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3 years ago

The graph of a system of equations with the same slope and the same y-intercepts will have no solution

Mathematics

2 answers:

kolezko [41]3 years ago

8 0

Answer:

False

Step-by-step explanation:

Bumek [7]3 years ago

5 0

Answer:

False.

Step-by-step explanation:

If they have the same slope and same intercept they will have the same line. So they will have infinite solutions.

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X2 - 6x + 12 and y = 2x - 4, algebraically are

olga_2 [115]

The solution is (4, 4)

Solution:

Given system of equations are:

$y = x^2 - 6x + 12 ------ eqn\ 1\\\\y = 2x - 4 ---------- eqn\ 2$

Substitute eqn 2 in eqn 1

$x^2 - 6x + 12 = 2x - 4$

Make the right side of equation 0

$x^2 - 6x + 12 - 2x + 4 = 0\\\\x^2 -8x + 16 = 0$

Solve by quadratic equation

$\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\mathrm{For\:}\quad a=1,\:b=-8,\:c=16:\\\\x=\frac{-\left(-8\right)\pm \sqrt{\left(-8\right)^2-4\cdot \:1\cdot \:16}}{2\cdot \:1}\\\\x=\frac{-\left(-8\right)\pm \sqrt{0}}{2\cdot \:1}\\\\x = \frac{8}{2}\\\\x = 4$

Substitute x = 4 in eqn 2

y = 2(4) - 4

y = 8 - 4

y = 4

Thus solution is (4, 4)

5 0

3 years ago

If n is a positive integer and the product all the integeres from 1 to n inclusive is a multiple of 990 what is the least possib

kolbaska11 [484]

Hello,

Since 990=2*3²*5*11 ==>n=11

6 0

3 years ago

1. Solve and verify each of the following systems of linear equations.

kakasveta [241]

5x - 2y = -6 ⇒ 10x - 4y = -12
2x - 1y = 1 ⇒ 10x - 5y = 5
 y = -17
 5x - 2(-17) = -6
 5x + 34 = -6
 - 34 - 34
 5x = -40
 5 5
 x = -8
 (x, y) = (-8, -17)

2x + 3y = 432 ⇒ 10x + 15y = 2160
5x + 2y = 16 ⇒ 10x + 4y = 32
 11y = 2128
 11 11
 y = 193.4545455
 2x + 3(193.4545455) = 432
 2x + 580.3636364 = 432
 - 580.3636364 - 580.3636364
 2x = -148.3636364
 2 2
 x = -74.1818182
 (x, y) = (-74.1818184, 193.4545455)

6 0

3 years ago

Read 2 more answers

F(x) has domain , and range

marta [7]

Domain: {-4, -2, 0, 2, 4}
range: {-2, -1, 0, 1, 2}

7 0

2 years ago

If f(x) = x2 – 1 and g(x) = 2x – 3, what is the domain

Ainat [17]

Begin by finding the lowest point the quadratic equation can be, the vertex;

x²-1= is just a translation down of the graph x²

vertex; (0, -1) and since the graph of x² would extend to infinity beyond that point, we can say {x| x≥0} for domain and {y| y≥-1}.

For the linear equation, it is possible to have all x and y values, therefore range and domain belong to all real numbers.

Hope I helped :)

5 0

3 years ago