Triangles def and hjk are similar. def has side lengths = 4, = 6, = 8. which of the following could be the side lengths of hjk? a.2, 6, 7 b. 8, 12, 16 c. 5, 7, 9 d. 2, 5, 7

Answer. Option B: 8,12,16

Solution:

Like the triangles are similar, their sides must be proportional, then if:

DE=4, EF=6 and FD=8; and the proportional sides are HJ, JK and KH respectively, then:

HJ/DE=JK/EF=KH/FD

Replacing DE=4, EF=6 and FD=8 in the equation above:

HJ/4=JK/6=KH/8

In option A or D, if HJ=2 (the smaller side)

2/4=JK/6=KH/8

Simplifying the fraction

1/2=JK/6=KH/8

Using the first equality:

1/2=JK/6

Solving for JK: Multiplying both sides of the equation by 6:

6(1/2)=6(JK/6)

6/2=6 JK/6

3=JK

JK=3

Then options A (JK=6) or D (JK=5) are no possibles.

Using HJ=8 (the smaller side) in the option B:

8/4=JK/6=KH/8

2=JK/6=KH/8

Using the first equality:

2=JK/6

Solving for JK: Multiplying both sides of the equation by 6:

6(2)=6(JK/6)

12=6 JK/6

12=JK

JK=12

Using the second equality:

2=KH/8

Solving for KH: Multiplying both sides of the equation by 8:

8(2)=8(KH/8)

16=8 KH/8

16=KH

KH=16

Option B is possible.

In option C, if HJ=5 (the smaller side)

5/4=JK/6=KH/8

Using the first equality:

5/4=JK/6

Solving for JK: Multiplying both sides of the equation by 6:

6(5/4)=6(JK/6)

30/4=6 JK/6

15/2=JK

JK=15/2=7.5

Then option B (JK=7) is no possible.

the f

last graph i believe

step-by-step explanation:

worked it out i believe

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.