helperid1839321

I can tell this is an isosceles triangle, since 2 of the sides have the same length. This means that the base of the triangle is \(2\sqrt{7}\). Because of this, I know that the base in each of the sides (if you figutre out the length via the Pythagorean Theorem) is the square root of 14 I subtract from the number inside the square root to get my height, which is \(2\sqrt{14}\). By multiplying these togther and simplifying the root, I get \(28\sqrt{2}\).

Cool! You're definitely going to pass me up at this rate! 

Next time, make sure not to confuse the x variables for multiplication signs. Here is the difference:

\(\times \ (multiplication \ sign)\\ x \ (variable)\)

Anyways:

\(-4x + 7=3x - 7\)

Add 4x to each side to remove the negative value of x (Rule: always subtract the lesser value when you are solving for a variable [this one was negative, so we added 4 instead of subtracting]):

\(7=7x-7\)

Add 7 to each side (Again, it is negative):

\(7x = 14\)

Divide by the coefficient of the variable you are solving for (x, coefficient is 7 so we divide each side by 7):

\(x=2\)

25 units = a line segment starting at (-24, 0) and ending at (0, n)

Pythagorean theorem: \(625 = 576 - n^2\)

625 - 576 = 49

\(\sqrt{49} = 7\)

n = 7

Now that we have the height and the width, we solve using \(a = \frac{1}{2}bh\)

\(7 \times 48 \div 2=7\times 24 = 168\)

The area of the triangle is 168 square centimeters.

^^^ I honestly don't know how I managed to use that method. ^^^

That looks kind of like a Fibonacci Spiral. It is based on the sequence \(t(n)=t(n-1)+t(n-2)\) . Eventually, this will leave you with the constant phi, which equals ​\(1+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{1}{\dots}}}}=\frac{3-\sqrt{5}}{2}\)

I assumed, based off of the wording, that this was based on displacement. The question is, "How many miles from the starting point was the traveler after completing these 4 legs of the journey"

I'm assuming this is absolute distance, not distance traveled on foot.

19 - 3 = 16

16 - 4 = 12

\(\sqrt{16^{2} + 12^{2}} = \sqrt{256 + 144} = \sqrt{400} =20\)

He moved an overall of 20 miles from the starting point.

3 facts:

QA is congruent to Q'A (QAQ' is an isosceles triangle)

QB is congruent to Q'B (QBQ' is an isosceles triangle)

QC is congruent to Q'C (\(\leftarrow QC \rightarrow\) is the same as \(\leftarrow Q'C \rightarrow\), C is the point where \(\leftarrow AB \rightarrow\) bisects CC')

B; this would give us 6 points on the circle, each equidistant. After connecting them, she would have the regular hexagon inscribed in the circle.

Do get the coordinates of the new image from the previous, divide the points of the original by the corresponding points, after translating them both so that the point of dilation is 0 (found by drawing lines through each corresponding point and seeing where they all intersect). In this case, A'B'C' has a relative scale factor of \(\frac{1}{4}\).