x^2-x-2=0 as a complete square

Answers

Answer 1

Answer:

[tex]x_1=2; x_2=-1[/tex]

Step-by-step explanation:

The square term is [tex]x^2[/tex] so we expect the complete square to be of the form [tex](x-a) ^2=x^2+2ax+a^2[/tex].

Let's compare the first degree terms now: we have [tex]2ax[/tex] on one side and [tex]-1x[/tex] on the other. That would make [tex]a=- \frac12[/tex]. At this point we have still the second squared term, so we add and subtract [tex]\frac14 = (\frac12)^2[/tex]

Our equation becomes:

[tex]x^2-x+\frac14 -\frac14-2 =0\\(x-\frac12)^2-\frac94=0[/tex]

(the [tex]\frac94[/tex] term comes from rewriting [tex]2= \frac84[/tex] and adding the terms out of the bracket).

At this point it's just solving the equation:

[tex](x-\frac12)^2 = \frac94 \rightarrow x-\frac12=\pm\frac32\\x=\frac12\pm\frac32\\x_1=\frac42 = 2; x_2=\fra-\frac22=-1[/tex]


Related Questions

A store is open for business while it is being renovated. The noise from the renovation is increasingly driving

away customers. The daily revenue, r (d), the store has made d days since renovation began is modeled by the

function r (d) = 10,000 (0. 939)d. What is the factor of decay in this function?

A

1. 9539

B

10,000

с

0. 0461

D

0. 9539

Answers

The factor of decay in the function that represents the daily revenue of the store is 0.939.

What is the factor that represents decay?

The factor that represents decay is the factor that reduces the growth rate of revenue for this store. In the given function, the factor that represents decay would have a value that is less than one.

To learn more about exponential functions, please check: https://brainly.com/question/26331578

HELP AGAIN I NEED IT DUE IN 10 MIN

Answers

Answer:

C: 28 inches

Step-by-step explanation:

Perimeter is when you add the length of each sides together.

Answer:

c

Step-by-step explanation: Because to get the perimeter you need to add all the sides of the figure for example 9+9+5+5=28 :]

Spencer owns a taxi cab company. He charges customers a base fee of $5 and an extra $2 for each mile traveled. If F represents a customer's fare (in dollars) and d represents the distance traveled (in miles draw a graph representing the relationship between F and d​

Answers

Answer:

Let F = customer's fare (in dollars)

Let d = distance traveled (in miles)

Given:

Base fee = $5Charge per mile = $2 per mile

Creating an equation from given information:

F = 2d + 5

This is a linear equation, with slope of 2 and y-intercept of (0, 5)

**see attached graph**

Answer:

See below ↓

Step-by-step explanation:

Given :

Base fee = $5Per extra mile = $2

Solving :

With F as the total customer fare and d is the distance covered the equation will be :-F = 2d + 5In terms of x and y, it can be written as :y = 2x + 5Graph is given below

A bus makes 28 stop every 2 hours. How many stops does it make in 5 hours?

Answers

Answer:

70 stops

Step-by-step explanation:

To find the amount of stops it makes in an hour, do 28 stops ÷ 2 hours, which will give you 14 stops in one hour.

Then do 14 stops × 5 hours, which would give you 70 stops.

Here's the notation if you want to make it look pretty:

 [tex]5(\frac{28}{2} )=70[/tex]

Find an ordered pair (x,y) that is a solution to the equation -x+6y=1

Answers

Answer:

(5,1)

is one of infinitely many possible order pairs.

Step-by-step explanation:

There are an infinite amount of x values that give you an answer to this question. You get to choose. But first let's start off with isolating y.

[tex]-x + 6y = 1\\6y = 1 + x\\y = \frac{1+x}{6}[/tex]

Now the equation is easier to interpret. [tex]y = \frac{1+x}{6}[/tex]

Now here's the part where you actually get to choose. Take any x, value, I'll choose 5.

