x^3+x^2+x+1 ÷x-1/2 find the remainder

[tex]\sf \: {x}^{2} - 5[/tex]

[tex]\sf \: Use \: the \: algebraic \: identity \\ \sf \: a {}^{2} - {b}^{2} = (a - b)(a + b)[/tex]

[tex]\sf \: Substitute \: the \: value \: of \: a \: and \: b \: in \: the \: identity.[/tex]

[tex]\sf \: a = \sqrt{x ^{2} } = x \\ \sf \: b = \sqrt{5} [/tex]

[tex]\sf \: the \: identity \: becomes \: [/tex]

[tex]\sf {x}^{2} - 5 \\ \sf = (x - \sqrt{5} )(x + \sqrt{5} ) \\ [/tex]

Answer ⟶ [tex]\boxed{\bf{(x - \sqrt{5} )(x + \sqrt{5} )}}[/tex]

Answer:

point 1 = (3, 6)

point 2 = (24, -15)

Step-by-step explanation:

8/x - 10/y = 1

x + y = 9

x = 9 - y

=>

8/(9-y) - 10/y = 1

8 - 10×(9-y)/y = 9 - y

-90/y + 10y/y = 1 - y

-90/y + 10 = 1 - y

-90 + 10y = y - y²

y² + 9y -90 = 0

the solution to a squared equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case we use y instead of x.

a = 1

b = 9

c = -90

y = (-9 ± sqrt(81 - -360))/2 = (-9 ± sqrt(441))/2 =

= (-9 ± 21)/2

y1 = 12/2 = 6

y2 = -30/2 = -15

8/x - 10/6 = 1

8 - 10x/6 = x

8 - 5x/3 = x

24 - 5x = 3x

24 = 8x

x = 3

8/x - 10/-15 = 1

8/x + 2/3 = 1

8 + 2x/3 = x

24 +2x = 3x

24 = x

======================================================

Explanation:

The rule we use is

a^b * a^c = a^(b + c)

This says that if we multiply exponential expressions with the same base, then we add the exponents. We keep the base the same the entire time.

For example, 2^3*2^4 = 2^(3+4) = 2^7

--------------

For this problem, we'll say,

5^(56)*5^(22)*5^(-96)

5^( 56+22+(-96) )

5^(-18)

Be sure that you use parenthesis so that you tell your teacher that all of the -18 is in the exponent. Saying 5^-18 could lead to ambiguity.

Answer:

sorry it he question isn't clear

Answer,

C

Step-by-step explanation:

I had the same question 2 days ago

Answer:

Step-by-step explanation:

Answer:

next 3 terms are -15, -28, -41. The formula would be n= (n-1)-13 to get the nth term

Step-by-step explanation:

Answer:

-2x-10=-2(x+5)

Step-by-step explanation:

Just multiply and find the pair that matches which happens to be the 3rd pair. you're welcome

Answer:

[tex]32\:\mathrm{m^2}[/tex]

Step-by-step explanation:

When cut by a diagonal, the parallelogram will be divided into two congruent triangles. By definition, congruent polygons have equal areas. Therefore, let the area of each of the triangle be [tex]x[/tex]:

[tex]x+x=64,\\2x=64,\\x=\frac{64}{2}=\boxed{32\:\mathrm{m^2}}[/tex]

yes it can be possible to do

Answer:

[tex]VR=5[/tex]

Step-by-step explanation:

From the question we are told that:

No of Pulleys =5

Generally Greatest VR is achieved if it has no friction to the pulleys

Therefore

[tex]W=5P[/tex]

Generally the equation for Efficiency  is mathematically given by

[tex]n=\frac{MA}{VR}[/tex]

Where

MA=mechanical advantage

Therefore  at Greatest VR

[tex]n=100 \%[/tex]

[tex]MA=VR[/tex]

[tex]VR=\frac{W}{P}[/tex]

[tex]\frac{W}{P}=5[/tex]

[tex]VR=5[/tex]

Answer:

Step-by-step explanation:

The answer is 4.

Once you add 4, you get:

x^2 -2x + 4 = 7.

The left side is factorable:

(x-2)^2 = 7.

