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If you have an equation where two number share the same base (ex: [tex]10 ^{x} * 10 ^{y}[/tex]), you keep the base the same and add the exponents ([tex]10 ^{x+y}[/tex]). So your first problem 10^5 * 10^7 = 10^12.
Dividing with exponents is just the opposite. If two numbers share the same base but have different exponents (ex: [tex] \frac{10 ^{x} }{10 ^{y} } [/tex]), you keep the base the same and subtract the exponents ([tex]10 ^{x-y} [/tex]). If this yields a negative exponent, you send it to the denominator and it becomes positive (ex: [tex]10 ^{-2} = \frac{1}{10 ^{2}} [/tex])
When simplifying expressions where you have the exponent of an exponent (ex: [tex](10 ^{x}) ^{y}[/tex]), you multiply the exponents together to create one power ([tex]10 ^{x*y}[/tex]. Same rule with yielding negative exponents applies but you should be okay looking at your worksheet.
If you need additional help still you can send me a message or reply in a comment and I'll come back. Same for if you need me to do examples from your piece of paper.
Related Questions
The Dalton’s completed 20% of their 2170 mile tripe the first day- how many miles did they travel the first day? How many miles of their trip did they still have to travel?
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round 76.3 to the nearest whole number
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185/100 + 50% + 4%
This is for a mastery challenge and for this lesson alone, I've been getting the answers wrong. If you can help me and explain it to me!
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= (185+50+4)/100
=239/100
=2.39
To do that with a fraction divide the numerator by the denominator.
185 divided by 100 = 1.85
To convert a percent to a demical move the number to the right twice. Or divide the number by 100. 50 divided by 100 = 0.5
4 divided by 100 = 0.04
Now add :)
1.85 + 0.5 + 0.04 = 2.39
Wally is playing with his toy robot. The robot's battery is 80% full when he starts playing with it. The battery drains to 74% after Wally plays with the robot for 40 minutes. If t represents the time elapsed in minutes and l represents the battery level, which of the following equations can be used to model this situation?
A. l = -0.15 + 80t
B. l = -0.15t + 80
C. l = 80t + 0.15
D. l = -0.15t - 80
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For your question
Answer:
B. l = -0.15t + 80
Step-by-step explanation:
From the options we can see that the relation between the battery level (I) and the time elapsed (t) is modeled by the equation of a line, that is:
I = a*t + b
where a and b are some constants, I is in % and t is in minutes.
At t = 0 (when Wally starts to play) the battery is 80%, that is:
80 = a*0 + b
80 = b
At t = 40 minutes the battery is 74%, then:
74 = a*40 + 80
74 - 80 = a*40
-6 = a*40
-6/40 = a
-0.15 = a
Then, the equation is I = -0.15*t + 80
Stock in Company XYZ decreased from $14 a share to $9 a share. What is the percent decrease in stock price?
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so:
9/14 × 100
can I get help with these questions
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A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $75. A season ski pass costs $400. The skier would have to rent skis with either pass for $20 per day. How many days would the skier have to go skiing in order to make the season pass less expensive than the daily passes?
(please help I suck at word problems)
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Which is a better estimate for the length of an ironing board?
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A better estimate for the length of an ironing board would be 120 inches, or 10 feet. This exercise illustrates the importance of carefully calculated approximations rather than relying on rough 'guesstimates'.
Explanation:A better estimate for the length of an ironing board would be 120 inches, or 10 feet. This estimate is closer to the final approximate value mentioned in the discussion. However, the early estimate of 3 inches was significantly off. This exercise illustrates the importance of carefully calculated approximations rather than relying on rough 'guesstimates'.
Given: l | | m
m∠4 = 105° and m∠6 = 50°.
m∠2 =
50°
55°
75°
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Answer:
x = 55°
Step-by-step explanation:
<4 = 105
<4 + <3 = 180 (supplementary angles, form a line)
180-105= 75
<3 = 75
The interior angles of a triangle always equal 180 degrees.
<3 = 75 degrees, <6 = 50, <2 = x
75+50+x = 180
125 + x = 180
x = 55°
I’m not sure how to “explain your math thinking”.
