Determine if a quadrilateral with the given vertices is an isosceles trapezoid. Show and explain all steps to prove or disprove.
A(-5,0) B(5,0) C(-3, 4) D(3, 4)
Answers
By satisfying all the four criteria, the quadrilateral with the vertices A(x, y) = (-5, 0), B(x, y) = (5, 0), C(x, y) = (-3, 4) and D(x, y) = (3, 4) is an isosceles trapezoid.
How to determine if a quadrilateral is an isosceles trapezoidBased on vectorial expressions, an isosceles trapezoid satisfies the following properties:
(i) [tex]\overrightarrow{CD} = k \cdot \overrightarrow{AB}[/tex], for k ∈ [tex]\mathbb{R}[/tex]
(ii) AB ≠ CD
(iii) [tex]\overrightarrow{AC} \neq \overrightarrow {BD}[/tex]
(iv) AC = BD
Now we proceed to prove each property:
Requisite I
(3 - (-3), 4 - 4) = (6, 0)
(5 - (-5), 0 - 0) = (10, 0)
(6, 0) = (5/3) · (10, 0)
Requisite II
AB = 6, CD = 10
AB ≠ CD
Requisite III
[tex]\overrightarrow{AC} = (2, 4)[/tex]
[tex]\overrightarrow{BD} = (-2, 4)[/tex]
[tex]\overrightarrow{AC} \neq \overrightarrow {BD}[/tex]
Requisite IV
[tex]AC = \sqrt{[-3-(-5)]^{2}+(4-0)^{2}}[/tex]
[tex]AC = \sqrt{2^{2}+4^{2}}[/tex]
[tex]AC = 2\sqrt{5}[/tex]
[tex]BD = \sqrt{(3-5)^{2}+(4-0)^{2}}[/tex]
[tex]BD = \sqrt{(-2)^{2}+4^{2}}[/tex]
[tex]BD = 2\sqrt{5}[/tex]
AC = BD
The figure with the entire quadrilateral is shown below. Therefore, the quadrilateral with the vertices A(x, y) = (-5, 0), B(x, y) = (5, 0), C(x, y) = (-3, 4) and D(x, y) = (3, 4) is an isosceles trapezoid.
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Related Questions
What is the first step in solving the following equation?
28 = -12 - 4x
Answers
Answer:
4x = - 12 - 28Step-by-step explanation:
When we transpose - 4x to the LHS then it becomes positive i.e +4x
Now we transpose 28 to the RHS then it becomes negative i.e - 28
So the first step you have to is,
4x = - 12 - 28
Find the volume of each square pyramid given its slant height. Round to the nearest tenth. It looks like a normal pyramid with a slant height of 2.8 and a base of one of the triangles is 1.2.
Answers
Answer:
1.344 cubic units
Step-by-step explanation:
Given data
Base edge a= 1.2
Hieght= 2.8
The expression for the volume of a pyramid is
V= a^2h/3
substitute
V= 1.2^2* 2.8/3
V= 1.44*2.8/3
V= 4.032/3
V= 1.34cubic units
HELP! i only have 5 minutes to turn it in if you already did it im on 50 percent give me all answers this is 5th grade
Answers
What is 4x/7 - 2/3
Fraction help
Answers
Answer:
2/21 * (6x-7)
Step-by-step explanation:
1/21 * (3*4x - 14)
1/21* (12x-14)
1/21* 2(6x-7)
2*1/21 * (6x-7)
2/21* (6x-7)
11,22,22,13,24,22 find the hunderds too
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Answer:
excuse me, but how do we answer this? This question is unanswerable without it being a question!
Step-by-step explanation:
please help!!!!!!!!!
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Answer:
that would be 1
Step-by-step explanation:
in this equation x=74 and 74/74 equals one
Solve |3x - 4| = 6
please help me solve
Answers
Step-by-step explanation:
|3x - 4| = 6
3x-4 = 6 or 3x-4 = -6
3x=6+4 3x=-6+4
3x=10 3x = -2
x= 10/3 x = -2/3
so, x1= 10/3 or x2 = -2/3
What is the total surface area of the rectangular prism below?
Answers
Answer:
solution given:
length[l]=3 in
breadth [b]=5in
height [h]=8in
total surface area of the rectangular prism=?
we have
total surface area of the rectangular prism
=2[lb+bh+lh]
=2[3*5+5*8+3*8]
=158 in²
total surface area of the rectangular prism is 158 in².
Answer:
158
Step-by-step explanation:
formula is 2(hL+wh+lw)
Length- 3
width- 5
height - 8
Substitue values and get answer.
2 (24+ 40+15)
2 (79)
= 158
have a wonderful day!
