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3 years ago

Classify each triangle with the given side lengths as Acute, Obtuse, or Right

Mathematics

2 answers:

Dahasolnce [82]3 years ago

4 0

Answer:

acute

Step-by-step explanation:

levacccp [35]3 years ago

4 0

Answer:

Right Triangle

Step-by-step explanation:

12, 16 > 20

$20^{2}$ = $12^{2}$ + $16^{2}$

400 = 144+256

400 = 400

Right Triangle

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Find the simultaneous solution of the following pairs of equations using an algebraic method: x=1+2y 2x+y=17. Please also give a

AnnyKZ [126]

The solution is x = 7 and y= 3

Solution:

Given pairs of equation are:

x = 1 + 2y ------- eqn 1

2x + y = 17 ------- eqn 2

We have to use algebraic method

Algebraic method involves substitution and elimination method

Let us use the substitution method

From equation 1, we can see that x is equal to 1 + 2y. If we substitute this for y in equation 2, we have:

2(1 + 2y) + y = 17

Solve for brackets

2 + 4y + y = 17

Combine the like terms which has same variable

2 + 5y = 17

5y = 17 - 2

5y = 15

Divide both sides of equation by 5

y = 3

So the value of y is 3. This value of y can be substituted into either equation 1 or 2 to find the value of x

Substitute y = 3 in eqn 1

x = 1 + 2(3)

x = 1 + 6

x = 7

So the solution is x = 7 and y = 3

6 0

3 years ago

Which expression is equivalent to 64y^18-1000z^6?

Shalnov [3]

For this case we must find an expression equivalent to: $64y ^ {18}-1000z ^ 6$

Then, we take common factor 8:

$8 (64y ^ {18}-125z ^ 6) =$

By definition of power properties we have to:

$(a ^ n) ^ m = a ^ {n * m}$

So:

$8 ((2y ^ 6) ^ 3- (5z ^ 2) ^ 3)$

Since both terms are perfect cubes, we factor using the cube difference formula:

$(a ^ 3-b ^ 3) = (a-b) (a ^ 2 + 2ab + b ^ 2)$

Where:

$a = 2y ^ 6\\b = 5z ^ 2$

So: $8 (2y ^ 6-5z ^ 2) ((2y ^ 6) ^ 2 + 2 (2y ^ 6) (5z ^ 2) + (5z ^ 2) ^ 2) =\\8 (2y ^ 6-5z ^ 2) (4y ^ {12} + 10y ^ 6z ^ 2 + 25z ^ 4)$

Answer:

$8 (2y ^ 6-5z ^ 2) (4y ^ {12} + 10y ^ 6z ^ 2 + 25z ^ 4)$

8 0

3 years ago

Please help me with math I need help and its suppose to be handed in today

Yakvenalex [24]

Answer:

A=B perioddddd

Step-by-step explanation:

7 0

4 years ago

Suppose that you were not given the sample mean and sample standard deviation and instead you were given a list of data for the

Troyanec [42]

Answer:

So, the sample mean is 31.3.

So, the sample standard deviation is 6.98.

Step-by-step explanation:

We have a list of data for the speeds (in miles per hour) of the 20 vehicles. So, N=20.

We calculate the sample mean :

$\mu=\frac{19 +19 +22 +24 +25 +27 +28+ 37 +35 +30+ 37+ 36+ 39+ 40+ 43+ 30+ 31+ 36+ 33+ 35}{20}\\\\\mu=\frac{626}{20}\\\\\mu=31.3$

So, the sample mean is 31.3.

We use the formula for a sample standard deviation:

$\sigma=\sqrt{\frac{1}{N-1}\sum_{i=1}^{N}(x_i-\mu)^2}$

Now, we calculate the sum

$\sum_{i=1}^{20}(x_i-31.3)^2=(19-31.3)^2+(19-31.3)^2+(22-31.3)^2+(24-31.3)^2+(25-31.3)^2+(27-31.3)^2+(28-31.3)^2+(37-31.3)^2+(35-31.3)^2+(30-31.3)^2+(37-31.3)^2+(36-31.3)^2+(39-31.3)^2+(40-31.3)^2+(43-31.3)^2+(30-31.3)^2+(31-31.3)^2+(36-31.3)^2+(33-31.3)^2+(35-31.3)^2\\\\\sum_{i=1}^{20}(x_i-31.3})^2=926.2\\$

Therefore, we get

$\sigma=\sqrt{\frac{1}{N-1}\sum_{i=1}^{N}(x_i-\mu)^2}\\\\\sigma=\sqrt{\frac{1}{19}\cdot926.2}\\\\\sigma=6.98$

So, the sample standard deviation is 6.98.

3 0

3 years ago

Does anyone understand this one? I am a little lost.

Harlamova29_29 [7]

Answer:

The graph is decreasing

Step-by-step explanation:

Starting at -1, the graph goes down to its value at 1

The graph is decreasing

6 0

3 years ago