All categories

1 year ago

Compare the process of solving |x – 1| + 1 < 15 to that of solving |x – 1| + 1 > 15.

Mathematics

2 answers:

Troyanec [42]1 year ago

6 0

Answer:

Both absolute values would need to be isolated first.

You would need to write a compound inequality for each.

Both compound inequalities would compare

x – 1 to –15 and 15.

The inequality with “<” would use an “and” statement, while the “>” would use an “or” statement.Step-by-step explanation:

kicyunya [14]1 year ago

4 0

In the first case we'd subtract 1 from both sides, obtaining |x-1|<14.

In the second case we'd also subtract 1 from both sides, and would obtain
|x-1|>14.

What would the graphs look like?

In the first case, the graph would be on the x-axis with "center" at x=1. From this center count 14 units to the right, and then place a circle around that location (which would be at x=15). Next, count 14 units to the left of this center, and place a circle around that location (which would be -13). Draw a line segment connecting the two circles. Notice that all of the solutions are between -13 and +15, not including these endpoints.

In the second case, x has to be greater than 15 or less than -13. Draw an arrow from x=1 to the left, and then draw a separate arrow from 15 to the right. None of the values in between are solutions.

You might be interested in

Tran has a credit card with a spending limit of $2000 and an APR (annual percentage rate) of 12%. During the first month, Tran c

MAXImum [283]

Step-by-step explanation:

Given data:

Tran has a credit card with a spending limit of $2000 and an APR (annual percentage rate) of 12%.

During the first month, Tran charged $450 and paid $150 of that in his billing cycle.

The expression which will find the amount of interest Tran will be charged after the first month is (0.012)(300)

Here 0.01 because it is 1 month tax.

300 is remaining amount as Tran used $450 but paid $150.

5 0

1 year ago

The height (in meters) of a projectile shot vertically upward from a point 2 m above ground level with an initial velocity of 22

NISA [10]

Answer:

a) $v(2\,s) = 2.9\,\frac{m}{s}$ , b) $v(4\,s) = -16.7\,\frac{m}{s}$ , c) $t = 2.296\,s$ , d) $h (2.296\,s) = 27.829\,m$ , e) $t \approx 4.679\,s$ , f) $v(4.679\,s) = -23.354\,\frac{m}{s}$

Step-by-step explanation:

The velocity function can be derived by the differentiating the height function:

$v = 22.5-9.8\cdot t$

Velocities after 2 and 4 seconds are, respectively:

a) $v(2\,s) = 2.9\,\frac{m}{s}$

b) $v(4\,s) = -16.7\,\frac{m}{s}$

The maximum height is reached when velocity is zero. Then:

$22.5-9.8\cdot t = 0$

c) $t = 2.296\,s$

The maximum height is:

d) $h (2.296\,s) = 27.829\,m$

The time required to hit the ground is:

$-4.9\cdot t^{2}+22.5\cdot t +2 = 0$

Roots of the second-order polynomial are:

$t_{1} \approx 4.679\,s$

$t_{2} \approx -0.087\,s$

Only the first root is physically reasonable.

e) $t \approx 4.679\,s$

The velocity when the projectile hits the ground is:

f) $v(4.679\,s) = -23.354\,\frac{m}{s}$

7 0

1 year ago

Which represents the reflection of f(x)= square root x over the x-axis?

antiseptic1488 [7]

The reflection of f(x)=sqrt(x) over x-axis will be represented by option a. This is because it is the reflection of the imaginary part of the function f(x)= sqrt(x). Hence the correct answer is a.

8 0

2 years ago

Read 2 more answers

If the measure of angle 5 equals 102 degrees, then the measure of angle 8 equals what?

kiruha [24]

I hope this helps you

7 0

1 year ago

A financial advisor tells you that you can make your child a millionaire if you just start saving early. You decide to put an eq

Blababa [14]

Answer:

$12159 per year.

Step-by-step explanation:

If I invest $x each year at the simple interest of 7.5%, then the first $x will grow for 35 years, the second $x will grow for 34 years and so on.

So, the total amount that will grow after 35 years by investing $x at the start of each year at the rate of 7.5% simple interest will be given by

$x( 1 + \frac{35 \times 7.5}{100}) + x( 1 + \frac{34 \times 7.5}{100}) + x( 1 + \frac{33 \times 7.5}{100}) + ......... + x( 1 + \frac{1 \times 7.5}{100})$