Find the volume of the cylinder shown. Use 3.14 for pi. Round your answer to the nearest hundredth.
Answers
Answer:
1847.26 yards cubed
Step-by-step explanation:
V=πr^2h
π*49*12= 1847.26
Have a good day :)
Shelly bought 53.6 gallons of orange juice and used 18.3 gallons of it to make popsicles how much orange juice dose shelly have left
Answers
Explanation:
53.6 - 18.3 = 35.3
Its subtraction since its asking for how much left.
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What is the initial value of the function represented by this table?
A. 0
B. 2
C. 3
D. 5
Answers
Answer:
C... 3
Step-by-step explanation:
Work out the surface area of this solid prism
Answers
Answer:
3220 cm²
Step-by-step explanation:
Lets find the area of the two triangles
I am making a modification:
Both of the triangles are the same, so I wont divide by 2 using the area of triangle formula 1/2(b * h) because we end up multiply by 2
Area of triangles = 15 cm x 28 cm = 420 cm²
Area of front facing parallelogram = 24 cm x 4(10)cm = 100(10)cm = 1000 cm²
Area of back facing parallelogram = 17 cm x 40 cm = 680 cm²
Area of bottom parallelogram = 40 cm x 28 cm = 1120 cm²
Total Surface area = 420 cm² + 1000 cm² + 680 cm² + 1120 cm² = 1100 cm² + 2120 cm² = 3220 cm²
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
During a sale, a store offered 60% discount on a particular camera that was originally priced $450. After the sale, the discounted price of the camera was increased by 60%. What was the price of the camera after this increase?
Answers
Answer:
$288.00
Step-by-step explanation:
Im just going off what my calculator told me, but im 95% sure its correc
450- 60%= 180
180+60%=288
Which has a slope of 4 and a y-intercept of -2
Answers
Answer:
C
Step-by-step explanation:
Have a good day :)
there are 4 trucks for every 5 cars in a parking lot. how many trucks and cars could be in the parking lot? A. 64 trucks and 80 cars B. 72 trucks and 73 cars C. 84 trucks and 100 cars D. 96 trucks and 110 cars
Answers
Answer:
A.
Step-by-step explanation:
64/4=16 80/5=16 They are multiplied by the same number so it is A
Find the circumference of the circle to the nearest hundredth
11cm
Answers
Question: Find the circumference of the circle to the nearest hundredth
d = 11cm
Answer:
34.54 cm
Step-by-step explanation:
Applying,
P = πd...................... Equation 1
Where P = Circumference of perimeter of the circle, d = diameter of the circle, π = pie
From the question
Given: d = 11 cm
Constant: π = 3.14
Substitute these values into equation 1
P = (3.14×11)
P = 34.54 cm
(x²- 3x) + (-2x²+ 5x - 3)
Answers
Answer:
[tex]-x^{2} +2x-3[/tex]
Answer :
-2x^2 + 2x - 3
What is the volume of a hemisphere with the radius of 24 ft?
Answers
Answer:
Toby began his math homework at 6:38 pm.
He finished at 7:09 pm.
How many minutes did Toby spend on his math homework?
Step-by-step explanation:
hhhhhhhheeeeeeeeelllllllllllpppppppp pls
Answers
Answer:
18
Step-by-step explanation:
2^3 = 8
4^2 = 16
8+16=24
3/4 of 24 Is 18
Answer:
18
Step-by-step explanation:
[tex] \frac{3}{4} (8 + 16) \\ \frac{3}{4}(24) \\ 3 \times 6 \\ 18[/tex]
Please answer quickly with explanation. I am in need of major help.
Suppose you work at a local radio station. You are in charge of a $180 budget for
new tapes and CDs. Record companies will give you 21 promotional (free) CDs. You
can then buy tapes for $8 and CDs for $12.
a. Write a linear inequality that models this situation.
Answer
b. Graph the inequality. Make sure to use proper scales and to label your axes
Answers
Answer:
0---22.5 and 21---36
Step-by-step explanation:
you will always have 21 free CDs so you can put a closed circle on 21 then you can have a max of 15 CDs (180/12) soo put another closed circle on 36
now time for tapes, which is easier, the minimum is 0 and the max is 22.5. Now put closed circles on each and you're done. Except that .5 might get you in trouble, use your own discretion on rather to leave it on the .5 or round. I don't know what your teacher is looking for so I will let you decide.
can yall or someone help
Answers
Answer:
x would equal 40
Step-by-step explanation:
x+(2x-5)+(x+25)=180
4x+20=180
x=40
Pls pls help I don’t understand
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Answer:
[tex]Given~quadratic ~function : 1=x^2-6x[/tex]
[tex]here,a=1,b=-6[/tex]
[tex]so, the~numbers~which ~we ~need ~to ~add....[/tex]
➜ [tex](\frac{b}{2} )^2[/tex]
➜ [tex]=(\frac{-6}{2})^2[/tex]
➜[tex]=(-3)^2[/tex]
➜ [tex]=9[/tex]
---------------------
hope it helps...
have a great day!!
