All categories

2 years ago

Solve the inequality -3x<54

Mathematics

1 answer:

kifflom [539]2 years ago

6 0

Answer:

x<-18

Step-by-step explanation:

you divide -3 by both sides.

You might be interested in

I dont understand how to do this, looking for someone who can help

earnstyle [38]

The answer should be a segment. have a great day :)))

8 0

3 years ago

Question 1:

Morgarella [4.7K]

Answer:

Step-by-step explanation:

KE = ½mv²

KE₁₀ = ½(1100)10² = 55000 = 55 kJ

KE₃₀ = ½(1100)30² = 495000 = 495 kJ

9 times greater

3 0

3 years ago

Dont really understand how to do this

bija089 [108]

Answers:

$t_{10} = -22 \ \text{ and } S_{10} = -85$

========================================================

Explanation:

$t_1 = \text{first term} = 5\\t_2 = \text{first term}-3 = t_1 - 3 = 5-3 = 2$

Note we subtract 3 off the previous term (t1) to get the next term (t2). Each new successive term is found this way

$t_3 = t_2 - 3 = 2-3 = -1\\t_4 = t_3 - 3 = -1-3 = -4$

and so on. This process may take a while to reach $t_{10}$

There's a shortcut. The nth term of any arithmetic sequence is

$t_n = t_1+d(n-1)$

We plug in $t_1 = 5 \text{ and } d = -3$ and simplify

$t_n = t_1+d(n-1)\\t_n = 5+(-3)(n-1)\\t_n = 5-3n+3\\t_n = -3n+8$

Then we can plug in various positive whole numbers for n to find the corresponding $t_n$ value. For example, plug in n = 2

$t_n = -3n+8\\t_2 = -3*2+8\\t_2 = -6+8\\t_2 = 2$

which matches with the second term we found earlier. And,

$tn = -3n+8\\t_{10} = -3*10+8\\t_{10} = -30+8\\t_{10} = \boldsymbol{-22} \ \textbf{ is the tenth term}$

---------------------

The notation $S_{10}$ refers to the sum of the first ten terms $t_1, t_2, \ldots, t_9, t_{10}$

We could use either the long way or the shortcut above to find all $t_1$ through $t_{10}$ . Then add those values up. Or we can take this shortcut below.

$Sn = \text{sum of the first n terms of an arithmetic sequence}\\S_n = (n/2)*(t_1+t_n)\\S_{10} = (10/2)*(t_1+t_{10})\\S_{10} = (10/2)*(5-22)\\S_{10} = 5*(-17)\\\boldsymbol{S_{10} = -85}$

The sum of the first ten terms is -85

-----------------------

As a check for $S_{10}$ , here are the first ten terms:

t1 = 5
t2 = 2
t3 = -1
t4 = -4
t5 = -7
t6 = -10
t7 = -13
t8 = -16
t9 = -19
t10 = -22

Then adding said terms gets us...

5 + 2 + (-1) + (-4) + (-7) + (-10) + (-13) + (-16) + (-19) + (-22) = -85

This confirms that $S_{10} = -85$ is correct.

6 0

2 years ago

Prove using coordinate geometry. Prove that the points (0,0), (4,0), (4, 4) and (0, 4) create a rhombus and then show that the m

BaLLatris [955]

Answer:

IDK

Step-by-step explanation:

IDK

5 0

3 years ago

In AOPQ, m2O = (2x – 5)º, m P = (3x – 8)°, and mZQ = (10x – 17).<br> What is the value of x?

Misha Larkins [42]

9514 1404 393

Answer:

x = 14

Step-by-step explanation:

The sum of angles in a triangle is 180°:

∠O +∠P +∠Q = 180°

(2x -5)° +(3x -8)° +(10x -17)° = 180°

15x -30 = 180 . . . . . divide by °, collect terms

x -2 = 12 . . . . . . . . . divide by 15

x = 14 . . . . . . . . . . . .add 2

3 0

3 years ago