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3 years ago

Solve this equation, and show work. worth 40 points.

Mathematics

1 answer:

ioda3 years ago

7 0

Answer:

$r=-3/5=-0.6$

Step-by-step explanation:

We have the equation:

$6^{-3r}=6^{2r+3}$

Since their bases are the same, the exponents must be equivalent. So:

$-3r=2r+3$

Solve for r, subtract 2r from both sides:

$-5r=3$

Divide both sides by -5:

$r=-3/5=-0.6$

So, the value of r is -3/5.

And we're done!

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irina1246 [14]

Turn the mixed number into an improper fraction, than multiply regularly. If it's an improper fraction than divide the top number by the bottom

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3 years ago

Please help it due in some time

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Answer:

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Step-by-step explanation:

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3 years ago

Find the 13th term of the arithmetic sequence -3x+7, -5x+3, -7x-1, ...

oksano4ka [1.4K]

Answer:

a₁₃ = - 27x - 41

Step-by-step explanation:

The nth term of an arithmetic sequence is

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 3x + 7

d = a₂ - a₁ = - 5x + 3 - (- 3x + 7)

= - 5x + 3 + 3x - 7

= - 2x - 4

Then

a₁₃ = - 3x + 7 + 12(- 2x - 4)

= - 3x + 7 - 24x - 48

= - 27x - 41

3 0

3 years ago

1. In a 30-60-90 triangle, the length of the hypotenuse is 6. What is the length of the shortest

PIT_PIT [208]

Answer:

b. 3

Step-by-step explanation:

In a 30°-60°-90° triangle, the short side is ½ the hypotenuse [the long side is double the short side].

30°-60°-90° Triangles

x√3 → long side

x → short side

2x → hypotenuse

45°-45°-90° Triangles

x → two legs

x√2 → hypotenuse

I am joyous to assist you anytime.

3 0

3 years ago

Cidnee is weighing combinations of geometric solids. She found that 4 cylinders and 5 prisms weigh 32 ounces and that 1 cylinder

vitfil [10]

Answer:

The weights of each cylinder and prism are 3 and 4 ounces, respectively.

Step-by-step explanation:

Let be $x$ and $y$ the masses of a cylinder and a prism, measured in ounces, respectively. After a careful reading of the statement we get the following linear equations by interpretation:

i) <em>She found that 4 cylinders and 5 prisms weigh 32 ounces:</em>

$4\cdot x +5\cdot y = 32\,oz$ (Eq. 1)

ii) <em>And that 1 cylinder and 8 prisms weigh 35 ounces:</em>

$x + 8\cdot y = 35\,oz$ (Eq. 2)

Now we solve the system of linear equations algebraically:

From (Eq. 2):

$x = 35 - 8\cdot y$

(Eq. 2) is (Eq. 1):

$4\cdot (35-8\cdot y) + 5\cdot y = 32$

$140-32\cdot y +5\cdot y = 32$

$32\cdot y - 5\cdot y = 140-32$

$27\cdot y = 108$

$y = 4\,oz$

From (Eq. 2):

$x = 35 - 8\cdot (4)$

$x = 35 - 32$

$x = 3\,oz$

The weights of each cylinder and prism are 3 and 4 ounces, respectively.

4 0

3 years ago