# Find an equation that models a hyperbolic lens with a = 12 inches and foci that are 26 inches apart. Assume that the center of the hyperbola is the origin and the transverse axis is vertical.

QUESTION POSTED AT 18/01/2020 - 07:36 AM

QUESTION POSTED AT 18/01/2020 - 07:36 AM

The general form for a hyperbola with the center at the origin and a vertical transverse axis is:

y2/a2 - x2/b2 = 1

From the given:

a = 12

To get b, we use the given distance between the foci.Since it's 26,

c = 26/2 = 13

Using this defintion:

c2 = a2 + b2

b = sqrt(c2 - a2) = sqrt (13^2 - 12^2) = 5

The equation therefore is:

y2/13^2 - x2/5^2 = 1

or

y2/169 - x2/25 = 1

y2/a2 - x2/b2 = 1

From the given:

a = 12

To get b, we use the given distance between the foci.Since it's 26,

c = 26/2 = 13

Using this defintion:

c2 = a2 + b2

b = sqrt(c2 - a2) = sqrt (13^2 - 12^2) = 5

The equation therefore is:

y2/13^2 - x2/5^2 = 1

or

y2/169 - x2/25 = 1

1 inch equals 2.54 centimeters. Can you work out from here ?

ANSWERED AT 20/02/2020 - 11:22 PM

QUESTION POSTED AT 20/02/2020 - 11:22 PM

Did your explanation include the following?

Some polynomial equations have complex solutions.

Therefore, complex solutions cannot be found by graphing the related system or function in the Cartesian (x-y) plane.

Polynomial functions with all complex solutions do not have x-intercepts, and the related system of equations will not intersect.

ANSWERED AT 20/02/2020 - 11:21 PM

QUESTION POSTED AT 20/02/2020 - 11:21 PM

If you estimate it the equation is -10+12=9+12=21 or 2=21=21 so the answer is false

ANSWERED AT 20/02/2020 - 11:21 PM

QUESTION POSTED AT 20/02/2020 - 11:21 PM

The answer to this question would be:

Jim =6 years

Harry =2 years

To answer this question, you need to translate the description into a mathematical equation. If H= Harry's ages and J= Jim's ages, then the equation should be look like this:

1. H+4= J

2. (J+2)= 2(H+2)

J+2= 2H+4

J= 2H +2

If you put the 1st and 2nd equation together, the result would be:

H+4= J

H+4= (2H +2)

H-2H= 2-4

-H= -2

H=2

After that insert the H value to either 1st or 2nd equation.

H+4= J

2+4=J

J= 6

Jim =6 years

Harry =2 years

To answer this question, you need to translate the description into a mathematical equation. If H= Harry's ages and J= Jim's ages, then the equation should be look like this:

1. H+4= J

2. (J+2)= 2(H+2)

J+2= 2H+4

J= 2H +2

If you put the 1st and 2nd equation together, the result would be:

H+4= J

H+4= (2H +2)

H-2H= 2-4

-H= -2

H=2

After that insert the H value to either 1st or 2nd equation.

H+4= J

2+4=J

J= 6

ANSWERED AT 20/02/2020 - 11:19 PM

QUESTION POSTED AT 20/02/2020 - 11:19 PM

Plug in negative 1 for x and do order of operations and u should get negative 8

ANSWERED AT 20/02/2020 - 11:18 PM

QUESTION POSTED AT 20/02/2020 - 11:18 PM

3-y=8

-y=8-3

y=-5

so just try to re arrange the equation to find the value for the variable

-y=8-3

y=-5

so just try to re arrange the equation to find the value for the variable

ANSWERED AT 20/02/2020 - 11:18 PM

QUESTION POSTED AT 20/02/2020 - 11:18 PM

Two forths is the same as one half ...so just take half of 36 which is 18

ANSWERED AT 20/02/2020 - 11:15 PM

QUESTION POSTED AT 20/02/2020 - 11:15 PM

2a = -12

5b = 10

Hope this helps

:)

5b = 10

Hope this helps

:)

ANSWERED AT 20/02/2020 - 11:14 PM

QUESTION POSTED AT 20/02/2020 - 11:14 PM

The nth term is 5n-7

ANSWERED AT 20/02/2020 - 11:14 PM

QUESTION POSTED AT 20/02/2020 - 11:14 PM

The two fractions that we can extract from the given rates above are:

(1) 12 pages / 20 minutes

(2) 20 pages / 32 minutes

We can reduce the fractions or rates to their lowest term by dividing the numbers by 4 such that,

(1) 3 pages / 5 minutes

(2) 5 pages / 8 minutes

Therefore, the rates are not equivalent.

