The sum of two numbers is 43. the smaller number is 19 less than the larger number. what are the numbers?

So the answer is 12 and 31.

Step-by-step explanation:

Let the smaller number be x and the larger number be y.

We can calculate this by using simultaneous equation, aka listing 2 equations out.

From given,

X + y = 43

Let this be equation no. 1

X + 19 = y

Let this number be equation 2.

We can do simultaneous equations either by substitute method or elimination. In this case I'm using substitute.

We can already obtain the value of y (in terms of x) in euqation no. 2, so all we gonna do is to put y into equation 1.

X + x + 19 = 43

Solve this by algebra.

2x = 43 - 19

X = 12

Now we know the exact value of x

Now substitute x = 12 into equation no. 2

12 + 19 = y

Y = 31

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.

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