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mixas84 [53]
3 years ago
11

Fill in the blank

Mathematics
2 answers:
vaieri [72.5K]3 years ago
6 0

Answer:

y=2/3x

Step-by-step explanation:

neonofarm [45]3 years ago
6 0
Your answer would be Y=2/3x
You might be interested in
How do you complete the other two?
Gwar [14]

For now, I'll focus on the figure in the bottom left.

Mark the point E at the base of the dashed line. So point E is on segment AB.

If you apply the pythagorean theorem for triangle ABC, you'll find that the hypotenuse is

a^2+b^2 = c^2

c = sqrt(a^2+b^2)

c = sqrt((8.4)^2+(8.4)^2)

c = 11.879393923934

which is approximate. Squaring both sides gets us to

c^2 = 141.12

So we know that AB = 11.879393923934 approximately which leads to (AB)^2 = 141.12

------------------------------------

Now focus on triangle CEB. This is a right triangle with legs CE and EB, and hypotenuse CB.

EB is half that of AB, so EB is roughly AB/2 = (11.879393923934)/2 = 5.939696961967 units long. This squares to 35.28

In short, (EB)^2 = 35.28 exactly. Also, (CB)^2 = (8.4)^2 = 70.56

Applying another round of pythagorean theorem gets us

a^2+b^2 = c^2

b = sqrt(c^2 - a^2)

CE = sqrt( (CB)^2 - (EB)^2 )

CE = sqrt( 70.56 - 35.28 )

CE = 5.939696961967

It turns out that CE and EB are the same length, ie triangle CEB is isosceles. This is because triangle ABC isosceles as well.

Notice how CB = CE*sqrt(2) and how CB = EB*sqrt(2)

------------------------------------

Now let's focus on triangle CED

We just found that CE = 5.939696961967 is one of the legs. We know that CD = 8.4 based on what the diagram says.

We'll use the pythagorean theorem once more

c = sqrt(a^2 + b^2)

ED = sqrt( (CE)^2 + (CD)^2 )

ED = sqrt( 35.28 + 70.56 )

ED = 10.2878569196893

This rounds to 10.3 when rounding to one decimal place (aka nearest tenth).

<h3>Answer: 10.3</h3>

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

Now I'm moving onto the figure in the bottom right corner.

Draw a segment connecting B to D. Focus on triangle BCD.

We have the two legs BC = 3.7 and CD = 3.7, and we need to find the length of the hypotenuse BD.

Like before, we'll turn to the pythagorean theorem.

a^2 + b^2 = c^2

c = sqrt( a^2 + b^2 )

BD = sqrt( (BC)^2 + (CD)^2 )

BD = sqrt( (3.7)^2 + (3.7)^2 )

BD = 5.23259018078046

Which is approximate. If we squared both sides, then we would get (BD)^2 = 27.38 which will be useful in the next round of pythagorean theorem as discussed below. This time however, we'll focus on triangle BDE

a^2 + b^2 = c^2

b = sqrt( c^2 - a^2 )

ED = sqrt( (EB)^2 - (BD)^2 )

x = sqrt( (5.9)^2 - (5.23259018078046)^2 )

x = sqrt( 34.81 - 27.38 )

x = sqrt( 7.43 )

x = 2.7258026340878

x = 2.7

--------------------------

As an alternative, we could use the 3D version of the pythagorean theorem (similar to what you did in the first problem in the upper left corner)

The 3D version of the pythagorean theorem is

a^2 + b^2 + c^2 = d^2

where a,b,c are the sides of the 3D block and d is the length of the diagonal. In this case, a = 3.7, b = 3.7, c = x, d = 5.9

So we get the following

a^2 + b^2 + c^2 = d^2

c = sqrt( d^2 - a^2 - b^2 )

x = sqrt( (5.9)^2 - (3.7)^2 - (3.7)^2 )

x = 2.7258026340878

x = 2.7

Either way, we get the same result as before. While this method is shorter, I think it's not as convincing to see why it works compared to breaking it down as done in the previous section.

<h3>Answer:  2.7</h3>
8 0
2 years ago
Is 6 a solution to the equation x^2 - 4 = 5x? Please tell me why or why not
TEA [102]

Answer:

6 is not a solution to the given equation.

Step-by-step explanation:

We are given the equation x^2-4=5x

We need to know whether or not x=6 is a solution. This means that we should substitute in 6 for each instance of x. Then, if both sides of the equation are equal, then 6 is a solution to the equation.

x^2-4=5x\\\\(6)^2-4=5(6)\\\\36-4=30\\\\32=30

As 32 ≠ 30, 6 is not a solution to the given equation.

3 0
2 years ago
Please add: 5 1\3 + 3 1\6
viva [34]

Answer:

17/2 or 8 and 1/2

Step-by-step explanation:

8 0
2 years ago
Write a simplified expression for the perimeter of the triangle.
Amiraneli [1.4K]

Answer: 2x + 4

Step-by-step explanation:

(x - 1) + (-x + 1) + (2x + 4)

Put like terms together

2x + x - x - 1 + 1 + 4

Combine like terms

2x + 0 + 0 + 4

2x + 4

7 0
3 years ago
What is this called?
guapka [62]

Answer:

This is a box and whisker plot.

Step-by-step explanation:

A box and whisker plot shows the distribution of data. It includes minimum and maximum values and the first, second, and third quartiles of the data.

5 0
3 years ago
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