A motorboat travels 275 kilometers in 5 hours going upstream. It travels 405 kilometers going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current?

The table suggests that f(x) approaches a value of 6.5 as x approches 3, or in other words, that

[tex]\displaystyle \lim_{x\to3}f(x) = 6.5[/tex]

Answer:

they are  proportional

Step-by-step explanation:

When one goes up so does the other

This is a simple problem of ranges, we will find that the ranges for the main floor and the balcony are:

[-6ft, 8ft] or {x ∈ R | -6ft ≤ x ≤ 8ft}

[26ft, 37ft] or {x ∈ R | 26ft ≤ x ≤ 37ft}

respectively.

We know that:

The main floor of the auditorium ranges from 6ft below the stage  to 8 feet above the stage.

The floor of the balcony ranges from 26 to 37 feet above the stage

The ranges relative to the stage will be, in interval notation, the interval that contains the two extremes of the range.

For the main floor, it goes from -6ft to 8ft (the first one is negative because is 6ft below the stage) then this interval will be: [-6ft, 8ft]

While in set-builder notation we want to specify that the variable must be a real number, so we start with: {x ∈ R

And we need to specify that x can go from -6ft to 8ft, then we add the restriction:

{x ∈ R | -6ft ≤ x ≤ 8ft}

Notice that we use a close interval here.

While for the balcony, the minimum is 26ft and the maximum is 37ft, then the interval will be [26ft, 37ft]

For the set-builder notation we will have:

{x ∈ R | 26ft ≤ x ≤ 37ft}

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Equations are represented with the = sign. It means both sides of the equation are equal. [tex]11=t+11.5-t[/tex] has no solution

Given that:

[tex]11=t+11.5-t[/tex]

Start by collecting like terms

[tex]11-11.5=t-t[/tex]

Evaluate like terms

[tex]-0.5 = 0[/tex]

-0.5 is not equal to 0.

Hence, the equation has no solution

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Step-by-step explanation:

Properties of the number 6425

Factorization5 * 5 * 257Square root80.156097709407Natural logarithm8.7679519097634Decimal logarithm3.8078731320033Sine-0.42867294834975

Answer:

g(x) =  |4x+3|

Step-by-step explanation:

Vertically translate f(x) two units down by subtracting 2 from f(x).

|4x+3|+2-2 = |4x+3|

f(x) = |4x + 3| + 2

To translate 2 units down, subtract 2

f(x) = |4x + 3| + 2 - 2

f(x) = |4x + 3|

Answer:

6 seconds

Step-by-step explanation:

h(x)=-(x-2)^2+16

We want h(x) to be 0 ( that is when the ball hits the ground)

0 = -(x-2)^2+16

Subtract 16 from each side

-16  = -(x-2)^2+16-16

-16 = -(x-2)^2

Divide by -1

16 = (x-2)^2

Take the square root of each side

sqrt(16) = sqrt((x-2)^2)

±4 = x-2

Add 2 to each side

2±4 = x-2+2

2±4 =x

2+4 = x   2-4 = x

6 =x  -2 =x

Time cannot be negative so x=6

Answer:

X = 6

Step-by-step explanation:

hope it will help you

Answer:

What?

Step-by-step explanation:

Answer:

3 times Mike's amount = 3h

Answer:

1. 8t+4v

A.9v+7t+6

S.14v+7t

Step-by-step explanation:

In A,

length=3units

width=2 units

area=length×width

area=3×2 sq.units

area=6 sq.units

In B,

length=1unit

width=4units

area=length × width

area=1unit × 4units

area= 4 sq.units

Note:if you need to ask any question please let me know.

Answer:

[tex]\frac{7}{20}[/tex]

Step-by-step explanation:

The difference 31 - 17 = 14

The product 10 × 4 = 40

Then

[tex]\frac{14}{40}[/tex] = [tex]\frac{7}{20}[/tex] ← in simplest form

The difference between thirty-one and seventeen divided by the product of ten and four will be 7 / 20.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

The difference between thirty-one and seventeen will be expressed as,

⇒ 31 - 17

⇒ 14

The product of ten and four will be expressed as,

⇒ 10 x 4

⇒ 40

Then the difference between thirty-one and seventeen divided by the product of ten and four will be expressed as,

⇒ 14 / 40

⇒ 7 / 20

Thus, the difference between thirty-one and seventeen divided by the product of ten and four will be 7 / 20.

