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svetlana [45]
3 years ago
7

24 + 8x + 10(2x) Terms: Constants: Coefficients:

Mathematics
1 answer:
Artemon [7]3 years ago
4 0
Terms: 24, 8x, 10(2x)
constants: 24
coefficients: 8, 10, 2
You might be interested in
Match the hyperbolas represented by the equations to their foci.
Arte-miy333 [17]

Answer:

1) (1 , -22) and (1 , 12) ⇔ (y + 5)²/15² - (x - 1)²/8² = 1

2) (-7 , 5) and (3 , 5) ⇔ (x + 2)²/3² - (y - 5)²/4² = 1

3) (-6 , -2) and (14 , -2) ⇔ (x - 4)²/8² - (y + 2)²/6² = 1

4) (-7 , -10) and (-7 , 16) ⇔ (y - 3)²/5² - (x + 7)²/12² = 1

Step-by-step explanation:

* Lets study the equation of the hyperbola

- The standard form of the equation of a hyperbola with

  center (h , k) and transverse axis parallel to the x-axis is

  (x - h)²/a² - (y - k)²/b² = 1

- the coordinates of the foci are (h ± c , k), where c² = a² + b²

- The standard form of the equation of a hyperbola with

  center (h , k) and transverse axis parallel to the y-axis is

  (y - k)²/a² - (x - h)²/b² = 1

- the coordinates of the foci are (h , k ± c), where c² = a² + b²

* Lets look to the problem

1) The foci are (1 , -22) and (1 , 12)

- Compare the point with the previous rules

∵ h = 1 and k ± c = -22 ,12

∴ The form of the equation will be (y - k)²/a² - (x - h)²/b² = 1

∵ k + c = -22 ⇒ (1)

∵ k - c = 12 ⇒ (2)

* Add (1) and(2)

∴ 2k = -10 ⇒ ÷2

∴ k = -5

* substitute the value of k in (1)

∴ -5 + c = -22 ⇒ add 5 to both sides

∴ c = -17

∴ c² = (-17)² = 289

∵ c² = a² + b²

∴ a² + b² = 289

* Now lets check which answer has (h , k) = (1 , -5)

  and a² + b² = 289 in the form (y - k)²/a² - (x - h)²/b² = 1

∵ 15² + 8² = 289

∵ (h , k) = (1 , -5)

∴ The answer is (y + 5)²/15² - (x - 1)²/8² = 1

* (1 , -22) and (1 , 12) ⇔ (y + 5)²/15² - (x - 1)²/8² = 1

2) The foci are (-7 , 5) and (3 , 5)

- Compare the point with the previous rules

∵ k = 5 and h ± c = -7 ,3

∴ The form of the equation will be (x - h)²/a² - (y - k)²/b² = 1

∵ h + c = -7 ⇒ (1)

∵ h - c = 3 ⇒ (2)

* Add (1) and(2)

∴ 2h = -4 ⇒ ÷2

∴ h = -2

* substitute the value of h in (1)

∴ -2 + c = -7 ⇒ add 2 to both sides

∴ c = -5

∴ c² = (-5)² = 25

∵ c² = a² + b²

∴ a² + b² = 25

* Now lets check which answer has (h , k) = (-2 , 5)

  and a² + b² = 25 in the form (x - h)²/a² - (y - k)²/b² = 1

∵ 3² + 4² = 25

∵ (h , k) = (-2 , 5)

∴ The answer is (x + 2)²/3² - (y - 5)²/4² = 1

* (-7 , 5) and (3 , 5) ⇔ (x + 2)²/3² - (y - 5)²/4² = 1

3) The foci are (-6 , -2) and (14 , -2)

- Compare the point with the previous rules

∵ k = -2 and h ± c = -6 ,14

∴ The form of the equation will be (x - h)²/a² - (y - k)²/b² = 1

∵ h + c = -6 ⇒ (1)

∵ h - c = 14 ⇒ (2)

* Add (1) and(2)

∴ 2h = 8 ⇒ ÷2

∴ h = 4

* substitute the value of h in (1)

