MATHEMATICS HIGH SCHOOL

8)What is the equation of a line that goes through the point (3, 12) and is perpendicular to the line given by the equation y = -1/3x - 7?(A) y = -3x - 12
(B )y = -1/3x + 6
(C) y = 3x + 3
(D) = (1/3x) - 6

Answers

Answer 1
Answer: The slope of the first line is m_1=(-1)/(3).
To be perpendicular the slope of the second line must be the negative reciprocal of the first: m_2=3
Use the slope-intercept formula: 
y=mx+b
Substitute known values:
12=3(3)+b
Solve for b:
b=3
Complete the formula:
y=3x+3

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A triangle has side lengths of 5, 9 and 12. Is it right acute or obtuse?

Answers

a\leq b\leq c\ (a;b;c-side\ lengths\ of\ the\ triangle)\n\nthere\ is\ a\ relationship:\n\na^2+b^2=c^2-right\ triangle\n\na^2+b^2 < c^2-obtuse\ triangle\n\na^2+b^2 > c^2-acute\ triangle

a=5;\ b=9;\ c=12\n\na^2+b^2=5^2+9^2=25+81=106\n\nc^2=12^2=144\n\na^2+b^2 < c^2\n\nAnswer:Obtuse\ triangle

0= (3 x^(2)-18x+24 )/( x^(2) -2x-8)Solve for x
Please show your work!!!
Thanks in advance :)

Answers

D:x^2-2x-8\not=0\nD:x^2-4x+2x-8\not=0\nD:x(x-4)+2(x-4)\not=0\nD:(x+2)(x-4)\not=0\nD:x\not =-2 \wedge x\not =4\n\n(3x^2-18x+24)/(x^2-2x-8)=0\n(3(x^2-6x+8))/((x+2)(x-4))=0\n(3(x^2-4x-2x+8))/((x+2)(x-4))=0\n(3(x(x-4)-2(x-4)))/((x+2)(x-4))=0\n(3(x-2)(x-4))/((x+2)(x-4))=0\n(3(x-2)(x-4))/((x+2)(x-4))=0\n(3(x-2))/((x+2))=0|\cdot(x+2)\n3(x-2)=0|:3\nx-2=0\n\boxed{x=2}

Find the volume of a sphere that is circumscribed about a cube with a volume of 216 cubic inches

Answers

 Volume Cube = Side^3 
Volume Sphere = 4/3 x PI x radius^3 
since radius sphere = 1/2 side cube 

V cube = 216 = Side^3 
Side cube = 6 inch 
Volume sphere = 4/3 x 3.1416 x (3)^3 
Volume sphere = 113.10 cubic inches

Christina is planning a dance routine. at the end of each measure of music, she will make a 1 1/4 turn. how many turns will she make after the first 3 measures of music

Answers

1 (1)/(4) is equal to (5)/(4)  ( (4)/(4) + (1)/(4) ). To get your answer all you need to do is multiply the numerator 5, by the number of times Christina goes through the routine. You therefore get the answer:
(5*3)/(4) = (15)/(4)
this simplifies to 3 (3)/(4)

What is the domain of the function y=3√6x+42 A. x ≥ 0
B. x ≤ 7
C. x ≥ –6
D. x ≥ –7

Answers

Answer:  The correct option is (D) x\geq -7.

Step-by-step explanation:  We are given to find the domain of the following function:

y=3√(6x+42)~~~~~~~~~~~~~~~~~~~~~~~~~(i)

The domain of a function y = f(x) is the set of all possible x-values which will make the function defined or will output real y-values.

That is, for the function (i), the domain will be given by all those values of x for which 3√(6x+42) is real.

Now, the values of y will be real only if the expression under square root is greater than or equal to 0.

Therefore, the domain of function (i) is

√(6x+42)\geq0\n\n\Rightarrow 6x+42\geq 0\n\n\Rightarrow 6x\geq -42\n\n\Rightarrow x\geq -(42)/(6)\n\n\Rightarrow x\geq -7.

Thus, the domain of the given function is x\geq -7.

Option (D) is CORRECT.
The domain of  the function:
y = 3 √ ( 6 x + 42 )
6 x + 42 ≥ 0
6 x ≥ - 42
x ≥ - 42 : 6
x ≥ - 7
Answer:
The domain is D ) x ≥ - 7
 

Pls pls u guys I promised u will get 15 points if u answer this

Answers

very easy
just add up all the meadals

japan is 38

so total=104+88+82+x+44+38=356+x
total of all medals is 421 so to find brittan or x you just subtrac the total from the big total so

356+x=421
subtract 356 from both sides
x=65
brittan won 65 medals
Total is 421, 
United States (104)+ China (88)+ Russia (82)+ Germany (44)+ Japan (3*)
= 104 + 88 + 82 + 44 = 318 (idk wat japan # is)

so because ur photo is cut off u need to do *318 + japan's number* then do 421 minus *that number* that is what great Britain ( x ) is 

so in the end x (great Britain) = 65
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