Mathematics College

How is multiplying and dividing numbers in scientific notation different from adding and subtracting numbers in scientific notation?

Answers

Answer 1
When you multiply or divide in scientific notation, you just add or subtract the exponents. When you add or subtract in scientific notation, you have to make the exponents the same before you can do anything else.
Answer 2
Final answer:

In scientific notation, multiplication involves multiplying the numbers before the exponents and adding the exponents, while division involves dividing the numbers before the exponents and subtracting the exponents. Addition and subtraction require the numbers to have the same exponent.

Explanation:

Multiplying and dividing numbers in scientific notation is different from adding and subtracting It's useful to know how to use scientific notation, especially in fields like astronomy where large numbers are common. Numbers in scientific numeration are written with one number to the left of the decimal point. For example, 500,000,000 will be expressed as 5 × 10⁸.

When we multiply two numbers in scientific notation, we multiply the numbers out front and then add the exponents. For instance, if we are multiplying (3 × 10⁵) × (2 × 10¹⁰), our answer will be 6 × 10¹⁵.

On the other hand, to divide two numbers in scientific notation, we divide the numbers out front and then subtract the exponents. For example, if we are dividing 1.2 x 10⁶ by 2 x 10³, our answer will be 0.6 x 10³ or 6 x 10².

When working with addition and subtraction in scientific notation, the numbers must have the same exponent in order for the operation to be performed.

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Related Questions

Two right triangles are congruent. Find the value of x.
right triangle with angle of 33 degrees, right triangle with angle of 9 x minus 15 degrees
Select one:
a. 5
b. 6
c. 8
d. 12

Answers

Given that the two right triangles are congruent, there are two possibilities.

9x - 15 is equal to the angle 33°  or 9x - 15 is equal to the other angle of the first triangle.

Let's probe with the first option:

9x - 15 = 33 => 9x = 33 + 15 = 48

=> x = 48 / 9 = 5,33, which is no in the list of options.

Now, let's probe the second option.

The other angle of the first right triangle is 90° - 33° = 57°

Then, 9x - 15 = 57

=> 9x = 57 + 15 = 72

=> x = 72 / 9 = 8

Which is the option c. 8.

So, I am sure that if you have a figure it will be compatible with that answer, else yet the procedure to find the answer is what I have used here.

Answer: option c. 8

Reina and Sam are multiplying (84)5 (73)9. Reina's Work Sam's Work (84)5 (73)9 = 84 + 573 + 9 = 89712 (84)5 (73)9 = 84⋅573⋅9 = 820727 Is either of them correct? Explain your reasoning.

Answers

None of this above 84⋅573⋅9  84*5*73*9  ( )= multiplication  all of them should multiply 

Algebra help me please ILL MARK BRAINIEST

Answers

The solution is optio D.

  0     4
- 6     1
  3    -4
 
Rember row times columns.

=>
a11 = 4*0 + 0*(-3) = 0

a12 = 4*1 + 0*1 = 4 + 0 = 4

a21 = -1*0 + 2*(-3) = 0 - 6 = -6

a22 = -1*1 + 2*1 = -1 + 2 = 1

a31 = -3*0 + (-1)*(-3) = 0 + 3 = 3

a32 = -3*1 + (-1)*1 = -3 - 1 = -4


on a certain day the temperature in Seattle was -1 degrees C and the temperature in the Hudson was 18 degrees C is how many degrees lower was the temperature in Seattle

Answers

18-(-1) or 18+1=19 degrees lower

The temperature in Seattle was 19 degrees lower than in the Hudson.

we subtract the temperature of Seattle from the temperature of the Hudson:

18°C - (-1°C) = 19°C

Therefore, the temperature in Seattle was 19 degrees lower than the temperature in the Hudson.

What was the total production of gasoline and kerosene combined?

Answers

それでも、日本人の食生活も急速に変化してきています。

(01.03) A box has dimensions of 14 inches long, 1.5 feet wide, and 7 inches high. What is the volume of the box

Answers

1.5 feet = 12 * 1.5 = 18 inches

14 x 18 x 7 = 1764 cubic inches

Michael sold his house for $548,900, which was 160% of the amount he paid for it. Calculate the amount he paid for the property.

