Lamar is solving the equation x2−12x=−6 by completing the square. Which shows Lamar's next step and the solution to the equation?

Step 1: x^2 - 12x = -6

Step 2: x^2 - 12x + 36= -6 + 36

Answers

Answer 1
Completing the square is a process to find the solutions, or the x-values, to a quadratic equation. This method can only work if it is in the format: x^2 + bx = c
In this equation, the b value is -12 and the c value is -6. The process for completing the square goes like this:

x^2 + bx + (b/2)^2 = c + (b/2)^2

Now let’s solve the equation above using this method.

Step 1: x^2 - 12x + (-12/2)^2 = -6 + (-12/2)^2

Step 2: x^2 - 12x + (-6)^2 = -6 + (-6)^2

Step 3: x^2 - 12x + 36 = -6 + 36

Step 4: x^2 - 12x + 36 = 30

Now, to factor it. After doing the process until now, the left side of the equation can ALWAYS be in the format: (x + a)^2

Step 5: x^2 - 12x + 36 can be factored in this format as (x - 6)^2

Step 6: (x - 6)^2 = 30

Step 7: x - 6 = √30

Step 8: x = 6 ±√30


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A bag of skittles contains 7 purple, 4 red, 6 yellow, and 5 green skittles. Randomly I will grab a skittle, eat it and then grab another to eat. What is the probability that I will get a purple and then red?

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Answer:

The probability will be [tex]\frac{1}{2}[/tex], since there are a total of 11 purple and red Skittles and an overall total of 22 Skittles in the bag.

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Answer:

14 nickels is the answer

Step-by-step explanation:

Description of a turn for those who have never done math / for a child​

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Answer:

Step-by-step explanation:

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What does it mean to be an independent student? A. You must pick your own study topics and research them. B. You can set your own deadlines, within a fixed time frame. C. You are responsible for your own study schedule and organization. D. You are expected to work without extra help from a teacher or tutor.

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Step-by-step explanation

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Answer:

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Find the points on x^2+3(y-2)^2 = 27
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Answers

[tex](-4.89, 3)[/tex] and [tex](4.89, 3)[/tex] are the farthest from the origin and [tex](0, -1)[/tex] is the closest from the origin.

Let be a curve of the form [tex]x^{2}+3\cdot (y-2)^{2} = 27[/tex]. The distance with respect to origin is found by using the following Pythagorean identity:

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

Where [tex]r[/tex] is the square distance function.

We can modify (1) as following:

[tex]r = [27-3\cdot (y-2)^{2}]+y^{2}[/tex]

[tex]r = 27-3\cdot (y^{2}-4\cdot y +4)+y^{2}[/tex]

[tex]r = 27-3\cdot y^{2}+12\cdot y -12 + y^{2}[/tex]

[tex]r = -2\cdot y^{2}+12\cdot y+27[/tex] (1b)

Now we apply the First and second derivative tests to determine the minimum and maximum distances from the origin:

First derivative test

[tex]-4\cdot y +12 = 0[/tex]

[tex]y = 3[/tex]

Second derivative test

[tex]r'' = -4[/tex]

The y-component represents a maximum.

Now we graph the function with the ressource of a graphing tool, we find the following points:

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Closest points: [tex](0, -1)[/tex].

[tex](-4.89, 3)[/tex] and [tex](4.89, 3)[/tex] are the farthest from the origin and [tex](0, -1)[/tex] is the closest from the origin.

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Answer: 42

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= 42

Answer:

6(9-2)

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Step-by-step explanation:

I think it help you I also you understand it

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Answer:

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u wanted expression ,  not answer.?

Step-by-step explanation:

can someone please find the slope for this?

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The gradient is 1/4.

As you take two points the line passes though, then use the rise/run equation to find the slope or gradient

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O A. 6^16
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Step-by-step explanation:

I am sorry but I cannot see your question

a coffee mug collection includes four red mugs, eight yellow mugs and two white mugs. What is the probability of selecting two white mugs one after another?

Answers

Assuming that the selection process was done without replacement, the probability of selecting two white mugs without replacement is 1/28

Given data

Sample Space

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Answers

774 watts so what he said is right

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What is average power?

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It can be expressed by the following relation:

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Answers

Answer:

This is the arithmetic sequence which has a common difference that equals to -4.

Step-by-step explanation:

An arithmetic sequence is a sequence with common difference. A common difference can be found by subtracting previous term with next term.

A common difference can be expressed in [tex]\displaystyle \large{d=a_{n+1}-a_n}[/tex] where d stands for common difference.

________

Moving to the question given. We have a sequence with given 15,11,7, ... first subtract 15 with 11.

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Therefore, we can conclude that the common difference is -4 thus making the given sequence an arithmetic.

Let me know if you have any question so regarding the sequence!

