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docker41 [41]
3 years ago
15

What is the solution set to the inequality (4x-3)(2x-1)=> 0?

Mathematics
2 answers:
Varvara68 [4.7K]3 years ago
6 0

Answer:

please send help thier is someone doing stupid noises

Step-by-step explanation:

eminem   ahhh shmalama what i gotta do to get it through to you super human elivated trying to get elimented you make elivator music.

Arturiano [62]3 years ago
5 0

Answer:

x <= 1/2 or x >= 3/4

In interval notation:

(-\infty, \dfrac{1}{2}] \land [\dfrac{3}{4}, \infty)

Step-by-step explanation:

First, solve the related equation for x.

(4x - 3)(2x - 1) = 0

4x - 3 = 0 or 2x - 1 = 0

4x = 3 or 2x = 1

x = 3/4 or x = 1/2

Now you have 2 points of interest, 1/2 and 3/4.

Plot these two numbers on a number line using solid dots.

The number line is now divided into three regions: left of 1/2, between 1/2 and 3/4, and right of 3/4. We need to test a point from each region to see which regions are part of the solution.

Test -1

(4x - 3)(2x - 1) => 0

[4(-1) - 3][2(-1) - 1] => 0 ?

(-7)(-3) => 0 ?

21 => 0 True

The interval left of 1/2 up to and including 1/2 is part of the solution.

Test 0.6

(4x - 3)(2x - 1) => 0

[4(0.6) - 3][2(0.6) - 1) => 0 ?

(-0.6)(0.2) => 0 ?

-0.12 => 0 False

The interval between 1/2 and 3/4 is not part of the solution.

Test 1

(4x - 3)(2x - 1) => 0

[4(1) - 3][2(1) - 1] => 0 ?

(1)(1) => 0 ?

1 => 0 True

The interval right of 1/2 including 1/2 is part of the solution.

Answer:

x <= 1/2 or x >= 3/4

In interval notation:

(-\infty, \dfrac{1}{2}] \land[\dfrac{3}{4}, \infty)

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Step-by-step explanation:

<u>Use points on the graph:</u>

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Give the equation of the line perpendicular to y +7= -2(x - 6) through the<br> point (6,-3)
lilavasa [31]

<u>Note: this answer assumes the equation of the line can be put in slope-intercept form. </u>

Answer:

y + 3 = \frac{1}{2}(x-6)

Step-by-step explanation:

1) First, find the slope of y + 7 = -2 (x - 6). We can see that it's already in point-slope form, or y-y_1 = m (x-x_1) format. Remember that the number in place of the m is the slope. Therefore, -2 is the slope of that equation.

What we need is the slope that is perpendicular to that, though. So, find the opposite reciprocal of -2. To do this, change its sign, convert it into a fraction (-\frac{2}{1}), and flip its numerators and denominators. Therefore, the perpendicular slope would be \frac{1}{2}.

2) Now that we have a slope and a point the line passes through, we can write an equation using the point-slope formula, y-y_1 = m (x-x_1). In order to write an equation, the x_1, y_1, and m have to be substitute for with real values.

The m represents the slope. We already calculated that in the last step, so put \frac{1}{2} in place of the m. The x_1 and y_1 represent the x and y values of a point the line passes through. We know that the line has to pass through (6, -3), so substitute 6 for x_1 and -3 for y_1:

y - (-3) = \frac{1}{2}(x -(6))\\y + 3 = \frac{1}{2}(x - 6)

Therefore, (again, assuming that the line can be put in point-slope form) the answer is y + 3 = \frac{1}{2}(x-6).

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