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1 year ago

Solve x2 + 6x = 7 by completing the square. Which is the solution set of the equation?

Mathematics

2 answers:

Doss [256]1 year ago

8 0

Answer:

x = 1; x = -7

Step-by-step explanation:

Given

x^2 + 6x = 7

we want to complete the square. If we have (x + a)^2 and expand it we get: x^2 + 2ax + a^2. The second term in the equation suggest that 2ax = 6x or a = 3. Then, adding 3^2 at both sides of the equation of the problem:

x^2 + 6x + 3^2 = 7 + 3^2

(x + 3)^2 = 16

x + 3 = sqrt(16)

That gives us two options

x + 3 = 4

x = 1

x + 3 = -4

x = -7

Ber [7]1 year ago

7 0

So first you have to find the perfect square that matches up with x^2 + 6x

so half of 6, and square it. your perfect square is 9

x^2 + 6x + 9 = 7 + 9

then, condense the left side of the equation into a squared binomial:

(x + 3)^2 = 16

take the square root of both sides:

x + 3 = ± √16

therefore:

x + 3 = ± 4

x = - 3 ± 4

so your solution set is:

x = 1, -7

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20 points<br> What is the linear function equation represented by the graph?

tigry1 [53]

Answer:

F(x) = 2/3x + 3

Step-by-step explanation:

I found this out by first starting off with the equation, f(x) = mx + b. (b is the y intercept, m is the slope.) The y intercept, where the line passes through the y axis, is 3. (f(x) = mx + 3) Now, look at rise over run, and see that the slope is 2/3, since for every one it goes over, it goes up 2/3. your final equation is f(x) = 2/3x + 3

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2 years ago

A computer store decides to increase the prices of all the items it sells by 15%. The store manager uses matrices to prepare the

Nitella [24]

The manager could perform scalar multiplication on Matrix A, using the scalar 1.15.

Increasing the price by 15% would mean we are taking 100% of the value + another 15%; 100+15 = 115%; 115% = 115/100 = 1.15.

Multiplying every value in Matrix A by 1.15 will give the price raised by 15%.

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2 years ago

An investor believes that investing in domestic and international stocks will give a difference in the mean rate of return. They

arlik [135]

Answer:

So on this case the 90% confidence interval would be given by $-4.137 \leq \mu_1 -\mu_2 \leq 2.087$

For this case since the confidence interval for the difference of means contains the 0 we can conclude that we don't have significant differences at 10% of significance between the two means analyzed.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X_1 =2.0233$ represent the sample mean 1

$\bar X_2 =3.048$ represent the sample mean 2

n1=15 represent the sample 1 size

n2=15 represent the sample 2 size

$s_1 =4.893387$ population sample deviation for sample 1

$s_2 =5.12399$ population sample deviation for sample 2

$\mu_1 -\mu_2$ parameter of interest at 0.1 of significance so the confidence would be 0.9 or 90%

We want to test:

H0: $\mu_1 = \mu_2$

H1: $\mu_1 \neq \mu_2$

And we can do this using the confidence interval for the difference of means.

Solution to the problem

The confidence interval for the difference of means is given by the following formula:

$(\bar X_1 -\bar X_2) \pm t_{\alpha/2}\sqrt{\frac{s^2_1}{n_1}+\frac{s^2_2}{n_2}}$ (1)

The point of estimate for $\mu_1 -\mu_2$ is just given by:

$\bar X_1 -\bar X_2 =2.0233-3.048=-1.0247$

The degrees of freedom are given by:

$df = n_1 +n_2 -2 = 15+15-2=28$

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,28)".And we see that $t_{\alpha/2}=\pm 1.701$

Now we have everything in order to replace into formula (1):

$-1.0247-1.701\sqrt{\frac{4.893387^2}{15}+\frac{5.12399^2}{15}}=-4.137$

$-1.0247+1.701\sqrt{\frac{4.893387^2}{15}+\frac{5.12399^2}{15}}=2.087$

So on this case the 90% confidence interval would be given by $-4.137 \leq \mu_1 -\mu_2 \leq 2.087$

4 0

1 year ago

Suppose that some country had an adult population of about 50 million, a labor-force participation rate of 60 percent, and an un

schepotkina [342]

Answer:

The Answer is b. 1.5Million

Step-by-step explanation:

Adult Population = 50 Million

Labor-Force Rate = 60%

Total Labor Force of Adult population = 50Million*60% = 30Million

Unemployment Rate = 5%

People Unemployment =

Total Labor force of Adult population * Unemployment rate

People Unemployment = 30Millon*5%

People Unemployment = 1.5Million

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1 year ago

Ariel weighed an object on her balance and recorded a mass of 24.3 grams.Her teacher told her that there was something wrong wit

grin007 [14]

For this case what we can do is the following rule of three:
24.3 -----> 130%
x ---------> 100%
We clear the value of x:
x = (100/130) * (24.3)
x = 18.7 grams
Answer:
the current mass of the object was:
x = 18.7 grams

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2 years ago