Find the equation of the line that passes through (1,4) and is parallel to3x+y+2=0

[tex]\large\underline{\sf{Solution-}}[/tex]

Given that

[tex] \purple{\rm :\longmapsto\:Dividend = {x}^{3} - {2x}^{2} - x + 2}[/tex]

and

[tex] \purple{\rm :\longmapsto\:Divisor = x + 1}[/tex]

So, By using Long Division Method, we have

[tex]\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\:\: {x}^{2} - 3x + 2\:\:}}}\\ {\underline{\sf{x + 1}}}& {\sf{\: {x}^{3}  -  {2x}^{2} - x + 2 \:\:}} \\{\sf{}}& \underline{\sf{- {x}^{3} - {x}^{2} \: \: \:  \:  \:  \:  \:  \:  \:  \: \:\:}} \\ {{\sf{}}}& {\sf{\: \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  - 3{x}^{2} - x +2  \:  \:  \:  \:   \:  \:  \:  \:\:}} \\{\sf{}}& \underline{\sf{\:\: \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  3{x}^{2} + 3x  \:  \:  \:  \:  \:  \: \:\:}} \\ {\underline{\sf{}}}& {\sf{\:\: \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: 2x + 2 \:\:}} \\{\sf{}}& \underline{\sf{\: \:  \:  \:  \:  \:  \:  \:  \:  \:  \: \: - 2x - 2\:\:}} \\ {\underline{\sf{}}}& {\sf{\:\: \:  \: \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: 0\:\:}}  \end{array}\end{gathered}\end{gathered}\end{gathered}[/tex]

So,

[tex]\bf\implies \:Remainder = 0[/tex]

Verification

[tex] \purple{\rm :\longmapsto\:Dividend = {x}^{3} - {2x}^{2} - x + 2}[/tex]

[tex] \purple{\rm :\longmapsto\:Divisor = x + 1}[/tex]

[tex] \purple{\rm :\longmapsto\:Remainder = 0}[/tex]

[tex] \purple{\rm :\longmapsto\:Quotient = {x}^{2} - 3x + 2}[/tex]

Now, Consider

[tex]\rm :\longmapsto\:Divisor \times Quotient + Remainder[/tex]

[tex]\rm \:  =  \: (x + 1)( {x}^{2} - 3x + 2) + 0[/tex]

[tex]\rm \:  =  \: {x}^{3} - {3x}^{2} + 2x + {x}^{2} - 3x + 2[/tex]

[tex]\rm \:  =  \: {x}^{3} - {2x}^{2} - x + 2[/tex]

[tex]\rm \:  =  \: Dividend[/tex]

Hence, Verified

CARRY ON LEARNING

CAN YOU BRAINLEST ME PLEASE

Answer:

[tex] \sf k = 1 \\\\ \sf y = x [/tex]

Step-by-step explanation:

A graph between the amount of time that backpacker hikes to the distance travelled is given .

According to the Question ,

[tex]\sf \implies y \propto x \\\\\sf \implies y = kx [/tex]

[tex]\sf\implies 5 = k(5) \\\\\sf \implies k =\dfrac{5}{5}\\\\\sf \implies \boxed{\frak{\pink{ k = 1 }}}[/tex]

Again the constant of proportionality is the slope of the line.

[tex]\sf\implies y = mx + c \\\\\sf \implies y = 1(x) + 0 \\\\\sf \implies \boxed{\pink{\frak{ y = x }}}[/tex]

Answer:

70m/s

Step-by-step explanation:

Velocity is distance by time so:

[tex]\frac{700}{10}=70m/s\\[/tex]

The sum of the measure of angle of a triangle = 180° .

Given two angles = 92° and 72°

92° + 72° = 164°

180° - 164° = 16° (Ans)

Answer:

the answer is  16!

Answer:

Thus, width is 6 and length is 25.

Step-by-step explanation:

Let us assume the width is x, then, the length is (4x+1).

Therefore, 2x + 2(4x+1) = 62

Or, 2x + 8x + 2 =62

Or, 10x = 60

Or, x = 6

Answer:

27 units.

Step-by-step explanation:

The perimeter is equal to 2 x length + 2 x width.

If the width is 4 then:

62 = 2 x length + 2 x 4

62 = 2 x length + 8

Then, we can subtract 8 from both sides.

54 = 2 x length

Next, divide both sides by 2

27 = length

so,

The length is 27 units.

Answer:

[tex]A = 48.815[/tex]

Step-by-step explanation:

[tex] \frac{a}{ \sin(A) } = \frac{b}{ \sin(B) } [/tex]

[tex] \frac{12.5}{ \sin(A) } = \frac{15.4}{ \sin(68) } [/tex]

[tex]12.5 \sin(68) = 15.4 \sin(A) [/tex]

[tex] \frac{12.5 \sin(68) }{15.4} = \frac{15.4 \sin(A) }{15.4} [/tex]

[tex] \sin(A) = \frac{12.5 \sin(68) }{15.4} [/tex]

[tex] A=\sin ^{ - 1} ( \frac{12.5 \sin(68) }{15.4} ) [/tex]

[tex]A = 48.815[/tex]

Answer:

180 out of 300

Step-by-step explanation:

Basically,

300÷120=2.5

Thereof,

72×2.5=180.

