Fine two integers that have a sum of -17 and a product of 52. What are the integers?

-4 x -13 are the two integers that have a product of 52 and a sum of -17!

Have a great day/night! ^^

{4, 13}

Step-by-step explanation:

Represent the integers by I and J.  Then I + J = -17 and I*J = 52.

Let's solve this system using substitution.  Solve the first equation for I as follows:  

I + J = -17 becomes I = -J - 17

Substitute -J -17 for   I   in the second equation:

(-J - 17)*J = 52

Performing the indicated multiplication, we get:

-J^2 - 17J - 52 = 0

Let's solve this using the quadratic formula.  The quadratic coefficients here are {-1, -17, -52}, and so the discriminant, b^2 - 4ac, is

(-17)^2 - 4(-1)(-52), or 289 - 208, or 81.  This result is positive, so we know that the quadratic equation has two real, unequal roots.  They are:

      17 ± √81         17 ± 9

J =   =

         2(-1)                  -2

Evaluating this last result, we get J = (17 + 9)/2, or J = 13, and

J = (17 - 9)/2 = 8/2, or J = 4

hello,

b) 62.47% of the students are between 14 and 18 years old.

step-by-step explanation:

mean = 15 and standard deviation = 2

student between 14 to 18

formula used z-score

for age 14 , z score

using z-table , p(z> -0.5)=0.3085

for age 18 , z score

using z-table , p(z< 1.5)=0.9332

p(-0.5< z< 1.5)=0.9332-0.3085 = 0.6247

thus, 62.47% of the students are between 14 and 18 years old.

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step-by-step explanation:

see explanation

step-by-step explanation:

a

(6r + 7) + (13 + 7r) ( remove brackets and collect like terms )

= 6r + 7 + 13 + 7r

= 13r + 20

b

remove brackets and collect like terms

13 - r - 1 + r

= 12 - r

c

remove brackets and collect like terms

= - 8 - r + 2r - 4

= - 12 + r

d

remove brackets and collect like terms

= 7r - - - 6r

[-   - = - - = - ]

= r -