(1) 12 pages / 20 minutes

(2) 20 pages / 32 minutes

We can reduce the fractions or rates to their lowest term by dividing the numbers by 4 such that,

(1) 3 pages / 5 minutes

(2) 5 pages / 8 minutes

Therefore, the rates are not equivalent.

ANSWERED AT 20/02/2020 - 11:12 PM

QUESTION POSTED AT 20/02/2020 - 11:12 PM

**Answer:**

**Required Equations are x + y = 24 & x - y = 6**

**Step-by-step explanation:**

let x be the no of yellow marbles that Charles has.

and y be the no of blue marbles that Charles has.

Total Marbles that Charles has = 24

**⇒ x + y = 24 ..............(1)**

Charles has 6 more yellow marbles than blue marbles.

**⇒ x = y + 6**

** x - y = 6 ......................(2)**

Therefore, **Required Equations are x + y = 24 & x - y = 6**

ANSWERED AT 20/02/2020 - 11:12 PM

QUESTION POSTED AT 20/02/2020 - 11:12 PM

B. And C. Is the correct answer

ANSWERED AT 20/02/2020 - 11:11 PM

QUESTION POSTED AT 20/02/2020 - 11:11 PM

D) 26 streamers x $0.50 = $13

25 balloons x $0.25 = $6.25

13+6.25 = 19.25

25 balloons x $0.25 = $6.25

13+6.25 = 19.25

ANSWERED AT 20/02/2020 - 11:10 PM

QUESTION POSTED AT 20/02/2020 - 11:10 PM

12/6 can be written as 2 because 6 can go into 12 two times.

ANSWERED AT 20/02/2020 - 11:07 PM

QUESTION POSTED AT 20/02/2020 - 11:07 PM

Answer:

Step-by-step explanation:

A

ANSWERED AT 20/02/2020 - 11:06 PM

QUESTION POSTED AT 20/02/2020 - 11:06 PM

Including the tax, the total would be $12,968.75

ANSWERED AT 20/02/2020 - 11:05 PM

QUESTION POSTED AT 20/02/2020 - 11:05 PM

21+33+15+20= 89 you started the day with $89

ANSWERED AT 20/02/2020 - 11:03 PM

QUESTION POSTED AT 20/02/2020 - 11:03 PM

Y=4+50x

Y=40+32x

Those are your answers

Y=40+32x

Those are your answers

ANSWERED AT 20/02/2020 - 11:02 PM

QUESTION POSTED AT 20/02/2020 - 11:02 PM

1 gallon / 350 ft^2 = x gallon / 182 ft^2

cross multiply (350 • x, 1 • 182)

350x = 182

x = 0.52 gallons

cross multiply (350 • x, 1 • 182)

350x = 182

x = 0.52 gallons

ANSWERED AT 20/02/2020 - 11:02 PM

QUESTION POSTED AT 20/02/2020 - 11:02 PM

1 hour and 25 minutes ~ 75 minutes. Divide: 75 / 5 = 15.

Multiply the numerator by 15. 15 x 3 = 45.

Now divide the denominator: 45/8 = 5 and a remainder of 5.

The answer is 5 5/8 inches.

Multiply the numerator by 15. 15 x 3 = 45.

Now divide the denominator: 45/8 = 5 and a remainder of 5.

The answer is 5 5/8 inches.

ANSWERED AT 20/02/2020 - 11:01 PM

QUESTION POSTED AT 20/02/2020 - 11:01 PM

Here, slope (m) = y2 - y1 / x2 - x1

m = 6-4 / 12-4

m = 2 / 8

m = 1/4

Equation, y - y1 = m(x - x1)

y - 4 = 1/4 (x - 4)

Also, y - 6 = 1/4 (x - 12)

**In short, Your Answers would be Option A & F**

Hope this helps!

m = 6-4 / 12-4

m = 2 / 8

m = 1/4

Equation, y - y1 = m(x - x1)

y - 4 = 1/4 (x - 4)

Also, y - 6 = 1/4 (x - 12)

Hope this helps!

