Answer:
9
Step-by-step explanation:
let the number
=
x
then 4 times the number
=
4
x
and 4 times the number increased by 15
=
4
x
+
15
also 6 times the number
=
6
x
and 3 less than 6 times the number
=
6
x
−
3
equating the two expressions gives the equation
4
x
+
15
=
6
x
−
3
←
solve for x
subtract 6x from both sides
4
x
−
6
x
+
15
=
6
x
−
6
x
−
3
⇒
−
2
x
+
15
=
−
3
subtract 15 from both sides
−
2
x
+
15
−
15
=
−
3
−
15
⇒
−
2
x
=
−
18
divide both sides by
−
2
−
2
x
−
2
=
−
18
−
2
⇒
x
=
9
As a check
(
4
×
9
)
+
15
=
36
+
15
=
51
(
6
×
9
)
−
3
=
54
−
3
=
51
⇒
the number is 9
Answer:
A
Step-by-step explanation:
The rate of change for the table is found using the slope formula. The rate of change for the linear function is the coefficient of x.
__
<h3>table</h3>
The slope formula tells us the rate of change is ...
m = (y2 -y1)/(x2 -x1)
m = (-9 -(-10))/(-1 -(-4)) = 1/3
<h3>equation</h3>
The coefficient of x in the equations of the offered answer choices are 1/4 and 6.
<h3>comparison</h3>
The relations between the various slopes are ...
1/4 < 1/3 < 6
That is, the equation with a slope of 1/4 has a rate of change less than that of the function represented by the table:
y = 1/4x +4 because ... table of values is 1/3
