All categories

2 years ago

x^2+1/2x+1/16=4/9 Factor the perfect-square trinomial on the left side of the equation. (x + )² = 4/9

Mathematics

2 answers:

viva [34]2 years ago

8 0

Answer:

$\frac{1}{4}$

Step-by-step explanation:

we have

$x^{2} +\frac{1}{2}x+\frac{1}{16}=\frac{4}{9}$

we know that

$(x+a)^{2}=x^{2}+2ax+a^{2}$

in this problem

$2ax=\frac{1}{2}x$ ------> $a=\frac{1}{4}$

$a^{2}=\frac{1}{16}$ -----> $a=\frac{1}{4}$

$x^{2} +\frac{1}{2}x+\frac{1}{16}=(x+\frac{1}{4})^{2}$

the missing number in the left side is $\frac{1}{4}$

Nezavi [6.7K]2 years ago

5 0

The missing number is the square-root of the constant term on the left-hand-side, which equals sqrt(1/16)=1/sqrt(16)=1/4.
Check:
(x+1/4)^2=x^2+2*(1/4)x+(1/4)^2=x^2+x/2+1/16. ok

Answer: x= 1/4

You might be interested in

Samantha wants to use her savings of $1150 to buy shirts and watches for her family. The total price of the shirts she bought wa

irakobra [83]

The cost of the shirts is stable, so we can subtract $1150 - $84, which = $1066. Now we want to find how many watches we can buy with $1066, or how many times $99 fits into $1066. So divide 1066 by 99 to get 10.77. You can't buy 77ths of a watch, so round it down to 10 and you have your answer. Samantha can buy 10 watches.

8 0

2 years ago

Read 2 more answers

Find the area of the triangle with the given measurements. Round the solution to the nearest hundredth if necessary. B = 74°, a

elena55 [62]

It is B 134,58 cm^2 i believe

6 0

1 year ago

Read 2 more answers

The score of golfers for a particular course follows a normal distribution that has a mean of 73 and a standard deviation of 3.

Artemon [7]

Answer:

P(X $\geq$ 74) = 0.3707

Step-by-step explanation:

We are given that the score of golfers for a particular course follows a normal distribution that has a mean of 73 and a standard deviation of 3.

Let X = Score of golfers

So, X ~ N( $\mu=73,\sigma^{2}=3^{2}$ )

The z score probability distribution is given by;

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

where, $\mu$ = population mean = 73

$\sigma$ = standard deviation = 3

So, the probability that the score of golfer is at least 74 is given by = P(X $\geq$ 74)

P(X $\geq$ 74) = P( $\frac{X-\mu}{\sigma}$ $\geq$ $\frac{74-73}{3}$ ) = P(Z $\geq$ 0.33) = 1 - P(Z < 0.33)

= 1 - 0.62930 = 0.3707

Therefore, the probability that the score of golfer is at least 74 is 0.3707 .

3 0

2 years ago

In estimating the mean score on a fitness exam, we use an original sample of size n = 30 and a bootstrap distribution containing

ioda

Answer:

C. 67.5 to 72.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The width of the interval is determined by it's margin of error, which is given by the following formula:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

So, as n increases, the margin of error decreases, and the interval gets smaller.

Using 10,000 bootstrap samples for the distribution:

We increase the sample size, which means that the interval gets smaller.

We had 67 to 73, since it got smaller, it will be from a value higher than 67 to a value lower than 73.

So the correct answer is:

C. 67.5 to 72.

8 0

2 years ago

Mr. mole left his burrow that lies 7 meters below the ground and started digging his way deeper into the ground, descending at a

Dimas [21]

Answer:

$f(t)=-\frac{3}{2}t-7$

Step-by-step explanation:

We know that:

The initial conditions are -7 meters at 0 minutes.
Then, after 6 minutes, he was 16 meters below the ground.

According to these two simple facts we can found the linear function that describes this problem. First, the problem says that Mr. Mole is descending at a constant rate, which is the slope of the function. Now, to calculate the slope we need to points, which are $(0;-7)$ and $(6;-16)$ , where t-values are minutes, and y-values are meters. You can see, that the first point is the initial condition and the second point is 6 minutes later.

So, we calculate the slope:

$m=\frac{y_{2}-y_{1}}{t_{2}-t_{1}} \\m=\frac{-16-(-7)}{6-0}=\frac{-16+7}{6}=\frac{-9}{6}=\frac{-3}{2}$

From the slope we can see that Mr. Mole is descending, because it has a negative sign. Also, the point $(0;-7)$ is on the y-axis, because t is null, so -7 is part of the function. Therefore the function that describes this problem is:

$f(t)=-\frac{3}{2}t-7$

7 0

2 years ago

Read 2 more answers