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Sedbober [7]
3 years ago
8

The sum of three consecutive odd integers is -75. What is the smallest number

Mathematics
1 answer:
pashok25 [27]3 years ago
3 0

Answer:

-27

Step-by-step explanation:

First, let's call the smallest number: n

Then, the next two consecutive odd numbers would be:

n+2 and n+4 (this is because it's only odd numbers so we add 2)

We know the sum of these is −75 so we can write this equation and solve for n:

n + (n + 2) + (n + 4) = -75

n + n + 2 + n + 4 = -75

n + n + n + 2 + 4 = -75

n + n + n + 6 = -75

1n + 1n + 1n + 6 = -75

3n + 6 = -75        Subtract 6 from each side, which cancels the 6 on the left.

3n + 6 - 6 = -75 - 6

3n = -75 - 6

3n = -81       Divide each side by 3

3n/3 = -81/3

n = -81/3

n = -27

n + 2 = -27 + 2 = -25

n + 4 = -27 + 4 = -23

The 3 consecutive odd integers would be:

-27, -25, -23

Let's check our work:

-27 + -25 + -23 = -75    We are correct!

The smallest number is -27

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The quarterback of a football team releases a pass at a height of 6 feet above the playing field, and the football is caught by
motikmotik

Answer:

t = 25.1seconds

Step-by-step explanation:

X(t)= 16cos75°t

Y(t)= 6 + (Vosin75°t - 16t^2)

Converting 78 yards to feet :

1 yard = 3 feet

78feet =?

78×3=234 feet

Y(t)= number of feet above the ground at t seconds

VoCos75° t = 234

t = 234/(VoCos75°)

At this time,4 = y(234/VoCos75°)

4 = 6 + VoSin75°(234/VoCos75) - 16(234/VoCos75°)^2

Vo= 140.66ft/s

Time,t= 234/(140.66× Cos75°)

t = 25.087seconds

t= 25.1 seconds (1 decimal place)

8 0
3 years ago
What group of numbers does -2 belong to?
Marizza181 [45]
Answer: Integers and Rational Numbers

Explanation: -2 is an integer because integers include positive an negative numbers. It would not be a whole number or a Naural number because both of those sets only include positive numbers. Here’s a better explanation:

Natural numbers: Natural Numbers are like (1,2,3....). They only include positive numbers. Therefore, -2 does not belong in this category.

Whole Numbers: Whole Numbers are like (0,1,2,3....). They include all the natural numbers with 0. Therefore, -2 does not belong in this set.

Integers: Integers include both positive and negative numbers. They are like (-3,-2,-1,0,1,2,3....). Since they both have positive and negative numbers, -2 would belong in this set.

Rational Numbers: Rational Numbers include ALL the sets that were described. (Natural, Whole, Integer). Since this set also includes positive and negative numbers, -2 would belong in this set.

So, -2 belongs in Integers and Rational Numbers

Hope this helps!
3 0
3 years ago
Trigonometry question! find the vaule of x. round to the nearest tenth!​
atroni [7]

Answer:

<h2>x = 88.2</h2>

Step-by-step explanation:

Look at the picture.

Use tangent:

tangent=\dfrac{opposite}{adjacent}

We have a measure of the angle and length of the adjacent:

\alpha=10^o,\ adjacent=500

\tan10^o\approx0.17633

Substitute:

\dfrac{x}{500}=0.17633             <em>multiply both sides by 500</em>

x=88.165\to x=88.2

8 0
3 years ago
A cylinder has a radius of 4 inches and a high of 10.5 inches what is the approximate volume of the cylinder
olga55 [171]

Answer:

V ≈ 527.79

Step-by-step explanation:

Formula is V= πr2h

therefore

V = π * 4 * 2 * 10.5

V = π * 8 * 10.5

V ≈ 527.79

5 0
3 years ago
If f and g are functions of time, and at time t = 2, f equals 5 and is rising at a rate of 6 units per second, and g equals 7 an
Yuliya22 [10]

Answer:

f/g at t =3 will be 9/8

d/ddx(f(x)/g(x))=f'(x)d(x)-f(x)g'(x)/(g'(x))^2

rate of change=(6*8)+(9*9)/9^2

rate of change =43/27=1.5925

8 0
3 years ago
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