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3 years ago

Which choice gives the center and radius of the circle represented by the equation?

1 answer:

3 0

$(x-h)^2+(y-k)^2=r^2$ is the equation of a circle centered at $(h,k)$ with radius $r$ .

Here $h=7$ , $k=-3$ , and $r^2=25\implies r=5$ . So the answer is (C)

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The 4th term of an arithmetic sequence is 12 and the 8th term is 36. Find the 17th term of the sequence.

Blizzard [7]

Answer: 90

Step-by-step explanation:

The formula for calculating the nth term of a sequence is given as :

$t_{n}$ = a + ( n - d )

Where a is the first term

d is the common difference and

n is the number of terms

This means that the 4th term of an arithmetic sequence will have the formula :

$t_{4}$ = a + 3d

And the 4th term has been given to be , 12 ,substituting into the formula we have

12 = a + 3d .............................. equation 1

Also substituting for the 8th term , we have

36 = a + 7d .............................. equation 2

Combining the two equations , we have

a + 3d = 12 ................... equation 1

a + 7d = 36 ------------ equation 2

Solving the system of linear equation by substitution method , make a the subject of formula from equation 1 , that is

a = 12 - 3d ................... equation 3

substitute a = 12 - 3d into equation 2 , equation 2 then becomes

12 - 3d + 7d = 36

12 + 4d = 36

subtract 12 from both sides

4d = 36 - 12

4d = 24

divide through by 4

d = 6

substitute d = 6 into equation 3 to find the value of a, we have

a = 12 - 3d

a = 12 - 3 ( 6)

a = 12 - 18

a = -6

Therefore , the 17th term of the sequence will be :

$t_{17}$ = a + 16d

$t_{17}$ = -6 + 16 (6)

$t_{17}$ = -6 + 96

$t_{17}$ = 90

Therefore : the 17th term of the sequence is 90

6 0

3 years ago

Write the ratio as a fraction in simplest form. 10 feet to 5 yards

Alex17521 [72]

Answer:

1:0.33

Step-by-step explanation:

This is because one foot= .333 yards

I hope this is what you were asking! :)

3 0

3 years ago

Help me please, please

Elina [12.6K]

Answer:

When used as a diacritic mark, the term dot is usually reserved for the interpunct, or to the glyphs 'combining dot above' and 'combining dot below' which may be combined with some letters of the extended Latin alphabets in use in Central European languages and Vietnamese.

Step-by-step explanation:

7 0

3 years ago

PLEASE HELPPPPPP!!!!! You are performing an experiment to determine how well plants grow under different light sources. Of the 3

PIT_PIT [208]

The probability that a plant in the experiment receives visible or ultraviolet light is 7/10.

Step-by-step explanation:

The total number of plants in the experiment = 30 plants

Plants that receive visible light alone = 12 plants

Plants that receive ultraviolet light alone = 15 plants

Plants that receive both visible and ultraviolet light = 6 plants

step 1 :

Probability = No. of required events / Total number

step 2 :

P(visible) = 12 / 30

P(ultraviolet) = 15 / 30

P(both) = 6 / 30

step 3 :

P(visible or ultraviolet) = P(visible) + P(ultraviolet) - P(both)

= 12/30 + 15/30 - 6/30

= 21/30

P(visible or ultraviolet) = 7/10

8 0

3 years ago

Which number from the data set 1, 1, 1, 2, 2, 3, 4, 5,5, and 25 is an outlier?

timofeeve [1]

Outliers are like outcasts of the group
Which number is farthest away from the average?
1-5 seems to be average

Solution: 25 is the outlier

6 0

3 years ago