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4 years ago

(x^2-10x+30)/(x-5) all it says is dividing polynomials

Mathematics

1 answer:

galina1969 [7]4 years ago

7 0

At each step, you determine the quotient term by dividing the highest-degree term of the dividend by the highest degree term of the divisor. When you can't do that anymore, you're done and the remaining dividend is the remainder.

Here, the highest-degree dividend term is x^2 and the highest-degree divisor term is x. Their ratio, x^2/x = x, is the first quotient term. In the usual manner of long division, you subtract the product of this quotient term and the divisor to get the new dividend.

For this problem, the quotient is (x -5) and the remainder is 5. You can write the result as
(x² -10x +30)/(x -5) = (x -5) +5/(x -5)

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Please help answer the two questions in the photo

Alex

The given pentagon can be divided into two figures : a triangle and rectangle as shown in figure.

Let us find area of each figure separately.

Triangle:

Area of triangle is given by:

$A=\frac{1}{2}*b*h$

where b=base and h=height

Height of triangle :

h=(3x+5)-(2x+1)

h=x+4

Base = 2x-2

$A=\frac{1}{2}*(x+4)(2x-2)$

Area of triangle= (x-1)(x+4) = x²+3x-4

Area of rectangle:

Area of rectangle is given by:

A=l*b

$A=(2x-2)(2x+1)$

Area of rectangle = 4x²-2x-2

Area of pentagon = Area of triangle + Area of rectangle

Area of pentagon = x²+3x-4 + 4x²-2x-2

Area of pentagon = 5x²+x-6

If area of pentagon is 42 cm², then solving for x,

$42=5x^{2}+x-6$

$5x^{2}+x-48=0$

Factorising to get x,

x=-3.2 and x=3

If we take x as negative the side will be negative, so we neglect x=-3.2

So x=3 is the answer.

3 0

3 years ago

PRS is isosceles with RP RS RQ is drawn such that it bisects PRS What additional fact can be used to prove PRQ SRQ by Sas in ord

SOVA2 [1]

Answer:

$\frac{PQR}{SQR}$

Step-by-step explanation:

An isosceles triangle has two equal sides and the two opposite angles to the sides to be equal.

Given that; RP = RS, RQ and PS are common,

RP = SQ (opposite sides of parallelogram RPQS)

PQ = RS (opposite sides of parallelogram RPQS)

ΔRPS = ΔQPS (congruence property)

Thus comparing triangles PQR and SQR,

$\frac{PQ}{SQ}$ = $\frac{PR}{SR}$ (similarity property)

<PRS = <PRQ + <SRQ (bisection of included <PRS)

<PQS = <PQR + <SQR (similatity property to <PRS)

$\frac{PRQ}{SRQ}$ = $\frac{SQR}{PQR}$ (congruence property)

But, SRQ = PQR

So that;

$\frac{PRQ}{SQR}$

Therefore by Side-Angle-Side (SAS), the required additional fact is: $\frac{PRQ}{SQR}$

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3 years ago

700 tickets were sold for a game for a total of $1,250.00. If adult tickets sold for $2.00 and children's tickets sold for $1.50

Vlad1618 [11]

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4 years ago

Read 2 more answers

Sin 30°-cos 30°÷ sin 60°<br><br>

Vilka [71]

Answer:

-1/2

Step-by-step explanation:

sin(30 degrees) = sin (pi/6) = 1/2

cos(30 degrees) = cos (pi/6) = [sqrt(3)]/2]

sin (60 degrees) = sin(pi/3) = [sqrt(3)]/2]

1/2 - [sqrt(3)/2] / [sqrt(3)/2] = -1/2