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[tex]10 + 7 - 1[/tex]
thats the way i would think about it
Answer:
9 + 7 = 16Step-by-step explanation:
The math thinking refers to the process you did to solve the sum 9 + 7.
To solve this we could think the following process:
1. We complete the first number to 10.
2. The completion subtracted one unit from 7, so now it's 6.
3. Then we sum the ten and the six, it's easier to operate with tens.
Therefore, the answer is 16.
Remember that not everyone solve math problems and exercises the same way, because we all are different from each other.
4a-|3b+2c|
solving equations involving absolute value please help
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Rohan is checking in poodles for a dog show. A miniature poodle must be between 10 in. and 15 in. at the shoulder. The body length must be no more than 16 in. In addition, the poodle’s shoulder height must be no more than 1 in. longer than its body length. The graph shows the feasible region, where x represents the poodle’s body length and y represents the shoulder height. Which ordered pairs meet all the constraints for a successful poodle measurement and make sense in context of the situation? Select each correct answer. (11, 9) (12, 10.5) (15, 11) (10, 12) (11, 14)
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it might be c...
A staircase has 105 blocks, how many stairs does it have?
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2 3
3 6
4 10
5 15
6 21
7 28
8 36
9 45
10 55
11 66
12 78
13 91
14 105
15 120
16 136
17 153
18 171
19 190
20 210
21 231
22 253
23 276
24 300
here is a spreadsheet to help you understand the stair problem notice for 1 step 1 block, 2 step, 3 block, 3 step, 6 block and so on notice the blocks for the number of a step is that step plus all the other blocks needed to make all the one(s) below it. Notice it takes 105 blocks to make 14 steps.
So if you are familiar with the summation process you would add the number that go with that stair with all the stairs below it. example step 5 blocks would be 5 + 4 + 3 + 2 +1 or 15 blocks. I hope this gets you started. The second part I do not understand the problems because they are not equations. NO equal signs
glad if it helps
The straight-line distance after walking 9 blocks east and 5 blocks north can be calculated using the Pythagorean theorem, resulting in a distance of approximately 10.3 blocks, which is shorter than the total 14 blocks walked.
Explanation:The question involves finding the straight-line distance between two points in a two-dimensional city grid.
When walking 9 blocks east and then 5 blocks north, you are creating a right-angled triangle where the straight-line distance is the hypotenuse of the triangle.
To calculate this, we can use the Pythagorean theorem.
To find the straight-line distance, you square the number of blocks walked east (9 blocks squared) and north (5 blocks squared), and then find the square root of their sum:
Hypotenuse = √((9 blocks)² + (5 blocks)²).
This results in a straight-line path of √(81 + 25) = √106, which is approximately 10.3 blocks.
Hence, even though you walked 14 blocks, the straight-line path is only about 10.3 blocks long, which is considerably shorter than the path you walked.
Which two steps are needed to multiply 4,087 × 5 using partial products?
Choose exactly two answers that are correct.
A.
Multiply 80 × 5.
B.
Write 4,087 in expanded form.
C.
Multiply 400 × 5.
D.
Add 4,087 and 5.
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Anna buys 24 seeds and plants 3 in each pot. She has 5 pots. How many more pots does Anna need to plant all of her seeds
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The number of pots required to plant 24 seeds will be 8.
What is an expression?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
Given that Anna buys 24 seeds and plants 3 in each pot. She has 5 pots.
The number of the pots will be calculated as Anna needs 3 more pots. 3 times 5 is 15 seeds. And she has 24 seeds. so 24 divided by 3 is 8. 8 minus 5 is 3.
Number = 24 / 3 = 8 pots
Therefore, the number of pots required to plant 24 seeds will be 8.
To know more about an expression follow
https://brainly.com/question/5174883
#SPJ5
A bakery makes 184 loaves of bread in 4 hours how many loaves of bread did the bakery make in one hour
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They made 46 loaves
The volume of a cube depends on the length of its sides. This can be written in function notation as a v(s). What is the best interpretation of v(3)= 27?
Please show all work.
