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vagabundo [1.1K]

2 years ago

15

If $f(x)$ is a polynomial of degree 3, and $g(x)$ is a polynomial of degree 5, then what is the degree of polynomial $2f(x) + 4g

(x)$?

1 answer:

worty [1.4K]2 years ago

6 0

Answer:

Degree 5

Step-by-step explanation:

Given

Degree of f(x) = 3

Degree of g(x) = 5

Required

Degree of 2f(x) + 4g(x)

<h2>Analyzing both polynomials</h2><h3>f(x)</h3>

2f(x) means 2 * f(x)

Since 2 is a constant

Multiplying f(x) by 2 will result in a polynomial with a degree of 3

Hence 2f(x) has a degree of 3

<h3 /><h3>g(x)</h3>

4g(x) means 4 * g(x)

Since 4 is also a constant

Multiplying g(x) by 4 will result in a polynomial with a degree of 5

Hence 4g(x) has a degree of 5

Having said that;

When 2 polynomials of different degrees are added together, the degree of the result will be the higher degree of both polynomials;

This means that;

Adding a polynomial of degree 3 and another of degree 5 will result in a polynomial of degree 5

You might be interested in

The cost C of hiring a lorry is partly constant and partly varies with the time T spent. If it cost ₦850 for 4 hours hire and ₦1

enot [183]

Answer:

$1800

Step-by-step explanation:

First, rewrite out the information you already have:

-for 4 hrs-cost $850

-for 7 hrs-cost $1300

-for 12 hrs-$?

Next, we have to find out the amount of cost for hire per hour, so we can multiply that by 12 hrs:

-start by subtracting $850 from $1300:

1300-850=$450

-now subtract 4 hrs from 7 hrs:

7-4=3 hrs

In doing this, we see that the cost for 3 hrs hire is $450. Now, to find the unit cost per hr hire, divide $450 by 3 hrs:

450÷3=$150/hr

It costs $150 per hr hire.

Now, we have to find the cost for 12 hrs hire, so just multipy the unit cost by 12:

150*12=$1800 for 12 hrs hire

It costs $1800 for 12 hrs hire.

6 0

2 years ago

Read 2 more answers

Rita is spending more time at home to study and practice math. Her efforts are finally paying off. On her first assessment she s

faltersainse [42]

<h2>Answer</h2>

She will be scoring above 85 after her 7 assessment.

<h2>Explanation</h2>

We can model this situation using a line equation.

We know that on her first assessment, Rita scored 58 points, so our first point is (1, 58)

We also know that on her second assessment, Rita scored 63 points, so our second point is (2, 63)

To find the rate, which is the slope of our line, we are using the slope formula:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

where

$(x_{1},y_{1})$ are the coordinates of the first point

$(x_{2},y_{2})$ are the coordinates of the second point

From our points we can infer that $x_{1}=1$ , $y_{1}=58$ , $x_{2}=2$ , $y_{2}=63$ . Let's replace the values in our slope formula:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$m=\frac{63-58}{2-1}$

$m=\frac{5}{1}$

$m=5$

Now we know that Rita's score is increasing 5 points every assessment.

To complete the equation of our line, we are using the point slope formula:

$y-y_{1}=m(x-x_{1})$

$y-58=5(x-1)$

$y-58=5x-5$

$y=5x+53$

Finally, we just need to replace $y$ with 85 in our line equation and solve for $x$ to find after which assessment she will score above 85:

$85=5x+53$

$32=5x$

$x=\frac{32}{5}$

$x=6.4$

Since we can't have 0.4 assessment, she will be scoring above 85 after her 7 assessment.

3 0

2 years ago

Read 2 more answers

The cup, on the 9th hole of a golf course, is located, dead center, in the middle of a circular green, which is 35 feet in radiu

ale4655 [162]

Answer:

± 27.33 ft

Step-by-step explanation:

For the given problem, we can estimate the initial and final coordinates of the line of the ball path as (-40,-50) and (0,0). Therefore, the slope is:

(-50-0)/(-40-0) = 50/40 = 1.25

Similarly, we can estimate the slope of a perpendicular line to the line of the ball path as: -1*(1/1.25) = -0.8.

