Answer:
x=13
Step-by-step explanation:
9^2 * 27^3 = 3^x
We need to get each term with a base of 3
9^2 = (3^2) ^2
We know that a^b^c = a^(b*c)
(3^2) ^2 = 3^(2+2) = 3^4
27^3 = (3^3) ^3 = 3^(3*3) = 3^9
Replacing these in the original equation
3^4 * 3^9 = 3^x
We know that a^b *a^c = a^(b+c)
3^4 * 3^9 =3^(4+9) = 3^13 = 3^x
The bases are the same, so the exponents must be the same
x=13
Step-by-step explanation:
37x + 41y = 70 --- R¹
41x + 37y = 86 --- R²
R¹ + R² : 78x + 78y = 156
78(x + y) = 156
x + y = 2 --- R³
R¹ - R² : -4x + 4y = -16
4(y - x) = -16
y - x = -4 --- R⁴
R³ + R⁴ : 2y = -2
y = -1
R³ - R⁴ : -2x = -6
x = 3
Answer:
5
Step-by-step explanation:
from the question:
15-5(p-6)
when p=8,
=15-5(8-6)
=15-5(2)
=15-10
=5
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Answer: y = x/2 + 3
Step-by-step explanation:
The equation of a straight line can be represented in the slope-intercept form, y = mx + c
Where c = intercept
Slope, m = change in value of y on the vertical axis / change in value of x on the horizontal axis
change in the value of y = y2 - y1
Change in value of x = x2 -x1
y2 = final value of y
y 1 = initial value of y
x2 = final value of x
x1 = initial value of x
Looking at the graph,
y2 = 6
y1 = 4
x2 = 6
x1 = 2
Slope,m = (6 - 4)/(6 - 2) = 2/4 = 1/2
To determine the intercept, we would substitute x = 2, y = 4 and m= 1/2 into y = mx + c. It becomes
4 = 1/2 × 2 + c
4 = 1 + c
c = 4 - 1
c = 3
The equation becomes
y = x/2 + 3