I'll sub it into the equation and get my y value, [tex]y = \frac{1 + (5)}{6}= 1[/tex]

Okay, we get that y = 1, when x = 5. That's an ordered pair:

(5,1)

Remember you could follow this same procedure for any x value you choose.

divide y⁴-2y³-7y²+8y+12 by (y-3) using long division method
please give answer​

Answers

Is this correct please ?

Flight Times (h)
.
.
Alrjet Express
2. The double dot plot shows the
times, in hours, for flights of two
different airlines flying out of the
same airport. Compare the shapes,
centers, and spreads of the two
populations. Which airline's flights
had shorter flight times? (Examples 3 and 4)
:
+
4 5 6 7 8 9
+ Cross Country Airlines
10
1 2 3

Answers

The dot plot that was illustrated simply shows that the airline's flights had shorter flight times is Airjet Express.

What is a dot plot?

It should be noted that a dot plot simply means a plot that is used to display the data values.

In this case, the dot plot that was illustrated simply shows that the airline's flights had shorter flight times is Airjet Express. This was depicted in the data visualization.

Learn more about dot plots on:

https://brainly.com/question/15853311

What is the area of this figure?

Answers

Answer:

56 im pretty sure not my level but if i did it right it should be but if it is wrong im sorry

Step-by-step explanation:

Answer:

58.5 ft ^2

Explanation:

You find the area of the 3 individual shapes then add them together.

A box of 15 cookies costs $9dollar sign, 9. What is the cost for 1 cookie?

Answers

Answer:

$1.66 or $1.70 if you round up

Step-by-step explanation:

A circle has (-1, -1) and (-25,-11) as endpoints of a diameter.
Find the center and radius of the circle.
Write the standard equation of the circle.

Answers

well, since we know the diameter points, half-way in between is the center

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{-1}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{-25}~,~\stackrel{y_2}{-11}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ -25 -1}{2}~~~ ,~~~ \cfrac{ -11 -1}{2} \right)\implies \left(\cfrac{-26}{2}~~,~~\cfrac{-12}{2} \right)\implies (-13~~,~~-6)[/tex]

and its radius will be half the length of the diameter

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-1}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{-25}~,~\stackrel{y_2}{-11})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[-25 - (-1)]^2 + [-11 - (-1)]^2}\implies d=\sqrt{(-25+1)^2+(-11+1)^2} \\\\\\ d=\sqrt{(-24)^2+(-10)^2}\implies d=\sqrt{676}\implies d=26~\hfill \stackrel{half~that}{r=13}[/tex]

[tex]\rule{34em}{0.25pt}\\\\ \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-13}{ h},\stackrel{-6}{ k})\qquad \qquad radius=\stackrel{13}{ r} \\\\[-0.35em] ~\dotfill\\\\\ [x-(-13)]^2~~ + ~~[y-(-6)]^2~~ = ~~13^2\implies (x+13)^2~~ + ~~(y+6)^2~~ = ~~169[/tex]

If the circumference of a circle is 88 cm find its area

Answers

I hope I can help you:)

A design for a garden is composed of a triangle and 2 rectangles. Some side lengths of the garden design are shown. 7.5 ft 12.5 ft 7.5 ft 12.5 ft What is the area of the garden in square feet?​

Answers

Answer:

215.625 square feet.

Step-by-step explanation:

The best way to approach this is by finding the area of each shape and then adding them together.

The area of a rectangle is Length · Width. Both rectangles have a length of 12.5 feet and a width of 7.5 feet. 12.5 · 7.5 = 93.75. And since both rectangles have the same dimensions, we can just multiply 93.75 by two to get 187.5 square feet for the rectangles.

The area of a triangle is Base · Height / 2. Since the sides of the triangle are the same as the sides of rectangles, the dimensions of the triangle are 7.5 feet and 7.5 feet.

7.5 · 7.5 / 2 = 28.125 square feet.

187.5 + 28.125 = 215.625 square feet.

Hope this helps! :)

Find the value of x. Round to the nearest tenth of a unit. Show work.