There is your perfect square.

Answer:

1) The length of [tex]DC[/tex] is 20.

2) The length of [tex]PS[/tex] is 17.

Step-by-step explanation:

1) If [tex]DR = RE[/tex] and [tex]CS = SB[/tex], then we can use the following proportionality ratio:

[tex]\frac{DE}{DR} = \frac{32 - x}{26 - x}[/tex] (1)

Where [tex]x[/tex] is the length of segment [tex]\overline{CD}[/tex].

If [tex]DE = 2\cdot DR[/tex], then the value of [tex]x[/tex] is:

[tex]2 = \frac{32-x}{26-x}[/tex]

[tex]52 - 2\cdot x = 32 - x[/tex]

[tex]20 = x[/tex]

The length of [tex]DC[/tex] is 20.

2) If [tex]QV = VP[/tex] and [tex]RW = WS[/tex], then we can use the following proportionality ratio:

[tex]\frac{QP}{QV} = \frac{x-7}{12-7}[/tex] (2)

Where [tex]x[/tex] is the length of segment [tex]\overline{PS}[/tex].

If [tex]QP = 2\cdot QV[/tex], then the value of [tex]x[/tex] is:

[tex]2 = \frac{x-7}{5}[/tex]

[tex]10 = x-7[/tex]

[tex]x = 17[/tex]

The length of [tex]PS[/tex] is 17.

Answer:

See graph

[tex](x +3)^{2}[/tex] + [tex](y + 1)^{2}[/tex] = 9

(-3 , -1) is the center.

[tex]\sqrt{9}[/tex] = 3 = radius

Step-by-step explanation:

[tex](x - h)^{2} + (y - k)^{2} = r^{2}[/tex]

center (h,k)

radius = r

Answer:

[tex]x = 4[/tex]

Step-by-step explanation:

Step 1:  Solve for x

Since there are two parallel lines and one perpendicular line through the middle, that means that all of the angles are equal.  Therefore, we can make an equation 21x + 6 = 90 and solve for x

[tex]21x + 6 - 6 = 90 - 6[/tex]

[tex]21x / 21 = 84 / 21[/tex]

[tex]x = 4[/tex]

Answer:  [tex]x = 4[/tex]

Answer:

1. 40

2. 52

Step-by-step explanation: 1. Subtract 16 from 36 then multiply by 2

2. Subtract 4 from 472 then divide by nine

Answer:

Step-by-step explanation:

The rectangle has 4 corners of 90 degrees.

Here a rectangle is divided into two right triangles. In right-angled triangles, the opposite side at a 30-degree angle is half a chord...I replace x instead of length.. So x / 2 = 4--->x:8

The perimeter of a rectangle is equal to (length + width) × 2--->(8+4)×2=24m^2

Answer:

[tex]\text{(D) }16\sqrt{3}\:\mathrm{m^2}[/tex]

Step-by-step explanation:

In all 30-60-90 triangles, the sides are in ratio [tex]x:2x:x\sqrt{3}[/tex], where [tex]x[/tex] is the side opposite to the 30 degree angle and [tex]2x[/tex] is the hypotenuse of the triangle.

The rectangle shown forms two 30-60-90 triangles. The side labelled 4 meters is opposite to the 30 degree angle. Therefore, the side on top must be [tex]x\sqrt{3}\text{ for }x=4[/tex]. Let the length of the top base be [tex]w[/tex]:

[tex]w=4\sqrt{3}[/tex]

The area of a rectangle with length [tex]l[/tex] and width [tex]w[/tex] is given by [tex]A=lw[/tex]. Thus, the area of the rectangle is:

[tex]A=4\cdot 4\sqrt{3},\\A=\boxed{16\sqrt{3}\:\mathrm{m^2}}[/tex]

Answer:

[see below]

Step-by-step explanation:

A functions input is assigned to exactly one output. This means that the inputs must not repeat.

{(-3, 5), (-2, 5), (0, 5), (1, 5), (2, 5)}

Since no inputs repeat, the relation given is a function.

Hope this helps.

Answer:

Yes, it's a function.

Step-by-step explanation:

X or input no repeated.