∴ 4 + c = -6 ⇒ subtract 4 from both sides

∴ c = -10

∴ c² = (-10)² = 100

∵ c² = a² + b²

∴ a² + b² = 100

* Now lets check which answer has (h , k) = (4 , -2)

  and a² + b² = 100 in the form (x - h)²/a² - (y - k)²/b² = 1

∵ 8² + 6² = 100

∵ (h , k) = (4 , -2)

∴ The answer is (x - 4)²/8² - (y + 2)²/6² = 1

* (-6 , -2) and (14 , -2) ⇔ (x - 4)²/8² - (y + 2)²/6² = 1

4) The foci are (-7 , -10) and (-7 , 16)

- Compare the point with the previous rules

∵ h = -7 and k ± c = -10 , 16

∴ The form of the equation will be (y - k)²/a² - (x - h)²/b² = 1

∵ k + c = -10 ⇒ (1)

∵ k - c = 16 ⇒ (2)

* Add (1) and(2)

∴ 2k = 6 ⇒ ÷2

∴ k = 3

* substitute the value of k in (1)

∴ 3 + c = -10 ⇒ subtract 3 from both sides

∴ c = -13

∴ c² = (-13)² = 169

∵ c² = a² + b²

∴ a² + b² = 169

* Now lets check which answer has (h , k) = (-7 , 3)

  and a² + b² = 169 in the form (y - k)²/a² - (x - h)²/b² = 1

∵ 5² + 12² = 169

∵ (h , k) = (-7 , 3)

∴ The answer is (y - 3)²/5² - (x + 7)²/12² = 1

* (-7 , -10) and (-7 , 16) ⇔ (y - 3)²/5² - (x + 7)²/12² = 1

7 0
3 years ago
The are of the shape is __ square centimeter
tensa zangetsu [6.8K]

Answer:

35 cm

Step-by-step explanation:

To find the area of the bottom portion, you would use the formula for finding out a triangle (B*H*1/2) which is:

(4+4)*5.75*1/2=<u>23</u>

Then, for the top portion, one would find the area of the triangles on the sides (with two marks going through). Since along the middle is 8cm, and along the top is 4, we can see that there is 2cm on either side, so that is the length of the base of the triangle. To solve for the top triangles, you would do almost the same thing as the last one:

2*2*1/2=2

But since there's two identical triangles on either side, we can multiply that by two, which would bring it to <u>4.</u>

That just leaves the rectangle that is left between the two triangles. To solve this, it's just B*H and luckily both of those are labeled for you already:

4*2=<u>8</u>  

Now, to find the total area, all you have to do is add up the areas of the different sections:

23+4+8=35 cm

Hope this helps!

4 0
3 years ago
The expression (X + 3)(x + 2) is the product of two binomials. Which expression is also a product of binomials?
kow [346]

Answer:

B

Step-by-step explanation:

Binomials are expressions containing the sum (or difference) of two terms.

A. is not the answer because pq and qp are <u>products</u>.

C. is not the answer because 3x is not a sum/difference.

D. is not the answer because it is one binomial, not two muliplied together.

6 0
3 years ago
In Hillsboro's wig shop, 1/2 of the wigs are blonde and 1/12 of the wigs are brunette. What fraction of the wigs are either blon
ella [17]

Answer:

7/12

Step-by-step explanation:

So, the probability of picking up a blonde wig = 1/2

The probabiliy of picking up a brunette wig = 1/12

The question asks to find th eprobability of picking up either of these types of wigs =

1/2 + 1/12

= 6/12 + 1/12 ( LCM of 12 and 1 is 12 )

= 7/12

Hope this helps

3 0
3 years ago
HELP PLS FOR 10 POINTS AND BRAINLIEST TO CORRECT ANSWER The cost, C, to ride in a taxi can be calculated using the function show
max2010maxim [7]

9514 1404 393

Answer:

  A.  $0.85

Step-by-step explanation:

Each time m increases by 1, the cost goes up by $0.85.

The cost per mile is $0.85.

7 0
3 years ago
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