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Answer:

10 areas

Step-by-step explanation:

5 minutes = 1 area

→ Divide the 50 by the 5

50 ÷ 5 = 10

→ Multiply this by the area

10 × 1 = 10

Answer:

AB = 4

Step-by-step explanation:

Since the line is horizontal then its length is the difference of the x- coordinates, that is

AB = | 8 - 4 | = 4 , or

AB = | 4 - 8 | = | - 4 | = 4

Answer:

Question is?

Step-by-step explanation:

what's the que for Points Z L and S are

Answer:

Step-by-step explanation:

[tex]0.8 = \dfrac{8}{10}=\dfrac{2*4}{2*5}=\dfrac{4}{5}[/tex]

Answer:

Each of the domain values, x, should only output a single unique range value, y.

This example is a relation and not a function because the the domain value of -1 output 2 distinct range values.

-1 outputs a 3

and

-1 outputs a 5

If I were to draw a vertical line at the domain value of -1 that vertical line would intersect the points (-1,3) and (-1,5). Which indicates that the relation is not a function.

Answer:

None of the following set of points represents a function .

Answer:

[tex]1275+0.2m=c[/tex]

m is the amount of miles driven, c is the total cost.

Step-by-step explanation:

Since she has a flat fee of 1275, that's the 1275 in the equation and since we don't know how many miles she drives, that's the m in the equation for miles driven. Since each mile costs 0.20, that's the 0.2 in the equation. And since c is the total cost in dollars, that's the c in the equation.

Answer:

Step-by-step explanation:

6x-3+2x-1=10x-18

8x-4=10x-18

18-4=10x-8x

14=2x

X=7

AB = (6*7)-3=39

BC=13

AC=39+13=52 or

AC=(10*7)-18=52

Step-by-step explanation:

v=s^3 s=3^4=81

v=(81)^3

v=531,441 cm^3

Answer:

The last one

Step-by-step explanation:

0.3333..., 30%, 3/10 are parts.

The last one ( 3 circles) are 3 wholes.

(whole numbers)

I hope this helped:)...

:-)

Hey there! I'm happy to help!

30% is the same thing as 0.3, which is 30% of 1.

0.3 is what you multiply numbers if you want to see what 30% of that number is as 0.3 is 30% of 1, the whole number.

3/10 is the same value as 30% because 3 divided by 10 is equal to 0.3, which is 30%.

The dots in the boxes are also the same thing as 3/10. There are 10 boxes, and 3 out of the 10 have dots, which is 3/10 and 30%.

The one that does not belong is 0.333333...... This is equivalent to 1/3, which is greater than 30%, 0.3, and 3/10.

Have a wonderful day and keep on learning! :D

Answer:

What do you mean

Step-by-step explanation:

Answer:

1) 1/2 *bh

2) 2s+4

3) 35+2m

Answer:

6

Step-by-step explanation:

6 decimal places

0.005011 has six decimal places.

'The place value of a decimal number is recognized according to the position of the dot or decimal point. The first digit to the right of the decimal point indicates the number of tenths and the second digit to the right indicates the number of hundreths.'

According to the given problem,

For the number 0.005011, after the decimal there are numbers up to the sixth place which is that there are six numbers.

For counting decimal places, we need to count the number of digits present to the right of decimal point.

Hence, we can conclude that 0.005011 has 6 decimal places.

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Answer

10.6

Explanation

Logic

Answer:

A

Step-by-step explanation:

This uses the sine law.

Sin(theta)/113 = sin(42)/120             Multiply both sides by 113

sin(theta) = 113*sin(42)/120

sin42 = 0.6691

sin(theta) = 113 * 0.6691 / 120

sin(theta) = 0.630008

theta = sin-1(0.63008)

theta = 39.1    Looks Like A