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3 years ago

True Or False: A triangle with the side lengths of 9, 12, 17 is a right triangle

Mathematics

1 answer:

alexdok [17]3 years ago

5 0

Answer:

not a right triangle

Step-by-step explanation:

We can use the Pythagorean theorem to see if it is a right triangle

a^2+b^2 = c^2

9^2+12^2 = 17^2

81+144 =289

225 = 289

This is not true so it is not a right triangle

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Explain how the difference of a fraction or a rational number and its additive inverse is equal to zero.

Jobisdone [24]

This question is in reverse (in two ways):

1. The definition of an additive inverse of a number is precisely that which, when added to the number, will give a sum of zero. 

The real problem, in certain fields, is usually to show that for all numbers in that field, there exists an additive inverse. 

Therefore, if you tell me that you have a number, and its additive inverse, and you plan to add them together, then I can tell you in advance that the sum MUST be zero. 

2. In your question, you use the word "difference", which does not work (unless the number is zero - 0 is an integer AND a rational number, and its additive inverse is -0 which is the same as 0 - the difference would be 0 - -0 = 0). 

For example, given the number 3, and its additive inverse -3, if you add them, you get zero: 
3 + (-3) = 0 

However, their "difference" will be 6 (or -6, depending which way you do the difference): 

3 - (-3) = 6 
-3 - 3 = -6 

(because -3 is a number in the integers, then it has an additive inverse, also in the integers, of +3). 

--- 

A rational number is simply a number that can be expressed as the "ratio" of two integers. For example, the number 4/7 is the ratio of "four to seven". 

It can be written as an endless decimal expansion 
0.571428571428571428....(forever), but that does not change its nature, because it CAN be written as a ratio, it is "rational". 

Integers are rational numbers as well (because you can always write 3/1, the ratio of 3 to 1, to express the integer we call "3") 

The additive inverse of a rational number, written as a ratio, is found by simply flipping the sign of the numerator (top) 

The additive inverse of 4/7 is -4/7 

and if you ADD those two numbers together, you get zero (as per the definition of "additive inverse") 

(4/7) + (-4/7) = 0/7 = 0 

If you need to "prove" it, you begin by the existence of additive inverses in the integers. 
ALL integers each have an additive inverse. 
For example, the additive inverse of 4 is -4 

Next, show that this (in the integers) can be applied to the rationals in this manner: 

(4/7) + (-4/7) = ? 
common denominator, therefore you can factor out the denominator: 

(4 + -4)/7 = ? 
Inside the bracket is the sum of an integer with its additive inverse, therefore the sum is zero 
(0)/7 = 0/7 = 0 

Since this is true for ALL integers, then it must also be true for ALL rational numbers.

5 0

3 years ago

Ive been doing this for 20 minutes now please help!!! I will give you brainliest if you give an actual answer!! SHOW YOUR WORK S

yanalaym [24]

Answer:

v= 3

Step-by-step explanation:

-19 + v = -8 ( v - 1 )

multiply -8(v - 1)= -8v + 8

-8v + 8v and then add the v with the +8v

Subtract -19 +19 and add the +19 with the +8= 27

27 divided by 9= 3

6 0

3 years ago

Read 2 more answers

1. A waste management service attempts to design routes so that each of their trucks pick-up on average four tons of garbage or

Galina-37 [17]

Answer:

We conclude that garbage collector's average picking is more than four tons of garbage per day.

Step-by-step explanation:

We are given the following information n the question:

First, we design the null and the alternate hypothesis

$H_{0}: \mu \leq 4\text{ tons}\\H_A: \mu > 4\text{ tons}$

Significance level = 5% = 0.05

P-value = 0.04

The p-value is the probability of obtaining the observed results of a test, assuming that the null hypothesis is correct.

P values evaluate how well the sample data support that the null hypothesis is true.
P-value is a measure or indicator that helps us to know that whether the sample belongs to the population or not.
Null hypothesis states that the sample belongs to the population.

A high p-values states that the null hypothesis is true ad the sample belongs to the population.ll.

A low p-value suggests that sample provides enough evidence that you the null hypothesis is not true and the sample does not belong to the population.
We compare p-value to significance level to obtain our result.

Here,

p-value = 0.04 < Significance level = 0.05

Since the p-value is lower than the significance level, we fail to accept the null hypothesis and reject it. That is there were enough evidence to support the fact that sample does not belong to the population and we conclude that garbage collector's average picking is more than four tons of garbage per day.

6 0

3 years ago

10. Make Sense and Persevere The flag of the

kumpel [21]

Answer:

$s=\frac{P}{3}$
Dimensions of the flag:

$lenght=6.65\ ft\\\\width=3.5\ ft$

Area of the flag: $23.275\ ft^2$

Step-by-step explanation:

The missing figure of the exercise is attached.

We know that the perimeter of the triangle is given by:

$P= 3s$

Where "s" is the side lenght of the triangle.

Solving for "s", we get:

$s=\frac{P}{3}$

Therefore, if the perimeter of the triangle is 126 inches, its side length is:

$s=\frac{126\ in}{3}\\\\s=42\ in$

Since $1\ ft=12\ in$ , we know that "s" in feet is:

$s=(42\ in)(\frac{1\ ft}{12\ in})=3.5\ ft$

The area of a rectangle can be calculated with this formula:

$A=lw$

Where "l" is the lenght and "w" is the width

We can observe in the figure that the lenght and the width of the flag are:

$l=1.9s\\w=s$

Then, the dimensions of the flag are:

$l=1.9(3.5\ ft)=6.65\ ft\\w=3.5\ ft$

And the area is:

$A=(6.65\ ft)(3.5\ ft)=23.275\ ft^2$

3 0

3 years ago

Oak Street and Elm Street run parallel to each other. When Main Street

Fiesta28 [93]

Answer:

50 Degrees

Step-by-step explanation:

They are parallel because, so 5, 8, 4, and 1 are all 50 degrees, and the angle is 180. That means the other sides angle is 130 degrees. 7, 6, 2, and 3 are 130 degrees

7 0

3 years ago

Read 2 more answers