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2 years ago

What is the solution to the system of equations?

Mathematics

1 answer:

Over [174]2 years ago

3 0

ANSWER

C) (6,-8)

EXPLANATION

The equations are:

$y = \frac{1}{3}x - 10$

and

$2x+y=4$

We substitute the first equation into the second equation to get:

$2x + \frac{1}{3}x - 10 = 4$

We multiply through by 3 to get:

$6x + x - 30= 12$

Group similar terms,

$6x + x = 30 + 12$

$7x = 42$

Divide both sides by 7 to get,

$x = \frac{42}{7} = 6$

Put this value of x into the first equation to get;

$y = \frac{1}{3} (6) - 10$

$y = 2 - 10 = - 8$

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We have that the equation of the volume of a sphere is given by:

$V=\frac{4}{3}\pi r^3$

We have that the radius of a sphere is half the diameter of it:

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<h2>Finding the volume of a sphere</h2>

We replace r by 3 in the equation:

$\begin{gathered} V=\frac{4}{3}\pi r^3 \\ \downarrow \\ V=\frac{4}{3}\pi\cdot3^3 \end{gathered}$

Since 3³ = 3 · 3 · 3 = 27

$\begin{gathered} V=\frac{4}{3}\pi3^3 \\ \downarrow \\ V=\frac{4}{3}\pi\cdot27 \end{gathered}$

If we use π = 3.14:

$\begin{gathered} V=\frac{4}{3}\pi\cdot27 \\ \downarrow \\ V=\frac{4}{3}\cdot3.14\cdot27 \\ \downarrow \\ V=4.18\bar{6}\cdot27 \end{gathered}$

Rounding the first factor to the nearest hundredth (two digits after the decimal), we have:

4.18666... ≅ 4.19

Then, we have that:

$\begin{gathered} V=\frac{4}{3}\pi\cdot27 \\ \downarrow \\ V=4.19\cdot27 \\ =113.13 \end{gathered}$

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<h2>Finding the volume of a cone</h2>

We have that the volume of a cone is given by:

$V=\frac{1}{3}\pi r^2h$

where r is the radius of its base and h is the height:

Then, in this case

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and

π = 3.14

Replacing in the equation for the volume:

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9 months ago

4z^3-3z^5+2z^4+z+1 please solve this question please!

lbvjy [14]

SOLUTION

TO DETERMINE

The degree of the polynomial

CONCEPT TO BE IMPLEMENTED

POLYNOMIAL

Polynomial is a mathematical expression consisting of variables, constants that can be combined using mathematical operations addition, subtraction, multiplication and whole number exponentiation of variables

DEGREE OF A POLYNOMIAL

Degree of a polynomial is defined as the highest power of its variable that appears with nonzero coefficient

When a polynomial has more than one variable, we need to find the degree by adding the exponents of each variable in each term.

EVALUATION

Here the given polynomial is

In the above polynomial variable is z

The highest power of its variable ( z ) that appears with nonzero coefficient is 5

Hence the degree of the polynomial is 5

FINAL ANSWER

The degree of the polynomial is 5

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