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3 years ago

Select one of the factors of x3y2 + 8xy2 + 5x2 + 40.

Mathematics

1 answer:

aniked [119]3 years ago

5 0

Answer:

Option a - $xy^2+5$

Step-by-step explanation:

Given : Polynomial $x^3y^2+8xy^2+5x^2+40$

To find : Select one of the factors of polynomial ?

Solution :

The polynomial $x^3y^2+8xy^2+5x^2+40$

We factor of above polynomial by taking common terms,

$xy^2(x^2+8)+5(x^2+8)$

$(xy^2+5)(x^2+8)$

From the given options,

$xy^2+5$ is one of the factors of polynomial.

Therefore, option a is correct.

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∆ABC has vertices A(–2, 0), B(0, 8), and C(4, 2)

Natali [406]

Answer:

Part 1) The equation of the perpendicular bisector side AB is $y=-\frac{1}{4}x+\frac{15}{4}$

Part 2) The equation of the perpendicular bisector side BC is $y=\frac{2}{3}x+\frac{11}{3}$

Part 3) The equation of the perpendicular bisector side AC is $y=-3x+4$

Part 4) The coordinates of the point P(0.091,3.727)

Step-by-step explanation:

Part 1) Find the equation of the perpendicular bisector side AB

we have

A(–2, 0), B(0, 8)

step 1

Find the slope AB

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{8-0}{0+2}$

$m=4$

step 2

Find the slope of the perpendicular line to side AB

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

therefore

The slope is equal to

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

step 3

Find the midpoint AB

The formula to calculate the midpoint between two points is equal to

$M(\frac{x1+x2}{2},\frac{y1+y2}{2})$

substitute the values

$M(\frac{-2+0}{2},\frac{0+8}{2})$

$M(-1,4)$

step 4

Find the equation of the perpendicular bisectors of AB

the slope is $m=-\frac{1}{4}$

passes through the point $(-1,4)$

The equation in slope intercept form is equal to

$y=mx+b$

substitute

$4=(-\frac{1}{4})(-1)+b$

solve for b

$b=4-\frac{1}{4}$

$b=\frac{15}{4}$

$y=-\frac{1}{4}x+\frac{15}{4}$

Part 2) Find the equation of the perpendicular bisector side BC

we have

B(0, 8) and C(4, 2)

step 1

Find the slope BC

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{2-8}{4-0}$

$m=-\frac{3}{2}$

step 2

Find the slope of the perpendicular line to side BC

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

therefore

The slope is equal to

$m=\frac{2}{3}$

step 3

Find the midpoint BC

The formula to calculate the midpoint between two points is equal to

$M(\frac{x1+x2}{2},\frac{y1+y2}{2})$

substitute the values

$M(\frac{0+4}{2},\frac{8+2}{2})$

$M(2,5)$

step 4

Find the equation of the perpendicular bisectors of BC

the slope is $m=\frac{2}{3}$

passes through the point $(2,5)$

The equation in slope intercept form is equal to

$y=mx+b$

substitute

$5=(\frac{2}{3})(2)+b$

solve for b

$b=5-\frac{4}{3}$

$b=\frac{11}{3}$

$y=\frac{2}{3}x+\frac{11}{3}$

Part 3) Find the equation of the perpendicular bisector side AC

we have

A(–2, 0) and C(4, 2)

step 1

Find the slope AC

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{2-0}{4+2}$

$m=\frac{1}{3}$

step 2

Find the slope of the perpendicular line to side AC

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

therefore

The slope is equal to

$m=-3$

step 3

Find the midpoint AC

The formula to calculate the midpoint between two points is equal to

$M(\frac{x1+x2}{2},\frac{y1+y2}{2})$

substitute the values

$M(\frac{-2+4}{2},\frac{0+2}{2})$

$M(1,1)$

step 4

Find the equation of the perpendicular bisectors of AC

the slope is $m=-3$

passes through the point $(1,1)$

The equation in slope intercept form is equal to

$y=mx+b$

substitute

$1=(-3)(1)+b$

solve for b

$b=1+3$

$b=4$

$y=-3x+4$

Part 4) Find the coordinates of the point of concurrency of the perpendicular bisectors (P)

we know that

The point of concurrency of the perpendicular bisectors is called the circumcenter.

Solve by graphing

using a graphing tool

the point of concurrency of the perpendicular bisectors is P(0.091,3.727)

see the attached figure

5 0

3 years ago

The chef took out 54.8 g of butter but then found out that he took out 6.9 g of butter more than he needed. How much butter did

stira [4]

Answer:

47.9 gm

Step-by-step explanation:

According to the scenario, calculation of the given data are as follows,

Total butter took = 54.8 gm

Extra butter quantity = 6.9g

So, we can calculate the exact quantity of butter needed by using following formula,

Exact butter needed = Total butter - Extra butter quantity

By putting the value, we get

Exact butter needed = 54.8 gm - 6.9gm

= 47.9 gm

Hence, he need 47.9gm butter.

6 0

3 years ago

Solve the inequality. 1/6w≥2.5

Viefleur [7K]

$\dfrac{1}{6}w\geq2.5\qquad\text{multiply both sides by 6}\\\\\not6^1\cdot\dfrac{1}{\not6_1}w\geq6\cdot2.5\\\\\boxed{w\geq15}$

7 0

3 years ago

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What is the y-intercept of the line represented by the equation y = 2x - 3?

cestrela7 [59]

Y =Mx + C
where M = gradient / slope
C = y intercept

comparing with y = 2x - 3
M = 2
C = -3

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3 years ago

If michelle rollerblades around a circular track with a radius of 80 meters, how far does she skate? use 3.14 for pi. round to t

Andrew [12]

I believe it’s A but not quite sure

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4 years ago

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