$\dfrac{2m}{5}+3=7(4m-3)\ \ \ \ |use\ distributive\ property:a(b-c)=ab-ac\\\\\dfrac{2m}{5}+3=28m-21\ \ \ \ \ |multiply\ both\ sides\ by\ 5\\\\2m+15=140m-105\ \ \ \ |subtract\ 140m\ from\ both\ sides\\\\-138m+15=-105\ \ \ \ |subtract\ 15\ from\ both\ sides\\\\-138m=-120\ \ \ \ |divide\ both\ sides\ by\ (-138)\\\\m=\dfrac{120:6}{138:6}\\\\\boxed{m=\frac{20}{23}}$

7 0

3 years ago

-6 < 2t - 5 < 3 Solve for T

natulia [17]

Answer:

I think it's 7

Step-by-step explanation:

-6 < 2T (-5+5) < 3+5

-6 < 2T < 8

+6 < 2T < 8 + 6

0 < 2T < 14

0 < ÷ 2 < ÷ 2

0 < T < 7

-0 < T < -0

T = 7

4 0

3 years ago

In triangle NOP p equals 600 inches angle P equals 96° and angle N equals 64° what is the area of triangle NOP to the nearest 10

DochEvi [55]

9514 1404 393

Answer:

55,637.8 square inches

Step-by-step explanation:

We can find side n using the Law of Sines:

n/sin(N) = p/sin(P)

n = p(sin(N)/sin(P)) = 600·sin(64°)/sin(96°)

n ≈ 542.246913 . . . . inches

The angle O is ...

O = 180° -N -P = 180° -64° -96° = 20°

Then the area is ...

A = 1/2·np·sin(O)

A = (1/2)(542.246913 in)(600 in)·sin(20°) ≈ 55,637.81008 in²

The area of ∆NOP is about 55,637.8 in².

7 0

3 years ago