Solve by completing the square: x^2-2x-1=0

Answers

Answer 1

Answer: $(a-b)^2=a^2-2ab+b^2\ (*)\n------------------------------\n\nx^2-2x-1=0\n\nx^2-2x\cdot1=1\n\n\underbrace{x^2-2x\cdot1+1^2}_((*))-1^2=1\n\n(x-1)^2-1=1\n\n(x-1)^2=1+1\n\n(x-1)^2=2\Rightarrow x-1=-\sqrt2\ \vee\ x-1=\sqrt2\n\n\underline{\underline{x=1-\sqrt2\ \vee\ x=1+\sqrt2}}$

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Factorise it step by step
4r²-7r+3

Answers

To factor the quadratic expression 4r² - 7r + 3, we can use the factoring method. We're looking for two binomials in the form (ar + b)(cr + d) where ac = 4, ad + bc = -7, and bd = 3. Here's how to factor it step by step:

Step 1: Multiply the leading coefficient (4) by the constant term (3). This gives us 4 * 3 = 12.

Step 2: Find two numbers that multiply to 12 (the result from step 1) and add up to the middle coefficient (-7). These numbers are -4 and -3 because (-4) * (-3) = 12, and (-4) + (-3) = -7.

Step 3: Rewrite the middle term (-7r) using the numbers from step 2 (-4 and -3). We split the middle term like this:
4r² - 4r - 3r + 3

Step 4: Group the terms and factor by grouping:
(4r² - 4r) - (3r - 3)

Step 5: Factor out the greatest common factor from each group:
4r(r - 1) - 3(r - 1)

Step 6: Now you can see that (r - 1) is a common factor in both terms. Factor it out:
(r - 1)(4r - 3)

So, the factored form of the quadratic expression 4r² - 7r + 3 is (r - 1)(4r - 3).

An igloo has a circular floor with a radius of 2 yards. What is the floor’s diameter?

Answers

Diameter

When we're given the radius, and asked to find the diameter, we use a simple formula, which is:

$\boldsymbol{\sf{Diameter=radius*2}}$

Since we know the radius, we substitute it into the formula:

$\boldsymbol{\sf{Diameter=2*2}}$

$\boldsymbol{\sf{Diameter=4\;yards}}$

Therefore, the diameter is 4 yards.

------------- Additional formulas -----------

$\sf{radius=\cfrac{diameter}{2}}$

$\sf{Circumference=\pi d}$

$\sf{Circumference=2\pi r}$

$\sf{Area=\pi r^2}$

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

The diameter of a circle is twice the length of its radius. In this case, the radius of the igloo's circular floor is 2 yards. Therefore, the diameter can be calculated as:

Diameter = 2 * Radius

Diameter = 2 * 2 yards

Diameter = 4 yards

So, the floor's diameter is 4 yards.

Dorothy is buying desks. This table shows how the cost depends onthe number of desks purchased.
Desks Cost ($)
8
24
9
27
10
30
11
33
What is the constant of proportionality of this relationship?

Answers

Answer:

one desk costs $3

Step-by-step explanation:

the increase in prices if another table were added on is $3 thus for every table you buy, $3 each

$=3x

x being the number of tables

furthermore, constant increase

What is one-fourth of four sevenths

Answers

The one-fourth of four sevenths is $(1)/(7)$ .

Given that,

The fraction is one-fourth of four sevenths.
We need to solve it.

Based on the above information, the calculation is as follows:

$= (1)/(4) * (4)/(7)\n\n= (4)/(28) \n\n= (1)/(7)$

Therefore, we can conclude that The one-fourth of four sevenths is $(1)/(7)$ .

Learn more: brainly.com/question/6201432

1/4 x 4/7
do the top numbers first. 1 x 4 is 4do bottom numbers next 4 x 7 is 28

that leaves you with 4/28. But you have to reduce.

4/28 = 2/14 = 1/7 (notice I just cut both the top and bottom numbers in half each time I reduced until I couldn't reduce any more).
So, final answer is 1/7

Can you solve for t in -100=12t-4?

Answers

$-100=12t-4\n\n12t-4=-100\ \ \ \ |both\ sides\ +4\n\n12t=-96\ \ \ \ |both\ sides\ :12\n\n\underline{\underline{t=-8}}$

The answer to your question is: Yes, I can.

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

Although you didn't ask for the solution, I'm here now, so
I might as well follow through and make good my boast.

-100 = 12t - 4

Add 4 to each side of the equation:

-96 = 12t

Divide each side by 12 :

-8 = t

A number changed to 193 after it was rounded. To what place was the number rounded?

Answers

The number was rounded to the nearest one.
Are there any answer choices?

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