All categories

3 years ago

Perform the following calculations without rewriting the numbers in decimal form.

Mathematics

1 answer:

RSB [31]3 years ago

6 0

Answer:

Answer will be $140\times 10^{13}$

Step-by-step explanation:

We have to perform the calculation $(1.42\times 10^{15}-2\times 10^{13})$ without changing into decimal

$1.42\times 10^{15}$ can be written as $142\times 10^{13}$

So $1.42\times 10^{15}-2\times 10^{13}=(142\times 10^{13}-2\times 10^{13})$

Now taking $10^{13}$ common

$10^{13}(142-23)=140\times 10^{13}$

You might be interested in

Nick will move a storage bin from its current location to the new location shown on the coordinate plane. Describe how Nick coul

nlexa [21]

Answer:

Move downward by 7 units

Move leftward by 6 units

$(x,y) \to (x -6,y-7)$

Step-by-step explanation:

Given

See attachment for grid

Required

The transformation from the current location to the new location

To do this, we pick two corresponding points on the current location and the new location.

We have:

$A = (3,2)$ -- Current location

$A' = (-6,-5)$ -- New location

First, move A downwards by 7 units.

The rule to this is:

$(x,y) \to (x,y-7)$

So, we have:

$(3,2) \to (3,2-7)$

$(3,2) \to (3,-5)$

Next, move the above points leftward by 6 units.

The rule to this is:

$(x,y) \to (x-6,y)$

So, we have:

$(3,-5) \to (3-6,-5)$

$(3,-5) \to (-3,-5)$

6 0

3 years ago

The quotient of (x^3+3x^2-4x-12)/(x^2+5x+6)

Elis [28]

Answer: The quotient is (x-2).

Step-by-step explanation:

Since we have given that

$f(x)=(x^3+3x^2-4x-12)\\\\and\\\\g(x)=x^2+5x+6\\\\So,\ \frac{\left(x^3+3x^2-4x-12\right)}{\left(x^2+5x+6\right)}$

Now, we have to find the quotient of the above expression.

So, here we go:

$Factorise\ (x^3+3x^2-4x-12)\\\\=\left(x^3+3x^2\right)+\left(-4x-12\right)\\\\=-4\left(x+3\right)+x^2\left(x+3\right)\\\\=\left(x+3\right)\left(x^2-4\right)$

Now, we will divide the above simplest form with g(x):

$\frac{\left(x+3\right)\left(x^2-4\right)}{\left(x+2\right)\left(x+3\right)}\\\\=\frac{x^2-4}{x+2}\\\\=\frac{\left(x+2\right)\left(x-2\right)}{x+2}\ using\ (a^2-b^2)=(a+b)(a-b)\\\\=x-2$

Hence, the quotient is (x-2).

6 0

3 years ago

Read 2 more answers

What is the range of the function shown in the graph?

natali 33 [55]

Answer:

Step-by-step explanation:

-∞<y<5

3 0

3 years ago

What's the average of 19 from 45

Naya [18.7K]

The average can be calclculated as follows:
average = sum of number/number of numbers
average = (19+45) / 2 = 64/2 = 32

4 0

3 years ago

Read 2 more answers

Graph the line with slope <br> −3/4<br><br> passing through the point <br> , (3,3)

Nookie1986 [14]

Y = mx + b
slope(m) = -3/4
(3,3)....x = 3 and y = 3
now we sub and find b, the y int
3 = -3/4(3) + b
3 = -9/4 + b
3 + 9/4 = b
12/4 + 9/4 = b
21/4 = b.....or 5.25 for graphing purposes

so ur equation is : y = -3/4x + 21/4

ur y int = (0,21/4) or (0,5.25)

ur x int can be found by subbing in 0 for y and solving for x
y = -3/4x + 21/4
0 = -3/4x + 21/4
3/4x = 21/4
x = 21/4 * 4/3
x = 84/12 = 7.....so ur x int is (7,0)

so plot ur points (7,0) and (0,5.25)....now start at (0,5.25) and since the slope is -3/4, come down 3 spaces and go to the right 4 spaces, then down 3, and to the right 4 and u will eventually cross the x axis at (7,0)

8 0

3 years ago