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julsineya [31]
3 years ago
15

The integer 6 is the product of two consecutive integers (6 = 2 × 3) and the product of three consecutive integers (6 = 1 × 2 ×

3). What is the next integer greater than 6 that is both the product of two consecutive integers and the product of three consecutive integers? A.153 B.210 C.272 D.336 E.600
Mathematics
1 answer:
Lelu [443]3 years ago
7 0

Answer:

B. 210

Step-by-step explanation:

Given:

6=2\times3

6=1\times2\times3

We need to find the next integer greater than 6 and is both the product of two consecutive integers and the product of three consecutive integers.

Solution:

From the given option we will find the factors of each.

a. 153

Now we will find the factors of 153.

Factors of 153 = 1, 3, 9, 17, 51, 153.

From above we can see that 153 doesn't have factors which are consecutive integers

Hence from Above we can say that 153 is not the number which is the product of two consecutive integers and the product of three consecutive integers.

b. 210

Now we will find the factors of 210.

Factors of 210 = 1,2,3,5,6,7,10,14,15,21,30,35,42,70,105,210,

So we can say that;

210 =5\times6\times7

Also;

210 =14\times15

From above we can see that;

210 is the number which is the product of two consecutive integers and the product of three consecutive integers.

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Answer:

1) A

2) min; min; max; max

3) y = x² + 5x - 3

Step-by-step explanation:

f(x) = x² + 2(x)(5) + 5² - 5² + 24

f(x) = (x + 5)² - 25 + 24

f(x) = (x + 5)² - 1

In ax² + bx + c,

if a > 0, it's a min

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y = ax² + bx + c

Using (0,-3)

-3 = a(0)² + b(0) + c

c = -3

y = ax² + bx - 3

Using (1,3)

3 = a + b - 3

a + b = 6

Using (-1,-7)

-7 = a(-1)² + b(-1) - 3

-7 + 3 = a - b

a - b = -4

b = a + 4

a + (a + 4) = 6

2a = 2

a = 1

b = 5

y = x² + 5x - 3

7 0
3 years ago
Scott wants to buy fencing to place around a circular rock garden. The diameter of the circle is 16 feet. Using 3.14 for π, Calc
denpristay [2]

Answer:

200.96 square feet

Step-by-step explanation:

The amount of fencing Scott will need to buy can be gotten by calculating the area of the circular rock garden .

Area of a circle is given by

Pi r^2

Where

r = radius

Given diameter of 16 feet

r = diameter/2

= 16/2

= 8 feet

Pi = 3.14

Therefore,

Area = 3.14 x 8^2

= 3.14 x 8 x 8

= 200.96 square feet

The amount of fencing Scott will need to buy is 200.96square feet

5 0
2 years ago
The average age of a preschool class is 4.5 years old. If there is one 3-year-old, five 5-year-olds, and two other children both
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Answer:

3.1

Step-by-step explanation:

5 x5 =25

25+3=28

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2 years ago
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Juliette [100K]

Answer:

C : -6

Step-by-step explanation:

Please Mark Me Brainliest!

4 0
1 year ago
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What is hundred-seventy as a fraction.
exis [7]
Hello,

To write 170 as a fraction ,you have to write 170 as the numerator and put it over 1 for the denominator.

After that, you now multiply numerator and denominator by 10.

170 = 170/1 (x 10) = 1700/10

The answer then is:
170 as a fraction<span> equals </span><span>1700/10
</span>
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