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3 years ago

Divide x³-4x²+5x-2 by x-2

Mathematics

2 answers:

tatyana61 [14]3 years ago

8 0

Answer:

p(x)=x^3-4x^2+5x-2

=(2)^3-4(2)^2+5(2)-2

=8-4(4)+10-2

=8-16+10-2

hope it helps mark as brainliest

Mekhanik [1.2K]3 years ago

4 0

Answer:

remainder is zero

quotient is x^2-2x+1

Step-by-step explanation:

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The ratio of boys to girls in homeroom is 2:3. If there<br> are 8 boys, how many girls are there?

Harrizon [31]

Let’s make 2:3 is the same as 8:12. This means that there are 12 girls in the home room.

4 0

4 years ago

I suck at math if you could help me with these questions that would be great

docker41 [41]

Answer:

Part 8) The triangles are not similar (see the explanation)

Part 12) The triangles are not similar (see the explanation)

Part 14) The area is increased by 125%

Part 15) $h=30\ ft$

Step-by-step explanation:

Part 8) we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

<em>Find the value of x in the larger triangle</em>

The sum of the interior angles in any triangle must be equal to 180 degrees

$64^o+85^o+x=180^o$

$149^o+x=180^o$

$x=180^o-149^o$

$x=31^o$

<em>Find the value of y in the smaller triangle</em>

The sum of the interior angles in any triangle must be equal to 180 degrees

$26^o+85^o+y=180^o$

$111^o+y=180^o$

$y=180^o-111^o$

$y=69^o$

The corresponding angles of both triangles are not congruent

therefore

The triangles are not similar

Part 12) we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

The measure of the interior angles of the triangle of the left are

88°

29° ----> by vertical angles

and

180°-(88°+29°)=63° ---> the sum of the interior angles in any triangle must be equal to 180 degrees

The measure of the interior angles of the triangle of the right are

180°-91°=89° ----> the sum of a exterior angle and a interior angle is equal to 180 degrees

29°

and

180°-(89°+29°)=62° ---> the sum of the interior angles in any triangle must be equal to 180 degrees

The corresponding angles of both triangles are not congruent

therefore

The triangles are not similar

Part 14) we know that

If two figures are similar then the ratio of its areas is equal to the scale factor squared

In this problem the scale factor is 1.5

Because

100%+50%=150%=150/100=1.5

The scale factor squared is $1.5^2=2.25$

That means that the new area is 2.25 times the original area

The area is increased by 125%

Part 15)

Let

h ----> the height of the pine

we know that

The height of the person divided by the length of his shadow is equal to the height of the pine tree divided by the length of its shadow

using proportion

$\frac{6}{3}=\frac{h}{15}$

solve for h

$2=\frac{h}{15}$

$h=2(15)=30\ ft$

6 0

3 years ago

The sum of two numbers, one of which is two-third of the other, is 45. find the smaller number

Travka [436]

Step-by-step explanation:

The smaller number is 18.

Step-by-step explanation:

Let larger number = x and smaller number = \dfrac{2}{3} x32x

To find, the smaller number = ?

According to question,

x+\dfrac{2}{3} x=45x+32x=45

⇒ \dfrac{3x+2x}{3} =4533x+2x=45

⇒ 5x=45\times 35x=45×3

⇒ 5x=1355x=135

⇒ x =\dfrac{135}{5} =27x=5135=27

∴ Smaller number =\dfrac{2}{3} \times 27=2\times 9 =18=32×27=2×9=18

Hence, the smaller number is 18.

6 0

3 years ago

I need help with these

3241004551 [841]

1. a= 60 (vertically opposite angles)

b= 360-(60+60)=240/2= 120 (angles at a point)

c= 120 (vertically opposite angles with b)

2. c= 90-40= 50 (vertically opposite angles)

b=a=360-90-90=180/2=90 (angles at a point)

3. a= 180-52-51= 77 (angles on a straight line)

b=52 (angles at a point)

d=51 (angles at a point)

c=77 (angles at a point)

4. a= 60 (vertically opposite angles)

b= 360-(60+60)=240/2= 120 (angles at a point)

c= 120 (vertically opposite angles with b)

e=65

d=f= 360-65-65=230/2=115

h=55

i=g=360-55-55=250/2=125

5. b=163

a=90

e=70

d=360-70-70=220/2=110

c=360-163-163=34/2=17

Hope this helps!

4 0

3 years ago

The temperature in degrees Celsius, c, can be converted to degrees Fahrenheit, f, using the equation f-c+32. Which

Basile [38]

It is a function because every Celsius temperature is associated with only one Fahrenheit temperature. Therefore, option B is true.

<h3>How to convert Celsius into Fahrenheit ?</h3>

We are given that the temperature in degrees Celsius C can be converted to degrees Fahrenheit F

We know that the formula

$\dfrac{C}{5} = \dfrac{F - 32}{9}$

If we are substituting c = -40

Then, we get

$\dfrac{C}{5} = \dfrac{F - 32}{9}\\\\\dfrac{-40}{5} = \dfrac{F - 32}{9}\\\\-8 \times 9 = F - 32\\\\F = -72 + 32\\\\F = -40$

For every Celsius temperature, we get only one value of Fahrenheit.

The function is one-one because for every value of Celsius we get a unique value of Fahrenheit.

Hence, it is a function because every Celsius temperature is associated with only one Fahrenheit temperature.

Therefore, option B is true.

Learn more about temperature scale here:

brainly.com/question/2919967

#SPJ1

7 0

3 years ago

Divide x³-4x²+5x-2 by x-2​

Divide x³-4x²+5x-2 by x-2