Write and solve a system of equations representing the following number puzzle. The sum of two numbers is 11. Four times the first number is 2 more than two times the second number. When you've found the two numbers, enter the value of the larger number as your answer.

7

Step-by-step explanation:

The sum of two numbers is 11

x + y = 11

Four times the first number is 2 more than two times the second number

4x = 2y + 2

x = 1/2y + 1/2 (divide by 4 on both sides)

(1/2y + 1/2) + y = 11 (substitute for x)

3/2y + 1/2 = 11 (simplify)

3/2y = 10 1/2 (subtract 1/2 from both sides)

y = 7 (divide both sides by 3/2)

x + (7) = 11 (substitute value for y)

x = 4

option a, c,d are correct.

step-by-step explanation:

from the given figure, it is given that z is equidistant from the sides of the triangle rst, then from triangle tzb and triangle szb, we have

tz=sz(given)

bz=zb(common)

therefore, by rhs rule,δtzb ≅δszb

by cpctc, sz≅tz

also, from δctz and δasz,

tz=sz(given)

∠tcz=∠saz(90°)

by rhs rule, δctz ≅ δasz, therefore by cpctc, ∠ctz≅∠asz

also,from δasz and δzsb,

zs=sz(common)

∠zbs=∠saz=90°

by rhs rule, δasz ≅δzsb, therefore, by cpctc, ∠asz≅∠zsb

hence, option a, c,d are correct.

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3