Answers

That would be 548,900  / 1.6  =  $343,062.50 

a large bag of cashews weighs 8 1/3 pounds one serving is 1/3 pound how many servings are in the bag

Answers

A large bag of cashews weighs is 8(1/3) pounds =  which is 25/3 in improper fraction form
one serving bag is 1/3
now,  how many servings are in the bag?
=> 25/3  ÷  1/3
=> 25/3 X 3/1 (changing division into multiplication form)
=> 25, bag are in serving .

Last year Jeremy had $7900 in medical expenses. If his AGI was $89,000, will he be able to deduct his medical expenses and if so, what amount?

Answers

medical expenses are deducted on schedule A - which is required to be over 7.5% of AGI

Answer:

He will be able to deduct his medical expenses by $1225.

Step-by-step explanation:

If his medical expenses are over 7.5% of his AGI he can reduce it to 7.5%.

His AGI was $89,000. How much is 7.5% of that?

0.075*89000 = $6675.

His expenses are over 7.5%, so yes, he can reduce.

He can reduce from $7900 to $6675, so 7900 - 6675 = $1225

ΔABC with vertices A(-3, 0), B(-2, 3), C(-1, 1) is rotated 180° clockwise about the origin. It is then reflected across the line y = -x. What are the coordinates of the vertices of the image?

A(. A'(0, 3), B'(2, 3), C'(1, 1)
B(. A'(0, -3), B'(3, -2), C'(1, -1)
C(. A'(-3, 0), B'(-3, 2), C'(-1, 1)
D(. A'(0, -3), B'(-2, -3), C'(-1, -1)

Answers

Answer: B

Picture 1 shows the reflection of ABC 180° clockwise about the origin. To draw A'B'C' we draw the line segments AO, BO, and CO and extend them such that O is the midpoint of line segments AA', BB', and CC' respectively.

Picture 2 shows the line y=-x (the yellow line.) This is the line containing all points of the form (x, -x), that is, this points contains (1, -1), (-2, 2) etc...

We see that point C' is already on this line, and we draw the reflections of points B and C with respect to this line, to find B'' and C'' with coordinates as shown in the figure.



Answer:

B (. A'(0, -3), B'(3, -2), C'(1, -1)

Step-by-step explanation:

A driveway is 40 yards long. About how many meters long is it? Round to the nearest hundredth

Answers

The driveway is 36.576 meters long.

F=J+Jrt solve following formula for t

Answers

F=j+jrt
F-j=jrt
t=(F-j)/jr
Final answer:

To solve the formula F=J+Jrt for 't', first, subtract 'J' from both sides to get F-J=Jrt. Then, divide both sides by 'Jr', for the final equation for 't' = (F-J)/Jr.

Explanation:

This physics-related mathematics question is asking you to solve the given formula F=J+Jrt for 't'. To isolate 't', we first want to eliminate 'J' from the right side. We do this by subtracting 'J' from both sides of the equation. This gives us F-J=Jrt.

Then, we divide both sides by 'Jr'. When we do this, we are left with t=(F-J)/Jr as the rearranged formula with 't' as the subject. This results in 't' being isolated in the equation, which answers the student's question.

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"how many terms are there in the algebraic expression""

Answers

so in this quistoon that you are asking there is 6 in here because you didnt show the problem so i cant help you out

Find each percent increase. From 24 teachers to 30 teachers.

Answers

percent increase or decrease is change divided by original x 100

then i solve for you





your welcome.


25%

Two different ways to find the difference for 12-3

Answers

You can either ask "How much is left when you take 3 away from 12?", or you can ask "How far apart are the numbers 12 and 3 on the number line?"

Another way you could think about it is "what number do I have to add to 3 to get to 12?"
First, you could count from 3 up to 12 and record the number between them. Second, you could use mental math and try to figure out mentally. The answer is 12-3= 9

What is the greatest common factor of 12 and 42

Answers

The greatest common factor for 12 and 42 is 6

The greatest common factor of 12 and 42 is 6.

What is Number system?

A number system is defined as a system of writing to express numbers.

We need to find the greatest common factor of 12 and 42.

The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share.

The factors of 12 are  1, 2, 3, 4,6 and 12.

The factor of 42 are 1, 2, 3, 6, 7, 14, 21 and 42.

Let us find the common factors of 12 and 42.

The common factors are 1, 2 , 3, 6.

Among the common factors which is greatest value.

Among 1,2,3 and 6 the number 6 is greatest.

Hence,  the greatest common factor of 12 and 42 is 6.

