MATHEMATICS MIDDLE SCHOOL

F(x) = √(x+7) -√(x^2+2x-15) find the domain

Answers

Answer 1
Answer:

Answer:

x >= -7  ................(1a)

x >= 3   ...............(2a1)

Step-by-step explanation:

f(x) =  √(x+7)-√(x^2+2x-15)  .............(0)

find the domain.

To find the (real) domain, we need to ensure that each term remains a real number.

which means the following conditions must be met

x+7 >= 0  .....................(1)

AND

x^2+2x-15 >= 0 ..........(2)

To satisfy (1),  x >= -7  .....................(1a) by transposition of (1)

To satisfy (2), we need first to find the roots of (2)

factor (2)

(x+5)(x-3) >= 0

This implis

(x+5) >= 0 AND (x-3) >= 0.....................(2a)

OR

(x+5) <= 0 AND (x-3) <= 0 ...................(2b)

(2a) is satisfied with x >= 3   ...............(2a1)

(2b) is satisfied with x <= -5 ................(2b1)

Combine the conditions (1a), (2a1), and (2b1),

x >= -7  ................(1a)

AND

(

x >= 3   ...............(2a1)

OR

x <= -5 ................(2b1)

)

which expands to

(1a) and (2a1)   OR  (1a) and (2b1)

( x >= -7 and x >= 3 )  OR ( x >= -7 and x <= -5 )

Simplifying, we have

x >= 3  OR ( -7 <= x <= -5 )

Referring to attached figure, the domain is indicated in dark (purple), the red-brown and white regions satisfiy only one of the two conditions.
Answer 2
Answer: f(x) = 
find the domain

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Answer:

31. Yes (Y)

WXYZ ~ DABC

S.F.=4


32. Yes (Y)

GHIJ ~ KLMN

S.F.=2/3


33. Missing length: 16


34. Missing length: 30


35. x=7


36. x=10


Step-by-step explanation:

31. The polygons are similar if:

WX/DA=XY/AB

Then:

WX/DA=24/6→WX/DA=4

XY/AB=16/4→XY/AB=4

Like WX/DA=4=XY/AB, the polygons WXYZ and DABC are similar

Scale Factor: S.F.=XY/DA=XY/AB→S.F.=4


32. The polygons are similar if:

GH/KL=HI/LM=IJ/MN=GJ/KN

Then:

GH/KL=6/9=(6/3)/(9/3)→GH/KL=2/3

HI/LM=4/6=(4/2)/(6/2)→HI/LM=2/3

IJ/MN=4/6=(4/2)/(6/2)→IJ/MN=2/3

GJ/KN=4/6=(4/2)/(6/2)→GJ/KN=2/3

Like GH/KL=HI/LM=IJ/MN=GJ/KN=4, the polygons GHIJ and KLMN are similar

Scale Factor: S.F.=GH/KL=HI/LM=IJ/MN=GJ/KN→S.F.=2/3


33. If the polygons are similar, their sides must be proportional, then:

x/24=10/15

Simplifying the fraction on the right sides of the equation, dividing the numerator ans denominator by 5:

x/24=(10/5)/(15/5)

Dividing:

x/24=2/3

Solving for x: Multiplying both sides of the equation by 24:

24(x/24)=24(2/3)

Multiplying:

x=8(2)

x=16


34. If the polygons are similar, their sides must be proportional, then:

54/63=(54/9)/(63/9)→54/63=6/7

48/56=(48/8)/(56/8)→48/56=6/7

x/35=6/7

Solving for x: Multiplying both sides of the equation by 35:

35(x/35)=35(6/7)

Multiplying:

x=5(6)

x=30


36. (8x-2)/63=42/49

Simplifying the fraction on the right sides of the equation, dividing the numerator ans denominator by 7:

(8x-2)/63=(42/7)/(49/7)

Dividing:

(8x-2)/63=6/7

Solving for x: Multiplying both sides of the equation by 63:

63(8x-2)63=63(6/7)

Multiplying:

8x-2=9(6)

8x-2=54

Adding 2 both sides of the equation:

8x-2+2=54+2

Adding:

8x=56

Dividing both sides of the equation by 8:

8x/8=56/8

Dividing:

x=7


37. (6x-6)/63=42/49=30/35

Simplifying the fractions

(6x-6)/63=(42/7)/(49/7)=(30/5)/(35/5)

Dividing:

(6x-6)/63=6/7

Solving for x: Multiplying both sides of the equation by 63:

63(6x-6)63=63(6/7)

Multiplying:

6x-6=9(6)

6x-6=54

Adding 6 both sides of the equation:

6x-6+6=54+6

Adding:

6x=60

Dividing both sides of the equation by 6:

6x/6=60/6

Dividing:

x=10

~~~15 POINTS~~~
Please help with this question!

Answers

I would see the numbers close to each other like in the number line. 

_1__2___3___4__5___6___7__8__9   10____
  *    *       *       *
  *    *        *
  *
  *

1 through 4 is all cluster together. 

Graph the data from the table below. Describe the parent function as linear, square root, cube root, cubic, or quadratic.

Answers

The function rule is g(x) = 2*sqrt(x) which is a transformation of the parent function f(x) = sqrt(x)

The g(x) function has been scaled by a factor of 2. In other words, each point on g(x) is twice as high as its corresponding point on f(x). Specifically for example, the point (1,1) has been doubled to (1,2). Overall, this vertically stretches out the parent function graph.

Both the parent function f(x) and the other g(x) curve are square root functions. 

See the attached image. The blue curve goes through the given points from the table. The red curve is the parent function. 

A store had a sale on art supplies. The pricep of each item was marked down 60%.
Which expression represents the new price?
A 0.4p C 1.4p
B 0.6p D 1.6p

Answers

The expression that marks the new price is choice A 0.4 p. Since we mark the prices down 60%, the customer will only be charged 40% of the p price which is 0.4 x p.  Think of a candy bar that originally costs $1 and is marked down 60% by a discount sale.  The new price is $0.40.  
100%-60%=40%=0.4
so new price is 0.4p
Answer: A=0.4p

How do you solve. 8-2(5x-3)

Answers

The answer is -10x+14
First you distribute the -2 into the 5x-3 to get -10x+6. Then you add the 6 and 8 to get 14 then add then on both sides of the equation to get 10x=14 then divide each by 10 to get x=1.4. Hope this helps you solve questions like this one.
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