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2 years ago

The sum of 5 consecutive integers is 100. What is the first number in this sequence?

1 answer:

5 0

So we can call first number "n"

Then all five integers would be n, n+1, n+2, n+3, n+4

So sum of them would be 5n + 10 = 100

Now you can solve for n:

5n + 10 = 100

5n = 90

n = 18

Verify: 18 + 19 + 20 + 21 + 22 = 100. All good.

So answer is 18

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How many feet of chain fence are necessary to enclosed a dog pen that is square and has a area of 64 sq feet

Oliga [24]

Answer:

32 feet

Step-by-step explanation:

area of square is given by side^2

Perimeter of square is given by 4*side

_______________________________

Given

area of square = 64 sq feet

side^2 = 64

side^2 = 8^2

side = 8

thus side = 8 feet

_______________________________________

The dog pen is fenced with chain, hence chain will be fence at the edge of square and at the perimeter.

Thus, length of chain required will be same as the Perimeter of square.

Perimeter of given dog pen with side length 8 feet = 4*8 = 32 feet.

Thus, 32 feet of chain fence is required.

6 0

3 years ago

Which expression is equivalent to 17s - 10 + 3(2s +1)?

klemol [59]

Answer:

Step-by-step explanation:

17s-10=3(2s+1)

17s-10 = 7s

2s+1=3s

7s+3s=10

10-3=7s

6 0

3 years ago

Which statement is not true about the pattern shown 2/3 , 4/6, 8/12, 16/24 , ...

natta225 [31]

They are multiplying by two .

8 0

2 years ago

The heights of the peach trees in an orchard are normally distributed with a mean of 12.5 feet and a standard deviation of 1.8 f

Zina [86]

Answer:

i think 1.8 not sure tho

8 0

2 years ago

Find the function value. tan495°

inysia [295]

Answer: -1

Step-by-step explanation:

You want to find an angle that is coterminal to 495. So, subtract 360 degrees until youre in the range of 0-360. I got 495 - 360 = 135°

Tangent is equal to $\frac{sin(theta)}{cos(theta)}$ , we already solved theta which was 135°

This next part is hard to explain to someone who doesnt know their trig circle, idk if you do. The angle 135 is apart of the pi/4 gang. So we know this is going to be some variant of √2/2. Sine of quadrant 1 and 2 is gonna be positive:

$sin135=\frac{\sqrt{2} }{2}$

Now lets do cosine of 135°, which again is apart of the pi/4 gang because its divisible by 45°. Its in quadrant 2 so the cosine will be negative.

$cos135=-\frac{\sqrt{2} }{2}$

The final step is to divide them. They are both fractions so you should multiply by the reciprocal.

$\frac{\sqrt{2} }{2} *-\frac{2}{\sqrt{2} } =-\frac{2\sqrt{2} }{2\sqrt{2} } =-1$

7 0

3 years ago

Read 2 more answers