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lidiya [134]
3 years ago
12

Solve for x 27^(2x+4)=1/9^(x-46)

Mathematics
1 answer:
lys-0071 [83]3 years ago
8 0
27^{2x+4}=(\frac{1}{9})^{x-46} \\
(3^3)^{2x+4}=(3^{-2})^{x-46} \\
3^{3(2x+4)}=3^{-2(x-46)} \\
3^{6x+12}=3^{-2x+92} \\
6x+12=-2x+92 \\
6x+2x=92-12 \\
8x=80 \\
x=10
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If cosine theta equals negative square root of three over two and pi over two less than theta less than pi, what are the values
Natalka [10]
<h2>Answer:</h2>

The values of sinθ and tanθ are:

\sin \theta=\dfrac{1}{2}

and

\tan \theta=-\dfrac{1}{\sqrt{3}}=-\dfrac{\sqrt{3}}{3}

<h2>Step-by-step explanation:</h2>

It is given that:

\cos \theta=-\dfrac{\sqrt{3}}{2}

where

\dfrac{\pi}{2}

i.e. the angle θ lie in the second quadrant.

Also, we know that in the second quadrant sine and cosecant function is positive.

whereas cosine,secant, tangent and cotangent functions are negative.

Now, we know that:

\cos (\dfrac{5\pi}{6})=-\dfrac{\sqrt{3}}{2}

i.e. here

\theta=\dfrac{5\pi}{6}

Hence, we have:

\sin (\theta)=\sin (\dfrac{5\pi}{6})\\\\i.e.\\\\\sin \theta=\dfrac{1}{2}

Also,

\tan \theta=\dfrac{\sin \theta}{\cos \theta}\\\\i.e.\\\\\tan \theta=\dfrac{\dfrac{1}{2}}{\dfrac{-\sqrt{3}}{2}}\\\\i.e.\\\\\tan \theta=\dfrac{1}{-\sqrt{3}}\\\\i.e.\\\\\tan \theta=-\dfrac{1}{\sqrt{3}}

Now, on rationalizing we have:

\tan \theta=-\dfrac{\sqrt{3}}{3}

7 0
4 years ago
Read 2 more answers
A company orders supplies from M distributors and wishes to place n orders (n &lt; M). Assume that the company places the orders
harkovskaia [24]

Answer:

a) 0.06048 b) 0.001344 c) 0.000294

Step-by-step explanation:

number of distributors = 10;

number of orders = 7

a)

There are 10 distributors for each order, so the no. of ways the 7 orders could be placed are = 10⁷ =10000000

no. of ways that orders goes to different distributors = ¹⁰C₇*7! = 604800

Probability = 604800/10000000 = 0.06048

b)

number of ways distributor 1 gets exactly 2 and distributor 2 gets exactly 3 orders = ⁷C₂*⁵C₃*8² = 13440

probability = 13440/10000000 = 0.001344

c)

number of ways distributor 1, 2,3 get exactly 2,3 and 1 order(s) = ⁷C₂*⁵C₃*²C₁*7¹ = 2940

probability = 2940/10000000 = 0.000294

3 0
4 years ago
What is the name of the relationship between ∠2 and ∠7?
kondaur [170]

Answer:

Alternate Exterior

Step-by-step explanation:

They are opposite angles from each other on different lines

5 0
3 years ago
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What is the las digit of the product of all the numbers between 11 and 29?
Tju [1.3M]

The last digit of the product of all the numbers between 11 and 29 is 0.

A product is something that has undergone one or more multiplications.

Here, we're looking for the final digit of the product of all whole numbers greater than 11 and less than 29.

Next, we have the product as: 12*13*14*15*16*17*18*19*20*21*22*23*24*25*26*27*28

Now take note of the 20 that is present.

Any number multiplied by 20 will result in a zero, so:

Product = 20*(12*13*14*15*16*17*18*19*21*22*23*24*25*26*27*28)

Using only that, we can infer that 0 represents the final digit in the product of all the numbers between 11 and 29.

Learn more about product here:

brainly.com/question/10873737

#SPJ1

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Please help will mark Brainly!
MakcuM [25]

Answer:

The table doesn't display a linear relationship because the slope doesn't stay constant throughout the whole table.

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4 years ago
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