Consider the equation: x^2 - 4x + 4 = 2x

Rewrite the equation by completing the square:
Your equation should look like (x+a)^2 = b or (x-c)^2 = d
______

What are the solutions to the equation? (1 right answer!)

Answer:

Answer:

2400

Step-by-step explanation:

2244 is the final price. it includes the VAT based on the actual sale price. and that is then actually 15% lower than the originally marked price.

so, let's calculate backwards :

2244 = 100% sale price + 10% VAT = 110%

1% = 2244 / 110 = 20.40

100% (actual sale price) = 20.40×100 = 2040

now, because of the 15% discount, these 2040 are only 85% of the originally marked price.

2040 = 85%

1% = 2040 / 85 = 24.00

100% (the original marked price) = 24×100 = 2400

Answer:

area of parallelogram=base *height

Answer:

area =36cm²

Step-by-step explanation:

area of parallelogram= b×h

Answer:

Rs4000

Step-by-step explanation:

Given data

Step one

Selling price =RS 4444

Gain =rs444

Cost price =???

We want to find the cost price

Cost price =selling price - gain

Cost =4444-444

Cost=Rs4000

Answer:

- [tex]\frac{17}{15}[/tex]      -1 [tex]\frac{2}{15}[/tex] , 1.13

Step-by-step explanation:

The line graph (A) represents the expression 5/2 + 3 the first term is 2 and-a-half units, and the second term is 3 units option (A) is correct.

It is defined as the representation of the numbers on a straight line that goes infinitely on both sides.

We have an expression:

= 5/2 + 3

Here 5/2 = 2.5 = 2 and half

= 2.5 + 3

The first arrow should indicate the 2 and-a-half unit

And the second arrow should represent the 3 unit

The line graph(A) represents the above situation or expression.

Thus, the line graph (A) represents the expression 5/2 + 3 the first term is 2 and-a-half units, and the second term is 3 units option (A) is correct.

Learn more about the number line here:

brainly.com/question/13189025

#SPJ1

Given:

AB formed by (-2,13) and (0,3).

CD formed by (-5,0) and (10,3).

To find:

Whether the segments AB and CD are parallel, perpendicular, or neither.

Solution:

Slope formula:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

AB formed by (-2,13) and (0,3). So, the slope of AB is:

[tex]m_1=\dfrac{3-13}{0-(-2)}[/tex]

[tex]m_1=\dfrac{-10}{2}[/tex]

[tex]m_1=-5[/tex]

CD formed by (-5,0) and (10,3). So, slope of CD is:

[tex]m_2=\dfrac{3-0}{10-(-5)}[/tex]

[tex]m_2=\dfrac{3}{10+5}[/tex]

[tex]m_2=\dfrac{3}{15}[/tex]

[tex]m_2=\dfrac{1}{5}[/tex]

Since [tex]m_1\neq m_2[/tex], therefore the segments AB and CD are not parallel.

[tex]m_1\times m_2=-5\times \dfrac{1}{5}[/tex]

[tex]m_1\times m_2=-1[/tex]

Since [tex]m_1\times m_2=-1[/tex], therefore the segments AB and CD are perpendicular because product of slopes of two perpendicular lines is always -1.

Hence, the segments AB and CD are perpendicular.

Answer:

AB is perpendicular to CD.

Step-by-step explanation:

AB formed by (-2, 13) and (0, 3)

CD formed by (-5, 0) and (10, 3)

Slope of a line passing through two points is

[tex]m= \frac{y''-y'}{x''- x'}[/tex]

The slope of line AB is

[tex]m= \frac{3- 13}{0+2} = -5[/tex]

The slope of line CD is

[tex]m'= \frac{3 -0 }{10+5} = \frac{1}{5}[/tex]

As the product of m and m' is -1 so the lines AB and CD are perpendicular to each other.