Answer:

(x-12)^2+(y-2)^2=4

Step-by-step explanation:

Answer:

the values of it is the first one. meaning: f(-2)

Answer:

Step-by-step explanation:

2

3

-1

Answer:

Para un rectángulo de largo L y ancho W, el área se define como:

A = L*W

Ahora sabemos que nuestro rectángulo tiene un área de 24cm^2

Entonces queremos encontrar 3 pares de valores L y W tal que:

L*W = 24cm

Esto es bastante trivial, podemos simplemente definir una de las dos variables, y así encontrar el valor de la otra.

Por ejemplo, si definimos L = 1cm

tenemos:

(1cm)*W = 24cm^2

W = (24cm^2)/(1cm) = 24cm

Entonces un posible rectángulo tiene un largo de 1cm y un ancho de 24cm

Si tomamos L = 3cm tenemos:

(3cm)*W = 24cm^2

W = (24cm^2)/(3cm) = 8cm

Un rectángulo con 8cm de ancho y 3cm de largo es otra opción.

Si tomamos L = 4cm tenemos:

(4cm)*W = 24cm^2

W = (24cm^2)/(4cm) = 6cm

Un rectángulo con 6cm de ancho y 4cm de largo también es un posible rectángulo.

Así, los 3 rectangulos que se piden pueden ser:

1) largo 1 cm, ancho 24cm

2) largo 3cm, ancho 8cm

3) largo 4cm, ancho 6cm

Answer:

the answer is as follows:

Step-by-step explanation:

a)

The equation has the following integer solutions:

5*x+25=-3*xy+8*y^2

Number of solutions found: 3

x1=-31; y1=-10

x2=-7; y2=-2

x3=-5; y3=-0

b)

The equation has the following integer solutions:

2*y^2+x+y+1=x^2+2*y^2+xy

Number of solutions found: 2

x1=0; y1=-1

x2=2; y2=-1

 Do not forget to give appriciation.

Answer:

63

Step-by-step explanation:

a=9

7a

7(9)

63

Answer:

20 degrees

Step-by-step explanation:

we can consider 33 to be the radius of a circle.

31 would then be the cos of the angle in that circle.

the regular cos function is defined for the standard circle with radius 1. so, that would be multiplied by 33 for this circle here.

31 = cos(?) × 33

cos(?) = 31/33 = 0.9393...

? = 20.05 ≈ 20 degrees

Step-by-step explanation:

First sentence

Let the number be X

second sentence

X-5

Third sentence

X-5=14

X=19

The number is 19

Hi there!  

»»————-　★　————-««

I believe your answer is:

19

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\text{"I am thinking of a number. l take away 5. The result is 14."}\\\\\text{5 taken away from 'said number' would be 14.}\\\\\boxed{n-5=14}\\\\\\\boxed{\text{Solving for 'n'...}} \\\\\rightarrow n - 5 + 5 = 14 + 5\\\\\rightarrow \boxed{n = 19}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

700 apples

Step-by-step explanation:

Let

x = Total number of apples in the cart

Percentage of apples sold = 40%

Number of apples sold = Percentage of apples sold * Total number of apples in the cart

= 40% * x

= 0.4 * x

= 0.4x

Number of apples left in the cart = 420

Total number of apples in the cart = Number of apples sold + Number of apples left in the cart

x = 0.4x + 420

x - 0.4x = 420

0.6x = 420

x = 420/0.6

x = 700

x = Total number of apples in the cart = 700

Lawrence started with 700 apples

Answer:

25.

Step-by-step explanation:

Let the number of pupils be x, then:

there are 0.6x girls and 0.4x boys.

From the given information:

0.6x - 0.4x = 5

0.2x = 5

x = 5/0.2

= 50/2

= 25.

hope this helps! feel free to clarify if unsure

Answer:

QXV=WXV

Step-by-step explanation:

Answer:

Triangle ISK

Step-by-step explanation:

Answer:

Triangle ISK

Step-by-step explanation:

if the angles and sides of one triangle are equal to the corresponding sides and angles of the other triangle, they are congruent.

∠Q = ∠I

∠R = ∠S

∠S = ∠K