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

Write an equation of each sentence. Use n to represent the unknown number. You can use the back page for your solution. (2 points each) 11. Six increased by a number is twenty. 12. A number decreased by seven is four. 13. The sum of two consecutive numbers is thirty-one. 14. The sum of twice a number and two is thirteen. 15. One less than a number is eighteen. 16. The square of a number increased by four is twice the number. 17. Twice a number is one-half. 18. The product of a number and its half is eighteen. 19. The average of a number and ninety is seventy. 20. Two more than a number is twelve.

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Answers

Answer:11. 6 + n = 2012. n - 7 = 2013. n + n + 1 = 3114. 2n + 2 = 1315. n - 1 = 18 16. n² + 4 = 2x17. 2n = 1/218. n²/2 = 1819. n/2 + 90/2 = 7020. 2 + n = 12

Hoped this helped.

[tex]-BrainaicUser1357-[/tex]

Let the number be x

#11

[tex]\\ \sf\longmapsto x+6=20[/tex]

#12

[tex]\\ \sf\longmapsto x-7=4[/tex]

#13

[tex]\\ \sf\longmapsto x(x+1)=31[/tex]

#14

[tex]\\ \sf\longmapsto 2x+2=13[/tex]

#15

[tex]\\ \sf\longmapsto x-1=18[/tex]

#16

[tex]\\ \sf\longmapsto x^2+4=17[/tex]

#17

[tex]\\ \sf\longmapsto x^2/2=18[/tex]

#18

[tex]\\ \sf\longmapsto x+90/2=70[/tex]

basically how to write y-3=4(x+2) in slope intercept form

Answers

Answer: y = 4x + 11

Step-by-step explanation:

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

y = mx + b

Rewrite in slope-intercept form.

Simplify the right side.

Simplify 4(x + 2).

y - 3 = 4x + 8

Move all terms not containing y to the right side of the equation.

Add 3 to both sides of the equation.

y = 4x + 8 + 3

Add 8 and 3.

y = 4x + 11

Your Welcome! :)

Solve for x: one over four (4x + 15) = 24

A: 45
B: 207/4
C: 81/4
D: 9

Answers

Answer:

[tex]C. x = \frac{81}{4} = 20.25[/tex]

Step-by-step explanation:

[tex]\frac{1}{4}\left(4x+15\right)=24[/tex]

[tex]\mathrm{Multiply\:both\:sides\:by\:}4[/tex]

[tex]4\cdot \frac{1}{4}\left(4x+15\right)=24\cdot \:4[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]4x+15=96[/tex]

[tex]\mathrm{Subtract\:}15\mathrm{\:from\:both\:sides}[/tex]

[tex]4x+15-15=96-15[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]4x=81[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}4[/tex]

[tex]\frac{4x}{4}=\frac{81}{4}[/tex]

[tex]Simplify[/tex]

[tex]x=\frac{81}{4}[/tex]

Find the equation of a line that intersects with y=2x-1 on the y-axis and is parallel to y=-x. Please explain.

Answers

Answer:

so where does that line intersect the y axis? just plug in x=0 and you see y= -1. so (0, -1)

y = -x -1 is parallel because it has the same slope and goes through the right point

Figures A and B at right are similar. Assuming that figure A is the original figure, find the scale factor and find the lengths of the missing sides of figure B.

A 4 sided polygon, labeled A, with sides labeled as follows: left, 15, top, 12, right, 18, bottom, 20. A smaller, 4 sided polygon, labeled b, oriented the same way, has left side labeled: 3.

Answers

The scale factor is: 1/5.

The missing sides of figure B are: 2.4, 3.6, and 4.

How to find Scale Factor?

Scale factor = dimension of new figure / dimension of original figure

The polygons given are shown in the diagram attached below.

Figure A is the original figure

Figure B is the new figure.

x, y, and z has been used to mark the missing sides of figure B.

One dimension of original figure = 15

Corresponding dimension of the new figure = 3

Scale factor = new/original = 3/15

Scale factor = 1/5

To find the missing sides of figure B, multiply each corresponding side lengths of Figure A by the scale factor:

x = 12 × 1/5 = 2.4

y = 18 × 1/5 = 3.6

z = 20 × 1/5 = 4

In summary:

The scale factor is: 1/5.

The missing sides of figure B are: 2.4, 3.6, and 4.

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In the New York marathon there were 45 360 runners. 7 /10 of the runners were women. How many of the runners were men? ​

Answers

Answer:

13,608

Step-by-step explanation:

If 7/10 of the runners were women, than 3/10 of the runners were men. 3/10 of 45,360 runners is 13,608.

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A line includes the points (-7, 1) and (7, -1). What is its equation in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.

Answers

Answer:

y=-1/7x

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-1-1)/(7-(-7))

m=-2/(7+7)

m=-2/14

simplify

m=-1/7

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

y-y1=m(x-x1)

y-1=-1/7(x-(-7))

y-1=-1/7(x+7)

y=-1/7x-7/7+1

y=-1/7x-1+1

y=-1/7x

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