A. 3 of these cubes will have a total of 27 cubic feet
B. 3 sides of the cube have a total length of 27 feet
C. A cube with side length's of 3 feet has a volume of 27 cubic feet.
D. A cube with a volume of 3 cubic feet has side lengths of 27 feet
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The best interpretation of the function given as v(3) = 27 would be a cube with side lengths of 3 feet has a volume of 27 cubic feet.
I hope this helps!
Use words to write 36427580
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Choose the point-slope form of the equation below that represents the line that passes through the point (−1, 6) and has a slope of −3. (1 point)
A) y − 6 = −3x − 3
B) y − 6 = −3(x + 1)
C) y = −3x + 3
D) 3x + y = 3
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The point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
We have the point (-1, 6) and the slope m = -3. Substitute:
[tex]y-6=-3(x-(-1))\\\\\boxed{y-6=-3(x+1)}\to\boxed{B)}[/tex]
8 gallons to fill tank
Gas cost $3.26
What was the gas mileage for 296 mil trip
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Jimmy made a 15% profit on the sale of a custom designed boat, and the original cost of the boat was $15,000. The boat sold for how much?
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Answer:
the boat was sold for $17,250
Step-by-step explanation:
Jimmy made a 15% profit, that means that the 15% of the cost is going to be his profit, so the 15% of $15,000 is:
$15,000(0.15)= $2,250
If his profit is 2,250, the price of the boat is going to be the initial cost plus the profit. So:
Price=$15,000 + $2,250 = $ 17,250
Then, the boat was sold for $17,250
Using proportions and the profit concept, it is found that the boat sold for $17,250.
This question is solved by proportions, using a rule of three.Profit of 15% means that the sales price was 15% more than the original cost. Thus, the original cost of $15,000 is worth 100% = 1, while the sales price of x is worth 100% + 15% = 115% = 1.15.The rule of three is:
$15,000 - 1
$x - 1.15
Applying cross multiplication:
[tex]x = 15000(1.15) = 17250[/tex]
The boat sold for $17,250.
A similar problem is given at https://brainly.com/question/24373628
What is 5374 multiplied by 345?
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1,854,030 is your answer
hope this helps
There are 3,812 people seated in a concert hall. There are 48 seats in each row. Estimate the number of rows of seats that are occupied
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15 POINTS! PLEASE ANSWER A.S.A.P.!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Rapid rental car charges a $40 rental fee, $15 for gas, and $0.25 per mile driven. For the same car, Capital Cars charges $45 for rental and gas and $0.35 per mile.
A. For how may miles is the rental cost at both companies the same?
B. What is that cost?
Explain both part A and part B!
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r1 + g1 + 0.25m = r2 + g2 + 0.35m now plug in and solve for m
40 + 15 + 0.25m = 45 + 0.35m
55 - 45 = 0.35m - 0.25m
10 = 0.1m
100 = m
for 100 miles the cost will be the same
now to find the cost
0.25m plug in 100 for m
0.25(100) = 80
for the course of 100 miles the cost will be $80
Nile had 20% less strike outs than last year. He had 124 strike outs last year. Which steps are needed to calculate the number of strike outs nile had this year?
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124 - 24.8 = 99.2 (if rounded, then = 100)
Nile has made 100 strikeouts this year
Next multiply 124*0.2=24.8
Now subtract 124-24.8=99.2
Now round the answer to 99
He had about 99 strike outs this year
A decimal number which ends after a finite number of digits after the decimal point is called a _______ decimal. Example: 6.875
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estimate the value of 98.5*13
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To estimate the value of 98.5*13, you round 98.5 to 100 and 13 to 10, and then multiply to get an estimated product of 1000, which is a simple calculation that provides a close approximation to the precise answer of 1,280.5.
To estimate the value of 98.5*13, you can round 98.5 to the nearest ten and 13 to the nearest ten. So, 98.5 is approximately 100 and 13 is approximately 10. To estimate the product, you multiply these two numbers:
100 * 10 = 1000
The estimated value of 98.5*13 is therefore around 1000. The calculator gives 1,280.5 as the precise answer, but our estimate simplifies the calculation while providing a close approximation.
2x+12 is greater than or equal to 6
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If x is more than -3, it's greater than 6.
If x is -3, it's equal to 6.
Can someone help me with these 3 questions please
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Can you help, i'm not to good with postulates and theorems.