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2 years ago

Solve for − ∣ x − 2 ∣ + 4 ≤ 0

Mathematics

1 answer:

MakcuM [25]2 years ago

5 0

Answer:

x ≥ 6 or x ≤ -2

Step-by-step explanation:

- I x - 2 I + 4 ≤ 0

- I x - 2 I ≤ -4

I x - 2 I ≥ 4

x - 2 ≥ 4 or x - 2 ≤ -4

x ≥ 6 or x ≤ -2

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Which expression is equivalent to (x Superscript one-half Baseline y Superscript negative one-fourth Baseline z) Superscript neg

Darina [25.2K]

By using exponent properties, we will get the simplified expression:

$x^{-1}*y^{1/2}*z^2$

<h3>How to simplify the given expression?</h3>

Here we have the expression:

$(x^{1/2}*y^{-1/4}*z)^{-2}$

Remember the exponent properties:

$(a^n)^m = a^{n*m}$

And:

$(a*b)^n = (a^n)*(b^n)$

So using these two properties, we can rewrite:

$(x^{1/2})^{-2}*(y^{-1/4})^{-2}*(z)^{-2}\\\\(x^{-2*1/2})*(y^{-2*-1/4})*(z^{-2}})\\\\x^{-1}*y^{1/2}*z^2$

So we conclude that the completely simplified expression is:

$x^{-1}*y^{1/2}*z^2$

If you want to learn more about exponents:

brainly.com/question/8952483

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8 0

2 years ago

(1/2)/(2/3) evaluate

nikitadnepr [17]

Answer:

$\frac{3}{4}$

Step-by-step explanation:

Find a common denominator for the 2 denominators: 6
Change the fractions: 2 × 3 = 6, 1 × 3 = 3, 3 × 2 = 6, 2 × 2 = 4
Re-write the fractions: $\frac{3}{6}$ and $\frac{4}{6}$
Write as an expression: $\frac{3}{6}$ ÷ $\frac{4}{6}$
$\frac{3}{6}$ ÷ $\frac{4}{6}$ = $\frac{3}{6}$ × $\frac{6}{4}$
$\frac{3}{6}$ × $\frac{6}{4} = \frac{18}{24}$
$\frac{18}{24} = \frac{3}{4}$

I hope this helps!

8 0

2 years ago

Solve with steps<br> 5^(x+3)=25^(x-2)

Taya2010 [7]

5^(x+3)=25^(x-2)

Apply the exponent rule ( 5 ^2 = 25, so remove the 5 and replace 25?with 2)

x + 3 = 2(x-2)

Simplify:

X + 3 = 2x -4

Add 4 to both sides:

X + 7 = 2x

Subtract x from both sides

X = 7

Answer: x = 7

6 0

2 years ago

Prachi was 555 kilometers east of her home when she began driving farther east at 707070 kilometers per hour. Let f(n)f(n)f, lef

vladimir2022 [97]

Answer:

Following are the solution to the given question:

Step-by-step explanation:

Whenever she began to drive farther east, at 70 km per hour, Prachi was 5 km east of her home.

Let f(n) at the beginning of her nth hour drive be Prachi's distance to her home.

f is a sequence of arithmetic.

Write a series explicit form.

$\to f(n) = 70n + 5$

3 0

2 years ago

Which of the following expressions are polynomials?

AlekseyPX

Answer:

1,3 and 5

Step-by-step explanation:

1) -2(7x + 1) − 5(3x2 + 3x + 2)

= -14x - 2 - 15x^2 - 15x - 10

= -15x^2 - 29x - 12

2) (5x2 − 10x + 8) − (10x2 + 19x + 20)

= 5x^2 - 10x + 8 - 10x^2 - 19x - 20

= -5x^2 -29x - 12

3) (-7x2 − 21x + 13) − (8x2 + 8x + 25)

= -7x^2 - 21x + 13 - 8x^2 - 8x - 25

= -15x^2 - 29x - 12

4) (-19x2 − 4x - 7) + (4x2 + 25x − 5)

= -15x^2 + 21x - 12

5) (-17x2 + 2x − 3) + (2x2 − 31x − 9)

= -15x^2 -29x - 12

6) -2(4x − 15) − 3(5x2 + 7x + 6)

= -8x + 30 - 15x^2 - 21x - 18

= -15x^2 - 29x + 12

5 0

3 years ago