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3 years ago

What is the product written in scientific notation? (5.91×10−3)⋅(8.7×1010)

2 answers:

5 0

$(5.91\cdot10^{-3})\cdot(8.7\cdot10^{10})=(5.91\cdot8.7)\cdot(10^{-3}\cdot10^{10})\\\\=51.417\cdot10^{-3+10}=51.417\cdot10^7=5.1417\cdot10\cdot10^7\\\\=\boxed{5.1417\cdot10^8}\to\boxed{B.}$

$Used:\\\text{Associative property}\ (a\cdot b)\cdot c=a\cdot(b\cdot d)\\\\a^n\cdot a^m=a^{n+m}$

romanna [79]3 years ago

4 0

(5.91×10^−3)⋅(8.7×10^10)

= (5.91 x 8.7) x 10^(- 3 + 10)

= 51.417 x 10^7

= 5.1417 x 10^8

Answer is

B. 5.1417 × 10^8

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Graph the image of this quadrilateral after a dilation with a scale factor of 4 centered at the origin

Brut [27]

Answer: The image is attached.

Step-by-step explanation:

A Dilation is defined as a transformation in which the image and the pre-image have the same shape, but their sizes are different.

When the scale factor is greater than 1, the image obtained after the dilation is greater than the pre-image and it is an "Enlargement".

When the scale factor is is between 0 and 1, the image obtained after the dilation is smaller than the pre-image and it is an "Reduction".

In this case we know that the scale factor is:

$scale\ factor=4$

Since:

$4>1$

It is an Enlargement.

You can identify that the vertices of the pre-image shown in the figure, are:

$(-2,1)\\\\(-1,2)\\\\(0,0)\\\\(-1,-2)$

So you need to multiply the coordinates of those vertices by 4 in order to get the coordinates of the image;

$((-2)(4),1(4))=(-8,4)\\\\((-1)(4),(2)(4))=(-4,8)\\\\((0)(4),(0)(4)=(0,0)\\\\((-1)(4),(-2)(4))=(-4,-8)$

Now you can draw it (The image is attached).

8 0

3 years ago

A geometric progression has a third term of 20 and a sum of infinity which is 3 times the first term. Find the first term

Anna007 [38]

Answer: the first term is 45

Step-by-step explanation:

Step 1: The formular for the nth term is ar^n-1 and since we're solving for the third term ar^3-1 = ar² which is equal to 20

So ar²= 20 and we make this equation i

Step 2: the formular for the sum of infinity is Sn = a/(1-r) and according the question the sum of infinity is equals to 3 *A ( A means the first term)

Further simplification gives us

3a= a/(1-r)

We simplify Futher by multiplying both sides by (1-r)

3a.(1-r) = a/(1-r).(1-r)

3a(1-r)=a

= 3a-3ar=a

Make 3ar the subject of the formula

3ar= 2a and lets make this equation (ii)

Step 3: From the first equation since ar²=20, let's make a the subject of the formula by dividing both sides by r²

Ar²/r² = 20/r²

A=20/r²lets make this equation (iii)

Step 4: subtitle a as 20/r² into equation (ii)

Since 3ar=2a

Then 3.(20/r²).r = 2. 20/r²

= (60/r²) .r = 40/r²

60/r = 40/r2

Multiplying both sides by r² gives us

60r = 40

Divide both sides by 20 gives us

= 3r= 2

Divide both sides by 3 gives us

= r = 2/3

Step 5: substitute r for 2/3 in equation i

ar²= 20

a. (2/3)2 = 20

= a.4/9 = 20

= 4a = 180

= a = 180/4

a = 45

5 0

3 years ago

Choose the correct simplification of the expression −3x2(5x − 4x2 − 6).

Bess [88]

Answer B.
$- 3 {x}^{2} (5x - 4 {x}^{2} - 6) \\ = - 15 {x}^{3} + 12 {x}^{4} + 18 {x}^{2} \\ = 12 {x}^{4} - 15 {x}^{3} + 18 {x}^{2}$

8 0

3 years ago

Read 2 more answers

The graph of an absolute value function opens up and has a vertex of (0, -3).

Ad libitum [116K]

Absolute value function domain is all real numbers

absolute value has vertex of(0,-3)
and it opens up
means that the lowest y value is -3
highest is infinity

domain=-inifnity to infinity
range=-3 to positive initnify

the answer is C for the domain and B for the range

4 0

2 years ago

Read 2 more answers

Jason complete 5/8 of his test and 10/25 of his homework. What fraction of his homework does he still need to complete?

sineoko [7]

Answer:

3/4

Step-by-step explanation:

Because the total homework would be 25/25

$\frac{25}{25}-\frac{10}{25} =\frac{15}{25}$

15/20 can be reduced to 3/4

4 0

3 years ago