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
Assoli18 [71]
3 years ago
9

Determine what shape is formed for the given coordinates for ABCD, and then find the perimeter and area as an exact value and ro

unded to the nearest tenth.
(help)

Mathematics
1 answer:
Helga [31]3 years ago
4 0

Answer:

Part 1) The shape is a trapezoid

Part 2) The perimeter is 25(4+\sqrt{2})\ units   or approximately  135.4\ units

Part 3) The area is 937.5\ units^2

Step-by-step explanation:

step 1

Plot the figure to better understand the problem

we have

A(-28,2),B(-21,-22),C(27,-8),D(-4,9)

using a graphing tool

The shape is a trapezoid

see the attached figure

step 2

Find the perimeter

we know that

The perimeter of the trapezoid is equal to

P=AB+BC+CD+AD

the formula to calculate the distance between two points is equal to

d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}

Find the distance AB

we have

A(-28,2),B(-21,-22)

substitute in the formula

d=\sqrt{(-22-2)^{2}+(-21+28)^{2}}

d=\sqrt{(-24)^{2}+(7)^{2}}

d=\sqrt{625}

d_A_B=25\ units

Find the distance BC

we have

B(-21,-22),C(27,-8)

substitute in the formula

d=\sqrt{(-8+22)^{2}+(27+21)^{2}}

d=\sqrt{(14)^{2}+(48)^{2}}

d=\sqrt{2,500}

d_B_C=50\ units

Find the distance CD

we have

C(27,-8),D(-4,9)

substitute in the formula

d=\sqrt{(9+8)^{2}+(-4-27)^{2}}

d=\sqrt{(17)^{2}+(-31)^{2}}

d=\sqrt{1,250}

d_C_D=25\sqrt{2}\ units

Find the distance AD

we have

A(-28,2),D(-4,9)

substitute in the formula

d=\sqrt{(9-2)^{2}+(-4+28)^{2}}

d=\sqrt{(7)^{2}+(24)^{2}}

d=\sqrt{625}

d_A_D=25\ units

Find the perimeter

P=25+50+25\sqrt{2}+25

P=(100+25\sqrt{2})\ units

simplify

P=25(4+\sqrt{2})\ units ----> exact value

P=135.4\ units

therefore

The perimeter is 25(4+\sqrt{2})\ units   or approximately  135.4\ units

step 3

Find the area

The area of trapezoid is equal to

A=\frac{1}{2}[BC+AD]AB

substitute the given values

A=\frac{1}{2}[50+25]25=937.5\ units^2

You might be interested in
Given f(x) = 3x + 1, solve for x when f(x) = 7.
irakobra [83]

Answer:

f(7) = 22 or x =2

Step-by-step explanation:

  1. f(x) = 3x + 1
  2. f(7) = 3(7) + 1
  3. f(7) = 21 + 1
  4. f(7) = 22

<u>Or if the equation meant it like this:</u>

  1. f(x) = 3x + 1
  2. 7 = 3x + 1
  3. 6 = 3x
  4. 2 = x
4 0
3 years ago
Read 2 more answers
Which equation are true for x=-2 and x=2 check all that apply
ki77a [65]
1 it is true
{x}^{2} - 4 = 0 \\ {x}^{2} = + 4 \\ x = \sqrt{4} = 2
2 it's not true
{x}^{2} = - 4
3 it's not true
3 {x}^{2} + 12 = 0 \\ 3 {x}^{2} = - 12 \\ {x}^{2} = \frac{ - 12}{3} = - 4 \\
4 it's true
4 {x}^{2} = 16 \\ {x}^{2} = \frac{16}{4} = 4 \\ x = \sqrt{4} = 2
5- it's true
{2(x - 2)}^{2} = 0 \\ {(x - 2)}^{2} = 0 \\ x - 2 = 0 \\ x = 2
4 0
3 years ago
Read 2 more answers
What is 5C3?<br> A. 35<br> B. 10<br> C. 14<br> D. 28
galben [10]

Answer: B. 10

-5C3 or 5 choose 3 refers to how many combinations are possible from 5 items, taken 3 at a time. To calculate combinations, we will use the formula nCr = n! / r! ... * (n - r)!, where n represents the total number of items, and r represents the number of items being chosen at a time.

-10 is the total number of all possible combinations for choosing 3 elements at a time from 5 distinct elements without considering the order of elements in statistics & probability surveys or experiments. The number of combinations for sample space 5 CHOOSE 3 can also be written as 5C3 in the format of nCr or nCk.

Step-by-step explanation: Hope this help :D

5 0
2 years ago
Read 2 more answers
Write an equation for the cubic polynomial function whose graph has zeroes at 2, 3, and 5.
TiliK225 [7]

we know that

For a polynomial, if x=a is a zero of the function, then (x−a) is a factor of the function. The term multiplicity, refers to the number of times that its associated factor appears in the polynomial.

So

In this problem

If the cubic polynomial function has zeroes at 2, 3, and 5

then

the factors are

(x-2)\\ (x-3)\\ (x-5)

Part a) Can any of the roots have multiplicity?

The answer is No

If a cubic polynomial function has three different zeroes

then

the multiplicity of each factor is one

For instance, the cubic polynomial function has the zeroes

x=2\\ x=3\\ x=5

each occurring once.

Part b) How can you find a function that has these roots?

To find the cubic polynomial function multiply the factors and equate to zero

so

(x-2)*(x-3)*(x-5)=0\\ (x^{2} -3x-2x+6)*(x-5)=0\\ (x^{2} -5x+6)*(x-5)=0\\ x^{3} -5x^{2} -5x^{2} +25x+6x-30=0\\ x^{3}-10x^{2} +31x-30=0

therefore

the answer Part b) is

the cubic polynomial function is equal to

x^{3}-10x^{2} +31x-30=0

7 0
2 years ago
Read 2 more answers
Please help I don’t get it
lidiya [134]

Answer:

4.718592

Step-by-step explanation:

To get to -14.4 from 18 you multiply 18 x 0.8

Repeat that until you get to the 7th term

18 (1st)

18 x 0.8 = -14.4 (2nd)

-14.4 x 0.8 = 11.52 (3rd)

11.52 x 0.8 = 9.216 (4th)

9.216 x 0.8 = 7.3728 (5th)

7.3728 x 0.8 = 5.89824 (6th)

5.89824 x 0.8 = 4.718592 (7th)

3 0
3 years ago
Other questions:
  • 87.5 ml = _____ liters?
    10·2 answers
  • PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
    12·1 answer
  • PLEASE HELP WITH THE QUESTION IN THE PICTURE!!!
    5·1 answer
  • How to describe each sequence using words and symbols
    10·1 answer
  • AB=1cm and AC=3cm. Find the radius of the circle. (Problem Number 13)
    11·1 answer
  • 3(2y-1)-2(2y)=2. what is the answer to this
    10·2 answers
  • To which subset of the real numbers does -18 belongs ( irrational, rational, integer, natural, real numbers, whole)
    14·1 answer
  • A rectangular box has length x and width 3. The volume of the box is given by y = 3x(8 – x). The greatest x-intercept of the gra
    13·1 answer
  • Look at this equation. 48 = 12x. Which value of x makes the equation true?
    7·2 answers
  • T/3+9=12 what does this mean in algerba
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!