The level of the top of the water in the ocean is considered to be at an altitude of zero (0) feet.

Romashka [77]

$-\dfrac{1}{2}x > 4\qquad|\text{change the signs}\\\\\dfrac{1}{2}x < -4\qquad|\cdot2\\\\x < -8\to\{x|x\in\mathbb{R},\ x < -8\}\to\boxed{B.}$

5 0

3 years ago

Mr johnson's students want to know his age. He tells them that this year his age is a multiple of 9, and next year it will be a

vladimir1956 [14]

Answer:

He is 27 years old.

Step-by-step explanation:

27 is a multiple of 9 (9 x 3)

28 comes after, and is a multiple of 4 (4 x 7)

Hope this answer helps you!! :)

8 0

2 years ago

Find the length of each side of the triangle determined by the three points P1,P2, and P3. State whether the triangle is an isos

Tanya [424]

Answer:

The triangle is both an Isosceles triangle and a right triangle.

Step-by-step explanation:

Given the vertices of a triangle.

$P_{1} = (- 1, 4)$

$P_{2} = (6, 2)$ and

$P_{3} = (4, - 5)$

We find the distance between all the points to determine the length of each side of the triangle.

Distance between any two points, say, $(x_1, y_1)$ and $(x_2, y_2)$ is:

$\sqrt{\bigg ( \textbf{x}_{\textbf{2}} \hspace{1mm} \textbf{- x}_{\textbf{1}} \bigg )^{\textbf{2}} \textbf{+} \bigg( \textbf{y}_{\textbf{2}} \hspace{1mm} \textbf{- y}_{\textbf{1}} \bigg)^ {\textbf{2}}$

Length between $P_1$ and $P_{2}$ , (Side 1) :

$(x_1, y_1) = (- 1, 4)$ and

$(x_2, y_2) = (6, 2)$

Distance = $\sqrt{\bigg(6 - (-1) \bigg)^{2} \hspace{1mm} + \hspace{1mm} \bigg( 2 - 4 \bigg )^2$

$= \sqrt{7^2 + 2^2}$

$= \sqrt{49 + 4}$

$= \sqrt{\textbf{53}}$

Length of Side 1 = $\sqrt{\textbf{53}}$ units.

Distance between $P_1$ and $P_2$ , (Side 2):

$(x_1, y_1) = (-1, 4)$

$(x_2, y_2) = (4, - 5)$

Distance = $\sqrt{ \bigg( 4 + 1 \bigg)^2 \hspace{1mm} + \bigg( - 5 - 4 \bigg ) ^2$

$= \sqrt{ 25 + 81 }$

$= \sqrt{\textbf{106}}$

Length of Side 2 = $\sqrt{\textbf{106}}$ units.

Distance between $P_2$ and $P_3$ , Side 3 :

$(x_1, y_1) = (4, 5)$

$(x_2, y_2) = (6, 2)$

Distance = $\sqrt{ 2^2 \hspace{1mm} + \hspace{1mm} 7^2}$

$= \sqrt{49 + 4}$

$= \sqrt{\textbf{53}$

Length of Side 3 = $\sqrt{\textbf{53}}$ units.

Note that the length of Side 1 = Length of Side 3.

That means the triangle is Isosceles.

Also, For a triangle to be right angle triangle, using Pythagoras theorem we have:

(Side 1)² + (Side 3)² = (Side 2)²

$\bigg( \sqrt{53} \bigg )^2 \hspace{1mm} + \hspace{1mm} \bigg( \sqrt{53} \bigg)^2 \hspace{1mm} = \hspace{1mm} \bigg ( \sqrt{106} \bigg ) ^2$

i.e, 53 + 53 = 106

Hence, the triangle is a right - angled triangle as well.

7 0

3 years ago

A rectangular garden has a length of 20 yards and a width of 42 yards. A diagonal path runs from one end of the garden to the ot

Marta_Voda [28]

Answer: 46.5 yards
*the answer may be C since it's the closest*

Explanation: With a diagonal in the rectangle it creates a triangle so you can use the Pythagorean Theorem to solve the problem.

3 0

3 years ago

Alexis uses toy blocks to build a model of a building. Each toy block is 1 cubic inch. The first three floors of the model are m

SIZIF [17.4K]

Answer:

For the 6 rows of 4 blocks the answer is 24, for the 4 rows of 4 blocks the answer is 16. Then you do 24x16.

Step-by-step explanation:

6 rows of 4 blocks = 6x4=24

4 rows of 4 blocks= 4x4=16

24

x16

___

124

+ 240

_____

364

So, your answer would be 346 cu in.!! Sorry if I'm wrong!! :(

6 0

3 years ago