Last year, Dana grew 1/2 of an inch and her brother grew 1/8 of an inch. How much more did Dana grow than her brother?

Answer:

D

Step-by-step explanation:

So we have the function:

[tex]f(x)=\frac{1}{5}x+4[/tex]

To find the inverse, simply switch x and f(x), change f(x) to f⁻¹(x), and solve for it. Thus:

[tex]x=\frac{1}{5}f^{-1}(x)+4[/tex]

Subtract 4 from both sides:

[tex]x-4=\frac{1}{5}f^{-1}(x)[/tex]

Multiply both sides by 5:

[tex]f^{-1}(x)=5x-20[/tex]

So that's our inverse :)

So, our answer is D

Answer:

D

Step-by-step explanation:

Answer:

He has 12 ten dollar bills

Step-by-step explanation:

Let t = number of 10 dollar bills

f = number of fifty dollar bills

t+f = 25  since he has 25 bills

solving for f

f = 25 -t

Then we know he has 770 dollars

10t+50f = 770

Using f = 25-t in the above equation

10t + 50 ( 25-t) = 770

Distribute

10t+ 1250 - 50t = 770

Combine like terms

-40t+1250 = 770

subtract 1250 from each side

-40t - 1250-1250 = 770-1250

-40t = -480

divide each side by -40

-40t/-40 = -480/-40

t =12

He has 12 ten dollar bills

We use the multiplicative property of equality to make Equation 1 and Equation 2 equivalent.

Given,

Equation 1 - 4.2x – 1.5 = 1.7x + 8.3

Equation 2 - 42x - 15 = 17x + 83

We have to Identify the property of equality that makes Equation 1 and Equation 2 equivalent.

We have,

Equation 1 - 4.2x – 1.5 = 1.7x + 8.3

Equation 2 - 42x - 15 = 17x + 83

If we multiply 10 on both sides of the equation, we get

10 (4.2x – 1.5)  = 10 (1.7x + 8.3)

10 x 4.2x - 10 x 1.5 = 10 x 1.7x + 10 x 8.3

42x - 15 = 17x + 8.3

We get,

42x - 15 = 17x + 8.3 which is equivalent to equation 2.

This property is called the multiplicative property of equality.

Thus we use the multiplicative property of equality to make Equation 1 and Equation 2 equivalent.

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Answer:A

Step-by-step explanation:

Answer: 9:14

Step-by-step explanation: So if he started if 1 bacteria, it becomes 2 bacteria at 9:01, etc. So at 9:13, it is 2^13 and if that is half, that means 2^14 is when it is full so 9:14.

The dish will be full at  9:14 am.

Given, the bacteria duplicates itself per minute.

The experiment started with a single cell at 9 am and at 9:13 am the dish was half full.

So it is clear that after 13 minutes of experiment started the dish was half full.

Now, let here is only 1 bacteria in the dish which is duplicating per minute,so after 1 minute it becomes 2 after that it becomes 4 and after that it becomes 8. Hence it is clear from the example the bacteria doubles itself in powers of her minute. ([tex]2^x[/tex])  here x is the number of minute.

Since after 13 minutes the dish was half full, it means there are [tex]2^{13}[/tex] bacteria in the dish. hence the full dish is [tex]2^{14}[/tex] bacteria. so the bacteria will take 1 more minute for the dish to be full.

Hence at 9:14 am the dish was full.

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Answer:

230.4

Step-by-step explanation:

11,979 divided by 52 is 230.365384615.

230.365384615 Rounded gets the answer

Answer:

[tex]\sqrt[3]{215}[/tex]

Decimal Form: 5.99072641

Look down for explanation

Step-by-step explanation:

[tex]\sqrt[3]{215}[/tex]

You have to simplify.

[tex]= \sqrt[3]{215}[/tex].

Decimal Form: 5.99072641

Now you have the answer to your question!

Hope this helps!

Answer:

The answer is 3.825 inches, the reduced picture will be 84% of the size of the original

Answer:

3.78 inches

Step-by-step explanation:

if the original length is 4.5 and we are making it 84 percent of that size we multiply 4.5 times 84 percent(that is 0.84).

If we type in 4.5 * 0.84 on a calculator the answer comes back as 3.78

so the answer is 3.78 inches

Answer:

X-17=22

X=22+17

X=39 this is the answer

Answer:

27

Step-by-step explanation:

15+5=20

20+7=27

Answer: 27

Step-by-step explanation:

15+5=20

20+7=27

Answer:

A. Graph B

Step-by-step explanation:

The reasoning is because the 2 lines are parallel; therefore, it is impossible for them to overlap or intersect, which is the only way a solution can be found. Parallel lines can never have a solution. Hope this helped!

