All categories

3 years ago

Complete the equation...

Mathematics

2 answers:

Nimfa-mama [501]3 years ago

8 0

Answer:

x^2 -14x +49

( x-7)^2

Step-by-step explanation:

x^2 -14x

We are completing the square

Take the coefficient of x

-14

Divide by 2

-14/2 = -7

Square it

(-7)^2 = 49

Add it

x^2 -14x +49

Take the -7

( x-7)^2

Lunna [17]3 years ago

7 0

Answer:

Step-by-step explanation:

x^2-14x+49=(x-7)^2

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Find the positive base $b$ in which the equation $5_b \cdot 23_b = 151_b$ is valid.

DanielleElmas [232]

Answer:

b=7

Step-by-step explanation:

We want to determine the positive base b in which:

$5_b \cdot 23_b = 151_b$

The easiest way to approach this is to convert all the numbers to base 10.

$5_b=5Xb^0=5\\23_b =(2Xb^1)+(3Xb^0)=2b+3\\151_b=(1Xb^2)+(5Xb^1)+(1Xb^0)=b^2+5b+1\\Therefore:\\5_b \cdot 23_b = 151_b\\5(2b+3)=b^2+5b+1\\10b+15=b^2+5b+1\\b^2+5b+1-10b-15=0$

$b^2-5b-14=0$

Next, we factorize the resulting expression.

$b^2-5b-14=b^2-7b+2b-14=0\\b(b-7)+2(b-7)=0\\(b-7)(b+2)=0\\b-7=0\: or \: b+2=0\\b=7\: or \: b=-2$

The positive value of b for which the equality hold is 7.

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2 years ago

Using your knowledge of inverse operations, what does 56 - 25 - 56 equal?

Ivan

Answer:

-25

Step-by-step explanation:

Using the commutative property of addition, we can rearrange the expression to 56-56-25. 56-56 = 0, so the answer is 0 - 25 = -25.

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