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Colt1911 [192]
3 years ago
13

Algebraically find three consecutive positive integers such that the square of the first is equal to the third.

Mathematics
1 answer:
dexar [7]3 years ago
7 0
Your numbers are 2, 3, 4.

The three consecutive numbers are x, x+1, x+2
The square of the first equals the third so x^2=x+2
Solve this quadratic as x^2-x-2=0
Factor into (x+1)(x-2)=0
So your answers are x=-1 and x=2
Since the question says they’re positive integers, use x=2
So the numbers are 2, 3, 4
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Which statements are correct? Check all that apply. A chord is sometimes a radius. A diameter is always a chord. A tangent is ne
katrin2010 [14]
1. (false) A chord is never a radius. A chord is the line segment whose 2 endpoints are points on the circle.

2. (true) A diameter is always a chord, in fact, it is the chord of largest length.

3. (true) A tangent is a line in the exterior of a circle, with only 1 common point with a circle. Whereas a secant has 2 common point with a circle and many more in the interior of the circle

4. (false) A chord can be at most equal to the length of the diameter.

5. (true) A chord can be very short. Consider 2 points on the circle which are very close to each other and the chord formed by them.

6. (true)  
7 0
3 years ago
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Compare the investment below to an investment of the same principal at the same rate compounded annually. ​
Marrrta [24]

Answer:

Can you please describe the problem more detailed pls?

5 0
3 years ago
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What are the next four terms in the following arithmetic sequence? (-7), (-2), 3, 8,... A. 18, 23, 28, 33 B. 13, 18, 23, 28 C. 8
Triss [41]
Ok..ur adding 5 each time to get the next term
so the next 4 terms are : 13, 18, 23, 28
5 0
3 years ago
Anna's math test grade was 7 points less than her science test grade. The average grade was 91.5%. What did she get on each test
denis23 [38]

Answer:

84.5%

Step-by-step explanation:

6 0
2 years ago
The manager wants to advertise that anybody who isn't served within a certain number of minutes gets a free hamburger. But she d
aksik [14]

Answer:

The number of minutes advertisement should use is found.

x ≅ 12 mins

Step-by-step explanation:

(MISSING PART OF THE QUESTION: AVERAGE WAITING TIME = 2.5 MINUTES)

<h3 /><h3>Step 1</h3>

For such problems, we can use probability density function, in which probability is found out by taking integral of a function across an interval.

Probability Density Function is given by:

f(t)=\left \{ {{0 ,\-t

Consider the second function:

f(t)=\frac{e^{-t/\mu}}{\mu}\\

Where Average waiting time = μ = 2.5

The function f(t) becomes

f(t)=0.4e^{-0.4t}

<h3>Step 2</h3>

The manager wants to give free hamburgers to only 1% of her costumers, which means that probability of a costumer getting a free hamburger is 0.01

The probability that a costumer has to wait for more than x minutes is:

\int\limits^\infty_x {f(t)} \, dt= \int\limits^\infty_x {}0.4e^{-0.4t}dt

which is equal to 0.01

<h3>Step 3</h3>

Solve the equation for x

\int\limits^{\infty}_x {0.4e^{-0.4t}} \, dt =0.01\\\\\frac{0.4e^{-0.4t}}{-0.4}=0.01\\\\-e^{-0.4t} |^\infty_x =0.01\\\\e^{-0.4x}=0.01

Take natural log on both sides

ln (e^{-0.4x})=ln(0.01)\\-0.4x=ln(0.01)\\-0.4x=-4.61\\x= 11.53

<h3>Results</h3>

The costumer has to wait x = 11.53 mins ≅ 12 mins to get a free hamburger

3 0
2 years ago
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