MATHEMATICS HIGH SCHOOL

The symmetry of a hyperbola with a center at (h, k) only occurs at y = k.

True or False

Answers

Answer 1
Answer:

Answer:

The given statement is a False statement.

Step-by-step explanation:

We know that the center of a hyperbola is the mid-point of the transverse axis of the hyperbola.

If the curves of hyperbola opens up and down such that the center is (h,k) then the symmetry of hyperbola is:

                             y=k

and if the curve opens to the right and to the left and the center is at (h,k) then the symmetry of hyperbola is:

                               x=h

Hence, the statement:

    The symmetry of a hyperbola with a center at (h, k) only occurs at y = k.

is FALSE.

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Solve 4/(x + 1) - 1/x = 1 over the real numbers.

Answers

( 4)/(x + 1) - (1)/(x) = 1 \n \nx+1\neq 0 \ \ \ and \ \ \ x\neq 0 \n \nx\neq -1 \ \ \ and \ \ \ x\neq 0 \n \nD=R\setminus \left \{ -1,0 \right \}

( 4x- (x+1))/(x(x + 1)) = 1 \n \n( 4x- x-1 )/(x^2+ x)=1 \n \n( 3x -1 )/(x^2 + x) = 1 \n \n3x-1=x^2+x\n \n x^2+x-3x+1=0

x^2-2x+1=0 \n \n (x-1)^2=0 \n \nx-1=0 \n \nx=1
 
Ok sorry I guessed this one but it was x = 1
4/(1+1) - 1/1 = 1
2 - 1 = 1
And it's right :)

What position is the 9 in the number 9,32805

Answers

( I think there's a typo. The comma should be in between 2 and 8 )

The 9 is in the hundred thousands place.

932805
 5- ones
0- tens
8-hundreds
2-thousands
3-ten thousands
9-hundred thousands
Solutions 

To solve the problem you can you place value. 

The number 9 is in the hundred thousands place.

 = Number (932805)

 5- ones

0- tens

8-hundreds

2-thousands

3-ten thousands

9-hundred thousands 

C(x) = 0.000002x3 − 0.03x2 + 400x + 80,000 where C(x) denotes the total cost incurred in producing x sets. Find the level of production that will yield a maximum profit for the manufacturer. Hint: Use the quadratic formula

Answers

Answer:

The producer will have maximum profit when x is 5000.

Step-by-step explanation:

Given C(x) = 0.000002x³ - 0.03x² + 400x + 80000

To find the level of production that will yield the maximum profit for the manufacturer, firstly, we differentiate C(x) to obtain C'(x), we then set the resulting quadratic expression to zero and solve. Whichever of the two values obtained from the quadratic equation will be tested to see what we want to find.

Differentiate C(x)

C'(x) = 3(0.000002)x² - 2(0.03)x + 400

= 0.000006x² - 0.06x + 400

Set C'(x) = 0

0.000006x² - 0.06x + 400 = 0

Solve using quadratic formula.

x = [-b ± √(b² - 4ac)]/2a

a = 0.000006

b = -0.06

c = 400

x = [-(-0.06) ± √((-0.06)² - 4(0.000006 × 400)]/2(0.000006)

= [0.06 ± √(0.0036 - 0.0096]/0.000012

= (0.06/0.000012) ± i√(0.006)/0.000012

= 5000 ± 6454.97i

x = 5000 + 6454.97i

Or

x = 5000 - 6454.97i

When registering their cars, owners must identify the color that covers the largest portion of the vehicle. In one region, the probability that car was mainly white was 0.24, the probability that it was mainly silver was 0.22, and the probability that it was mainly black was 0.19. In this region, are the events "silver" and "black" mutually exclusive:? Choose 1 answer A) Yes
B) No
Find the probability that a randomly selected car from this region is mainly silver OR mainly black.
P (silver OR black)=

Answers

Answer:

A) Yes

Step-by-step explanation:

Yes, the events silver and black are mutually exclusive, meaning they cannot not happen at the same time. While a car can certainly be black and silver, a car cannot be mainly silver AND mainly black at the same time. One color is going to be dominant

P (silver OR black)= P(silver) + P(black)

                              = 0.22 + 0.19

                              = 0.41

Answer:

yes, 0.41

Step-by-step explanation:

Got it right on Khan

Which solid has a volume that is 3 times the volume of a cone with the same base and height?a.cylinder
b.prism
c.pyramid eliminate
d.sphere?

Answers

Answer: (a) Cylinder

The formula for volume of a cone = 1/3 π r² h

The formula for volume of a cylinder = π r² h
The answer is  A. Cylinder

What is the value of n in the equation below?StartFraction a Superscript n Over a cubed EndFraction = a Superscript 9
3
6
12
27

Answers

Answer

12

Step-by-step explanation:

in this equation , since its a fraction you would divide. With the exponents it would be subtraction. therefore, making it 12 I hope this helps :)

Answer:

12

Step-by-step explanation:

got 100 on the test.
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