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1 year ago

Find the value of the expression.

Mathematics

1 answer:

Olegator [25]1 year ago

5 0

$( (\frac{3}{5}) {}^{0} ) {}^{ - 2} = (1) {}^{ - 2} = \frac{1}{1 {}^{2} } = \frac{1}{1} = 1$

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What is the best approximation for the input value when f(x)=g(x)?

Lostsunrise [7]

Answer:

$x=0$ and $x=1$ .

Step-by-step explanation:

If we have to different functions like the ones attached, one is a parabolic function and the other is a radical function. To know where $f(x)=g(x)$ , we just have to equalize them and find the solution for that equation:

$x^{2}=\sqrt{x} \\(x^{2} )^{2}=(\sqrt{x} )^{2}\\x^{4}=x\\x^{4}-x=0\\x(x^{3}-1)=0\\$

So, applying the zero product property, we have:

$x=0\\x^{3}-1=0\\x^{3}=1\\x=\sqrt[3]{1}=1$

Therefore, these two solutions mean that there are two points where both functions are equal, that is, when $x=0$ and $x=1$ .

So, the input values are $x=0$ and $x=1$ .

8 0

2 years ago

Read 2 more answers

How many solutions does the equation have, x1 + x2 + x3 = 10 , where x1 , x2, and x3 are non-negative integers?

MAVERICK [17]

Non-negative integers are positive integers or zero.

1. When $x_1=0,$ then there are such possible cases for $x_2$ and $x_3:$

$x_2=0,\ x_3=10;$
$x_2=1,\ x_3=9;$
$x_2=2,\ x_3=8;$
$x_2=3,\ x_3=7;$
$x_2=4,\ x_3=6;$
$x_2=5,\ x_3=5;$
$x_2=6,\ x_3=4;$
$x_2=7,\ x_3=3;$
$x_2=8,\ x_3=2;$
$x_2=9,\ x_3=1;$
$x_2=10,\ x_3=0.$

In total 11 solutions for $x_1=0.$

2. For $x_1=1,$ there are such possible cases for $x_2$ and $x_3:$

$x_2=0,\ x_3=9;$
$x_2=1,\ x_3=8;$
$x_2=2,\ x_3=7;$
$x_2=3,\ x_3=6;$
$x_2=4,\ x_3=5;$
$x_2=5,\ x_3=4;$
$x_2=6,\ x_3=3;$
$x_2=7,\ x_3=2;$
$x_2=8,\ x_3=1;$
$x_2=9,\ x_3=0.$

In total 10 solutions for $x_1=1.$

3. This process gives you

for $x_1=2$ - 9 solutions;
for $x_1=3$ - 8 solutions;
for $x_1=4$ - 7 solutions;
for $x_1=5$ - 6 solutions;
for $x_1=6$ - 5 solutions;
for $x_1=7$ - 4 solutions;
for $x_1=8$ - 3 solutions;
for $x_1=9$ - 2 solutions;
for $x_1=10$ - 1 solution.

4. Add all numbers of solutions:

$11+10+9+8+7+6+5+4+3+2+1=66.$

Answer: there are 66 possible solutions (with non-negative integer variables)

8 0

2 years ago

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4x2 minus 20+48 factorise this polynomial completely

bulgar [2K]

Answer:

Step-by-step explanation:

With no parenthesis

7 0

2 years ago

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It takes 1 hour (t) to fill the water tank of volume (V) 750 m3. Identify the dependent and the independent variables.

Natalija [7]

Answer:

The time t is the independent variable while the volume V is the dependent variable

Step-by-step explanation:

A variable is a parameter that changes.

We have two types namely dependent and independent variables.

A dependent variable is a variable which its value needs to be determined based on the value of another variable while and independent variable is a variable which its value independent of other parameters.

In our question, It takes 1 hour (t) to fill the water tank of volume (V) 750 m3.

The volume of the tank V changes as time changes. So the volume of the tank V is dependent on time, t.

So V is proportional to t

Since the volume of the tank is the variable that needs to be determined based on another variable-which is time,t- it is the dependent variable, while the time,t is the independent variable since its value is not determined based on other parameters.

4 0

2 years ago

Lxl=10 what is the answer

Svetradugi [14.3K]

Answer:

Step-by-step explanation:

The absolute value of 10 is 10. Algebraically speaking, the absolute value of a number x takes x and makes it positive.

6 0

2 years ago