What do we put in the first boxes

A circle is centered at the point (7,1) and passes through the point (8,7). what is the radius

Scorpion4ik [409]

Easy

the radius is the distance from the center to a point on the circle

we are given
center=(7,1)
a point=(8,7)
find the distance
distance formula
D= $\sqrt{(x2-x1)^2+(y2-y1)^2}$

so the distance between point and center is radius
D= $\sqrt{(8-7)^2+(7-1)^2}$
D= $\sqrt{(1)^2+(6)^2}$
D= $\sqrt{1+36}$
D=√37 units

radius is √37 units

7 0

3 years ago

Write the equation of a line that passes a given point and has the given slope. Answer in standard form. 1. Point (-3,5), m = -7

Likurg_2 [28]

Answer:

y -5 = -7(x +3)
y = 7

Step-by-step explanation:

The point-slope form of the equation can be used for this. It is generally written as ...

y -k = m(x -h) . . . . . line with slope m through point (h, k)

__

1. For m=-7, (h, k) = (-3, 5), the equation is ...

y -5 = -7(x +3)

__

2. For m=0, (h, k) = (4, 7), the equation is ...

y -7 = 0(x -4)

y = 7

_____

Comment on the form of the answer

Since a point and slope are given, "the equation" is appropriately written in point-slope form. For the second problem the simplified version would be ...

y -7 = 0

Sometimes, "the equation" means the answer is expected in slope-intercept form. In that case, a little rearranging is necessary for the first answer. It becomes ...

y = -7x -16

There are perhaps a dozen different forms that a linear equation can be written in. Considering those, "the equation" is somewhat ambiguous. Your curriculum materials may offer a clue as to the form intended.

5 0

3 years ago

$28,000 invested at a rate of 4% compounded annually; 5 years

sasho [114]

$28 compounded on a Yearly basis over the course of 5 years at a 4% interest rate would be worth:

$34

4 0

3 years ago

Read 2 more answers

The formula K=59(F−32)+273.15 converts temperatures from Fahrenheit F to Kelvin K.

Semmy [17]

Answer:

9/5 (K-273.15) + 32=F

Step-by-step explanation:

K=5 /9(F−32)+273.15

Subtract 273.15 from each side

K-273.15=5/9(F−32)+273.15-273.15

K-273.15=5/9(F−32)

Multiply by 9/5 on each side

9/5 (K-273.15)= 9/5 *5/9(F−32)

9/5 (K-273.15)=(F−32)

Add 32 to each side

9/5 (K-273.15) + 32=F−32 +32

9/5 (K-273.15) + 32=F

4 0

3 years ago

Read 2 more answers

2. In your own words, explain HOW to find the standard deviation of this data set. (20 points) 3. What does the standard deviati

Ket [755]

Answer:

$\sigma = 11.28$ --- Standard deviation

Step-by-step explanation:

Given

See attachment for graph

Solving (a): Explain how the standard deviation is calculated.

Start by calculating the mean

To do this, we divide the sum of the products of grade and number of students by the total number of students;

i.e.

$\bar x = \frac{\sum fx}{\sum f}$

So, we have:

$\bar x = \frac{50 * 1 + 57 * 2 + 60 * 4 + 65 * 3 +72 *3 + 75 * 12 + 77 * 10 + 81 * 6 + 83 * 6 + 88 * 9 + 90 * 12 + 92 * 12 +95 * 2 + 99 * 4 + 100 * 5}{1 + 2 + 4 + 3 +3 + 12 + 10 + 6 + 6 + 9 + 12 + 12 +2 + 4 + 5}$

$\bar x = \frac{7531}{91}$

$\bar x = 82.76$

Next, calculate the variance using the following formula:

$\sigma^2 = \frac{\sum f(x - \bar x)^2}{\sum f}$

i.e subtract the mean from each dataset; take the squares; add up the squares; then divide the sum by the number of dataset

So, we have:

$\sigma^2 = \frac{1 * (50 - 82.76)^2 +...................+ 5 * (100 - 82.76)^2}{91}$

$\sigma^2 = \frac{11580.6816}{91}$

$\sigma^2 = 127.26$

Lastly, take the square root of the variance to get the standard deviation

$\sigma = \sqrt{\sigma^2}$

$\sigma = \sqrt{127.26}$

$\sigma = 11.28$ --- approximated

Hence, the standard deviation is approximately 11.28

Considering the calculated mean (i.e. 82.76), the standard deviation (i.e. 11.28) is small and this means that the grade of the students are close to the average grade.

8 0

2 years ago