MATHEMATICS MIDDLE SCHOOL

Three vertices of a rectangle are (–3, 4), (5, 4), and (5, –2). 

What are the coordinates of the fourth vertex of the rectangle? 

         A. (–3, –4)                                               

        B. (–3, –2)                                               

     C. (5, –3)      

       D. (5, 2)

Answers

Answer 1
Answer: A =(-3, 4), \ \ B= (5, 4),\ \ C= (5, -2)\n \n The \ slope \ of \ AB : \n \n \n m= (y_(2)-y_(1))/(x_(2)-x_(1) ) = (4-4)/(5+3)=(0)/(8)=0\n \n The \ slope \ of \ CB :\n \n m= (y_(2)-y_(1))/(x_(2)-x_(1) ) = (5-5)/(-2-4)=0

The \ slope \ of \ lines \ parallel \ is \ the \ same \n \nTo \ find \ the \ coordinates \ of \ the \ fourth \ vertex, \ add \ the \ coordinates \n of \ A \ and \ C \ together, \ and \ subtract \ the \ coordinates \ of \ B. \n \n The \ fourth \ vertex \ is: (-3+5-5; 4-2-4) = (-3, -2) \n \n Answer: \ B. \ \ (-3, -2)

 
 
Answer 2
Answer: The rectangle doesn't necessarily have to be standing up straight or laying down flat
on the graph.  It could be tilted ... leaning.  Dealing with those coordinates would be
a nightmare, and since you're in Middle School and just learning this stuff, we can be
pretty sure that the rectangle in this problem is straight on the graph.

If we think about it for a second, and visualize a rectangle in our mind, we realize that:

-- Both top corners have the same y-coordinate.
-- Both bottom corners have the same y-coordinate.
-- Both corners on the left side have the same x-coordinate.
-- Both corners on the right side have the same x-coordinate.

The first two points given in the question are ( -3, 4) and (5, 4).

-- They have the same y-coordinate, so they must be either the top
or the bottom two corners.

-- We also know right away that the left side of the rectangle is at x = -3
and the right side of the rectangle is at x = 5 .

Now look at the third given point ... (5, -2) . 

-- Its x-coordinate is 5 so we know it's a corner on the right side.

-- But we already had one corner on the right side ... the point at (5, 4).
This new one is lower.

-- So now we know that (5, 4) was the upper right corner, (-3, 4) was the
upper left corner, and this new point is the lower right corner.

All we're missing is the lower left corner.

We know now that the left side is at x = -3 and the right side is at 5 .
We also know now that the top is at y = 4 and the bottom is at y = -2 .

So the bottom left corner is (-3, -2).  That's choice - 'B' .

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The diameter of circles A,C and E are 32 cm, 24cm and 14 cm respectively Which of the following statements are true? Select all that apply

Answers

Answer:

AG = 4

AH = 21

EC = 12

CH = 5

HE = 7

Step-by-step explanation:

The complete question is

The diameters of circles A, C and E are 32 cm, 24 cm and 14 cm respectively.

Which of the following statements are true? Select all that apply.

•AG = 4

•GC = 10

•AH = 21

•EC = 12

•EH = 5

•CH = 5

•HE = 7

The picture of the question in the attached figure

Verify each statement

1) AG = 4

we know that

AG=AC-GC

AC=32\2=16\ cm ----> radius of circle A

GC=24/2=12\ cm ----> radius of circle C

substitute

AG=16-12=4\ cm

therefore

The statement is true

2) GC = 10

we know that

GC=24/2=12\ cm ----> radius of circle C

therefore

The statement is false

3) AH = 21

we know that

AH=AC+CH

we have

AC=16\ cm ----> radius of circle A

CH=CE-HE

CE=12\ cm ----> radius of circle C

HE=14/2=7\ cm ----> radius of circle E

so

CH=12-7=5\ cm

AH=16+5=21\ cm

therefore

The statement is true

4) EC = 12

we know that

EC=24/2=12\ cm ----> radius of circle C

therefore

The statement is true

5) EH = 5

we know that

EH=14/2=7\ cm ----> radius of circle E

therefore

The statement is false

6) CH = 5

we know that

CH=CE-HE

CE=12\ cm ----> radius of circle C

HE=14/2=7\ cm ----> radius of circle E

so

CH=12-7=5\ cm

therefore

The statement is true

7) HE = 7

we know that

HE=14/2=7\ cm ----> radius of circle E

therefore

The statement is true

Please help I FORGOT ??? what to do and I'm a need of HELP ugh !!!!!!!!!!!!!!!!!!!!!!!

Answers

The larger lines are ur whole numbers...the smaller lines in between each large line are in increments of 1/3. I did not draw the larger lines....they are where the whole numbers are...the lines I inserted are the 1/3 increments.

                                    -6 2/3                 -4 1/3
                                     ^                        ^
< ----------------------------|---|--------------|---|-------------------------------->
   -10     -9     -8       -7       -6        -5         -4       -3      -2      -1    0

does that make sense ? 

Answer:

ok

Step-by-step explanation:

Glenn’s favorite number is very special because it reminds him of the day his daughter, Sarah, was born. The factors of this number do not repeat, and all the prime numbers are less than 12. What is Glenn’s number? When was Sarah born?

Answers

Answer:

2/3/10

Step-by-step explanation:

the number is such that its factors do not repeat and factors are all prime numbers less than 12.

prime numbers less than 12 are 2,3,5,7,11

so if the number is N then

N= 2×3×5×7×11= 2,310

Hence the Number N is 2310

and DOB of the daughter must be 2/3/10

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Answers

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Answers

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