Answer:

9.1 x 10²

Step-by-step explanation:

Answer:

Any number greater than 6,300

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

-27+(-3) can be simplified to -27-3

-27-3= -30

Answer: Yes you are correct. The answer is -30

Explanation:

We are adding 2 negatives. So we effectively add the positive versions of each number, and then make the result negative.

You can think of it in terms of money: you start off 27 dollars in debt and then borrow 3 more dollars to be a total of 27+3 = 30 dollars in debt.

Or you can think of it like you're under the ocean. Writing -27 could mean you're 27 feet below sea level. Adding on -3, ie subtracting 3, would then move you down 3 feet to get to 27+3 = 30 feet below sea level.

Answer:

2 hours

Step-by-step explanation:

at one hour, you would be on lvl 10 and he would be on lvl 9, at 2 hour you would be on lvl 14, and he would be on lvl 14.

Answer:

96 miles.

Step-by-step explanation:

2 hours = 2*60*60 = 7200 seconds.

So the required distance = 7200/75

= 96 miles.

Answer:

96 miles

Step-by-step explanation:

i did this a few months ago (coincidence I think not)

Answer:

its a irrational number

Answer:

4,200 g. of aluminum

Step-by-step explanation:

42x100=4,200

The 42 grams of aluminum implies that the chemist has 0.06429ml of aluminum

The mass is given as:

Mass = 42 grams

The density of aluminum is:

Density = 2.7 g/cm³

So, we have:

Volume = Density/Mass

This gives

Volume = 2.7/42

Evaluate

Volume = 0.06429cm³

Convert to ml

Volume = 0.06429ml

Hence, the chemist has 0.06429ml of aluminum

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Answer:

Complementary angles

Step-by-step explanation:

The sum of the 2 angles = 27° + 63° = 90°

This is the definition of Complementary angles

Answer:

The first one BED and DEA. AEC and BEC.

Step-by-step explanation:

Supplementary angles are 2 angles that when added equals 180. Also, if there are no numbers given, the 2 angles should make a straight line when next to each other.

Answer:

No

Step-by-step explanation:

The time it takes Timothy to drive to his friends' houses is not proportional. This is because when going to the first house, he is going at 4km per minute, but when visiting the second and third houses he is no longer traveling at that speed.

In a directly proportional relationship, increasing one variable will increase another. The given relationship is not proportional.

In a directly proportional relationship, increasing one variable will increase another.

This directly proportional relationship between p and q is written as

p∝q where that middle sign is the sign of proportionality.

Inversely proportional relationship increasing one variable will decrease the other variable if both are inversely proportional.

This directly proportional relationship between p and q is written as

p∝1/q where that middle sign is the sign of proportionality.

Given that the table shows the distance and time it takes him to drive to each of his friends’ houses.

Now, to know if the time it takes Timothy to drive to his friends’ houses proportional to the distance, find the ratio of distance to time for each row. Therefore, the ratios can be written as,

R₁ = 5km / 10 min = 0.5 km per min

R₂ = 11 km / 15 min = 0.7334 km per min

R₃ = 18 km / 20 min = 0.9 km per min

Since the ratio of distance and time in different cases is different, therefore, the given relationship is not proportional.

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The answer is $1282.66

Explanation:

The sales tax rate (in this case 6.8%) is paid as part of selling a product. Also, to find the final price of a product, find the tax rate (percentage) of the price of the product and add this number to the price. The process to know the final price of the fridge is shown below:

1. Determine the 6.8% of $1201

 1.1. Write the values

1201  = 100  

 x     =  6.8

 1.2. Cross multiply and solve the equation

x100 = 8166

x= 8166 ÷ 100

x = 81.66

2. Add this value to the original price

$1201 + $ 81.66 = $1282.66 (Total price including the sales tax)

Answer:

b

Step-by-step explanation:

BECAUSE x-25 = 3

shows something mines 25 that equals 3

Answer:

the answer is 0

Step-by-step explanation:

6 (4) -2 (3)(4)

24-24=0

Answer: 8x^2-2x-5

Step-by-step explanation:

13. -5/6

14. -7/8

15 -7/10

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

3x+x=4x

40+20=60

180-60=120

120/4=30

Answer:

21

Step-by-step explanation:

5x-3x=18+15-9

2x=42 /:2

x=21