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3 years ago

Find three consecutive integers such that twice the sum of the first two is to less than three times the third

Mathematics

1 answer:

drek231 [11]3 years ago

7 0

Answer:

Step-by-step explanation:

Let the consecutive integers be x - 1 , x , x + 1

Equation

2*(x - 1 + x) = 3*(x+1) - 2

Solution

2(2x - 1) = 3(x + 1) - 2 After the first two have been combined remove the brackets.

4x - 2 = 3x + 3 - 2 Combine the right

4x - 2 = 3x + 1

4x - 2 + 2 = 3x + 1 + 2 Add 2 to both sides

4x = 3x + 3 Subtract 3x from both sides

4x-3x = 3x - 3x + 3 Combine

x = 3

Check

Left hand side

2(2 + 3)

2(5)

Right hand side

3*(x+1) - 2

3*(4) - 2

12 - 2

The answers at least agree.

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A new toy hits the local store. Sales (in hundreds) increase at a steady rate for several months, then decrease at about the sam

Montano1993 [528]

Answer:

Option A.

Step-by-step explanation:

It is given that, sales (in hundreds) for several months can be modeled by the function:

$S(m)=-0.625|m-8|+5$

We need to find the month in which 400 toys were sold.

Substitute S(m)=4 in the given function.

$4=-0.625|m-8|+5$

$4-5=-0.625|m-8|$

$-1=-0.625|m-8|$

$\dfrac{-1}{-0.625}=|m-8|$

$1.6=|m-8|$

Now,

$\pm 1.6=m-8$

$1.6=m-8$ or $-1.6=m-8$

$1.6+8=m$ or $-1.6+8=m$

$9.6=m$ or $6.4=m$

Approx the value to the next whole number.

$m\approx 10$ or $m\approx 7$

It means, 400 toys were sold on 7th and 10th month.

Therefore, the correct option is A.

5 0

3 years ago

A crew will arrive in one week and begin filming a city for a movie. The mayor is desperate to clean the city streets before fil

Zigmanuir [339]

Answer:

See below in bold.

Step-by-step explanation:

You work in fractions of the city streets done per hour:

1/200 + 1/400 = 1 /x where x is the number of hours taken by 2 teams.

Multiply through by the LCM 400x:

2x + x = 400

3x = 400

x = 133.33 hours.

As there are 168 hours in a week they will have enough time.

6 0

4 years ago

Angles formed by Parallel lines 8th grade

pashok25 [27]

None since parallel lines never intersect.

I hope this helps!

6 0

4 years ago

Use the given information to determine if the geometric series converges or

lana66690 [7]

Answer:

c) The series diverges. There is no sum.

Step-by-step explanation:

A geometric series is a series of the form:

$S = \Sigma_{i=0}^{n} a\cdot r^{i}$ , $\forall i \in \mathbb{N}_{O}$

Where:

$a$ - First term of the series, dimensionless.

$r$ - Common ratio, dimensionless.

A geometric series converges only if $|r| < 1$ . As $r > 1$ , the geometric series diverges. Hence, the right answer is C.

8 0

3 years ago

Determine whether each table represents a linear, quadratic, or exponential function and justify your answer. Write the correct

Oksanka [162]

Answer:

exponential

Step-by-step explanation:

it gets smaller as the x increases

6 0

3 years ago