Answer:

[tex]{ \tt{sum = \frac{a(r {}^{n - 1} )}{n - 1} }} \\ 27 = \frac{a(r {}^{2 - 1} )}{2 - 1} \\ { \bf{27 = ar - - - (i)}} \\ \\ 54 = \frac{a( {r}^{3 - 1} )}{3 - 1} \\ { \bf{108 = a {r}^{2} - - - (ii) }} \\ { \tt{(ii) \div (i) : }} \\ r = \frac{108}{27} \\ { \bf{common \: ratio = 4}} \\ { \bf{first \: term = \frac{27}{4} }}[/tex]

Answer:

C.7, -2

Step-by-step explanation:

A quadratic equation is a polynomial of degree two. A quadratic equation is in the form:

ax² + bx + c = 0; where a, b, c are constants.

Quadratic equation can be solved using different methods, such as completing the square method, quadratic formula.

Solving the equation 2x² - 10x - 20 = 8 using completing the square:

2x² - 10x - 20 = 8

2x² - 10x = 28

Divide through by 2, to make the coefficient of x² to be 1:

x² - 5x = 14

Add to both sides, the square of half of the coefficient of x [i.e. (-5/2)² = 6.25]

x² - 5x + 6.25 = 14 + 6.25

(x - 2.5)² = 20.25

taking square root of both sides:

x - 2.5 = √20.25

x - 2.5 = ±4.5

x = 2.5 ± 4.5

x = 2.5 + 4.5; or x = 2.5 - 4.5

x = 7 or x = -2

Answer: Personally I would do option "B" 2 1/3 because it sounds right.

Answer:

[tex]y - 2 = - \frac{6}{5} (x - 0)[/tex]

Step-by-step explanation:

The Point Slope formula is a algebraic formula used for

The formula is

[tex]{y - y _1} = m(x - x_1)[/tex]

We are given its slope and we know a pair of points

Note a y intercept is (0,b). Where b is any real number so our points are (0,2).

Plug it in the expression

[tex]y - 2 = - \frac{6}{5} (x - 0)[/tex]

Answer:

152-88 = 64

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer: The quotient of 28 and 4 minus the sum of a number and 7

Step-by-step explanation:

Answer: f(3)=-7

Step-by-step explanation:

To evaluate f(3), we want to plug in x=3 into f(x)=-4x+5.

f(3)=-4(3)+5       [multiply]

f(3)=-12+5          [add]

f(3)=-7

Now, we know that f(3)=-7.

Answer:

40°

Step-by-step explanation:

As sum of angles of the triangle is 180°

therefore the third angle will be 180 -( 75 + 65)=40°

x=40°= vertically opposite angle

Answer:

x = 40°

Step-by-step explanation:

a + 65 + 75 = 180  {Angle sum property}

a + 140 = 180

     a = 180 - 140

    a = 40

x = a  {Vertically opposite angles}

x = 40°

Answer:

y=2x

Step-by-step explanation:

Answer:

Supongo que la pregunta completa es:

"Una recta pasa por los puntos A(-4, 0) y B(2, -3)"

Luego dice "calcular su área", pero una recta es un elemento unidimensional (los cuales no tienen área, el área es un concepto bidimensional).

Por lo que el área de esta recta no está definida.

Ignorando esto, podemos encontrar la ecuación que define a nuestra recta.

Sabemos que una recta se escribe como:

y = a*x + b

donde a es la pendiente y b es la ordenada al origen.

Sabemos que para una recta que pasa por los puntos (x₁, y₁) y (x₂, y₂), la pendiente será:

a = (y₂ - y₁)/(x₂ - x₁)

Entonces, para nuestra recta que pasa por los puntos (-4, 0) y (2, - 3) la pendiente será:

a = (-3 - 0)/(2 - (-4) )

a = -3/6 = -1/2

Entonces nuestra línea es algo como:

y = (-1/2)*x + b

para encontrar el valor de b, usamos el hecho de que esta línea pasa por el punto (2, -3)

esto significa que cuando x = 2, tenemos que tener y = -3

reemplazando esos dos valores obtenemos

-3 = (-1/2)*2 + b

-3 = -1 + b

-3 + 1 = b

-2 = b

La ecuación que define a esta recta es:

y = -(1/2)*x  - 2

Nuevamente, el área de esta recta no está definida, por lo que no podemos calcular el área de esta recta.

Answer:

[tex]a \div (b + c) = (a \div b) + (a \div c) \\ 6 \div (5 + 7) = (6 \div 5) + (6 \div 7) \\ 0.5 = 1.2 + 0.86 \\ 0.5 = 2.06[/tex]

Answer:

The value of x is 8 .

