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azamat
3 years ago
15

The graph shows the number of laps that Jan runs as her coach times her.

Mathematics
2 answers:
Lena [83]3 years ago
6 0
The slope of the line is +2

this means that Jan runs 2 laps every 1 minute
lara31 [8.8K]3 years ago
5 0

Answer:

The slope of the line is 2. It means Jan runs 2 laps every minute.

Step-by-step explanation:

From the given graph it is noticed that the line passing through the points (2,4) and (5,10).

The slope of lines is

m=\frac{y_2-y_1}{x_2-x_1}

The slope of given line is

m=\frac{10-4}{5-2}

m=\frac{6}{3}

m=2

The slope of the line is 2.

In the given graph x axis represents the time in min and y-axis represents the laps run. The slope defines the number of laps in each minute.

The slope is 2, it means Jan runs 2 laps every minute.

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The _____ _____, f(x) = x, is formed by the composition of a function and its inverse. (2 words)
jonny [76]

Answer:

Identity function    

Step-by-step explanation:

We are given the following in the question:

Let f(x) be a function.

Then, inverse of f(x) can be written as:

f^{-1}(x)

The composition function of the function and the reverse function can be found as:

(f\circf^{-1})(x) = f(f^{-1})(x) = x

which is an identity function.

Thus, the correct answer is

The identity function, f(x) = x, is formed by the composition of a function and its inverse.

8 0
2 years ago
Simplify: Log3 27 = x can anybody help me with this?? Thank you!!
Allushta [10]

Answer:3

Step-by-step explanation:

3 ^x= 27

X=3

5 0
3 years ago
A house that costs $125,400 appreciates at a rate of 3% each year. What is the value of the
ser-zykov [4K]

Answer:

The value after three years is $137,027.97

Step-by-step explanation:

Here, we want to get the value of the home after 3 years

Generally, we have the exponential formula as follows;

y = P(1 + r)^t

where P is the original cost which is $124,400

r is the rate of increase which is 3% = 3/100 = 0.03

t is the time which is 3 years

Substituting these values;

y = 125400(1 + 0.03)^3 = $137,027.97

6 0
2 years ago
Solve for x: 3/4x+5/8=4x
kompoz [17]
So, you have 3/4x + 5/8 = 4x. We can do this in two ways. Since fractions are harder to deal with, we can turn the fractions into whole numbers.

First we need to find the LCD (Least Common Denominator) between 4 and 8, which is 8. So multiply the 3/4x by 2/2, which gives you an equivalent fraction of 6/8x.

So now we have 6/8x + 5/8 = 4x. Now multiply both sides by 8, to get rid of the denominators of the fractions. That gives us 6x + 5 = 32x. Now use the subtraction property of equality to subtract 6x from both sides giving us 5 = 26x. 

Now you can use the division property of equality to divide 26 on both sides, which gives us x = 5/26.

Hope this helps. :D Feel free to ask any other questions, and if you have any questions about my explanation, don't hesitate to ask.
6 0
3 years ago
Evaluate for x = 3 and y = 4: x^-2y^2/x^0y^3 1/36 4/9 1024/9
GrogVix [38]

Answer:

\frac{1}{36}

Step-by-step explanation:

Evaluating the numerator and denominator before evaluating

Using the rule of exponents

a^{-n} ⇔ \frac{1}{a^{n} }, a^{0} = 1

Thus

x^{-2}y² ← substitute values into expression

= 3^{-2} × 4² = \frac{1}{9} × 16 = \frac{16}{9}

and denominator

x^{0}y^{3} = 1 × 4³ = 1 × 64 = 64

Now dividing

\frac{16}{9} ÷ 64

= \frac{16}{9} × \frac{1}{64} ( cancel 16 and 64 )

= \frac{1}{9(4)} = \frac{1}{36}

4 0
2 years ago
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