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3 years ago

What is the equation and solution for the sentence?

Mathematics

1 answer:

frez [133]3 years ago

4 0

Answer:

Write the equation as n + 31 = 113 and subtract 31 from both sides. The answer is 82.

Step-by-step explanation:

The sum of a number and 31 would be 'n + 31'. The sum equaling 113 would be '= 113'.

You would get 'n' by subtracting 31 for each side.

$n+31 = 113\\n+31-31=113-31 \leftarrow \text{Subtraction Property of Equality} \\\boxed{n=82}$

The statement: "Write the equation as n + 31 = 113 and subtract 31 from both sides. The answer is 82." should be the correct answer.

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Which function represents a reflection of f(x) = 5(0.8)^x across the x-axis?

Vikki [24]

Answer: The correct option is second.

Explanation:

The given function is,

$f(x)=5(0.8)^x$

If we graph a function is f(x), then its coordinates is defined as (x,f(x)).

When the graph of f(x) is reflect across the x-axis, then the the x-coordinate remains the same and the sign of y-coordinate is changed. It means after reflecting across the x-axis,

$(x,y)\rightarrow(x,-y)$

The given given equation can be written as,

$y=5(0.8)^x$

To find the equation of the graph after reflection across the x-axis multiply both sides by -1.

$-y=-5(0.8)^x$

Because f(x)=y and g(x)=-y.

$g(x)=-5(0.8)^x$

Therefore the second option is correct and the graph of both function is given below.

6 0

3 years ago

Read 2 more answers

What is the distance between (-2 1/2,3)and(1,-3)

nikklg [1K]

Answer:

Step-by-step explanation:

due to the fact I really don't know

6 0

3 years ago

On the Bologna-Rome route of a high-speed train, 3/4 of the reservations are with departure from Bologna, while the remainder ar

svlad2 [7]

Step-by-step explanation:

First, we consider the calculation towards finding the total number of passengers who had booked the train in Florence. The main question to ask in answering this problem is

$\text{``If 20 passengers that board the train from Florence correlates to only} \ \displaystyle\frac{2}{5} \\ \text{of the bookings from Florence, then what is the total number of passengers} \\ \text{that booked regardless if the passengers boarded the train or not?"}$

This statement can be phrase mathematically using the method of ratio and proportion as shown below

$\displaystyle\frac{2}{5} : 1 \ = \ 20:x$ ,

in which the variable $x$ is the total number of passengers who booked the train from Florence.

Now, rewriting the above ratio into the form of fractions, yields

$\displaystyle\frac{\displaystyle\frac{2}{5}}{1} \ = \ \displaystyle\frac{20}{x} \\ \\ \displaystyle\frac{2}{5} \ = \ \displaystyle\frac{20}{x} \\ \\ x \ = \ \displaystyle\frac{20}{\frac{2}{5}} \\ \\ x \ = \ 20 \ \times \ \displaystyle\frac{5}{2} \\ \\ x \ = \ 50$

Given that a quarter out of all reservations is from Florence, then using the same method as before to evaluate the number of passengers that had booked the train (from both Bologna and Florence).

$\displaystyle\frac{\displaystyle\frac{1}{4}}{1} \ = \ \displaystyle\frac{50}{y} \\ \\ y \ = \ \dsiplaystyle\frac{50}{\frac{1}{4}} \\ \\ y \ = \ 50 \ \times \ 4 \\ \\ y \ = \ 200$ ,

where the variable $y$ denotes the total number of bookings.

Therefore, the total number of passengers that had booked the train is 200.

Now, it is stated that all passengers who booked had boarded the train from Bologna which is 150 passengers (three-quarters of total bookings). Then, 36 passengers from earlier got off in Florence, while 20 passengers boarded.

Number of passengers left when arriving Rome = 150 - 36 + 20

= 134 passengers

8 0

2 years ago

Solve the equation:<br>39 = 3m - 12

Fed [463]

Answer: m = 17

Step-by-step explanation:

3m = 39+12

3m = 51

m = 17

3 0

3 years ago

Read 2 more answers

Find the distance between the two points in simplest radical form.<br> (1.5) and (-5,8)

Nuetrik [128]

Answer:

exact: 3 √ 5

decimal: 6.70820393 …

Hope this helps

3 0

3 years ago