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3 years ago

The solutions of x^2= 16x-28

Mathematics

2 answers:

-BARSIC- [3]3 years ago

6 0

The answer it (4,14)

STALIN [3.7K]3 years ago

5 0

Answer:

Simplifying

x2 = 16x + -28

Reorder the terms:

x2 = -28 + 16x

Solving

x2 = -28 + 16x

Solving for variable 'x'.

Reorder the terms:

28 + -16x + x2 = -28 + 16x + 28 + -16x

Reorder the terms:

28 + -16x + x2 = -28 + 28 + 16x + -16x

Combine like terms: -28 + 28 = 0

28 + -16x + x2 = 0 + 16x + -16x

28 + -16x + x2 = 16x + -16x

Combine like terms: 16x + -16x = 0

28 + -16x + x2 = 0

Factor a trinomial.

(2 + -1x)(14 + -1x) = 0

Subproblem 1

Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying

2 + -1x = 0

Solving

2 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.

2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0

0 + -1x = 0 + -2

-1x = 0 + -2

Combine like terms: 0 + -2 = -2

-1x = -2

Divide each side by '-1'.

x = 2

Simplifying

x = 2

Subproblem 2

Set the factor '(14 + -1x)' equal to zero and attempt to solve:

Simplifying

14 + -1x = 0

Solving

14 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-14' to each side of the equation.

14 + -14 + -1x = 0 + -14

Combine like terms: 14 + -14 = 0

0 + -1x = 0 + -14

-1x = 0 + -14

Combine like terms: 0 + -14 = -14

-1x = -14

Divide each side by '-1'.

x = 14

Simplifying

x = 14

Solution

x = {2, 14}

Step-by-step explanation:

I type fast lol

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i have been trying to solve this compound and double angle question please help me find the answer to these question guys

natali 33 [55]

Answer:

These type of questions are super tricky b/c you have to remember all the different versions of the identities, and then they put the question in some odd form, I feel like this should land math professors in jail , for dishonesty , b/c it's really a form of "how tricky can I make a question and still have a way to solve it" anyway,

Step-by-step explanation:

next the question asks 1-cos 2A and this is total abuse of notation. the way this should be written is 1- cos( 2A) so we know that the A is part of the cosine functions input... btw.. in any computer program, it would never ever let you get away with that top form of the expression. :/ anyway... I keep ranting.. huh... sorry :P

1-cos(2A) is an odd form of the identity 1/2(1-cos(2A) = $sin^{2}$ (A) the 1/2 is missing but we can add that pretty easy, we just have to remember to take it out too. I usually forget to do that. and my professor marks me off completely, totally wrong, but I just miss one small thing :/ anyway....

our 1-cos(2A) needs the 1/2 added to it. or if we move that 1/2 to the other side it looks like 2* $sin^{2}$ (A) = 1-cos(2A) and this is that "odd" from of the identity that I was talking about.

next let's deal with sin(2A) it has an identity of 2 sin(A)cos(A) which is really nice for us b/c it will cancel out the 2 in then numerator for us, nice !

now our fraction looks like [2* $sin^{2}$ (A)] / 2 sin(A)cos(A)

so cancel out one of the sines

2*sin(A) / 2 cos(A)

cancel the 2s

Sin(A) / Cos(A) = Tan(A)

nice it worked out :P

by the above that we just worked out, then

Tan(15) = Sin(15) / Cos(15)

I had to look up what sin of 15 is b/c it's not one of those special angles but it does have an exact form of

Sin(15) = (√3 - 1) / 2√2

Cos(A) = (√3 + 1) / 2√2

you can use rule of Cos(A-B) = Cos(A)Cos(B)+Sin(A)Sin(B) to get the above and a similar rule for Sin(A-B)

back to our problem, the 2√2 will cancel out

then we have

Tan(15) = (√3 - 1) /(√3 + 1)

in the form that is above that's exact, the roots could be approximated but i'll just leave that in the form that is exact. Most math professors like that form.

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2 years ago

You have just timed a person doing a job a four times. the first time it took the person 120 minutes, the second time it took 90

Oksanka [162]

treonvty trwqnty ewuit

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3 years ago

Need help!!!!!!!!!!!!!!

lisov135 [29]

It is the last answer that is the correct one

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2 years ago

Jacob throws an acorn into the air. It lands in front of him. The acorn's path is

Burka [1]

Answer:

hits the ground at x = -0.732, and x = 2.732
only the positive solution is reasonable

Step-by-step explanation:

The acorn will hit the ground where the value of x is such that y=0. We can find these values of x by solving the quadratic using any of several means.

<h3>graphing</h3>

The attachment shows a graphing calculator solution to the equation

-3x^2 + 6x + 6 = 0

The values of x are -0.732 and 2.732. The negative value is the point where the acorn would have originated from if its parabolic path were extrapolated backward in time. Only the positive horizontal distance is a reasonable solution.

<h3>completing the square</h3>

We can also solve the equation algebraically. One of the simplest methods is "completing the square."

-3x^2 +6x +6 = 0

x^2 -2x = 2 . . . . . . . . divide by -3 and add 2

x^2 -2x +1 = 2 +1 . . . . add 1 to complete the square

(x -1)^2 = 3 . . . . . . . . written as a square

x -1 = ±√3 . . . . . . . take the square root

x = 1 ±√3 . . . . . . . add 1; where the acorn hits the ground

The numerical values of these solutions are approximately ...

x ≈ {-0.732, 2.732}

The solutions to the equation say the acorn hits the ground at a distance of -0.732 behind Jacob, and at a distance of 2.732 in front of Jacob. The "behind" distance represents and extrapolation of the acorn's path backward in time before Jacob threw it. Only the positive solution is reasonable.

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1 year ago

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The eggs of birds and other animals come in many different shapes and sizes. Eggs often have a shape that is nearly spherical. W

vekshin1

Answer:

696.9 cm^3 to the nearest tenth.

Step-by-step explanation:

Radius of the egg = 1/2 * 11 = 5.5 cm.

Volume = 4/3 * pi * 5.5^3

= 696.9099703

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2 years ago