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3 years ago

Let 3.27<<5.89 represent an interval on the number line. Find the value that is in the middle of the interval.

Mathematics

1 answer:

laila [671]3 years ago

4 0

Answer:

The middle value of the interval is 4.58

Step-by-step explanation:

Consider the provided interval.

We need to find the value that is in the middle of the interval.

We can find the middle value of the interval by adding the upper and lower limit and divide the sum of the upper and lower limits by 2.

Here the upper limit is 3.27 and lower limit is 5.89.

$\frac{3.27+5.89}{2}=\frac{9.16}{2}=4.58$

Hence, the middle value of the interval is 4.58

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Answer:

Step-by-step explanation:

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3 years ago

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Given the system of linear equations. x=y+3 y=-4x-3 Part A: Solve the linear system of equations by graphing Part B: Use substit

Radda [10]

Answer:

see below

Step-by-step explanation:

x=y+3

Subtract 3 from each side

x-3 = y

y = x-3

y=-4x-3

We have both equations in slope intercept form

y = mx +b where m is the slope and b is the y intercept

graph is below

They both have the same y intercept so they intersect at (0,-3)

Substitution

x=y+3

y=-4x-3

Substitute the second equation into the first equation

x=y+3

x = -4x-3 +3

x = -4x

Add 4x to each side

5x =0

x=0

y = -4x-3

y = 0-3

y = -3

(0,-3)

Additon

x=y+3

Subtract y from each side

x-y = 3

y=-4x-3

Add 4x to each side

4x+y =-3

Add the equations together to eliminate y

x-y = 3

4x+y =-3

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5x +0y =0

5x = 0

x=0

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y = 0-3

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3 years ago

Let f (x)=1/x and g (x)=x^2+5x. A. Find (f×g)(x). B. Find the domain and range of (f×g)(x).

Ira Lisetskai [31]

we are given

$f(x)=\frac{1}{x}$

$g(x)=x^2+5x$

(A)

(f×g)(x)=f(x)*g(x)

now, we can plug it

$(fXg)(x)=\frac{1}{x} (x^2+5x)$

we can simplify it

$(fXg)(x)=\frac{1}{x} (x(x+5))$

$(fXg)(x)=x+5$

(B)

Domain:

Firstly, we will find domain of f(x) , g(x) and (fxg)(x)

and then we can find common domain

Domain of f(x):

$f(x)=\frac{1}{x}$

we know that f(x) is undefined at x=0

so, domain will be

$(-\infty,0)$ ∪ $(0,\infty)$

Domain of g(x):

$g(x)=x^2+5x$

Since, it is polynomial

so, it is defined for all real values of x

now, we can find common domain

so, domain will be

$(-\infty,0)$ ∪ $(0,\infty)$ ..............Answer

Range:

Firstly, we will find range of f(x) , g(x) and (fxg)(x)

and then we can find common range

Range of f(x):

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we know that range is all possible values of y for which x is defined

since, horizontal asymptote will be at y=0

so, range is

$(-\infty,0)$ ∪ $(0,\infty)$

Range of g(x):

$g(x)=x^2+5x$

Since, it is quadratic equation

so, its range will be

$[-6.25,\infty)$

now, we can find common range

so, range will be

$(-6.25,0)$ ∪ $(0,\infty)$ .............Answer

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3 years ago

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Step-by-step explanation:

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