16 sq inches
Translate the sentence into an equation.
Two more than the quotient of a number and 5 is equal to 4.
Use the variable Y for the unknown number.
Answers
Answer:
Step-by-step explanation:
y/5 That's your quotient
y/5 + 2 That's the quotient with 2 added on.
y/5 + 2 = 4 And that's your answer.
Always break the statements into the smallest possible steps that you can. Notice that I broke it down to 3 parts that are not quite equal in length.
helppp please i need this answered fast please :⊂
Answers
Answer:
dang good luck
Step-by-step explanation:
Find the area of the triangle.
24 in.
32 in.
Answers
Answer:
A = 384 inches^2
Step-by-step explanation:
The area of a triangle is given by
A = 1/2 bh where b is the length of the base and h is the height
A = 1/2 ( 32) *(24)
A = 384 inches^2
Answer:
The area of triangle is 384 inches².
Step-by-step explanation:
Given : -Base of triangle = 24 inchesHeight of triangle = 32 inches To Find :-Area of triangleFormula Used :-Area of triangle = 1/2 × base × height
Solution :-Using Formula
Area of triangle = 1/2 × base × height
substitute the values into the formula
Area of triangle = 1/2 × 32 inches × 24 inches.
multiply,
Area of triangle = 1/2 × 768 inches ²
Divide, we get
Area of triangle = 384 inches ²
Therefore, The area of triangle is 384 inches².
Jose bought a plant. The height, h, of the plant is 2 feet. He noticed that every month, m,
the plant grows by 0.5 feet. What equation represents the height of the tree?
Answers
Answer:
the answer is h=0.5m+2 I think
A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 423 gram setting. Is there sufficient evidence at the 0.05 level that the bags are underfilled or overfilled
Answers
Necesito ayuda con este ejercicio hay que determinar el valor de la a: [tex]a^{20} : a^{2x} = a^{12}[/tex]
Answers
Answer:
x = 10 + log(1/a^12)/(2 log(a)) + (i π n)/log(a) for n element Z
Step-by-step explanation:
Solve for x:
a^(20 - 2 x) = a^12
Take reciprocals of both sides:
a^(2 x - 20) = 1/a^12
Take the logarithm base a of both sides:
2 x - 20 = log(1/a^12)/log(a) + (2 i π n)/log(a) for n element Z
Add 20 to both sides:
2 x = 20 + log(1/a^12)/log(a) + (2 i π n)/log(a) for n element Z
Divide both sides by 2:
Answer: x = 10 + log(1/a^12)/(2 log(a)) + (i π n)/log(a) for n element Z
when does two plus two equal five
Answers
Please help me with this as quickly as possible
Answers
3 hour 30 minutes : 36 minutes
1 hour = 60 minutes
3 hour = 3×60 minutes = 180 minutes
3hour 30 minutes = 180 minutes + 30 minutes
= 210 minutes
210 minutes : 60 minutes
3 hours 30 minutes : 60 minutes = 6:2
Let g(x) be the indicated transformation of f(x). Write the rule for g(x) f(x)=3x + 1: translation 2 units right
Answers
Answer:
3x +3
Step-by-step explanation:
3x + 1 + 2units(on the x axis)= 3x +3
Can someone please help me? I'm stuck.
Answers
Answer:
Sure i can help you
Step-by-step explanation:
Answer:
Sure! What’s the question?
Step-by-step explanation:
Jane was baking cookies. She needed 1/3 cup sugar and 1 2/4 cups flour. How much more flour does she need than sugar?
(Common core)
Answers
Answer:
1 and 1/6 cups more
Step-by-step explanation:
1/3 cup sugar
*1 2/4 cups flour = 6/4 cups flour
*assuming it’s 1 and 2/4 and not 12/4 =3
6/4 - 1/3 = (18-4)/ 12 = 14/ 12 = 1 and 1/6
Ricardo has a wooden board that measures 5 feet in length. How many 1/4 foot long pieces can Ricardo cut from the board
Answers
Answer:
20 pieces of wood
Step-by-step explanation:
5 divided by 1/4: 20
another way to look at it is if there are 4 of these pieces in a foot, and there are 5 feet, 4 times 5 is also 20.
How many feet are in 18 yards?
6 feet
30 feet
54 feet
216 feet
Answers
Answer:
54 is the answer
have a great dayyyy
Answer:
there are 64 feet in18 yards
Step-by-step explanation:
1 yard equals 3 feet
Help please I don’t understand
Answers
looks like something around 14, yet not quite sure
guys please help me :(((((((((( crying
Answers
Answer:
18
Step-by-step explanation:
2/6
4/12
6/18
Answer:
x = 18
Step-by-step explanation:
We can write ratios
2 2+4
---- = -----
6 x
Using cross products
2x = 6(2+4)
2x = 6(6)
2x = 36
Divide by 2
2x/2 = 36/2
x = 18
