All categories

3 years ago

The answer is D. explain how to get the answer??

Mathematics

1 answer:

ivolga24 [154]3 years ago

6 0

Answer:

$- 5 \leqslant x - 2 < 4$

$- 5 + 2 \leqslant x < 4 + 2$

$3 \leqslant x < 6$

Step-by-step explanation:

add +2 for both sides

to make x as a subject

You might be interested in

I need help please!?

astra-53 [7]

Its 3 and 7 so write the as a equation

3 is on the y axis and 7 is on the x axis

so 3y and 7x

3 0

3 years ago

Write the standard form of the line that passes through the point (-2, 4) and is parallel to x - 2 y = 6.

Alex787 [66]

x-2y=6

-2y=-x+6

2y=x-6

y=0.5x-3

Parallel=same slope

y=0.5x+5

5 0

4 years ago

What is the nth term rule of the quadratic sequence below?

Ahat [919]

Answer:

The nth term = n^2 - 2n - 3.

Step-by-step explanation:

Here, we will be finding the nth term of a quadratic number sequence. A quadratic number sequence has nth term = an² + bn + c

Example 1

Write down the nth term of this quadratic number sequence.

-3, 8, 23, 42, 65...

Step 1: Confirm the sequence is quadratic. This is done by finding the second difference.

Sequence = -3, 8, 23, 42, 65

1st difference = 11,15,19,23

2nd difference = 4,4,4,4

Step 2: If you divide the second difference by 2, you will get the value of a.

4 ÷ 2 = 2

So the first term of the nth term is 2n²

Step 3: Next, substitute the number 1 to 5 into 2n².

n = 1,2,3,4,5

2n² = 2,8,18,32,50

Step 4: Now, take these values (2n²) from the numbers in the original number sequence and work out the nth term of these numbers that form a linear sequence.

n = 1,2,3,4,5

2n² = 2,8,18,32,50

Differences = -5,0,5,10,15

Now the nth term of these differences (-5,0,5,10,15) is 5n -10.

So b = 5 and c = -10.

Step 5: Write down your final answer in the form an² + bn + c.

2n² + 5n -10

Example 2

Write down the nth term of this quadratic number sequence.

9, 28, 57, 96, 145...

Step 1: Confirm if the sequence is quadratic. This is done by finding the second difference.

Sequence = 9, 28, 57, 96, 145...

1st differences = 19,29,39,49

2nd differences = 10,10,10

Step 2: If you divide the second difference by 2, you will get the value of a.

10 ÷ 2 = 5

So the first term of the nth term is 5n²

Step 3: Next, substitute the number 1 to 5 into 5n².

n = 1,2,3,4,5

5n² = 5,20,45,80,125

Step 4: Now, take these values (5n²) from the numbers in the original number sequence and work out the nth term of these numbers that form a linear sequence.

n = 1,2,3,4,5

5n² = 5,20,45,80,125

Differences = 4,8,12,16,20

Now the nth term of these differences (4,8,12,16,20) is 4n. So b = 4 and c = 0.

Step 5: Write down your final answer in the form an² + bn + c.

5n² + 4n

5 0

3 years ago

Christy went on a round-trip bicycle ride starting at her house. When she left, she traveled downhill at a rate of 24 kilometers

vazorg [7]

Since this is a round-trip, Christy covered the same distance in both journey.

Let the distance covered be
$d$

When she left the house, she travelled at
$24 \: kph$

We were given the average speed to be
$20 \: kph$

Meaning if we add the speed in the return journey to 24 kph and find the average , we must obtain 20 kph.

Let
$x$
be the speed in the return trip.

Then
$\frac{24 + x}{2} = 20$

We solve for x to obtain;

$24 + x = 40$

$x = 40 - 24 = 16 \: kph$

We were also told that she took half an hour longer in the return trip.

If we let
$t$
represent the time the first journey took, then the return trip will take

$(t + 0.5) \: hours$

Now we have the following:

$First Journey$

$speed = \frac{d}{t}$

$24 = \frac{d}{t}$

$\Rightarrow d = 24t - - - (1)$

$Second Journey$

$16 = \frac{d}{t + 0.5}$

$\Rightarrow d = 16(t + 0.5) - - - (2)$

Now let us equate the two equations to obtain,

$16(t + 0.5)= 24t$

We expand and simplify to obtain;

$16t + 8= 24t$

This implies that,

$8= 24t - 16t$

.
$8= 8t$

$t = 1$

Hence the return trip took,

$t + 0.5 = 1 + 0.5 = 1.5$

hours.

4 0

4 years ago

The polynomial 4x^3 - 6x^2 + 8x – 12 can be grouped in different ways to factor by

zubka84 [21]

Answer:

(4x3-6x) + (8x-12)= 2x

(4x3+8x) + (-6x2-12)= 2(2x-3) (x^2+2)

Step-by-step explanation:

All you have to do is simplify.

8 0

4 years ago