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What are the quotient and remainder when
a.19 is divided by 7?
b.−111 is divided by 11?

Answers

a. quotient when 19÷7 = 2
the remainder = 5

b quotient = -10
remainder = 1

How many pounds of cashew nuts worth 75 cents a pound must be mixed with 10 pounds of pecans worth $1.50 a pound to make a mixture worth $1.00 a pound? Which of the equations could be used to solve for p, the pounds of cashew nuts?

Answers

Let c represent the weight of cashews and p the weight of pecans.

Then c + 10 = total weight of the nut mixture.

An equation for the value of the mixture follows:

 $1.50(10 lb) + $0.75c = (c+10)($1.00)

Solve this equation for c:  15 + .75c = c + 10.  Subtract .75c from both sides:

15 = 1c - 0.75c + 10.  Then 5=0.25c, and c = 5/0.25, or 20.

Need 20 lb of cashews.


Check:  the pecans weigh 10 lb and are worth $1.50 per lb, so the total value of the pecans is $15.  The total value of the cashews is (20 lb)($0.75/lb), or $15.     Does (20 lb + 10 lb)($1/lb) = $15 + $15?  Yes.  So c= 20 lb is correct.

y=-2/5x+4 in standard form

Answers

1、 -10
2、 4
4、 Y=-2/5x+4

Solve the equation by the zero factor property 6x^2 -5x -6=0

Answers

First, you need to factor the polynomial.

I'll use the trial and error method.

6x^2 - 5x - 6 = 0

6 has factors
6 and 1
3 and 2

I'll try 3 and 2 first.

(3x     )(2x      ) = 0

Now we need to factor -6.
-6 factors into
-1, 6
-6, 1
-2, 3
-3, 2

Now we need to see if one of these pairs of factors placed correclty will factor the trinomial.

(3x + 2)(2x - 3) = 0

That did it.

Now we use the zero factor property.

3x + 2 = 0 or 2x - 3 = 0

3x = -2      or 2x = 3

x = -2/3     or x = 3/2

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You want to find out how many baseball cards Ryan had to begin with. Which situation about his card collection best represents the equation
x/2-1=24

A. Half of his cards were ruined after they got wet, and then he lost 1 card. After that, he had 24 cards left.

B. He lost 1 card, and then half of his cards were ruined after they got wet. After that, he had 24 cards left.

C. Half of his cards were ruined after they got wet, and then he bought 1 more card. After that, he had 24 cards left.

D. He bought 1 card, and then half of his cards were ruined after they got wet. After that, he had 24 cards left.

Which situation about Connor’s commission best represents the inequality 40 + 10x ≥ 100?



A.Connor earns $10 per day plus a $40 commission on each item he sells. How much will he earn if he sells 100 items?

B.Connor earns $40 per day plus a $10 commission on each item he sells. How much will he earn if he sells 100 items?

C.Connor earns $40 per day plus a $10 commission on each item he sells. How many items must he sell to earn at least $100?

D.Connor earns $40 per day plus a $10 commission on each item he sells. How many items must he sell to earn no more than $100?

Answers

The first one is a. If you solve for x, equals 50. And if you retrace the steps described in a, describes the situation. Lost half, then one more.

The second is c, the inequality describes the condition and solves how many commissions he needs to earn at least 100 or more dollars a day.

Three friends all live on the same street that runs west to east. Ben lives 4 blocks from Ann. Carl lives 2 blocks from Ben. If the street is represented by a number line and Ann​'s house is located at​ 0, what are the possible locations for Carl​'s ​house?

Answers

Answer:

The possible locations are,

2, -2, 6 or -6

Step-by-step explanation:

Given,

The location of Ann's house in the number line = 0,

∵ Ben lives 4 blocks from Ann.

So, the possible location of Ben's house =  4 ( right of ann's house ) or - 4 ( left of ann's house )

Now, Carl lives 2 blocks from Ben,

So, the possible location of Carl's house

Case 1 : If Ben's house location is 4 = 2 ( left of ben's house ) or 6 ( right of ben's house )

Case 2 : If Ben's house location is -4 = -2 ( right of ben's house ) or -6 ( left of ben's house )

The possible locations of Carl's house are - 6, 6, 2 or - 2

Let :

Ben's location = B

Carl's position = C

Ann's position = A

Using the Number line illustration :

Ann's position = 0

Ben's possible positions :

4 blocks(units) from Ann = ± 4

Carl's location :

2 blocks from Ben-4 ± 2 = (-4 - 2) or (-4 + 2) = - 6 or - 2 +4 ± 2 = (4 + 2) or (4 - 2) = 6 or 2

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there are 3/4 of a pizza left over from last night how many 1/8 portions are there

Answers

3/4 of the pizza is left

3/4 = 6/8

There are 6 "1/8" portions left

hope this helps

Evaluate the dot product a⃗ ⋅b⃗ of a⃗ =3i^−8j^ and b⃗ =−2i^−6j^.