ANSWERED AT 20/02/2020 - 10:58 PM

QUESTION POSTED AT 20/02/2020 - 10:58 PM

A statement that has mathematical expressions that are equal.

Examples:

2+1=3

11x4=44

Examples:

2+1=3

11x4=44

ANSWERED AT 20/02/2020 - 10:58 PM

QUESTION POSTED AT 20/02/2020 - 10:58 PM

The y intercept would be 3, from there go up 4 and right 1 .

ANSWERED AT 20/02/2020 - 10:57 PM

QUESTION POSTED AT 20/02/2020 - 10:57 PM

Here, Slope (m) = y2 - y1 / x2 - x1

m = 10 - 2 / 1 - (-3)

m = 8 / 4

m = 2

y - 10 = 2 (x - 1)

Also, y - 2 = 2(x + 3)

**In short, Your Answers would be A & B**

Hope this helps!

m = 10 - 2 / 1 - (-3)

m = 8 / 4

m = 2

y - 10 = 2 (x - 1)

Also, y - 2 = 2(x + 3)

Hope this helps!

ANSWERED AT 20/02/2020 - 10:57 PM

QUESTION POSTED AT 20/02/2020 - 10:57 PM

Harriet at 1/4 of all pieces

4/4-1/4=3/4

nisha ate 1/2 of remaining (3/4)

1/2 of 3/4=3/8 eaten

ok, so eaten=1/4+3/8=2/8+3/8=5/8 eaten

8/8-5/8=3/8 left

3/8=6 pices

1/8=2 pieces

8/8=16 pices

origainally divided into 16 pieces

4/4-1/4=3/4

nisha ate 1/2 of remaining (3/4)

1/2 of 3/4=3/8 eaten

ok, so eaten=1/4+3/8=2/8+3/8=5/8 eaten

8/8-5/8=3/8 left

3/8=6 pices

1/8=2 pieces

8/8=16 pices

origainally divided into 16 pieces

ANSWERED AT 20/02/2020 - 10:56 PM

QUESTION POSTED AT 20/02/2020 - 10:56 PM

1. I belive this is in simplest form already.

2. 4s+9

3. 8s+4r

4. -2r+4

5. 6s

Hope that helps a little bit!

2. 4s+9

3. 8s+4r

4. -2r+4

5. 6s

Hope that helps a little bit!

ANSWERED AT 20/02/2020 - 10:55 PM

QUESTION POSTED AT 20/02/2020 - 10:55 PM

Since the problem is 4(x+8)=44 you will first need to distribute. 4 times x equals 4x. And 4 times 8 equals 32. So that leaves you with a neat problem, 4x+32=44. Next, you must subtract 32 from both sides. You need to do this to both sides to make she that they stay even. So minus 32 on both sides leaves the equation at, 4x=12. Lastly, you must divide both sides by four to get the x alone and the answer is 3. Hope this helped.

ANSWERED AT 20/02/2020 - 10:55 PM

QUESTION POSTED AT 20/02/2020 - 10:55 PM

They bought granola the most

5/6 = 10/12

10/12 > 1/12

5/6 = 10/12

10/12 > 1/12

ANSWERED AT 20/02/2020 - 10:54 PM

QUESTION POSTED AT 20/02/2020 - 10:54 PM

Assuming simple interest

I=PRT

Interset=principal times rate times time

principal=1500

rate=9%=0.09

time=2

I=1500 times 0.09 times 2

I=1500 times 0.18

I=270

interest=270

total is 1500+270=1770 total paied

I=PRT

Interset=principal times rate times time

principal=1500

rate=9%=0.09

time=2

I=1500 times 0.09 times 2

I=1500 times 0.18

I=270

interest=270

total is 1500+270=1770 total paied

ANSWERED AT 20/02/2020 - 10:53 PM

QUESTION POSTED AT 20/02/2020 - 10:53 PM

4 times 3 equals 12.

ANSWERED AT 20/02/2020 - 10:53 PM

QUESTION POSTED AT 20/02/2020 - 10:53 PM