Hope this helps!

tag brainliest please...

Answer:

3x - 2 = 4

x = 2

Step-by-step explanation:

3x - 2 = 4 ---> plus 2 on both sides

3x = 6 --> divide by 3 on both sides

x = 2

Answer: 7200

Step-by-step explanation:

40 percent of leaves are green so 60 percent of leaves are no longer green.

there are 12000 total leaves so [tex]\frac{60}{100}[/tex] × [tex]12000[/tex] = 7200

please give me a brainliest answer

Answer:

m<b=107º

Step-by-step explanation:

180-41-32=107

D and B are congruent

Answer:

Step-by-step explanation:

Take 2 points:

Find the slope:

Find the y- intercept:

The line is:

Answer:

b = 2S/n - a.

Step-by-step explanation:

S=n/2(a + b)

a + b = S / n/2

a + b = 2S/n

b = 2S/n - a.

If the formula for determining the sum of the given arithmetic sequence is S = n/2(a + b), then 'b' can be expressed as b = [(2S/n) - a].

An arithmetic sequence is a sequence where the difference between any to consecutive terms are always equal.

Here, a and b are the first and the last terms respectively and n is the number of terms.

Therefore, the sum of the arithmetic sequence is:

S = n/2(a + b)

⇒ 2S/n = (a + b)

⇒ b = (2S/n) - a

Learn more about an arithmetic sequence here: https://brainly.com/question/25715593

#Tag #SPJ2

A) multiply the price of the game by 5%

42.99 x 0.05 = 2.1495 rounds to 2.15

Amount of tax = $2.15

B) add the amount of tax to the price of the game:

42.99 + 2.15 = 45.14

Total cost = $45.14

Answer:

V = 665,012 cm^2 (centímetros cuadrados)

Step-by-step explanation:

V= (pi) x (r^2) x (h)

V = 3.14 x 1764 x 120cm = 665012 cm^2

Answer:

Step-by-step explanation:

[tex]a) x_{1+1}=\dfrac{(x_{1})^{3}-5}{10}\\\\x_{2}=\dfrac{(-1)^{3}-5}{10}=\dfrac{-1-5}{10}=\dfrac{-6}{10}= - 0.6\\\\\\ii) x_{2+1}=\dfrac{(x_{2})^{3}-5}{10}\\\\x_{3}=\dfrac{(-0.6)^{3}-5}{10}=\dfrac{-0.216-5}{10}=\dfrac{-5.216}{10}= - 0.5216\\\\\\[/tex]

Answer:

AA   as the angles are similar the sides are not similar so AA is the answer

Step-by-step explanation:

Answer:

-72

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]a^{-m}=\dfrac{1}{a^{m}}\\\\8^{-3}=\dfrac{1}{8^{3}}=\dfrac{1}{8*8*8}=\dfrac{1}{512}[/tex]

Answer:

x = 1, y = 1

x = -2, y = -8

x = 3, y = 7

Step-by-step explanation:

Answer and explanation:

Temperature:

If it was -5°C, you know that it is very cold and below freezing point (0°C), but if it was 20°C you know the weather is quite warm.

0°C is freezing point and is used as a reference point to be able to tell if the temperature is warm or not.

The question provides the measures of two angles, (one of which contains

a variable), and the relationship between the angles.

The value of x is 6 degrees

Reason:

The given parameters are;

The base angles of the isosceles triangles are; 61° and (7·x + 19)°

Required:

To find the value of x

Solution:

By definition of an isosceles triangle, we have;

The base angles of an isosceles triangle are equal, therefore;

(7·x + 19) = 61

Which gives;

[tex]x = \dfrac{61 - 19}{7} = 6[/tex]

The value of x = 6

Learn more here:

https://brainly.com/question/16350203

Answer:

20N

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

1) Subtract 44 from both sides of the equation

3x + 44 - 44 = 50 - 44

2) Simplify

a. Subtract the numbers

3x = 50 - 44

b. Subtract the numbers

3x = 6

3) Divide both sides of the equation by the same term

3x/3 = 6/3

4) Simplify

a. Cancel terms that are in both the numerator and denominator

x = 6/3

b. Divide the numbers

x = 2

Answer:

The answer is 500

Step-by-step explanation:

When you round to the hundred, you look at the 10s place. If the 10s place is 5,6,7,8, or 9, you round the hundred up. In this case, it is 459 so you would round up to 500. Have a nice day!!!

Answer:

continuous becasue the arrows point out meaning the go on forever

Step-by-step explanation:

Answer:

8.) Rational

10.) Irrational

Step-by-step explanation:

8.) This is rational because although it is a decimal, it is terminating, meaning it has an end.

10.) This is irrational because it is a repeating decimal with seemingly no pattern.

Answer:

Hey there, first let's find the slope.

M=y2-y1/x2-x1.

M=7-3/2-1 which is 4/1.

So your slope is 4

So now we have y=4x+b.

Now we need our Y-intercept (B). which is -1

So your answer is Y=4x-1

Answer:

any function which can be written as the ratio of two polynomial functions.

have a nice day <3

the answer is -6.

the negative 7 turns the answer negative.