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3 years ago

Determine the integer value of n that satisfies the the equation. 4^n=16 3^n=1/81

Mathematics

1 answer:

tresset_1 [31]3 years ago

7 0

Answer:

Step-by-step explanation:

$4^{n} = 16 \\\\4^{n} = 4^2\\\\$

n = 2

$3^{n} =\frac{1}{81}\\\\ = \frac{1}{3^{4}}\\\\3^{n} = 3^{-4}$

n = -4

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For what value of x is the figure a rhombus? x=6 x=7.5 x=12 x=18.75

nika2105 [10]

The value of $x$ in the given figure is $\boxed{{\mathbf{12^\circ}}}$ and it matches with $\boxed{{\mathbf{OPTION}}\,\,{\mathbf{C}}}$ .

Further explanation:

A rhombus is shown below in Figure 1.

Now, from Figure 1 it is observed that a rhombus has 4 sides.

A rhombus is a quadrilateral in which opposite sides are equal as well as parallel to each other. In rhombus, all sides are equal; adjacent angles are supplementary to each other.

The property of rhombus is diagonal bisect each other at right angles and diagonal also bisect the angle forming from two sides of rhombus.

In rhombus, diagonals bisect the angles so it is observed from Figure 1, the rhombus angles are equal to each other that is expressed as,

$2x+39=6x-9$

Further simplify the above equation to obtain the value of $x$ as follows:

$\begin{aligned}2x+39-6x+9&=0\\-4x+48&=0\\x&=\frac{{48}}{4}\\x&=12\\\end{aligned}$

Therefore, the value of $x$ in the given rhombus is $12^\circ$ .

Now, the four options are given below.

$\begin{gathered}{\text{OPTION A}}\to x=6\hfill\\{\text{OPTION B}}\to x=7.5\hfill\\{\text{OPTION C}}\to x=12\hfill\\{\text{OPTION D}}\to x=18.75\hfill\\\end{gathered}$

Since OPTION C matches the obtained value of $x$ that is $12^\circ$ .

Thus, the value of $x$ in the given figure is $\boxed{{\mathbf{12^\circ}}}$ and it matches with $\boxed{{\mathbf{OPTION}}\,\,{\mathbf{C}}}$ .

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Answer Details:

Grade: Junior High School

Subject: Mathematics

Chapter: Lines and angles

Keywords: angle, regular rhombus, $12$ degree, measure, angle of a rhombus, $2x+39$ , degree, sum of interior angles, $6x-9$ , quadrilateral, $12^\circ$ .

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3 years ago

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Passengers traveling by airplane have two options for their bags: carry-on (for smaller bags) or check (for large bags). An airl

erica [24]

<h3>Answer: 342/601</h3>

==============================================================

Explanation:

We're told that "given the customer has a carry-on bag". This means we know 100% that the customer has a carry-on bag and we don't need to worry about the other rows. We'll only focus on row 1.

Of the 601 people who had a carry-on, there are 342 people who had a short flight.

This leads to the fraction 342/601

It cannot be reduced because 342 and 601 don't have any factors in common (other than 1).

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3 years ago

Number Talk: Missing Addend

nignag [31]

Answer:

A) C = 211

B) C = 15.05

Step-by-step explanation:

To get your answer you need to subtract the final answer with the number in the equation. So... 458 - 247 = 211. Hence C is 211

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A meteorologist said it rained during 30% of the past 70 days. How many days did it rain?

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21 days. To solve on your own you do 0.3 • 70

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4 years ago

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Gnom [1K]

4.0987 rounded to the nearest tenth.

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Look at the number after it, if it's 5 or more, round up, if it's 4 or less, round down.

It's 9, so we round up to 4.1

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3 years ago

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