One number is 19 larger than the other, and the sum of these numbers is 97. What is the larger number? Plz help asap

58

Step-by-step explanation:

I have attached an image with this answer that will help you to visualise this question. I will now explain it.

The smaller number (Number 1) has 1 unit.

The bigger number (Number 2) has 1 unit, and 19.

If you add 19 to the smaller number, you will make two of the bigger number.

This is equivalent to two of the bigger number. (Try to visualise it!)

Hence, divide it by 2 to get one of the bigger number.

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

)

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4