Alexander found the means-to-MAD ratio of two data sets to be 3.4.

An acute triangle has sides measuring 10 cm and 16 cm. The length of the third side is unknown.

saveliy_v [14]

Answer: Choice B

12.5 < x < 18.9

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Explanation:

We have a triangle with these side lengths:

a = 10
b = 16
c = x = unknown

Let's assume that b = 16 is the largest side of this triangle.

By the converse of the pythagorean theorem, we need $b^2 < a^2+c^2$ to be true in order for an acute triangle to happen.

So,

$b^2 < a^2 + c^2\\\\c^2 > b^2 - a^2\\\\c > \sqrt{b^2-a^2}\\\\x > \sqrt{16^2-10^2}\\\\x > \sqrt{156}\\\\x > 12.4899959967968 \ \text{(approximate)}\\\\x > 12.5$

Now let's consider the possibility that the missing side x is actually the longest side.

Using the same theorem as before, we would say,

$c^2 < a^2 + b^2\\\\c < \sqrt{a^2 + b^2}\\\\x < \sqrt{10^2 + 16^2}\\\\x < \sqrt{356}\\\\x < 18.8679622641132 \ \text{(approximate)}\\\\x < 18.9\\\\$

We found that x > 12.5 and x < 18.9

This is the same as saying 12.5 < x and x < 18.9

Put together, they form the approximate answer of 12.5 < x < 18.9

6 0

3 years ago

The slope of the line whose equation is given

rosijanka [135]

The slope is 9/1 hope i helped

8 0

3 years ago

Segment PH is graphed on the coordinate grid where P is (-31,8) and H is (29,-10). Point E is the midpoint of segment PH. If poi

maks197457 [2]

Answer:

The coordinates of point A are (-11 , 2)

Step-by-step explanation:

- The coordinates of point P are (-31 , 8)

- The coordinates of point H are (29 , -10)

- Point E is the mid-point of segment PH

- The coordinates of the the mid-point are:

→ $x=\frac{x_{1}+x_{2}}{2}$ and $y=\frac{y_{1}+y_{2}}{2}$

∵ E is the mid-point of segment PH

∴ The x-coordinate of point E is $x=\frac{-31+29}{2}=-1$

∴ The x-coordinate of point E is -1

∴ The y-coordinate of point E is $y=\frac{8+-10}{2}=-1$

∴ The y-coordinate of point E is -1

∴ The coordinates of point E are (-1 , -1)

- Point A is graphed $\frac{2}{3}$ of the way along the segment from P to E

- That mean the distances from points P to A is 2 parts and from P to E

is 3 parts, then the distance from A to E is "3 - 2" = 1 part

- So point A divides the line segment PE at ratio 2 : 1 from P

- The coordinates of the division point are:

→ $x=\frac{x_{1}m_{2}+x_{2}m_{1}}{m_{1}+m_{2}}$ and $y=\frac{y_{1}m_{2}+y_{2}m_{1}}{m_{1}+m_{2}}$

∵ Point A divides PE at ratio 2 : 1

∵ The coordinates of point P are (-31 , 8)

∵ The coordinates of point E are (-1 , -1)

∴ The x-coordinate of point A is $x=\frac{(-31)(1)+(-1)(2)}{2+1}= -11$

∴ The x-coordinate of point A is -11

∴ The y-coordinate of point A is $x=\frac{(8)(1)+(-1)(2)}{2+1}=2$

∴ The y-coordinate of point A is 2

∴ The coordinates of point A are (-11 , 2)

* The coordinates of point A are (-11 , 2)

3 0

3 years ago

Write a ratio for the situation in three ways, comparing the first quantity to the second quantity. In Largo City, about one in

saul85 [17]

Answer:

Step-by-step explanation:

1/9

(1*4) / (9*4) = 4/36

(1*4) / (9*4) = 5/45

The first one is the ratio as it is stated in the problem.

The second one multiplies top and bottom by 4

The third one multiplies top and bottom of the top ratio by 5.

3 0

3 years ago

Geomertry Tangents Chords Sectors Arcs and segments! whichever one helps

8_murik_8 [283]

Answer:

1

Step-by-step explanation:

(195 - 85)/2 = 54x+1 -->

110/2 = 54x + 1 -->

55 = 54x + 1 -->

54 = 54x -->

1 = x

3 0

3 years ago