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2 years ago

Find the term that must be added to the equation x2 6x=1 to make it into a perfect square.

Mathematics

1 answer:

andrezito [222]2 years ago

3 0

The value added to the equation $$x^2-6x=1$ exists $$x^2-6x+9=10$ .

<h3>What is a perfect square?</h3>

A perfect square exists as a number that can be described as the product of an integer by itself or as the second exponent of an integer.

The perfect square trinomial exists

$(a$ ± $b)^2$ = $a ^2$ ± 2ab + $b ^2$

$$x^2-6x=1$

$x^2-2*3x=1$

then $$2ab = 2 * 3*x = 2 * x *3$

The value of a = x and b = 3

$$b^2=3^2=9$

$$x^2-6x+9=1+9$

$$x^2-6x+9=10$

The value added to the equation $$x^2-6x=1$ exists $$x^2-6x+9=10$ .

To learn more about perfect square refer to: brainly.com/question/6946048

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Read 2 more answers

The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 460 seconds and a

AlekseyPX

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The time that the boys need to beat in order to earn a certificate of recognition from the fitness association is 511.264 seconds.

Step-by-step explanation:

We are given that the time for this event for boys in secondary school is known to possess a normal distribution with a mean of 460 seconds and a standard deviation of 40 seconds.

The fitness association wants to recognize the fastest 10% of the boys with certificates of recognition.

Let X = time for this event for boys in secondary school

SO, X ~ Normal( $\mu=460,\sigma^{2} =40^{2}$ )

The z-score probability distribution for normal distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = mean time = 460 seconds

$\sigma$ = standard deviation = 40 seconds

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

Now, it is given that the fitness association wants to recognize the fastest 10% of the boys with certificates of recognition, which means;

P(X > x) = 0.10 {where x is the required time which boy need to beat}

P( $\frac{X-\mu}{\sigma}$ > $\frac{x-460}{40}$ ) = 0.10