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slamgirl [31]
3 years ago
6

Solve the equation. Round to the nearest hundredth. Show work.

Mathematics
1 answer:
denis-greek [22]3 years ago
8 0

Answer:

Final answer is approx x=-0.66.

Step-by-step explanation:

Given equation is 5^{-2x-1}=4^{4x+3}.

Now we need to solve equation 5^{-2x-1}=4^{4x+3} and round to the nearest hundredth.

5^{-2x-1}=4^{4x+3}

\log(5^{-2x-1})=\log(4^{4x+3})

(-2x-1)\log(5)=(4x+3)\log(4)

-2x \log(5)- \log(5)=4x \log(4)+3 \log(4)

-2x \log(5) -4x \log(4)=3 \log(4) +\log(5)

x=\frac{\left(3\log(4)+\log(5)\right)}{\left(-2\log(5)-4\log(4)\right)}

Now use calculator to calculate log values, we get:

x=-0.65817959094

Round to the nearest hundredth.

Hence final answer is approx x=-0.66.

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39.39÷3 Show ur work plz
kiruha [24]

Answer:

13.13

Step-by-step explanation:

39.39 ÷ 3

13.13

There is not a lot of work

Looking at it we can tell that 3 will go into 3 one time, and 3 will go into 9 three times because:

1 x 3 = 3

3 x 3 = 9

3 0
3 years ago
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Scott collects hats. He has 65 hats an plans on buying 80 per year.
kicyunya [14]

Answer:

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Step-by-step explanation:

x being the number of years so in ten years he will have 80x10=800+65=865

80x5=400+65=465 so 5 is the number of years it would take

and i do not understand number 1 but i put a formula just in case that was it

7 0
3 years ago
If sin(theta) =4/5 and is in quadrant 2, the value of cot(theta
iren [92.7K]
\sin\theta= \frac{4}{5} 
\\
\\\sin^2\theta+\cos^2\theta=1
\\ \cos\theta=\pm \sqrt{1-\sin^2\theta} =\pm \sqrt{1-( \frac{4}{5})^2 } =\pm \sqrt{1- \frac{16}{25} } =\pm \sqrt{\frac{9}{25} }=\pm \frac{3}{5}}

\theta \in II \Rightarrow \cos\theta\ \textless \ 0 \Rightarrow \cos\theta=-\frac{3}{5}

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5 0
3 years ago
Katie has a bag of 15 marbles. There are 3 green, 4 blue, and 5 red marbles. The rest of the marbles are yellow. If Katie random
son4ous [18]

Answer:

P(yellow or red)   =8/15

Step-by-step explanation:

There are 15 marbles, 3 green, 4 blue, and 5 red marbles.

3+4+5 = 12

That means there are 15-12 = 3  3 yellow marbles.

3 green,

4 blue

5 red

3 yellow

To find the probability of yellow or red, we add the number of yellow and red marbles together over the total number of marbles

P(yellow or red) = (yellow +red)/ total

                           = (3+5)/ 15

                             =8/15

8 0
3 years ago
A punch recipe says to mix 4 cups pineapple juice 8 cups orange juice and 12 cups seltzer in order to make 18 servers of punch.H
lesya692 [45]
81 servings. I found this by making a ratio:
24 c            108 c
-------     =    -------
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I then cross multiplied to get the equation: 24x=1,944. I solved this equation to find x, the number of servings in 108 cups, which was 81. 

I remember doing this back in elementary school. I had a hard time with it too!
6 0
3 years ago
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