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2 years ago

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Mathematics

1 answer:

const2013 [10]2 years ago

4 0

The equation in the given standard form is $(x+10)^2+(y+6)^2=5^2$

<h3>Equation of a circle</h3>

The standard equation of a circle is expressed as:

$(x-a)^2+(y-b)^2=r^2$

Given the equation $x^2 + y^2 + 20x + 12y + 111 =0$

Group the function to have:

$(x^2 +20x)+(y^2+ 12y) + 111 =0$

Complete the squares to have:

$(x^2 +20x)+(y^2+ 12y) + 111 =0\\(x^2+20x+10^2-10^2)+(y^2+12y+6^2-6^2)+111=0\\(x+10)^2+(y+6)^2 -100-36+111=0\\(x+10)^2+(y+6)^2-25=0\\(x+10)^2+(y+6)^2=25\\(x+10)^2+(y+6)^2=5^2$

Hence the equation in the given standard form is $(x+10)^2+(y+6)^2=5^2$

Learn more on equation of a circle here: brainly.com/question/1506955

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The perimeter of a rectangle is 24 inches. Find the dimension If the length of the rectangle is 3 inches more than it’s width.

GuDViN [60]

Answer:

length is 7.5 and width is 4.5

Step-by-step explanation:

Its given that perimeter of the triangle is 24 units.

The condition is that length is 3 units more than the width.

l=w+3;

Formula for perimeter is 2(l+w).

so ,

2(w+w+3)=24,

2w+3=12,

w=4.5,

l=w+3=7.5

Hence for the given conditions length is 7.5 and width is 4.5.

8 0

2 years ago

Which expression is equivalent to 16^2 − 36? (Explain)

seropon [69]

Answer:

4(2x-3)(2x + 3)

Step-by-step explanation:

Here, we want to simplify the given expression

we can have;

16x^2-36

= 4(4x^2 -9)

we can use the difference of two squares

where;

a^2 - b^2 = (a-b)(a + b)

= 4(2x-3)(2x+ 3)

6 0

2 years ago

Brainliest question please help me now plz I need it

Alenkasestr [34]

Answer:

As shown in picture:

A(-4, 1)

Z(-2, 3)

P(3, -4)

The length of AZ is calculated by:

L = sqrt((-4 - -2)^2 + (1 - 3)^2) = 2.83

The length of AP is calculated by:

L = sqrt((3 - -4)^2 + (-4 - 1)^2) = 8.60

THe length of ZP is calculated by:

L = sqrt((3 - -2)^2 + (-4 - 3)^2) = 8.60

=>Perimeter of triangle AZP is calculated by:

P = AZ + AP + ZP = 2.83 + 8.60 + 8.60 = 20.3

Hope this helps!

7 0

3 years ago

An object has volume 36 cubic inches. A box has side lengths 1 foor by 3 inches by 4 inches.

nevsk [136]

Answer:

<u>4 Objects can fit in the box</u>

Step-by-step explanation:

First, translate the box's 1-foot side into 12 inches. Now multiply all the box's sides together to get 12*3*4. This will equal 144 cubic inches. Now divide 144 by 36 to get 4.

5 0

2 years ago

Suppose a lawn and garden company wants to determine the current percentage of customers who use fertilizer on their lawns. How

marishachu [46]

Answer:

n=601

Step-by-step explanation:

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".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

The confidence interval for the mean is given by the following formula:

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.04$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

Since we don't have a prior estimation for the proportion we can use 0.5 as estimation. And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.04}{1.96})^2}=600.25$

And rounded up we have that n=601

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3 years ago