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ExtremeBDS [4]
3 years ago
12

Which solution set describes the solutions to the inequality below?

Mathematics
1 answer:
Nuetrik [128]3 years ago
7 0
<h2>Hello!</h2>

The answer is:

The sixth option,

[-6,6]

<h2>Why?</h2>

To solve the problem, we need to find which of the given options match with the solution to the inequality. As we know, solving inequalities is almost the same that solving equalities, we need to isolate the variable and then, find where it satisfies the given condition (inequality)

So, solving the inequality we have:

-3x^{2} +1\leq -107\\-3x^{2}\leq -107-1\\-3x^{2} \leq -108\\3x^{2} \leq 108\\x^{2} \leq \frac{108}{3}\\\sqrt{x^{2} } \leq \sqrt{36}\\ x^{2\leq } +-36\\(x-6)(x+6)\leq 0

Therefore, we have that the solutions to the inequality are:

First solution:

x-6\leq 0\\x\leq 6

Second solution:

x+6\leq 0\\x\leq-6

Hence, the correct option is the sixth option, the solution is described by the following solution set :

[-6,6]

Have a nice day!

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Two lines intersect to form a linear pair with equal measures. One angle had the measure 2x and the other angle had the measure
rosijanka [135]

Answer:

x = 45, y = 5

Step-by-step explanation:

It is given that two lines form a linear pair with equal measures. Therefore, the angle between the two lines will be 90. Now, according to the question,

2x + 20y - 10 =90

2x+20y = 100

x + 10y = 50

And

2x = 20y-10

x = 10y -5

x - 10 y = -5

Now, adding x + 10y = 50 and x - 10y =-5, the value of x can be found. The required value will be:

x + 10y =50

x - 10y = -5

------------------

x = 45

Therefore, the value of y after substitution of the value of x in one of the equations will be:

90 = 20y - 10

20 y = 100

y = 5

Hence, the required value of x and y are 45 and 5 respectively.

4 0
3 years ago
Find the volume: A cone with a diameter of 16cm and a height of 16cm.
soldier1979 [14.2K]
<h2><em>The formula for a cone is in the attachment below. Substitute Pie for 3.14.</em></h2><h2><em>3.14 x 8 x 8 x 16/3 = 1071.78667. You can round this up and you get 1072.33.</em></h2><h2><em></em></h2><h2><em>Final Answer: 1072.33cm^3</em></h2><h2><em>Hope this helps and have a nice day! o/</em></h2>

6 0
3 years ago
Boris buys 5 markers and a 29 cent eraser for a total of $3.24. How much does each marker cost?
Minchanka [31]
$.58 ; 3.24-.29is 2.95 and 2.95 divided by 5 is .58
4 0
3 years ago
Read 2 more answers
skew-symmetric 3 x 3 matrices form as subspace of all 3 x 3 matrices and find a basis for this subspace.
Neporo4naja [7]

Answer:

a) ∝A ∈ W

so by subspace, W is subspace of 3 × 3 matrix

b) therefore Basis of W is

={ {\left[\begin{array}{ccc}0&1&0\\-1&0&0\\0&0&0\end{array}\right] ,\left[\begin{array}{ccc}0&0&1\\0&0&0\\-1&0&0\end{array}\right] ,\left[\begin{array}{ccc}0&0&0\\0&0&1\\0&-1&0\end{array}\right]}

Step-by-step explanation:

Given the data in the question;

W = { A| Air Skew symmetric matrix}

= {A | A = -A^T }

A ; O⁻ = -O⁻^T        O⁻ : Zero mstrix

O⁻ ∈ W

now let A, B ∈ W

A = -A^T       B = -B^T

(A+B)^T = A^T + B^T

= -A - B

- ( A + B )

⇒ A + B = -( A + B)^T

∴ A + B ∈ W.

∝ ∈ | R

(∝.A)^T = ∝A^T

= ∝( -A)

= -( ∝A)

(∝A) = -( ∝A)^T

∴ ∝A ∈ W

so by subspace, W is subspace of 3 × 3 matrix

A ∈ W

A = -AT

A = \left[\begin{array}{ccc}o&a&b\\-a&o&c\\-b&-c&0\end{array}\right]

= a\left[\begin{array}{ccc}0&1&0\\-1&0&0\\0&0&0\end{array}\right] +b\left[\begin{array}{ccc}0&0&1\\0&0&0\\-1&0&0\end{array}\right] +c\left[\begin{array}{ccc}0&0&0\\0&0&1\\0&-1&0\end{array}\right]

therefore Basis of W is

={ {\left[\begin{array}{ccc}0&1&0\\-1&0&0\\0&0&0\end{array}\right] ,\left[\begin{array}{ccc}0&0&1\\0&0&0\\-1&0&0\end{array}\right] ,\left[\begin{array}{ccc}0&0&0\\0&0&1\\0&-1&0\end{array}\right]}

8 0
3 years ago
How can victoria justify step 3 of her work
Wittaler [7]
A little more info please?
4 0
3 years ago
Read 2 more answers
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