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3 years ago

X² − 12x + 36 = 0 Solutions?

2 answers:

8 0

X² - 12x + 36 = 0
We know this is in standard form so we can use the quadratic formula. Indeed like a previous solution posted you can use factors, that is quicker but this will always work so let's see.

Now let's fill the gaps in the formula

x = 12 +- square root of (144 - 4(1)(36) )/ 2

X = 12 +- square root of (144 - 144) / 2

X = 12 / 2

X = 6

Alika [10]3 years ago

5 0

Factors of 36 that add up to -12

-6 and -6

<span>(x − 6)(x − 6)
</span>
Set them both to equal 0 and solve for x

x - 6 = 0

x - 6 = 0

x = 6

x = 6

You might be interested in

Which explanation can be used to derive the formula for the circumference of a circle?

Gelneren [198K]

Answer: The answer is the first explanation.

Step-by-step explanation: We are given five different options and we are to select which explanation is correct to derive the formula for a circumference of a circle.

Let 'C' be the circumference and 'd' be the diameter of a circle. Now, we will write the ratio of the circumference to the diameter as

$\dfrac{\textup{C}}{\textup{d}}.$

Also, we know that

$\dfrac{\textup{C}}{\textup{d}}=\pi.$

And diameter of a circle is twice the radius, so

$d=2r.$

Therefore,

$\dfrac{\textup{C}}{2\textup{r}}=\pi\\\\\Rightarrow \textup{C}=2\pi \textup{r}.$

This is the formula for the circumference of a circle. Since this explanation matches exactly with the first option, so the correct option is

(a). Find the relationship between the circumference and the diameter by dividing the length of the circumference and length of the diameter. Use this quotient to set up an equation to showing the ratio of the circumference over the diameter equals to π . Then rearrange the equation to solve for the circumference. Substitute 2 times the radius for the diameter.

8 0

2 years ago

A person starts walking from home and walks: 4 miles east 3 miles southeast 3 miles south 4 miles southwest 3 miles east find to

Fantom [35]

A geometry program can show you the total displacement is about 10.14 miles.

_____
You can use a vector calculator to find the solution, too. Using bearing angles, the sum is
4∠90° + 3∠135° + 3∠180° + 4∠225° + 3∠90° ≈ 10.1390∠141.6354°

_____
If you want to do it by hand, you can recognize the sum will be
7 miles east + 3 miles south + 3 miles southeast + 4 miles southwest

Distances that are not in the direction of one of the coordinate axes can be translated to rectangular coordinates by
displacement*(cos(angle), sin(angle))
Angles can be measured in the conventional way—from the positive x-axis. A direction of southeast will be +315° or -45°. A direction of southwest will be +225° or -135°.

Then the sum of the displacements in rectangular coordinates is ...
= (7, -3) + 3*(cos(-45°), sin(-45°)) + 4*(cos(-135°), sin(-135°))
= (7, -3) + ((√2)/2)*((3, -3) + (-4, -4))
= (7, -3) + 0.707107*(-1, -7)
= (6.2929, -7.9497)
Then the Pythagorean theorem is used to find the direct distance from home to this displaced location.
d = √(6.2929² +(-7.9497)²) ≈ √102.7990
d ≈ 10.1390 . . . . miles

4 0

3 years ago

Can someone explain this? :)

Alchen [17]

I'll do part (a) to get you started.

The angle 'a' pairs up with the 123 degree angle as a corresponding angle pair. Due to the parallel lines, the corresponding angles are congruent. Therefore a = 123.

We also see that b = 123 as well since a = b (they are vertical angles).

Notice how angle c is adjacent to the 123 degree angle. These two angles form a straight line, so they must add to 180 degrees.

c+123 = 180

c = 180-123

c = 57

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

To summarize, we have these three angles

a = 123

b = 123

c = 57

6 0

3 years ago

Read 2 more answers

Find the missing angle measure.<br><br> m

Alexeev081 [22]

Answer:43 degrees

Step-by-step explanation: 47+90=137 and 180-137= 43

5 0

2 years ago

Read 2 more answers

Each answer choice below represents a relation by a set of ordered pairs. In which of the answer choices is the relation a funct

alexdok [17]

Answer:

A - Not Function

B - Function

C - Function

D - Not Function

E - Function

Step-by-step explanation:

For a relation to be a function, each value of input should have exactly one output. Which means that for one value of x, there should only one value of y. If the relation has repetition of x in its ordered pairs, it means that for one value of x, there are two or more values of y, hence the relation is not a function

(Consult the diagram below)

As x = 6 is being repeat, it means that x=6 has two values of y that are 12 and 4. IT IS NOT A FUNCTION.

No repetition of x, IT IS A FUNCTION.

No repetition of x, IT IS A FUNCTION.

As x = -1 is being repeat, it means that x=-1 has two values of y that are 4 and -2. IT IS NOT A FUNCTION.

No repetition of x, IT IS A FUNCTION.

5 0

2 years ago