All categories

3 years ago

Which is true about the degree of the sum and difference of the polynomials 3x5y – 2x3y4 – 7xy3 and –8x5y + 2x3y4 + xy3?

Mathematics

2 answers:

Anit [1.1K]3 years ago

7 0

Answer:

The sum has a degree of 6, but the difference has a degree of 7.

Step-by-step explanation:

tankabanditka [31]3 years ago

6 0

Answer:

The option " The sum has degree of 6 , but the difference has a degree of 7 " is correct.

Step-by-step explanation:

Given that the sum and difference of the polynomials $3x^5y-2x^3y^4-7xy^3$ and $-8x^5y+2x^3y^4+xy^3$

<h3>Now sum the given polynomials :</h3>

$3x^5y-2x^3y^4-7xy^3+(-8x^5y+2x^3y^4+xy^3)$

$=3x^5y-2x^3y^4-7xy^3-8x^5y+2x^3y^4+xy^3$

$=-5x^5y+0-6xy^3$

$=-5x^5y-6xy^3$

Therefore $3x^5y-2x^3y^4-7xy^3+(-8x^5y+2x^3y^4+xy^3)=-5x^5y-6xy^3$

In the simplified <u>sum of the polynomials</u> $-5x^5y-6xy^3$ we have <u>the degree is 6</u>

<h3>Now difference the polynomials </h3>

$3x^5y-2x^3y^4-7xy^3-(-8x^5y+2x^3y^4+xy^3)$

$=3x^5y-2x^3y^4-7xy^3+8x^5y-2x^3y^4-xy^3$

$=11x^5y-4x^3y^4-8xy^3$

Therefore $3x^5y-2x^3y^4-7xy^3-(-8x^5y+2x^3y^4+xy^3)=11x^5y-4x^3y^4-8xy^3$

In the simplified <u>difference of polynomials</u> $11x^5y-4x^3y^4-8xy^3$ we have <u>the degree is 7</u>

Therefore the option " The sum has degree of 6 , but the difference has a degree of 7 " is correct

You might be interested in

Since it's Wednesday, Buy for Less gives a 5% discount for purchases. The items in Rhonda's cart total $53.75. She needs to know

Aleksandr-060686 [28]

First we need to know how much the discount was so 5% is actually 0.05 then we need to multiply it by 53.75 which would equal 2.6875 then subtract it by 53.75 which would equal -51.0625.

B) .95(53.75)

This is a trick question because D) could also be correct if they said you could subtract it but it's not saying use the distributive property.

5 0

3 years ago

Read 2 more answers

0-6

dybincka [34]

<h3>Given :-</h3>

Pranav ran 20.3 km more than Branda

Pravin ran 38.6 km

$\\ \\$

To find :

No. of kilometers did Brenda run.

$\\ \\$

No. of kilometers ran by Brenda be x.

$\\ \\$

<h3>Solution:</h3>

$\\ \\$

Equation formed:-

$\\ \\$

Total distance covered by Pravan = More distance covered by Pravan + distance covered by Brenda.

Therefore:-

$\\ \\$

$\leadsto \sf38.6 = 20.3 + x$

Write the equation

$\\ \\$

$\leadsto \sf38.6 - 20.3 =x$

When we transfer 20.3 to left side the positive sign (+) will change into negative sign (–)

$\\ \\$

$\leadsto \sf x = 38.6 - 20.3$

Arrange the equation because x is always represented at left side.

$\\ \\$

$\leadsto \boxed {\pmb{\sf x = 18.3}}\star$

After subtracting 38.6 with 20.3 we will get result as 18.3 .

$\\ \\$

$\therefore \red{ \underline{ \pmb{\frak{Distance ~ covered ~by ~Brenda~ is ~equal ~to~18.3~kilometers}}}}$

7 0

2 years ago

find the equation of the perpendicular bisector of the line segment joining the points (3,8) and (-5,6).

IgorLugansk [536]

Answer:

y = - 4x + 3

Step-by-step explanation:

The perpendicular bisector is positioned at the midpoint of AB at right angles.

We require to find the midpoint and slope m of AB

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = A(3, 8) and (x₂, y₂ ) = B(- 5, 6)

m = $\frac{6-8}{-5-3}$ = $\frac{-2}{-8}$ = $\frac{1}{4}$

Given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{\frac{1}{4} }$ = - 4

mid point = [0.5(x₁ + x₂ ), 0.5(y₁ + y₂ ) ]

Using the coordinates of A and B, then

midpoint AB = [0.5(3 - 5), 0.5(8 + 6) ] = (- 1, 7 )

Equation of perpendicular in slope- intercept form

y = mx + c ( m is the slope and c the y- intercept )

with m = - 4

y = - 4x + c ← is the partial equation

To find c substitute (- 1, 7) into the partial equation

Using (- 1, 7), then

7 = 4 + c ⇒ c = 7 - 4 = 3

y = - 4x + 3 ← equation of perpendicular bisector

3 0

3 years ago

Read 2 more answers

PLEASE PLEASE ANSWER!

muminat

The area of the shaded region is $$8(\pi \ -\sqrt{3})\ \text{cm}^2$ .

Solution:

Given radius = 4 cm

Diameter = 2 × 4 = 8 cm

Let us first find the area of the semi-circle.

Area of the semi-circle = $\frac{1}{2}\times \pi r^2$

$$=\frac{1}{2}\times \pi\times 4^2$

$$=\frac{1}{2}\times \pi\times 16$

Area of the semi-circle = $$8\pi$ cm²

Angle in a semi-circle is always 90º.

∠C = 90°

So, ABC is a right angled triangle.

Using Pythagoras theorem, we can find base of the triangle.

$AC^2+BC^2=AB^2$

$AC^2+4^2=8^2$

$AC^2=64-16$

$AC^2=48$

$AC=4\sqrt{3}$ cm

Base of the triangle ABC = $4\sqrt{3}$ cm

Height of the triangle = 4 cm

Area of the triangle ABC = $\frac{1}{2}\times b \times h$

$$=\frac{1}{2}\times 4\sqrt{3} \times 4$

Area of the triangle ABC = $8\sqrt{3}$ cm²

Area of the shaded region

= Area of the semi-circle – Area of the triangle ABC

= $$8\pi \ \text{cm}^2-8\sqrt{3}\ \text{cm}^2$

= $$8(\pi \ -\sqrt{3})\ \text{cm}^2$

Hence the area of the shaded region is $$8(\pi \ -\sqrt{3})\ \text{cm}^2$ .

3 0

3 years ago

Isaac bought seven new magic cards to add to his collection this year the next day he gave half his entire collection to his fri

OverLord2011 [107]

Answer:

35 cards

Step-by-step explanation:

21x2=42

42-7=35

3 0

3 years ago

Read 2 more answers