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Olenka [21]
3 years ago
8

Whats the solution to the system of inequalities? -3x-y+z=6 -3x-y+3z=0 -3z=3

Mathematics
1 answer:
Naya [18.7K]3 years ago
3 0

Answer:

  This system of equations has <em>no solution</em>. It is inconsistent.

Step-by-step explanation:

The last equation tells you z = -1.

Substituting this value for z in the other two equations allows them to be written as ...

  -3x -y = 7

  -3x -y = 3

There are no values of x and y that can make both these equations true.

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Find the value of tan(B)<br><br> please help quickly
elena55 [62]

Answer:

it is 4/3

Step-by-step explanation:

because tan(B) = opposite/adjacent

4 0
3 years ago
The shape below is constructed from six squares, and the lengths of the sides of the three smallest squares are written inside o
Maurinko [17]

Answer:

78

Step-by-step explanation:

Smallest square: 1

Small Square: 2, Area of 4

Mid Square: 3, Area of 9

Mid White Square: 5, Area of 25

Big Square: 8, Area of 64

1 + 4 + 9 + 64 = 78

5 0
3 years ago
2y+3x² +5+y+2x+x²+2 what are the coefficients?
saw5 [17]

Answer: 200

The quadratic function f(x) = a(x - h)2 + k, a not equal to zero, is said to be in standard form. If a is positive, the graph opens upward, and if a is negative, then it opens downward. The line of symmetry is the vertical line x = h, and the vertex is the point (h,k).

Any quadratic function can be rewritten in standard form by completing the square. (See the section on solving equations algebraically to review completing the square.) The steps that we use in this section for completing the square will look a little different, because our chief goal here is not solving an equation.

Note that when a quadratic function is in standard form it is also easy to find its zeros by the square root principle.

Example 3.

Write the function f(x) = x2 - 6x + 7 in standard form. Sketch the graph of f and find its zeros and vertex.

f(x) = x2 - 6x + 7.

= (x2 - 6x )+ 7.        Group the x2 and x terms and then complete the square on these terms.

= (x2 - 6x + 9 - 9) + 7.

We need to add 9 because it is the square of one half the coefficient of x, (-6/2)2 = 9. When we were solving an equation we simply added 9 to both sides of the equation. In this setting we add and subtract 9 so that we do not change the function.

= (x2 - 6x + 9) - 9 + 7. We see that x2 - 6x + 9 is a perfect square, namely (x - 3)2.

f(x) = (x - 3)2 - 2. This is standard form.

From this result, one easily finds the vertex of the graph of f is (3, -2).

To find the zeros of f, we set f equal to 0 and solve for x.

(x - 3)2 - 2 = 0.

(x - 3)2 = 2.

(x - 3) = ± sqrt(2).

x = 3 ± sqrt(2).

To sketch the graph of f we shift the graph of y = x2 three units to the right and two units down.

If the coefficient of x2 is not 1, then we must factor this coefficient from the x2 and x terms before proceeding.

Example 4.

Write f(x) = -2x2 + 2x + 3 in standard form and find the vertex of the graph of f.

f(x) = -2x2 + 2x + 3.

= (-2x2 + 2x) + 3.

= -2(x2 - x) + 3.

= -2(x2 - x + 1/4 - 1/4) + 3.

We add and subtract 1/4, because (-1/2)2 = 1/4, and -1 is the coefficient of x.

= -2(x2 - x + 1/4) -2(-1/4) + 3.

Note that everything in the parentheses is multiplied by -2, so when we remove -1/4 from the parentheses, we must multiply it by -2.

= -2(x - 1/2)2 + 1/2 + 3.

= -2(x - 1/2)2 + 7/2.

The vertex is the point (1/2, 7/2). Since the graph opens downward (-2 < 0), the vertex is the highest point on the graph.

Exercise 2:

Write f(x) = 3x2 + 12x + 8 in standard form. Sketch the graph of f ,find its vertex, and find the zeros of f. Answer

Alternate method of finding the vertex

In some cases completing the square is not the easiest way to find the vertex of a parabola. If the graph of a quadratic function has two x-intercepts, then the line of symmetry is the vertical line through the midpoint of the x-intercepts.

The x-intercepts of the graph above are at -5 and 3. The line of symmetry goes through -1, which is the average of -5 and 3. (-5 + 3)/2 = -2/2 = -1. Once we know that the line of symmetry is x = -1, then we know the first coordinate of the vertex is -1. The second coordinate of the vertex can be found by evaluating the function at x = -1.

Example 5.

Find the vertex of the graph of f(x) = (x + 9)(x - 5).

Since the formula for f is factored, it is easy to find the zeros: -9 and 5.

The average of the zeros is (-9 + 5)/2 = -4/2 = -2. So, the line of symmetry is x = -2 and the first coordinate of the vertex is -2.

The second coordinate of the vertex is f(-2) = (-2 + 9)(-2 - 5) = 7*(-7) = -49.

Therefore, the vertex of the graph of f is (-2, -49).

8 0
2 years ago
What is the greatest common factor of 15x^3y^2 and 20x^4y^4?
Vanyuwa [196]
<h3>What is the greatest common factor of 15x³y² and 20x⁴y⁴? ​</h3>

​<em>First we have to find the factors of 15x³y²</em>

<em>15x³y² = 3 * 5x³y² ​</em>

<em>​Then we have to find the factors of 20x⁴y⁴</em>

<em>​20x⁴y⁴ = 2²x¹y² * 5x³y²</em>

<em>Now we have to find the common factors to both numbers.​</em>

<em>The common factors are </em><em>5x³y²</em>

Answer : GCF = (15x³y²,20x⁴y⁴) = 5x³y²​

​Hope this helps!​​​​

​​\textit{\textbf{Spymore}}​​​​​​

6 0
3 years ago
Assume that y varies inversely
Marina86 [1]

Answer:

y = 2

Step-by-step explanation:

y varies inversely with x setup is:

y = k/x

7 = \frac{k}{2/3}  (find 'k')

k = 7/1 · 2/3

k = 14/3

use what you know about 'k' and 'x' to solve for 'y'

y = 14/3 ÷ 7/3  (remember to multiply by the reciprocal when dividing fractions)

y = 14/3 · 3/7

y = 2

3 0
3 years ago
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