What is the length of AC ?
Answers
Answer:
there is no enough data to find the answer
Solve the equation for y. Then find the value of y for each value of x.
y + 5x = 8; x = - 2, 0,3
Solve the equation for y.
Answers
Answer:
y = 8 - 5x, y(-2) = 18, y(0) = 8, y(3) = -7
Step-by-step explanation:
y + 5x = 8
y = 8 - 5x
y(-2) = 8 - 5*(-2) = 8 + 10 = 18
y(0) = 8 - 5*(0) = 8 - 0 = 8
y(3) = 8 - 5*(3) = 8 - 15 = -7
14. Michelle purchased three stuffed bears for the price shown. The sales tax on her
purchase was 8.5%. What was the total cost for the stuffed bears? Round to the nearest
cent.
$9.49
w
F. $10.30
G. $30.89
H $80.67
3. $2.42
Answers
Answer: $30.89
Step-by-step explanation: you time $9.49 by three (28.47) then you find 8.5% of that total (2.41995) and then you add that to the total for the three bears and round to the nearest cent
No links please ASAP!!! Find the slope of the line that passes through (5,3) and (4,2).
Answers
Answer:
1
Step-by-step explanation:
y2 - y1/ x2 - x1
3-2/ 5-4 = 1/1 = 1
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
PLEASE HELP 20 points
Answers
Answer:
2.greatest common factor is 4
3.[tex]x^{2}[/tex]-3x-10
[tex]x^{2}[/tex]-(5-2)x-10
[tex]x^{2}[/tex]-5x+2x-10
x(x-5)+2(x-5)
(x+2)(x-5)
Step-by-step explanation:
Answer:
2. 4
3. (x+2)(x−5)
Step-by-step explanation:
Question One.
Factor 8x+12
8x+12
4(2x+3)
Question Two.
Factor [tex]x^{2}[/tex]−3x−10
The middle number is -3 and the last number is -10.
Factoring means we want something like:
(x+_)(x+_)
We need to figure out which numbers go in the blanks.
You will need two numbers. They need to...
Add together to get -3.
Multiply together to get -10.
2+-5=-3
2·-5=-10
Fill in the blanks.
(x+2)(x-5)
Answer:
(x+2)(x−5)
Tonia contributes 5% of her paycheck to her 401(k) plan in order to save for her retirement, and she pays state income tax at a rate of 5% on the rest of her paycheck. If p represents Tonia's paycheck and t represents the amount she pays in state income tax, which of these equations represents this Situation? А t = 0.0025p t = 0.025p С 1 = 0.0475p D 1 = 0.475p
Answers
Answer:
t = 0.0475p
Step-by-step explanation:
If
p = paycheck ; t = amount paid in state income tax
Amount contributed towards retirement :
5% of p ; 0.05p
Amount left :
Paycheck - contribution
p - 0.05p = 0.95p
Amount paid in state income tax :
5% of amount left
5% of 0.95p
5/100 * 0.95p
0.05 * 0.95p
= 0.0475p
Hence, state income tax, t = 0.0475p
Convert the following equation into slope intercept form y-6=2(x+4)
Answers
Answer:
y = 2x +14
Step-by-step explanation:
We need to convert the given equation into slope intercept form ,
=> y - 6 = 2(x+4)
=> y -6= 2x + 8
=> y = 2x +8+6
=> y = 2x + 14
• Hence the required answer is y = 2x + 14Solve for x. Answer as a whole number.
Answers
Given:
In triangle ABC, AE is the angle bisector.
[tex]AB=4, BE=2, AC=x, CE=3[/tex]
To find:
The value of x.
Solution:
According to the angle bisector theorem, the angle bisector of a triangle divides the opposite side of the triangle into two parts. These two parts are proportional to the other two sides of the triangle.
Using the angle bisector theorem, we get
[tex]\dfrac{AB}{AC}=\dfrac{BE}{CE}[/tex]
[tex]\dfrac{4}{x}=\dfrac{2}{3}[/tex]
On cross multiplication, we get
[tex]4\times 3=2\times x[/tex]
[tex]12=2x[/tex]
Divide both sides by 2.
[tex]\dfrac{12}{2}=x[/tex]
[tex]6=x[/tex]
Therefore, the value of x is 6.