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Georgia [21]
3 years ago
6

The sum of two integers is 23 and the positive difference of the same two integers is 13. What is the product of these two integ

ers?
A) 90 B) 75
C) 46 D) 299
Mathematics
1 answer:
Lady_Fox [76]3 years ago
7 0

Answer:

A) 90

Step-by-step explanation:

"The sum of two integers is 23" becomes

a + b = 23

"the positive difference of the same two integers is 13" becomes

a - b = 13        (difference means subtract)

Now solve the system..

a + b = 23

a - b = 13            *use addition or elimination method, since b has opposite coefficients...

2a = 36             ( we add the two equations together)

   a = 18             (divide by 2 on both sides)

Since a = 18,   18 + b = 23, gives us b = 5.     (18 + 5 = 23)

ab = (18)(5) = 90

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Find the vertices and foci of the hyperbola with equation quantity x plus one squared divided by sixteen minus the quantity of y
katrin2010 [14]

Answer:

The vertices are (3 , -5) , (-5 , -5)

The foci are (4 , -5) , (-6 , -5)

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 length of the transverse axis is 2 a

- The coordinates of the vertices are  (h  ±  a  ,  k)

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

- The distance between the foci is  2c

* Now lets solve the problem

- The equation of the hyperbola is (x + 1)²/16 - (y + 5)²/9 = 1

* From the equation

# a² = 16 ⇒ a = ± 4

# b² = 9 ⇒ b = ± 3

# h = -1

# k = -5

∵ The vertices are (h + a , k) , (h - a , k)

∴ The vertices are (-1 + 4 , -5) , (-1 - 4 , -5)

* The vertices are (3 , -5) , (-5 , -5)

∵ c² = a² + b²

∴ c² = 16 + 9 = 25

∴ c = ± 5

∵ The foci are (h ± c , k)

∴ The foci are (-1 + 5 , -5) , (-1 - 5 , -5)

* The foci are (4 , -5) , (-6 , -5)

4 0
3 years ago
Read 2 more answers
Thank you in advance for the help !!
babymother [125]

The Answer is C, my good friend.

4 0
3 years ago
someone, please help me asap, that would be great, offering 15 points, and please do not attach a link for the answer, thanks.
algol13
Pretty sure the answer is 288
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3 years ago
A baby weights 18 pounds at her four month appointment. Six months later she weights 24 pounds. By what percentage did the baby’
Anna11 [10]

Answer: 25%

Step-by-step explanation:

Given : Previous baby's weight = 18 pounds

New baby's weight =  24 pounds.

Increase in weight = New weight -Previews weight

=24 pounds - 18 pounds  =6 pounds

Percentage increase in baby's weight ==\dfrac{\text{Increase in baby's weight}}{\text{previous weight}}\times100

\\\\=\dfrac{6}{24}\times100=25\%

Hence, the percentage increase in baby's weight = 25%

4 0
3 years ago
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