Answers

Answer:

x = 41.16

Step-by-step explanation:

The value of the top angle in the triangle is equal to 90° - 27° = 63° as they are complementary anglesTo find x, take the tan ratio of the angletan63° = 1.96tan63° = x/21⇒ x/21 = 1.96⇒ x = 21 * 1.96⇒ x = 41.16

Answer:

x=41.2

Step-by-step explanation:

Assuming that the dotted line and the vertical line form a 90 degree angle, we can find the angle measurements of the triangle.

Since there is a 90 degree angle formed between the dotted line and the vertical line, subtracting 27 from 90 will get us the angle measure of one of the vertex of the triangle.

90-27=63 degrees

Now we can use trig. ratios to help us figure out the missing side.

tan(63)=x/21

x=tan(63)*21

x=41.21482062

x=41.2

Hope this helps!!!

In the figure below, BC=7 and AB= 16. Find AC.

Answers

The expressions BC and AB are illustrations of straight lines

The length AC is 25 units

How to determine the length of AC?

The given parameters are:

BC =7

AB = 16

Assume that AB and BC are straight lines.

Then , we have:

AC =AB + BC

Substitute known values

AC = 16 + 7

Evaluate the sum

AC = 25

Hence, the length AC is 25 units

Read more about lengths at:

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Which inequality is shown in the graph?

Answers

Answer:

Step-by-step explanation:

Today only, a table is being sold for 134.40 . This is 32% of its regular price. What was the price yesterday?

Answers

Answer:

$177.41

Step-by-step explanation:

when it says 32% OF , of always means multiply in word problems so we multiple 132% (1.32) times 134.40

$177.41

Answer:

420

Step-by-step explanation:

32% of its original price

32%=134.40

100%=?

cross multiply

100/100 x 134.40 × 100/32

1×134.40×3.125

=420

Can someone please help me?

Answers

Question 4:

   2x + 3y = 17    -- equation 1

   5x + 6y = 32  -- equation 2

    (equation 1) * 2

    4x + 6y = 34 -- equation 3

    (equation 2) - (equation 3)

     x = -2 -- equation 4

     plug (equation 4)'s value of x into (equation 1)

     2(-2) + 3y = 17

     3y - 4 = 17

      3y = 21

         y = 7

      Thus the answer is x = -2 and y = 7

Question 5:

  The vertex form of a quadrilateral looks like this:

      [tex]y = a(x-h)^2 + k[/tex]

a : coefficient of [tex]x^2\\[/tex](h,k): coordinate of the vertex.

    The x-coordinate of the vertex is equal to '-b/2a'. Where b is the

     coefficient of x, so:

          [tex]h = -\frac{b}{2a} =-\frac{-8}{2*1} =4[/tex]

     

    There is also another formula to find the y-value of the vertex

    coordinate, but the easier way to find it is to plug it into the original

    equation:

        [tex]k=(4)^2-8(4) + 12= 16 -32 + 12 = -16 + 12 = -4[/tex]

    Since we know now that h = 4 and k = -4 and that a = 1, lets plug it into

    the original equation.

       [tex]y = 1*(x-4)^2 - 4 =(x^2-4)-4[/tex]

     Thus the answer is [tex]y = (x-4)^2 -4[/tex]

Hope that helps!

       

 

what are the slope and y - intercept of the equation 6x+3y=-12

Answers

Answer:

Slope= -2

y-intercept= -4

Step-by-step explanation:

To find the slope and y-intercept of a given equation, first rearrange the equation such that it is in the slope-intercept form. In the slope-intercept form, the coefficient of y is 1 and the rest are moved to the left hand side of the equation.

[tex]\textcolor{steelblue}{\text{Slope-intercept form}}[/tex]

y= mx +c, where m is the slope and c is the y-intercept

Given equation: 6x +3y= -12

Let's leave the y term on the left of the equation and bring the rest to the right.

3y= -6x -12

To ensure that the coefficient of y is 1, divide both sides by 3.

y= -2x -4

The equation is now in the slope-intercept form.

