7. Emma says that Function A and Function B have the same initial
value. Is Emma correct? Justify your
response.
Function A
ly У
6
4
2
х
0
0 2 4 6
Function B
4
6
8
10
2
х
4
6
3
5
2
у

NO. Emma is not correct.

Step-by-step explanation:

✔️Initial value for Function A:

The initial value is the y-intercept of the graph. The y-intercept is the point at which the line intercepts the y-axis. From the graph given, the line intercepts the y-axis, at y = 2, when x = 0.

Initial value for Function A is therefore = 2

✔️Initial Value of Function B:

To find the initial value/y-intercept for Function B, do the following:

Using two pairs of values form the table, (2, 2) and (4, 3), find the slope:

Slope (m) = ∆y/∆x = (3 - 2) / (4 - 2) = 1/2

Slope (m) = ½

Next, substitute (x, y) = (2, 2) and m = ½ into y = mx + b, to find the intial value/y-intercept (b).

Thus:

2 = ½(2) + b

2 = 1 + b

2 - 1 = b

1 = b

b = 1

The initial value for Function B = 1

✅The initial value for Function A (2) is not the same as the initial value for Function B (1). Therefore, Emma is NOT CORRECT.

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)