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djverab [1.8K]
2 years ago
15

Write an equation of the circle with center (3,-2) and radius 6

Mathematics
1 answer:
Lubov Fominskaja [6]2 years ago
8 0

Answer:

\displaystyle (x-3)^2 + (y+2)^2 = 36

Step-by-step explanation:

We want to write the equation of a circle with a center at (3, -2) and a radius of 6 units.

Recall that the equation of a circle is given by:

\displaystyle (x-h)^2 + (y-k)^2 = r^2

Where (<em>h, k</em>) is the center and <em>r</em> is the radius.

Since our center is at (3, -2), <em>h</em> = 3 and <em>k</em> = -2. <em>r</em> = 6. Substitute:

\displaystyle (x-(3))^2  +(y-(-2))^2 = (6)^2

Simplify:

\displaystyle (x-3)^2 + (y+2)^2 = 36

In conclusion, the equation of the circle will be:

\displaystyle (x-3)^2 + (y+2)^2 = 36

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Simplify the expression 21z - 6z + 13
Bess [88]

Answer:

15z+13

Step-by-step explanation:

hey! all we have to do is combine like terms.

21z-6z+13

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there's your answer.

3 0
3 years ago
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Factorize 2x^4-7x^3-13x^2+63x-45 using factor theorem.
zheka24 [161]
Find the possible rational roots and use synthetic division to find the first zero.
I chose x=1 (which represents the factor "x-1")

1║2  -7  -13    63  -45
  ║     2    -5  -18    45
    2  -5  -18    45    0
(x-1) is a factor, (2x³ - 5x² - 18x + 45) is the other factor.

Use synthetic division on the decomposed polynomial to find the next zero.
I chose x = 3 (which represents the factor "x-3")

3║2  -5  -18    45 
  ║     6     3   -45   
    2   1  -15     0   

Using synthetic division, we discovered that (x-1), (x-3), & (2x² + x -15) are factors.  Take the new decomposed polynomial (2x² + x -15) and find the last two factors using any method.

Final Answer: (x-1)(x-3)(x+3)(2x-5)




8 0
3 years ago
Neighbor Fred built a retaining wall that was 2 feet outside his property line. What has Fred created?
yulyashka [42]

Answer:

An encroachment.

Step-by-step explanation:

In real estate,encroachment is building a structure between the boundaries of your property or land and your neighbor's property or land.

The retaining wall Fred build that was 2ft outside his property line is called encroachment

4 0
3 years ago
Between what two integer powers of 2 does 2√7 lie?
prisoha [69]

Answer:

Between 5 and 6

Step-by-step explanation:

Integers refer to positive whole numbers.

Firstly, we need to know the value of the surd

By calculating, the value of the surd is 5.29

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5 0
3 years ago
A major retail clothing store is interested in estimating the difference in mean monthly purchases by customers who use the stor
mixer [17]

Answer:

Critical value is t = 1.9901

Step-by-step explanation:

We are given the results of the sampling :

                                     In-House Credit Card                National Credit Card                    <u>Sample Size</u> :                              32                                                    50

<u>Mean Monthly Purchases </u>:      $45.67                                            $39.87

<u>Standard Deviation </u>:                $10.90                                             $12.47

Also, the managers wished to test whether there is a statistical difference in the mean monthly purchases by customers using the two types of credit cards, using a significance level α of 0.05.

<em>Firstly, we will specify our null and alternate hypothesis;</em>

Let \mu_1 = Mean Monthly Purchases of In-House Credit Card

     \mu_2 = Mean Monthly purchases of National Credit Card

So, Null Hypothesis, H_0 : \mu_1-\mu_2 = 0  {means that there is no difference in the mean monthly purchases by customers using the two types of credit cards}

Alternate Hypothesis, H_0 : \mu_1-\mu_2\neq 0  {means that there is statistical difference in the mean monthly purchases by customers using the two types of credit cards}

The test statistics that will be used here is <u>Two-sample t-test statistics</u>;

              T.S. = \frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p \sqrt{\frac{1}{n_1}+\frac{1}{n_2}  } }  ~ t_n___1+n_2-_2

where, \bar X_1 = Sample mean Purchases of In-House Credit Card = $45.67

           \bar X_2 = Sample mean Purchases of National Credit Card = $39.87

            s_p = pooled variance

            n_1 = In-house credit card sample = 32

            n_2 = National credit card sample = 50

So, degree of freedom of t-value here is (32 + 50 - 2) = 80

Now, at 0.05 significance level, t table gives critical value of t = 1.9901 at 80 degree of freedom.

<em>Therefore, the critical value assuming the population standard deviations are not known but that the populations are normally distributed with equal variances is t = 1.9901.</em>

4 0
3 years ago
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