The slope is the coefficient of x (the number that comes before x), thus the slope is -2. The y-intercept is -4.

what is 1/100 of 2.14

Answers

Answer:

.0214

Step-by-step explanation:

2.14 * .01 = .0214

to check:

.0214 * 100 = 2.14

Anthony is six years older than Juntao. In three years' time, the ratio of Juntao's age to Anthony's age will be 2 : 5. How old is Juntao now?

Answers

he is now 69 years old because i am smarter than you.

the coordinating grid shows points L, M, N, and O. all the coordinates for these points are integers. what is the value of the x-coordinates of point M

Answers

Answer:

-6

Step-by-step explanation:

Hope this helps!!!

pls help ASAP first correct answer gets brainleist ​

Answers

Answer:

4.58257569 meters (Could probably get away with rounding it to 4.6 meters)

Step-by-step explanation:

Pythag theorem

a^2 +b^2 =c^2

Insert your numbers

10^2+b^2=11^2

Simplify squares

100+b^2=121

subtract 100 from both sides

b^2=21

sqrt both sides

sqrt(b^2)=sqrt(21)

simplify sqrts to get b

b= 4.58257569

PLEASE HELP ME WITH THIS

Answers

The answer is 68 degrees

What is the vertex of the function below?

Answers

Answer:

lol thts 26

Step-by-step explanation:

ABSOLUTE VALUE FUNCTION
PLS HELP WILL GIVE BRAINLY FOR CORRECT ANSWER ONLYY

Answers

B) [tex]\sf y=\left|x-3\right|[/tex]

The original graph has x-intercept : 3   ||  y-intercept : 3

Calculate the y-intercept and x-intercept for every function.

Here in option B,

y-intercept:

y = |x-3|

y = |0-3|

y = 3

x-intercept:

0 = |x-3|

x - 3 = 0

x = 3

Thus option B is correct.

In this lab, you observed how pollutants affected the ________


of water. You also modeled and observed how pollution affected freshwater sources, including surface water and the water in the _________

Answers

Answer: PH, ground

Step-by-step explanation: edge2022

In this lab, you observed how pollutants affected the" PH "of water. You also modeled and observed how pollution affected freshwater sources, including surface water and the water in the" ground "

What is water pollution?

Water pollution can be defined as the abnormal accumulation of strange elements in the water with harmful consequences to natural ecosystems.

Water pollution involves all the possible ways in which any water body can be contaminated with harmful elements.

The source of water pollution is human activities, producing the biggest damage to natural ecosystems.

Contaminating elements might be either gasses, solid material, or liquid material Such as Chemical elements, microbiota, heavy metals, and sediments affect all forms of life.

You can learn more about water pollution at

brainly.com/question/19920929

#SPJ2

ixl math question im very lazy and i dont understand

Answers

Answer:

1/21

Step-by-step explanation:

We start with 7 cards. The probability of picking a 4 is 1/7. Since the first card is not put back, there are 6 cards left. Of these 6 cards, there are two which have divisors of 63: 3 and 7. So the probability of picking a divisor of 63 is 2/6, which reduces to 1/3. Multiplying these probabilities gives 1/21.

Solve the system of equations at right. 2^(x+y)=16 2^(2x+y)= 1/8

Answers

Answer:

  (x, y) = (-7, 11)

Step-by-step explanation:

The system of exponential equations can be solved by the use of logarithms. Equivalently, the equations can be written so that exponents can be equated. This system is equivalent to two linear equations.

First equation:

  2^(x+y) = 16

  2^(x +y) = 2^4 . . . . use the same base to write the constant

  x +y = 4 . . . . . . . . equate exponents of 2 (take log₂ of both sides)

Second equation:

  2^(2x +y) = 1/8

  2^(2x +y) = 2^(-3) . . . . use the same base to write the constant

  2x +y = -3 . . . . . . equate exponents of 2

Solve the linear equations:

We can subtract the first equation from the second to get ...

