Which of the following integers is in the solution set of │1 – 3x│ < 5 ?I -1
II 1
III 2

Answers

Answer 1

Answer: $|1-3x| < 5\n\nx=-1\n\n|1-3\cdot(-1)| < 5\n\n|1+3| < 5\n\n|4| < 5\n\n4 < 5-the\ true$

$x=1\n\n|1-3\cdot1| < 5\n\n|1-3| < 5\n\n|-2| < 5\n\n2 < 5-the\ true$

$x=2\n\n|1-3\cdot2| < 5\n\n|1-6| < 5\n\n|-5| < 5\n\n5 < 5-the\ false$

$|1-3x| < 5\n\n1-3x < 5\ \wedge\ 1-3x > -5\n\n-3x < 5-1\ \wedge\ -3x > -5-1\n\n-3x < 4\ /:(-3)\ \wedge\ -3x > -6\ /:(-3)\n\nx > -(4)/(3)\ \wedge\ x < 2\n\nx\in(-(4)/(3);\ 2)\n\nI\ x=-1\in(-(4)/(3);\ 2)\n\nII\ x=1\in(-(4)/(3);\ 2)\n\nIII\ x=2\notin(-(4)/(3);\ 2)$

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The number line is a graph of the _____. A)real numbers. B)integers. C)rational numbers

Answers

The number line is a graph of the A)real numbers. Because number line includes rational and irrational numbers.

Theo used to drive 60 miles to work each day. His new home is now 20 miles awayfrom his job. What is the percent of
decrease in the distance Theo travels to
work? Round to the nearest tenth if
necessary.

Answers

The percentage of decrease in the distance Theo travels to work is 66.7%.

Used concept of percentage;

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating the hundredth part of any quantity is called a percentage.

Given that;

Theo used to drive 60 miles to work each day.

And, His new home is now 20 miles away from his job.

Hence the percentage of decrease in the distance Theo travels to work is,

P = (60 - 20)/60 x 100

P = 40/60 x 100

P = 66.7%

So, The percentage of decrease in the distance Theo travels to work is 66.7%.

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Answer:

66.6% decrease in distance

Rounded 67%

He is traveling 1/3 of what he used to travel

Step-by-step explanation:

Determine the type and number of solutions of 4x^2-5x+1=0.A. Two real solutions
B. One real solution
C. Two imaginary solutions

Answers

4x² - 5x + 1 = 0
a = 4; b = - 5, c = 1
Δ = b² - 4.a.c
Δ = (-5)² - 4.4.1
Δ = 25 - 16
Δ = 9

x = - b ± √Δ / 2.a
$x = (-5\± √(9) )/(2*4)$
$x = (-5\±3)/(8)$
$x' = (-5-3)/(8) = (-8)/(8) = -1$
$x' = (-5+3)/(8) = (-2)/(8) (/2) = (-1)/(4)$

A. Two real solutions (x' = -1 and x'' = -1/4)

equation of the circle in standard form with the center and radius given. Center (5,-3), the radius = 1 Please explain. Thank you so much

Answers

The equation of a circle is (x-h)²+(y-k)²=r², given that the center of the circle is (h, k). So the equation for this circle is (x-5)²+(y+3)²=1.

What would my final balance be if i put $650 in the bank for 60 months with an interest rate of 6%?

Answers

Your final balance would be $2,340.

I = Prt
Percent (6%) x rate (650) x time (60 months) = 2,340

6% = 0.06

0.06 x 60 x 650 = 2,340

Final answer:

You would end up with approximately $871.89 in your bank account after investing $650 for 60 months at an annual interest rate of 6%, if the bank compounds the interest yearly.

Explanation:

In this case, we are calculating the compound interest over a certain period. The formula for compound interest is:

P = C * (1 + r/n)^(nt)

C is the initial deposit (the principal). In your case, this is $650.
The interest rate (r) is 6%. To use this in the formula, we need to convert it to decimal form by dividing by 100, so r = 0.06.
n is the number of times that interest is compounded per unit t. Since it's not stated in the question, we'll assume it is once per year.
t is the time the money is invested for in years. Converting your 60 months to years gives t = 60/12 = 5 years.

Substitute the values into the formula:

P = $650 * (1 + 0.06/1)^(1*5)

Applying mathematics, we get an approximate final balance of $871.89