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3 years ago

BRAINLIEST IF ANSWERED*

Mathematics

1 answer:

goblinko [34]3 years ago

6 0

Answer:

(D)7 in.

Step-by-step explanation:

A regular hexagon can be divided into six equilateral triangles.

Therefore:

$b=\dfrac{c}{2}$

Applying Pythagoras Theorem

$c^2=12^2+b^2\\c^2=12^2+(\frac{c}{2})^2\\c^2-(\frac{c}{2})^2=12^2\\c^2-\dfrac{c^2}{4}=144\\\dfrac{4c^2-c^2}{4}=144\\\dfrac{3c^2}{4}=144\\$Cross multiply\\3c^2=144 \times 4\\3c^2=576\\$Divide both sides by 3\\c^2=192\\$Therefore:\\c=\sqrt{192}\\c=8\sqrt{3}$ in.$

Recall that b=c/2

Therefore:

$b=4\sqrt{3} \approx 7$ in.$

The value of b is 7 inches.

You might be interested in

If the police have 9 suspects how many different ways can they select 5 for a lineup

kow [346]

Assuming the order does not matter, you want the number of combinations of 9 things taken 5 at a time. The combinations can be shown as C(9,5), 9C5.

C(9, 5) =
9/5(9-5) =
9*8*7*6*5 / 5*4

The 5 terms cancel.

9*8*7*6 / 4*3*2 =
9*7*2 =
126

The above change is because 4*2 cancels the 8 in the numerator and 6/3 = 2
Therefore, the solution is 126.

4 0

3 years ago

For the system of equations that follows, use Gaussian elimination to obtain an equivalent system whose coefficient matrix is in

Rainbow [258]

Answer:

$\begin{Vmatrix}1 & 0 & 0& 46/41 &180/41\\0 & 1 & 0&1/41 &-5/41\\0&0 & 1 & -8/41& -42/41\end{Vmatrix}$

Step-by-step explanation:

From the question we are told that

System of equations given as

x₁ + 3x₂ + x₃ + x₄ = 3;

2x₁ - 2x₂ + x₃ + 2x₄ = 8;

x₁ - 5x₂ + x₄ = 5

Matrix form

$\begin{Vmatrix}1 & 3 & 1&1&3\\2 & -2 & 1&2&8\\0&1 & -5 & 1& 5\end{Vmatrix}$ $\begin{Vmatrix}x_1\\x_2\\x_3\\x_4\end{Vmatrix}$

Generally the echelon reduction is mathematically applied as

$\begin{Vmatrix}1 & 3 & 1&1&3\\2 & -2 & 1&2&8\\0&1 & -5 & 1& 5\end{Vmatrix}$

Add -2 times the 1st row to the 2nd row

$\begin{Vmatrix}1 & 3 & 1&1&3\\0 & -8 & -1&0&2\\0&1 & -5 & 1& 5\end{Vmatrix}$

Multiply the 2nd row by -1/8

$\begin{Vmatrix}1 & 3 & 1&1&3\\0 & 1 & 1/8&0&-1/4\\0&1 & -5 & 1& 5\end{Vmatrix}$

Add -1 times the 2nd row to the 3rd row

$\begin{Vmatrix}1 & 3 & 1&1&3\\0 & 1 & 1/8&0&-1/4\\0&0 & -41/8 & 1& 21/4\end{Vmatrix}$

Multiply the 3rd row by -8/41

$\begin{Vmatrix}1 & 3 & 1&1&3\\0 & 1 & 1/8&0&-1/4\\0&0 & 1 & -8/41& -42/41\end{Vmatrix}$

Add -1/8 times the 3rd row to the 2nd row

Add -1 times the 3rd row to the 1st row

$\begin{Vmatrix}1 & 3 & 0&49/41&165/41\\0 & 1 & 0&1/41 &-5/41\\0&0 & 1 & -8/41& -42/41\end{Vmatrix}$

Add -3 times the 2nd row to the 1st row

$\begin{Vmatrix}1 & 0 & 0& 46/41 &180/41\\0 & 1 & 0&1/41 &-5/41\\0&0 & 1 & -8/41& -42/41\end{Vmatrix}$

3 0

3 years ago

What is the greatest number you can multiply by 4 and not go over 12?

taurus [48]

Answer:

Step-by-step explanation:

3 x 4 = 12

7 0

2 years ago

The box plots below show the average daily temperatures in July and August for a U.S. city: two box plots shown. The top one is

sergey [27]

The <em>correct answer</em> is:

The mean for July is smaller than the median; and

the mean for August is larger than the median.

Explanation:

A distribution with a positive skew would have a longer whisker in the positive direction than in the negative direction. A larger mean than median would also indicate a positive skew.

Alternatively, a distribution with a negative skew would have a longer whisker in the negative direction than in the positive direction. A smaller mean than median would also indicate a negative skew.

The whisker in the negative direction for July is longer than the whisker in the positive direction. This indicates a negative skew.

The whisker in the positive direction for August is longer than the whisker in the negative direction. This indicates a positive skew.

7 0

3 years ago

10. Convert 45 miles per hour into<br> kilometers per minute.<br> Hint: 1 mile = 1.6 km

andreev551 [17]

Answer: 72km per minute

Step-by-step explanation:

Given that 1mile = 1.6km

45 mile = x

Cross multiply to find the value of x

x = 45 x 1.6km

= 72km per minute

8 0

4 years ago

**BRAINLIEST IF ANSWERED***

BRAINLIEST IF ANSWERED*