MATHEMATICS MIDDLE SCHOOL

If x and y are real numbers such that x > 1 and y < −1,then which of the following inequalities must be true?
A. x/y> 1
B. |s|^2 > |y|
C. x/3− 5 > y/3 − 5
D. x^2 + 1 > y^2 + 1
E. x^(−2) > y^(−2)

Answers

Answer 1
Answer: x > 1\ \wedge\ y < -1\n\nA.\ (x)/(y) > 1-FALSE;example:x=2;\ y=-2\ then\nL=(2)/(-2)=-1;R=1;\ L < R\n\nB.\ |x|^2 > |y|-FALSE;example:x=2;\ y=-6\ then\nL=|2|^2=2^2=4;R=|-6|=6;\ L < R\n\nC.\ (x)/(3)-5 > (y)/(3)-5-TRUE;(x)/(3)-5 > (y)/(3)-5\to(x)/(3) > (y)/(3)\to x > y

D.\ x^2+1 > y^2+1-FALSE;example:x=2;\ y=-3\ then\nL=2^2+1=4+1=5;R=(-3)^2+1=9+1=10;L < R\n\nE.\ x^(-2) > y^(-2)-FALSE;example:x=3;\ y=-2\ then\nL=3^(-2)=(1)/(9);R=(-2)^(-2)=(1)/(4);\ L < R

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Find the missing number.

32/52 = ?/13

Answers

Answer:  The required missing number is 8.

Step-by-step explanation:  We are given to find the missing number in the following proportion :

(32)/(52)=(?)/(13).

Let the missing number be represented by x.

Then, according to the given information, we have

(32)/(52)=(x)/(13)\n\n\n\Rightarrow (8)/(13)=(x)/(13)\n\n\n\Rightarrow x=(8)/(13)*13\n\n\Rightarrow x=8.

Thus, the required missing number is 8.
32,52 
to get the third no add 5+2 =7 is the first digit of the 3rd no 
to get the second digit u need to find the difference between (addition of the digits of second no and addition of digits of the first no) i.e. (5+2)-(3+2)=7-5=2 
so the third no is 72 
similarly for the fourth no. 
first digit (7+4)=11 
second digit ((7+4)-(5+2))=11-7=4 
next no should be 114 
.... 
last number 135 
13+5 = 18 
The last digit is the difference between the last two answers, in this case, 18-13 = 5. 

ANSWER: 185 = 17

a window shaped like a parallelogram has an area of 18 1/3 square feet. The height of a window is 3 1/3 feet. How long is the base of the window?

Answers

You must first realize that
     base times height equals the area

Now that you remember that, all you have to do is work backwards...
     
18 1/3 
--------  
 3 1/3       

18 1/3 = 55/3

3 1/3 = 10/3

55/3 divided by 10/3
   =5 1/2

Expand the brackets and simplify
a. 5(x+4) + 2(x+3)

b. 3(y+6) + 4(y-5)​

Answers

Answer:

Step-by-step explanation:

a. 5(x+4) + 2(x+3)  = 5*x + 5*4 + 2*x + 2*3

                             = 5x + 20 + 2x + 6  

                            = 5x + 2x + 20 +6  {bring like terms together}

                            = 7x + 26

b. 3(y+6) + 4(y-5)​ = 3*y + 3*6 + 4*y - 4*5

                           = 3y + 18 + 4y - 20  

                           = 3y + 4y + 18 - 20   {bring like terms together}

                          = 7y - 2

Answer:

a. 7x+26

b.7y-2

Step-by-step explanation:

for question a

1.Do 5 multiplied by x (5x) and 5 multiplied by 4 (20) and do the same with the other brackets

2. simplify the expression (collect the like terms)

5x+20+2x+6=6x+26

3.calculate the sum

DO THE SAME FOR QUESTION b

Angles U and V are supplementary angles. The ratio of their measures is 7:13 Find the measure of each angle

Answers

If u and v are supplementary angles, then

u+v=180^(\circ)~~~~~\mathbf{(i)}


The ratio of u and v is (7)/(13):

(u)/(v)=(7)/(13)\n\n\n u=(7v)/(13)~~~~\mathbf{(ii)}


Substitute \mathbf{(ii)} into \mathbf{(i)}:

(7v)/(13)+v=180^(\circ)\n\n\n \left((7)/(13)+1 \right )\cdot v=180^(\circ)\n\n\n \left((7)/(13)+(13)/(13) \right )\cdot v=180^(\circ)\n\n\n (20)/(13)\cdot v=180^(\circ)\n\n\n v=180^(\circ)\cdot (13)/(20)\n\n\n \boxed{\begin{array}{c} v=117^(\circ) \end{array}}


From \mathbf{(i)}, we find the measure of u:

u=180^(\circ)-v\n\n u=180^(\circ)-117^(\circ)\n\n \boxed{\begin{array}{c} u=63^(\circ) \end{array}}

How can i use models to relate fractions and decimals?

Answers

You can make visual (model) witch helps you see what you are doing
you can use different colors
 

Find the volume of the composite figure. please!

Answers

Volume= Length * width ( aka Base ) * height 

Break up the figure into easier figures, a small square and a bigger square.

Small square- 3*2*1 = 6 cm

Large Square- 7*6*1 = 42 cm

42 + 6 = 48 cm. But wait! You have to take one more step, which is minus-ing 6 from 48. Why? Notice that there is a little area where a side of the small square meets the bigger square. That little area is worth 3 cm ( length is 3, height is 1 cm ) times 2 ( 3 cm is one side, another 3 cm is the other side from the other square ) = 6 cm.

Your total answer should be 42. ( or 48, if your teacher doesn't count the area where the squares meet/join together ).
3times2times1equals 6
7times6times1equals 42
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