Step-by-step explanation:

It is known that EF = x cm , GH = (x + 6) cm , RS = 16 cm and NP = 28 cm . Knowing that EF ,GH , RS , and NP are, in that order, proportional segments, determine the value of x .

As EF, GH, RS and NP are in proportion

So,

EF : GH = RS : NP

[tex]\frac{x}{x+6}=\frac{16}{28}\\\\7 x = 4 (x + 6)\\\\7 x = 4 x + 24 \\\\3 x = 24 \\\\x = 8[/tex]

Answer:

no solution

Step-by-step explanation:

Answer:

63/70 = 9 : 10

Step-by-step explanation:

Given ratio:

9/10

a 70/63

= 10/9

= 10 : 9

b 19/70

= 19:70

c 19/20

= 19 : 20

d 63/70

= 9/10

= 9 : 10

The equivalent ratio to 9/10 = 63/70

= 9 : 10

Answer

6x<-12

Step-by-step explanation:

Answer:

There would be 2 answers in this case:

C. 6x > 32

and

D. 21 + x < 28

Step-by-step explanation:

A. Incorrect

6-13 = -7, and -7 is NOT greater than 7

B. Incorrect

6(6) = 36, and 36 is NOT less than -12.

C. Correct

6*6 = 36, which is greater than 32.

D. Correct

21+6 = 27, which is less than 28.

Answer:

[tex]f^{-1}[/tex] (x) = [tex]\frac{5x}{x-2}[/tex]

Step-by-step explanation:

let y = f(x) and rearrange making x the subject

y = [tex]\frac{2x}{x-5}[/tex] ( multiply both sides by x - 5 )

y(x - 5) = 2x ← distribute left side

xy - 5y = 2x ( subtract 2x from both sides )

xy - 2x - 5y = 0 ( add 5y to both sides )

xy - 2x = 5y ← factor out x from each term on the left side )

x(y - 2) - 5y ← divide both sides by y - 2

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

Change y back into terms of x with x = [tex]f^{-1}[/tex] (x) , then

[tex]f^{-1}[/tex] (x) = [tex]\frac{5x}{x-2}[/tex]

Look into the image. I hope it helps❤

Answer:

30 seconds

Step-by-step explanation:

→ Work out how many floors it's going to travel

15 - 3 = 12 floors

→ Work out how many meters 12 floors is

12 × 5 = 60 meters

→ Work out how long that will take

60 ÷ 2 = 30 seconds

Answer:

R = (-3, 8).

Step-by-step explanation:

Recall the midpoint formula:

[tex]\displaystyle M=\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)[/tex]

Where M is the midpoint, (x₁, y₁) is one point and (x₂, y₂) is another.

We are given that Q is the midpoint of PR, where P = (11, -2) and Q = (4, 3) and we want to find the coordinates of R.

Substitute Q for M and let P(11, -2) be (x₁, y₁). Hence:

[tex]\displaystyle (4, 3)=\left(\frac{11+x_2}{2}, \frac{-2+y_2}{2}\right)[/tex]

Split into two separate equations:

[tex]\displaystyle \frac{11+x_2}{2}=4\text{ and } \frac{-2+y_2}{2}=3[/tex]

Solve for each case:

[tex]\displaystyle 11+x_2=8\Rightarrow x_2=-3[/tex]

[tex]\displaystyle -2+y_2=6\Rightarrow y_2=8[/tex]

Therefore, our second point (x₂, y₂) is (-3, 8).

Hence, R = (-3, 8).

Answer:

(15/2),(1/2)

Step-by-step explanation:

(x1 + x2 / 2)  ,   (y1 + y2) / 2)

(11 + 4 / 2) , (-2 + 3 / 2)

(15/2) , (1/2)

GCF=4

4(4x^2/4+-28x/4+-32f/4)

=4(x^2-7x-8f)

Hello,

[tex]4x^2-28x-32\\\\=4(x^2-7x-8)\\\\=4(x^2-8x+x-8)\\\\=4[x(x-8)+1(x-8)]\\\\=4(x-8)(x+1)\\[/tex]

Answer:

7 students

Step-by-step explanation:

1+2+4=7students