Answers

The "dot product" of two vectors has several different formulas.

Since you are given the x- and y-coordinates of both vectors a and b, we can apply the formula

a dot b  = ax*bx + ay*by, where ax=x-component of vector a, by=y comp of vector b, and so on.  

So, for the problem at hand, ax * bx + ay * by becomes

3(-2) + (-8)(-6) = -6 + 48 = 42 (answer).  Note that the dot product (or "scalar product" is itself a scalar.
Final answer:

The dot product of vectors a⃗ =3i^−8j^ and b⃗ =−2i^−6j^ is calculated by multiplying the corresponding components of the vectors and summing the results, giving a final dot product of 42.

Explanation:

The dot product of two vectors a and b is calculated by multiplying the corresponding components of the vectors and summing the results. So, given the vectors a⃗ =3i^−8j^ and b⃗ =−2i^−6j^, the dot product can be found as follows:

a⃗ ⋅b⃗ = (a_x * b_x) + (a_y * b_y)

Therefore, substituting the known values: a⃗ ⋅b⃗ = (3 * -2) + (-8 * -6) = -6 + 48 = 42

So, the dot product a⃗ ⋅b⃗ for vectors a⃗ =3i^−8j^ and b⃗ =−2i^−6j^ is equal to 42.

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A person who is 6ft tall walks away from a streetlight. When the person is 15 feet away from the light, the tip of his shadow is 5 feet in front of him. Find the height of the streetlight

Answers

We essentially have a ratio here:
[tex]\frac{shadow}{actual}[/tex]

Since we know the ratio is going to stay constant at [tex]\frac{5}{6}[/tex], we can use this to find the height of the lamp along with the information that the total distance from the lamp to the tip of his shadow is 20:
[tex]\frac{5}{6}=\frac{20}{h}[/tex]
[tex]5h=120[/tex]
[tex]h=24[/tex]

Solve the absolute value equation. |x| = –45

Answers

Absolute value of x=-45 is x=45             Absolute value just means that you make everything positive.






how much apple juice does each person get if 6 people share 2 and 2/3 quarts equally

Answers

First convert 2 2/3 to an improper fraction. That comes out to 8/3. Then multiply 8/3 with the inverted fraction 1/6. It comes out to be 8/18, but most require simplification, which is 4/9 quart per person.

The fraction of apple juice shared by 6 people is A = 4/9 of the apple juice

What is a Fraction?

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given data ,

Let the fraction of apple juice shared by 6 people be A

Let the total number of people be represented as n = 6 people

Now , the fraction of total amount of apple juice = 2 2/3

The fraction of total amount of apple juice T = ( 8/3 ) of apple juice

And , the equation is

A = fraction of total amount of apple juice T / total number of people n

On simplifying , we get

A = ( 8/3 ) / 6

A = ( 8/18 )

Divide by 2 on both numerator and denominator of the fraction , we get

A = 4/9 of the apple juice

Therefore , the value of A is 4/9

Hence , the fraction of apple juice is ( 4/9 ) equally

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Find the simple interest. Principal ​$200 rate 13​% time 33 months. The interest is ​$ nothing. ​(Round to the nearest​ cent.)

Answers

there are 12 months in a year, so in 33 months, there are 33/12 years then.

[tex]\bf \qquad \textit{Simple Interest Earned}\\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\to& \$200\\ r=rate\to 13\%\to \frac{13}{100}\to &0.13\\ t=years\to &\frac{33}{12} \end{cases} \\\\\\ I=200\cdot 0.13\cdot \cfrac{33}{12}[/tex]

how many times can 36 go into 300

Answers

8.333333 so lets just say 8 
36 can go into 300 around 8 times. 8.3 to be more accurate.

A car is driving at the speed of 58 km/h.How much time will it take to drive for distance 32 miles?

Answers

53 Minutes and 16 seconds
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