  (2x +y) -(x +y) = (-3) -(4)

  x = -7

  y = 4 -x = 4 -(-7) = 4 +7 = 11 . . . . use the first equation to find y

The solution to the system is (x, y) = (-7, 11).


¿ A que distancia se encuentran dos masas de 60 kg y 80 kg, si la fuerza de
atracción entre ellas es de 3x10-31N.

Answers

Teniendo en cuenta la Ley Universal de la Gravitación, la distancia a la que se encuentran dos masas de 60 kg y 80 kg, si la fuerza de atracción entre ellas es de 3×10⁻³¹ N, es 1.033 ×10¹² m.

Ley Universal de la Gravitación

La Ley Universal de la Gravitación establece que los cuerpos, por el simple hecho de tener masa, experimentan una fuerza de atracción hacia otros cuerpos con masa, llamada fuerza gravitacional.

Esta ley dice que la fuerza gravitacional entre dos cuerpos es directamente proporcional al producto de sus masas e inversamente proporcional al cuadrado de la distancia que los separa.

Matemáticamente se expresa de la siguiente manera:

[tex]F=G\frac{Mm}{d^{2} }[/tex]

donde:

G es la constante gravitatoria universal, con un valor de 6,67×10⁻¹¹[tex]\frac{Nm^{2} }{kg^{2} }[/tex].M y m son las masas de los cuerpos que interactúan.d es la distancia que los separa.

Distancia entre dos masas

En este caso, sabes:

F= 3×10⁻³¹ NM=  60 kgm= 80 kg

Reemplazando en la Ley Universal de la Gravitación:

[tex]3x10^{-31}N =6,67x10^{-11}\frac{Nm^{2} }{kg^{2} } \frac{60 kg x80 kg}{d^{2} }[/tex]

Resolviendo:
[tex]\frac{3x10^{-31}N}{6,67x10^{-11}\frac{Nm^{2} }{kg^{2} }} = \frac{60 kg x80 kg}{d^{2} }[/tex]

[tex]4,4977x10^{-21} \frac{kg^{2} }{m^{2} } = \frac{4800 kg^{2} }{d^{2} }[/tex]

[tex]d^{2} x4,4977x10^{-21} \frac{kg^{2} }{m^{2} } =4800 kg^{2}[/tex]

[tex]d^{2} = \frac{4800 kg^{2} }{4,4977x10^{-21} \frac{kg^{2} }{m^{2} } }[/tex]

[tex]d = \sqrt{\frac{4800 kg^{2} }{4,4977x10^{-21} \frac{kg^{2} }{m^{2} } }}[/tex]

[tex]d = \sqrt{1,0672x10^{24} m^{2} }[/tex]

d= 1.033 ×10¹² m

Finalmente, la distancia a la que se encuentran dos masas de 60 kg y 80 kg, si la fuerza de atracción entre ellas es de 3×10⁻³¹ N, es 1.033 ×10¹² m.

Aprende más acerca de la Ley Universal de la Gravitación:

brainly.com/question/15967105

brainly.com/question/11359658

please solve this question faaaast​

Answers

Answer:

300-400

Step-by-step explanation:

The first step is finding the total of the data we have. So, we take 5 + 10 + 15 + 20 + 25 + 15 + 10 which equals 80.

The median is the middle point of all the data. If it's an odd number, you can calculate the median with the equation (n+1) / 2, plugging in the total amount of data for n.

When it's an even number though, there is no one middle point since the data splits evenly in 2, so we have to use 2 equations: n/2 & (n/2) + 1. Then, we find the average of those two data points. (Although, you don't have to do that for this particular question).

When we plug 80 in for n in both of these equations, we get 40 and 41.

To where this is in the question, we have to count up from the bottom of the chart. 1-5 is below 100, 6-15 is 100-200, 16-30 is 200-300, and 31-50 is 300-400.

Since 40 and 41 are between 31 and 50, the answer is 300-400.

Hope this helps! :)

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