All categories

2 years ago

Why is the inequality x≤6 equivalent to the inequality x−5≤6−5

Mathematics

1 answer:

Monica [59]2 years ago

8 0

Two inequalities are equivalent if they have the same set of solutions.

x - 5 ≤ 6 - 5

x - 5 ≤ 1 |add 5 to both sides

x ≤ 6

You might be interested in

Pre Calc work, I need help with writing piece wise functions from graphs. Can anyone help? Giving brainliest

Andrei [34K]

The definition of the piece-wise function is:

$f(x) = 2.5x + 1, -2 \leq x \leq 2$

$f(x) = -3, 2 < x < 6$ .

<h3>What is a piece-wise function?</h3>

A piece-wise function is a function that has different definitions, depending on the input.

In this problem, for inputs between -2 and 2, the function is a line that goes through (-2,-4) and (2,6). The slope is:

m = (6 - (-4))/(2 - (-2)) = 2.5.

The y-intercept is of b = 1, hence the rule is:

$f(x) = 2.5x + 1, -2 \leq x \leq 2$

For x greater than 2 and less than 6, the function is constant at -3, hence the rule is:

$f(x) = -3, 2 < x < 6$ .

More can be learned about piece-wise functions at brainly.com/question/27262465

#SPJ1

5 0

1 year ago

F(x) = 3x^3 - 2x^2 - 11x + 10; (x + 2) I need to factor and find the zeros.

Ratling [72]

Answer:

$\textsf{Factored function}: \quad f(x)=(x+2)(3x-5)(x-1)$

$\textsf{Zeros}: \quad x=-2, \quad x=\dfrac{5}{3},\quad x=1$

Step-by-step explanation:

Given function:

$f(x)=3x^3-2x^2-11x+10$

If (x + 2) is a factor then:

$\implies f(x)=(x+2)(ax^2+bx+c)$

Expand:

$\implies f(x)=ax^3+bx^2+cx+2ax^2+2bx+2c$

$\implies f(x)=ax^3+2ax^2+bx^2+2bx+cx+2c$

$\implies f(x)=ax^3+(2a+b)x^2+(2b+c)x+2c$

To find a, compare the coefficients of x³:

$\implies a=3$

To find b, substitute the found value of a into the coefficient for x² and compare:

$\implies 2a+b=-2$

$\implies 2(3)+b=-2$

$\implies b=-8$

To find c, compare the constants:

$\implies 2c=10$

$\implies c=5$

Therefore:

$\implies f(x)=(x+2)(3x^2-8x+5)$

Now factor (3x²-8x+5):

$\implies 3x^2-3x-5x+5$

$\implies 3x(x-1)-5(x-1)$

$\implies (3x-5)(x-1)$

Therefore the factored function is:

$\implies f(x)=(x+2)(3x-5)(x-1)$

Zero Product Property

$\boxed{\text{If \; $a \cdot b = 0$ \; then either \; $a = 0$ \;or \;$b = 0$ (or both)}.}$

To find the zeros, set each factor equal to zero and solve for x:

$\implies x+2=0 \implies x=-2$

$\implies 3x-5=0 \implies x=\dfrac{5}{3}$

$\implies x-1=0 \implies x=1$

Therefore, the zeros of the function are:

$x=-2, \quad x=\dfrac{5}{3},\quad x=1$

3 0

10 months ago

What type of sequence is the following numbers? 2.5,5,10,...

Aliun [14]

Answer:

its doubling every time

Step-by-step explanation:

2.5 add 2.5 is 5

5 add 5 equals 10 etc.

5 0

2 years ago

Please solve these 2 ;-; y = 2x – 6 y = –4x + 3

Yuri [45]

Answer:

x = 3/2 | y = -3

Step-by-step explanation:

Given equations:

y = 2x - 6. . . .(i)
y = -4x + 3. . . . (ii)

Substituting from equation (i) for y:

==> 2x - 6 = -4x + 3

==> 2x + 4x = 6 + 3

==> 6x = 9

dividing both sides by 3:

==> 2x = 3

==> x = 3/2

Substituting 3/2 for x in equation (i):

==> y = 2(3/2) - 6

==> y = 3 - 6

==> y = -3

3 0

2 years ago

Read 2 more answers

Multiply by hundreds: 545 times 200

fiasKO [112]

Answer:

109000

Step-by-step explanation:

5 0

2 years ago