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
ella [17]
3 years ago
12

Which statement explains how you could use coordinate geometry to prove that quadrilateral ABCD is a square

Mathematics
1 answer:
mixer [17]3 years ago
3 0

Answer:

Prove that all sides are congruent and that the slopes of consecutive sides are opposite reciprocals. Step-by-step explanation: In order to two segmets to be perpendicular, the slope of both lines must be opposite and reciprocals, having a 90° interception and forming a square.

You might be interested in
Work out the Perimeter of the Triangle For 100 Points
WINSTONCH [101]

Answer:

P = 4x + 14

Step-by-step explanation:

P=(3x-5)+(19-x)+(2x)=(3x-x+2x)+(-5+19)=4x+14

Hope this helps

5 0
2 years ago
Thanks for any help provided to my question! &lt;3<br>5m + 2(m + 8) + 3
disa [49]
5m+2(m+8)+3
5m+2m+16+3
7m+19
3 0
3 years ago
The point (-2, -1) satisfies which of the following inequalities?
satela [25.4K]

Answer:

C

Step-by-step explanation:

4 0
3 years ago
Calculus Problem
Roman55 [17]

The two parabolas intersect for

8-x^2 = x^2 \implies 2x^2 = 8 \implies x^2 = 4 \implies x=\pm2

and so the base of each solid is the set

B = \left\{(x,y) \,:\, -2\le x\le2 \text{ and } x^2 \le y \le 8-x^2\right\}

The side length of each cross section that coincides with B is equal to the vertical distance between the two parabolas, |x^2-(8-x^2)| = 2|x^2-4|. But since -2 ≤ x ≤ 2, this reduces to 2(x^2-4).

a. Square cross sections will contribute a volume of

\left(2(x^2-4)\right)^2 \, \Delta x = 4(x^2-4)^2 \, \Delta x

where ∆x is the thickness of the section. Then the volume would be

\displaystyle \int_{-2}^2 4(x^2-4)^2 \, dx = 8 \int_0^2 (x^2-4)^2 \, dx \\\\ = 8 \int_0^2 (x^4-8x^2+16) \, dx \\\\ = 8 \left(\frac{2^5}5 - \frac{8\times2^3}3 + 16\times2\right) = \boxed{\frac{2048}{15}}

where we take advantage of symmetry in the first line.

b. For a semicircle, the side length we found earlier corresponds to diameter. Each semicircular cross section will contribute a volume of

\dfrac\pi8 \left(2(x^2-4)\right)^2 \, \Delta x = \dfrac\pi2 (x^2-4)^2 \, \Delta x

We end up with the same integral as before except for the leading constant:

\displaystyle \int_{-2}^2 \frac\pi2 (x^2-4)^2 \, dx = \pi \int_0^2 (x^2-4)^2 \, dx

Using the result of part (a), the volume is

\displaystyle \frac\pi8 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{256\pi}{15}}}

c. An equilateral triangle with side length s has area √3/4 s², hence the volume of a given section is

\dfrac{\sqrt3}4 \left(2(x^2-4)\right)^2 \, \Delta x = \sqrt3 (x^2-4)^2 \, \Delta x

and using the result of part (a) again, the volume is

\displaystyle \int_{-2}^2 \sqrt 3(x^2-4)^2 \, dx = \frac{\sqrt3}4 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{512}{5\sqrt3}}

7 0
2 years ago
Is x = 7 a solution to the equation 3x - 4 = 15? No Yes
Elis [28]

Answer:

No, because 3 x 7 = 21 - 4 = 17

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Other questions:
  • What is the absolute value of -12|3x+12|5=43
    7·1 answer
  • The volume of a cube depends on the length of its sides. This can be written in function notation as v(s). What is the best inte
    10·1 answer
  • What is the area of a right triangle 21 centimeters wide and 13 centimeters tall?
    12·2 answers
  • Which describes the relationship between Angle 1 and Angle 2? Line C intersect angle A B D to form angles 1 and 2. Angle 1 and A
    7·2 answers
  • Suppose that attendance at the concerts by the band "Keane" is a normally distributed random variable X with a mean of 18,500. Y
    5·1 answer
  • The dimensions of a standard tennis court are 36 ft. 78 ft. with a net that is 3 ft. high in the center. The
    15·1 answer
  • Who would benefit most from obtaining a loan with a fixed interest rate? A. A student seeking a credit card to use for daily exp
    7·2 answers
  • Simplify (3x^2y^3)^3
    10·1 answer
  • 2/
    9·1 answer
  • Please help me with the question below (also please explain).
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!