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Y_Kistochka [10]
3 years ago
5

How do you solve 3^2x=81

Mathematics
2 answers:
Jobisdone [24]3 years ago
7 0

Answer:

x=ln(81) over 2ln(3)

Step-by-step explanation:

Using ln as its base thing instead of log and the formula usually is log over log. Plus you have to bring down the power that way.

qwelly [4]3 years ago
4 0

Answer:

x=2

Step-by-step explanation:

3^2x = 81

3^2x = 3^4

Compare powers

2x = 4

x = 2

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Keith drives 5.3 miles east, then he drives 9.2 miles north. How far is he from his starting point?
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Answer:

14.5 miles

Step-by-step explanation:

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3 years ago
Which is the simplified form of the expression?
Scorpion4ik [409]

Answer:

1 / q^30.

Step-by-step explanation:

[(p^2)(q^5)]^-4 * [(p^-4)(q^5)]^-2

Using the law (a^b)^c =  a^bc :-

=  p^-8 * q^-20 * p^8 * q^-10

= p^(-8+8) * q^(-20-10)

= p^0 * q^-30

= 1 * q^-30.

= 1 / q^30.

8 0
3 years ago
The final exam scores in a statistics class were normally distributed with a mean of
IRISSAK [1]

Answer:

68.27%

Step-by-step explanation:

By the Empirical Rule, as 65% and 75% are both one standard deviation apart from the mean of 70%, then this represents 68.27% of the data.

4 0
2 years ago
The prime factorizations of 54 and 72 are shown below.
Karo-lina-s [1.5K]
Your answer is 2’3’3!! (2*3*3 = 18)

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5 0
3 years ago
Read 2 more answers
A homeowner has an octagonal gazebo inside a circular area. Each vertex of the gazebo lies on the circumference of the circular
Tcecarenko [31]

If we draw the diagonals of the octagonal gazebo, the 4 diagonals divide the octagon into 8 triangles.

Note that each triangle is an isosceles triangle whose equal sides are x, the radius of the circle.

The top angle of each triangle is obtained by dividing the full angle by 8.

So, each top angle = \frac{360}{8}

= 45°

Now, in fig., consider one of the triangles Δ OAB. Draw an altitude OC from O to the opposite side AB.

This altitude OC bisects the top angle 45°.

Therefore, ∠ AOC = 22.5°.

Now, in Δ AOC,

sin 22.5=\frac{AC}{OA}

=\frac{AC}{x}

So, AC = x sin 22.5°

Note that, AB = 2 AC.

Therefore, AB = 2x sin 22.5°.

Also, cos 22.5=\frac{OC}{OA}

=\frac{OC}{x}

So, OC = x cos 22.5°.

Area of Δ AOB = \frac{1}{2}(AB)(OC)

= \frac{1}{2} × (2x sin 22.5°) × (x cos 22.5°)

= \frac{1}{2} x^{2} (2 sin 22.5° cos 22.5°)

= \frac{1}{2} x^{2} sin 45°

= x^{2} / 2\sqrt{2}

Area of the octagonal gazebo = 8 × one triangular area

= 8 × (x^{2} / 2\sqrt{2})

=2\sqrt{2} x^{2}

=2.828x^{2}

Area required for mulch = circular area - area of the gazebo

=3.14x^{2} -2.828x^{2}

=0.312x^{2}

Now, cost per unit area = $1.50.

Hence, total cost g(m) = area × cost per unit area

Total cost g(m) = 0.312x^{2} × 1.5

=0.468x^{2}

Hence, total cost g(m) = 0.468x^{2}.

4 0
3 years ago
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