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3 years ago

What is the solution to 0.4(12-3x)=0.3(12x-16)

Mathematics

1 answer:

Pavel [41]3 years ago

6 0

Step 1: Simplify both sides of the equation.

0.4(12−3x)=0.3(12x−16)

(0.4)(12)+(0.4)(−3x)=(0.3)(12x)+(0.3)(−16)(Distribute)

4.8+−1.2x=3.6x+−4.8

−1.2x+4.8=3.6x−4.8

Step 2: Subtract 3.6x from both sides.

−1.2x+4.8−3.6x=3.6x−4.8−3.6x

−4.8x+4.8=−4.8

Step 3: Subtract 4.8 from both sides.

−4.8x+4.8−4.8=−4.8−4.8

−4.8x=−9.6

Step 4: Divide both sides by -4.8.

−4.8x /−4.8 = −9.6 /−4.8

x = 2

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In Exercises 5-7, find all the exact t-values for which the given statement is true,

bearhunter [10]

Answer: See Below

Step-by-step explanation:

NOTE: You need the Unit Circle to answer these (attached)

5) cos (t) = 1

Where on the Unit Circle does cos = 1?

Answer: at 0π (0°) and all rotations of 2π (360°)

In radians: t = 0π + 2πn

In degrees: t = 0° + 360n

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$6)\quad sin (t) = \dfrac{1}{2}$

Where on the Unit Circle does $sin = \dfrac{1}{2}$

Hint: sin is only positive in Quadrants I and II

$\text{Answer: at}\ \dfrac{\pi}{6}\ (30^o)\ \text{and at}\ \dfrac{5\pi}{6}\ (150^o)\ \text{and all rotations of}\ 2\pi \ (360^o)$

$\text{In radians:}\ t = \dfrac{\pi}{6} + 2\pi n \quad \text{and}\quad \dfrac{5\pi}{6} + 2\pi n$

In degrees: t = 30° + 360n and 150° + 360n

******************************************************************************

$7)\quad tan (t) = -\sqrt3$

Where on the Unit Circle does $\dfrac{sin}{cos} = \dfrac{-\sqrt3}{1}\ or\ \dfrac{\sqrt3}{-1}\quad \rightarrow \quad (1,-\sqrt3)\ or\ (-1, \sqrt3)$

Hint: sin and cos are only opposite signs in Quadrants II and IV

$\text{Answer: at}\ \dfrac{2\pi}{3}\ (120^o)\ \text{and at}\ \dfrac{5\pi}{3}\ (300^o)\ \text{and all rotations of}\ 2\pi \ (360^o)$

$\text{In radians:}\ t = \dfrac{2\pi}{3} + 2\pi n \quad \text{and}\quad \dfrac{5\pi}{3} + 2\pi n$

In degrees: t = 120° + 360n and 300° + 360n

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3 years ago

What is the least common denominator of the fractions 1/3 5/6 5/9

hichkok12 [17]

Answer:

Step-by-step explanation:

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3 years ago

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A line passes through the point (-8,-9) and has a slope of (-3,-4)

Colt1911 [192]

Answer:

y = -3/4x + 3

Step-by-step explanation:

y - 9 = -3/4 (x-8)

y-9 = -3/4x -6

y = -3/4x - 6 + 9

y = -3/4x + 3

hope this helps if not sorry

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3 years ago

The metro theater has 20 rows of seats with 18 seats in each row. Tickets cost $5. The theaters income in dollars if all seats a

jarptica [38.1K]

In a Metro there are:
20 rows of seats
18 seats in a row
and $5 per ticket

Using commutative property of Multiplication:
Therefore.
=> (20 x 18) x 5 = 5 x (18 x 20)
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Therefore, they have $1800 income.

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3 years ago

10 POINTS! NO LINKS!

Deffense [45]

Answer:

164.48 or 164.5

Step-by-step explanation:

So, to make it simpler, you can do the circle like this: 3.14×(8×8). Then you can work down!

3.14 × 64

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and then because it's halved, you divide by 2

100.48

then that's the half circle

The square would just be 8×8=64

then add the circle and the square and viola!

164.48

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3 years ago

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