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1 year ago

Solve x2 = 12x – 15 by completing the square. Which is the solution set of the equation?

2 answers:

4 0

The answer is x = 6 + √21. The general form of quadratic function is ax2 + bx + c = 0. So, the equation x2 = 12x – 15 in the general form will be look like: x2 - 12x + 15 = 0. Now, move the number term on the right side of the equation: x2 - 12x = -15. Since b = 12, (b/2)2 = (12/2)2 = (6)2 = 36. Add this number on the both side of equation: x2 - 12x + 36 = -15 + 36. From here: (x-6)2 = 21. Take square root on both sides: x - 6 = √21. Solve for x: x = 6 + √21

Nady [450]1 year ago

3 0

For this case we have the following polynomial:
$x ^ 2 = 12x - 15
$
The first thing to do is to place the variables on the same side of the equation.
We have then:
$x ^ 2 - 12x = -15
$
We complete the square by adding the term (b / 2) ^ 2 on both sides of the equation.
We have then:
$x ^ 2 - 12x + (-12/2) ^ 2 = -15 + (-12/2) ^ 2
$
Rewriting we have:
$x ^ 2 - 12x + (-6) ^ 2 = -15 + (-6) ^ 2

x ^ 2 - 12x + 36 = -15 + 36
 
(x-6) ^ 2 = 21$
$x-6 =+/- \sqrt{21}$
Therefore, the solutions are:
$x = 6 - \sqrt{21}$
$x = 6 + \sqrt{21}$
Answer:
the solution set of the equation is:
$x = 6 - \sqrt{21}$
$x = 6 + \sqrt{21}$

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Which shows how to solve the equation Three-fourths x = negative 6 for x in one step?

My name is Ann [436]

option A i.e. Three-fourths (four-thirds) x = negative 6 (four-thirds).

Step-by-step explanation:

We have , The given expression as Three-fourths x = negative 6 , which can be written as $\frac{3}{4} (x) = -6$ . Now in order to solve this equation in one step , we must notice that coefficient of x must be 1 but it's $\frac{3}{4}$ , Let's make coefficient of x as 1 by multiplying both side of equations by 4/3:

$\frac{3}{4} (x) = -6$

⇒ $\frac{3}{4} (x) = -6$

⇒ $\frac{3}{4}(\frac{4}{3} ) (x) = -6(\frac{4}{3} )$

⇒ $x = -6(\frac{4}{3} )$

⇒ $x = -2(4)$

⇒ $x = -8$

Therefore, x= -8 & correct option to solve the equation Three-fourths x = negative 6 for x in one step is option A i.e. Three-fourths (four-thirds) x = negative 6 (four-thirds).

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1 year ago

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Aliun [14]

Answer:

Positive Linear Association

Step-by-step explanation:

It was right on Khan

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1 year ago

Malcolm has $638.54 in his checking account. He must maintain a $500 balance to avoid a fee. He wrote a check for $159.50 today.

e-lub [12.9K]

Your answer is c, 638.54 − 159.50 + x ≥ 500; x ≥ $20.96

5 0

2 years ago

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Please answer all of them need this

VikaD [51]

First Question

For a better understanding of the solution provided here please find the first attached file which has the diagram of the the isosceles trapezoid.

We dropped perpendiculars from C and D to intersect AB at Q and P respectively.

As can be seen in $\Delta BCQ$ , we can easily find the values of CQ and BQ.

Since, $Sin(75^0)=\frac{CQ}{8}$

$\therefore CQ=8\times Sin(75^0)\approx 7.73$ ft

In a similar manner we can find BQ as:

$Cos(75^0)=\frac{BQ}{8}$

$BQ\approx2.07$ ft

All these values can be found in the diagram attached.

Thus, because of the inherent symmetry of the isosceles trapezoid, PQ can be found as:

$PQ=22-(AP+QB)=22-(2.07+2.07)=17.86$

Let us now consider $\Delta AQC$

We can apply the Pythagorean Theorem here to find the length of the diagonal AC which is the hypotenuse of $\Delta AQC$ .

$AC=\sqrt{(AQ)^2+(QC)^2}=\sqrt{(AP+PQ)^2+(QC)^2}=\sqrt{(2.07+17.86)^2+(7.73)^2}\approx21.38$ feet.

Thus, out of the given options, Option B is the closest and hence is the answer.

Second Question

For this question we can directly apply the formula for the area of a triangle using sines which is as:

Area= $\frac{1}{2}$ (First Side)(Second Side)(Sine of the angle between the two sides)

Thus, from the given data,

Area= $\frac{1}{2}\times 218.5\times 224.5\times sin(58.2^0)\approx20845$ $m^2$

Therefore, Option D is the correct option.

Third Question

For this question we will apply the Sine Rule to the $\Delta ABC$ given to us.

Thus, from the triangle we will have:

$\frac{AB}{Sin(\angle C)}=\frac{BC}{Sin(\angle A)}$

$\frac{c}{Sin(\angle C)}=\frac{a}{Sin(\angle A)}$

$\frac{17}{Sin(25^0)}=\frac{a}{Sin(45^0)}$

This gives $a$ to be:

$a\approx28.44$

Which is not close to any of the given options.

Fourth Question

Please find the second attachment for a better understanding of the solution provided her.

As can be clearly seen from the attached diagram, we can apply the Cosine Rule here to find the return distance of the plane which is CA.

$AC=\sqrt{(AB)^2+(BC)^2-2(AB)(BC)\times Cos(\angle B)}$

$\therefore AC=\sqrt{(172.20)^2+(111.64)^2-2(172.20)(111.64)\times Cos(177.29^0)}\approx283.8$ miles.

Thus, Option D is the answer.

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2 years ago

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Zayed is helping his classmates get ready for their math test by making them identical packages of pencils and calculators. He h

oee [108]

So 72 pencils and 24 calculators
so greates number of identical calculators

this means
what is the biggest number that we can divide 72 and 24 by and get a whole number
this is called the GCM or greatest common multipule

to find the GCM, you factor 72 and group the like ones
72=2 times 2 times 2 times 3 times 3
24=2 times 2 times 2 times 3
so the common group is 2 times 2 times 2 times 3 or 24
so the greates number of packs is 24

so pencils
72 divided by 24=72/24=3
3 pencils per pack

24 divided by 24=24/24=1
1 calulator per pack

answer is 3 pencils and 1 calculator per pack

6 0

2 years ago

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