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o-na [289]
3 years ago
7

Part A: Find a rational number that is between 7.7 and 7.9. Explain why it is rational. (2 points)

Mathematics
1 answer:
8_murik_8 [283]3 years ago
6 0
A rational number is any number that can be written as the ratio between two other numbers i.e. in the form \frac{a}{b}

Part A:
An easy choice that makes sense is 7.8, right in the middle. To prove that it's rational we need to write it as a ratio. In this case we have 7.8=\frac{78}{10}

Part B:
We need a number that can't be written as a ratio (because it neither terminates nor repeats). Some common ones are \sqrt{2}, e, \phi and \pi so it makes sense to try and use those to build our number. In this case \frac{11\sqrt{2}}{5}\approx7.78 works nicely. 
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Antonio is a biologist studying life in a pond. He needs to know how deep the water is. He notices a water lily sticking straigh
quester [9]
For this problem we can represent the situation as a rectangle triangle.
 x: depth of water.
 40: Base. "Antonio pulls the lily to one side, keeping the stem straight, until the blossom touches the water at a spot"
 x + 8: Hypotenuse. "He notices water lily sticking straight up from the water, whose blossom is 8 cm above the water's surface." Antonio pulls the lily to one side, keeping the stem straight, until the blossom touches the water at a spot".
 By the Pythagorean theorem we have:
 x ^ 2 + 40 ^ 2 = (x + 8) ^ 2
 Clearing x:
 x ^ 2 + 1600 = x ^ 2 + 16x + 64
 x ^ 2 - x ^ 2 = 16x + 64 - 1600
 0 = 16x -1536
 1536 = 16x
 1536/16 = x
 x = 96
 answer:
 1) x ^ 2 + 40 ^ 2 = (x + 8) ^ 2
 2) the depth of the water is
 x = 96
6 0
3 years ago
The scale of a truck is 3.7 cm
Tju [1.3M]

Answer:

that truck must be straight fire

7 0
3 years ago
Read 2 more answers
R+6> 13 solving one step inequalities
Sidana [21]

Answer:

R > 7

Step-by-step explanation:

R+6> 13   (subtract 6 from both sides)

R > 13 - 6

R > 7

6 0
3 years ago
Given that $x \le -7,$ identify all the correct conclusions. (A) $3x \le -21.$ (B) $3x \ge -21.$ (C) $-3x \le 21.$ (D) $-3x \ge
exis [7]

Answer:

Options A and D are correct choices.

Step-by-step explanation:

We have been given an inequality x\leq -7 and we are asked to find the correct options from our given choices.

Let us solve inequalities in our given options one by one to see which of these matches with our given inequality.

(A) 3x\leq -21  

x\leq \frac{-21}{3}

x\leq -7

We can see that option A gives the same answer as our given inequality, therefore, option A is the correct choice.

(B) 3x\geq -21

x\geq \frac{-21}{3}

x\geq -7

This inequality represented in option C gives solution that x should be greater than or equal to -7, which is opposite to our given inequality, therefore, option B is incorrect.

(C) -3x\leq 21

Dividing inequality by a negative number swaps inequality sign.

x\geq \frac{21}{-3}

x\geq -7

This inequality gives solution that x should be greater than or equal to -7, which is opposite to our given inequality, therefore, option C is incorrect.

(D) -3x\geq 21  

Dividing inequality by a negative number swaps inequality sign.

x\leq \frac{21}{-3}

x\leq -7

We can see that option D gives the same answer as our given inequality, therefore, option D is the correct choice.  

8 0
3 years ago
PLEASE HELP ME I"M DYING FOR AN ANSWER.
Nata [24]

Answer:

The answer to the first one is number 2

Step-by-step explanation:

They are parralel because they do not cross either in the front or in the back

8 0
3 years ago
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