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Pani-rosa [81]
3 years ago
12

Solve this absolute value inequality. {14-2x]<8

Mathematics
1 answer:
prohojiy [21]3 years ago
6 0

|14-2x|6\ \wedge\ 2x3\ \wedge\ x

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Use Cramer’s Rule to solve system of equation.
alisha [4.7K]

\left\{\begin{array}{ccc}5x+2y=4\\3x+4y+2z=6\\7x+3y+4z=29\end{array}\right\\\\A=\left[\begin{array}{ccc}5&2&0\\3&4&2\\7&3&4\end{array}\right]\\\\\det A=5\cdot4\cdot4+3\cdot3\cdot0+2\cdot2\cdot7-7\cdot4\cdot0-3\cdot2\cdot5-3\cdot2\cdot4=54\\W_x=\left[\begin{array}{ccc}4&2&0\\6&4&2\\29&3&4\end{array}\right]\\\det W_x=4\cdot4\cdot4+2\cdot2\cdot29+6\cdot3\cdot0-29\cdot4\cdot0-3\cdot2\cdot4-6\cdot2\cdot4=108

W_y=\left[\begin{array}{ccc}5&4&0\\3&6&2\\7&29&4\end{array}\right]\\\det W_y=5\cdot6\cdot4+3\cdot29\cdot0+4\cdot2\cdot7-7\cdot6\cdot0-29\cdot2\cdot5-3\cdot4\cdot4=-162\\W_z=\left[\begin{array}{ccc}5&2&4\\3&4&6\\7&3&29\end{array}\right]\\\det W_z=5\cdot4\cdot29+3\cdot3\cdot4+6\cdot2\cdot7-7\cdot4\cdot4-3\cdot6\cdot5-3\cdot2\cdot29=324\\\\x=\dfrac{\det W_x}{\det A}=\dfrac{108}{54}=2\\\\y=\dfrac{\det W_y}{\det A}=\dfrac{-62}{54}=-3\\\\z=\dfrac{\det W_z}{\det A}=\dfrac{324}{54}=6

5 0
3 years ago
What is -9x-(2x/-3) When x equals 7
yuradex [85]
-9x- \frac{2x}{-3}

-9*(7) -  \frac{2*7}{-3}

9*7 = 63

\frac{2*7}{-3}  =  \frac{14}{-3}

Apply the fraction  rule : \frac{a}{-b} = -  \frac{a}{b}

= - \frac{14}{3}

-63-( -\frac{14}{3} )

Apply rule  - ( - a) = a

-63+ \frac{14}{3}

Convert  element to fraction :

63 =  \frac{63}{1}

-\frac{63}{1} + \frac{14}{3}

Find the LCD 1*3 = 3

- \frac{63*3}{3}+ \frac{14}{3}

\frac{-3+63+14}{3} =  \frac{-175}{3}

<span>Apply the fraction  rule : \frac{a}{-b} = - \frac{a}{b}</span>

= - \frac{175}{3}

hope this helps!

4 0
3 years ago
Please help me get the answer i’ll give you a thanks and 10 points pls
vitfil [10]
586 cm squared i believe
7 0
3 years ago
Read 2 more answers
The Johnson twins were born five years after their older sister. This​ year, the product of the three​ siblings' ages is exactly
Mamont248 [21]

Answer:

13 years.

Step-by-step explanation:

Suppose, today, the Johnson twins' age is x years. Then the age of their elder sister will be (x + 5) years old. It is given that product of the three​ siblings' ages is exactly 2998 more than the sum of their ages. Therefore:

x + x + x + 5 + 2998 = (x)(x)(x + 5).

3x + 3003 = x^3 + 5x^2.

x^3 + 5x^2 - 3x - 3003 = 0.

To solve the question, factor theorem will be used. It states if any number c satisfies the equation f(c) = 0, then c is the factor of f(x). By observation, it can be seen that x = 13 can be a possible candidate for the factor of f(x). To verify, check f(13).

f(13) = 13^3 + 5(13^2) - 3(13) - 3003 = 2197 + 845 - 39 - 3003 = 0.

Since f(13) = 0, therefore x = 13 is the factor of f(x).

Now applying synthetic division:

Column 1       2       3       4            5

     13    |         1       5      -3        -3003  (Row 1)

______|______<u>  _13__234___3003</u>   (Row 2)

            |         1       18      231          0    (Row 3)

The method requires to write the coefficients of all the powers in the Row 1 on the right hand side of the table. Put the factor x = 13 on the left hand side of the table (Row 1 Column 1). The first step involves the second column elements to be added. Since there is only 1, thus there will be 1 below the line. Next step involves multiplying 1 with the factor (which is 13) and this will be the element for row 2 column 3. The add the elements of the column 3. The answer comes out to be -3. Repeat the above steps for the columns 4 and 5. The sum of the column 5 (the last column) should be 0, which is the case. The elements of the last row are actually the coefficients of the quadratic equation which is resultant from dividing f(x) by (x - 13). Thus:

x^2 + 18x + 231 = 0.

Using completing the square:

x^2 + 18 = -231.

(x)^2 + 2*(x)*(9) + (9)^2 = -231 + (9)^2.

(x + 9)^2 = -231 + 81.

(x + 9)^2 = -150.

Taking square root on both sides shows that rest of the 2 answers of this polynomial will be complex roots since square root of -150 does not exist in real numbers. Therefore, since the age is a real quantity and not a complex quantity, the age of the twins is 13 years!!!

8 0
3 years ago
For this right triangle, find the measure of angle g.<br> angle g = ?°
love history [14]

The sum of the interior angles of all triangles is 180 degrees. This is a right triangle, thus we know two interior angle values (90 degrees and 29 degrees). To find the third, set the sum of all interior angle values equal to 180 and solve for g.

180 = 90 + 29 + g

Collect like terms.

180 = 119 + g

Subtract 119 from both sides.

61 = g

Find the sum using 61 for g to check work.

180 = 90 + 29 + g

180 = 90 + 29 + 61

180 = 180

Answer:

m∠g = 61°

6 0
3 years ago
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