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3 years ago

17.

Mathematics

2 answers:

Hitman42 [59]3 years ago

8 0

<h3>Solution:</h3>

Using formula (a-b)^2 = a^2-2ab+b^2

$4x^{2} - 12x + k \\ = > (2x) ^{2} - 2(2x)(3) + {3}^{2} \\ \\ = > {(2x)}^{2} - 2(2x)(3) + 9$

<h3>Answer:</h3>

k = 9

vagabundo [1.1K]3 years ago

4 0

Answer:

Using formula (a-b)^2 = a^2-2ab+b^2

4x 2 −12x+k

=>(2x) 2 −2(2x)(3)+3 2

=>(2x) 2 −2(2x)(3)+9

=> k = 9

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Answer: 0.5 < x < 16.5.

Step-by-step explanation:

Given: Two sides of triangle: 8.0 units and 8.5 units

Measure of third side = x

According to the triangle's inequality,

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If x is the third side, then

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Also, x > 8.5-8 [Using (ii)]

i.e. x> 0.5

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3 years ago

The sum of the digits of a 2-digit number is 10. If 18 is added to the number, the digits of the new number are those of the ori

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Answer:

Step-by-step explanation:

Let $(ab)$ represent a number with $a$ in the ten's position and $b$ is the one's position.

This means $(ab)$ actually has value of $10a+b$ .

We are given the sum of those digits of $(ab)$ is 10; this means $a+b=10$ .

It says if 18 is added to the number $(ab)$ , then the result is $(ba)$ .

So $(ab)$ has value $10a+b$ and

$(ba)$ has value $10b+a$ .

We are given then:

$(ab)+18=(ba)$

$10a+b+18=10b+a$

Subtract $10a$ on both sides:

$b+18=10b+a-10a$

Simplify:

$b+18=10b-9a$

Subtract $b$ on both sides:

$18=10b-b-9a$

$18=9b-9a$

Divide both sides by 9:

$2=b-a$

Rearrange by commutative property:

$2=-a+b$

So the system of equations we want to solve is:

$a+b=10$

$-a+b=2$

-------------------------Add equations together (this will eliminate the variable $a$ and allow you to go ahead and solve for $b$ :

$0+2b=12$

$2b=12$

Divide both sides by 2:

$b=\frac{12}{2}$

Simplify:

$b=6$

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So the original number is (46).

18 more than 46 is 18+46=(64) which is what we wanted.

We also have the sum of 4 and 6 is 10 as well.

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