Therefore, using (0,0) and the slope -0.8, the equation of the perpendicular line is: -0.8 = (y-0)/(x-0);

-0.8 = y/x

y = -0.8x

Furthermore, we are given the circle radius as 35 ft and we can use the distance formula to find the two points 35 ft far from the origin:

35^2 = x^2 + y^2

y = -0.8x

35^2 = x^2 + (-0.8x)^2

1225 = (x^2 + 0.64x^2)

1225 = 1.64x^2

x^2 = 1225/1.64 = 746.95

x = sqrt(746.95) = ± 27.33 ft

5 0

2 years ago

The weight of a person on or above the surface of the earth varies inversely as the square of the distance the person is from th

bazaltina [42]

$\bf \qquad \textit{ inverse proportional variation}\\\\\\
\begin{array}{llllll}
\textit{something}&&\textit{varies inversely to}&\textit{something else}\\ \quad \\
\textit{something}&=&\cfrac{{{\textit{some value}}}}{}&\cfrac{}{\textit{something else}}\\ \quad \\
y&=&\cfrac{{{\textit{k}}}}{}&\cfrac{}{x}

&&y=\cfrac{{{ k}}}{x}
\end{array}$

"<span>The weight of a person on or above the surface of the earth varies inversely as the square of the distance the person is from the center of the earth"

namely "w" varies inversely to </span> $\bf d^2$ or $\bf w=\cfrac{k}{d^2}$

then
"<span>A particular person weighs 192 pounds on the surface of the earth and the radius of the earth is 3900 miles. "
</span>namely when w = 192, d = 3900

so $\bf w=\cfrac{k}{d^2}\qquad 
\begin{cases}
w=192\\
d=3900
\end{cases}\implies 192=\cfrac{k}{3900^2}
\\\\\\
\textit{solve for "k", to find the}\\
\textit{"constant of variation"}\\
\textit{once you've found it, plug it back in at }w=\cfrac{k}{d^2}$

7 0

2 years ago

Polygons are a subcategory of parallograms

dolphi86 [110]

Answer:

Step-by-step explanation:

Category:Parallelograms. ... A parallelogram is a quadrilateral whose opposite sides are parallel to each other, and whose sides may or may not all be the same length.

We know many quadrilaterals by their special shapes and properties, like squares. Remember, if you see the word quadrilateral, it does not necessarily mean a figure with special properties like a square or rectangle! In word problems, be careful not to assume that a quadrilateral has parallel sides or equal sides unless that is stated.

Special Quadrilaterals

A parallelogram has two parallel pairs of opposite sides.

A rectangle has two pairs of opposite sides parallel, and four right angles. It is also a parallelogram, since it has two pairs of parallel sides.

A square has two pairs of parallel sides, four right angles, and all four sides are equal. It is also a rectangle and a parallelogram.

A rhombus is defined as a parallelogram with four equal sides. Is a rhombus always a rectangle? No, because a rhombus does not have to have 4 right angles.

Trapezoids only have one pair of parallel sides. It's a type of quadrilateral that is not a parallelogram. (British name: Trapezium)

Kites have two pairs of adjacent sides that are equal.

We can use a Venn diagram to help us group the types of quadrilaterals.

A Venn diagram uses overlapping circles to show relationships between groups of objects. All "quadrilaterals" can be separated into three sub-groups: general quadrilaterals, parallelograms and trapezoids.

Is a rectangle always a rhombus? No, because all four sides of a rectangle don't have to be equal. However, the sets of rectangles and rhombuses do intersect, and their intersection is the set of squares—all squares are both a rectangle and a rhombus.

We can put squares in the intersection of the two circles.

From this diagram, you can see that a square is a quadrilateral, a parallelogram, a rectangle, and a rhombus!

Is a trapezoid a parallelogram? No, because a trapezoid has only one pair of parallel sides. That is why we must show the set of trapezoids in a separate circle on the Venn diagram.

What about kites? Kites are quadrilaterals that can be parallelograms. If their two pairs of sides are equal, it becomes a rhombus, and if their angles are equal, it becomes a square.

Related Links:

Area Formulas

Perimeter Formulas

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8 0

2 years ago