Las edades de paulina y monica suman 36, las de monica y andrea 40, mientras que la suma de las edades de paulina y andrea es 44¿cuantos años tiene cada una?

Defining variables we have:

x: Paulina's age

y: Age of monica

z: Age of Andrea

We write the system of equations:

The ages of Pauline and Monica sum 36:

x + y = 36

Monica and Andrea 40:

y + z = 40

the sum of the ages of Pauline and Andrea is 44:

x + z = 44

From equation three we have:

z = 44-x

From equation 2:

y + z = 40

y + (44-x) = 40

y = 40-44 + x

y = -4 + x

From equation 1:

x + (- 4 + x) = 36

2x = 36 + 4

2x = 40

x = 20

Then, the age of monica is:

y = -4 + x

y = -4 + 20

y = 16

Finally, Andrea's age is:

z = 44-x

z = 44-20

z = 24

Paulina is 20 years old

Monica is 16 years old

Andrea is 24 years old

The question in English is

The ages of Paulina and Monica are 36, the ages of Monica and Andrea 40, while the sum of the ages of Paulina and Andrea is 44. How old is each one?

Let

x> Paulina's age

y> Monica's age

z> Andrea's age

we know that

x+y=36> equation 1

y+z=40> y=40-z> equation 2

x+z=44> x=44-z> equation 3

Substitute equation 2 and equation 3 in equation 1

[44-z]+[40-z]=36

84-2z=36

2z=84-36

z=48/2> z=24 years

Find the value of x

x=44-z> x=44-24> x=20 years

Find the value of y

y=40-z> y=40-24> y=16 years

therefore

the answer is

Paulina's age is 20 years old

Monica's age is 16 years old

Andrea's age is 24 yeras old

The answer in Spanish

Hagamos

x> La edad de Paulina

y> La edad de Monica

z> la edad de Andrea

Sabemos que

x+y=36> ecuacion 1

y+z=40> y=40-z> ecuacion 2

x+z=44> x=44-z> ecuacion 3

sustituya ecuacion 2 y ecuacion 3 en la ecuacion 1

[44-z]+[40-z]=36

84-2z=36

2z=84-36

z=48/2> z=24

Encuentre el valor de x

x=44-z> x=44-24> x=20

Encuentre el valor de y

y=40-z> y=40-24> y=16

por lo tanto

La respuesta es

La edad de Paulina es igual a 20

La edad de Monica es igual a 16

La edad de Andrea es igual a 24

answer:

(-8,7)

explanation:

we know that  

f

(

−

3

)

=

7

therefore, if we wish to get the output as 7, in the function, we need to have our input to be -3.

looking at the function  

f

(

x

+

5

)

, what should the value of x be, such that the input in the function becomes 7?

we simply equate the terms,

x

+

5

=

−

3

x

=

−

8

thus, the point on the new function would be  

(

−

8

,

7

)

answer

a,b, and d

explanation

a reflection angle is more than

but less than;

an angle that measures

is a reflex angle.(true)

an angle that measures less than

is acute.(true)

provided we are considering angles greater or equal to zero.

an acute angle lies in the range.

an obtuse angle is less than 180° but more than 90°

an angle that measures 300° is obtuse (false)

an angle that measures 65° is an acute angle.(true)