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3 years ago

Solve for X:

Mathematics

2 answers:

galben [10]3 years ago

4 0

Answer:

A. -61/9

Step-by-step explanation:

(7x + 28) + (7x +28) = 5x - 5 . . . . . . . given equation

14x +56 = 5x -5 . . . . . . . . . . . . . . . . . collect terms

9x = -61 . . . . . . . . . . . . . . . . . . . . . . . . subtract 5x+56

x = -61/9 . . . . . . . . . . . . . . . . . . . . . . . . divide by the coefficient of x

Nesterboy [21]3 years ago

3 0

Answer:

A. -61/9

good luck

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Prove that the sum of all natural numbers is -1/12.

ankoles [38]

This is not true. The infinite series

$\displaystyle\sum_{n=1}^\infty n$

converges if and only if the sequence of its partial sums converges. The $k$ -th partial sum is

$\displaystyle\sum_{n=1}^kn=\frac{k(k+1)}2$

but clearly this diverges as $k$ gets arbitrarily large.

5 0

3 years ago

I will give BRAINLIEST to the correct answer Find the measure of angle 6.

True [87]

Answer:

m∠6 = 116°

Step-by-step explanation:

first find x:

7x - 17 = 2x + 78

subtract 2x from both sides: 5x - 17 = 78

add 17 to both sides: 5x = 95

divide by 5: x = 19

plug x into 7x - 17

7(19) - 17 = 116

∠6 and 7x - 17 are vertical angles and therefore congruent, so m∠6 also = 116°

3 0

2 years ago

A shopper purchased 4 tables and 2 chairs for $200 and 2 tables and 7 chairs for $400. What is the cost of each table and each c

I am Lyosha [343]

4t+2c=200
2t+7c=400

I will solve for c in terms of t first
4t+2c=200
2c=200-4t
c=100-2t

Then I will substitute this in for c in the second equation to make it single variable
2t+7c=400
2t+7(100-2t)=400
2t+700-14t=400
300t=12
t=25
Tables cost $25 each

Plug t back into one of the ORIGINAL equations to find the cost of chairs
4(25)+2c=200
100+2c=200
2c=100
c=50
Chairs cost $50 each

Hope this helps! :)

6 0

3 years ago

One month Ravi rented4 movies and8video games for a total of $57 The next month he rented2 movies and3 video games for a total o

e-lub [12.9K]

SOLUTION

Given the question in the question tab, the following are the solution steps to get the rental cost for each movie and each video game.

Step 1: Write the representation for the two rentals

Let m represents movies

Let v represent video games

Step 2: Write the statements in form of a mathematical equation

$\begin{gathered} \text{Month 1: }4m+8v=57 \\ \text{Month 2: }2m+3v=23 \end{gathered}$

Step 3: Solve the equations above simultaneously using elimination method to get the values of m and v

$\begin{gathered} 4m+8v=57----(1) \\ 2m+3v=23----(2) \\ \text{ multiply equation 1 by 2 and equation 2 by }4 \\ 8m+16v=114----(3) \\ 8m+12v=92----(4) \\ \text{subtract equation (4) from equation (3)} \\ 4v=22 \\ v=\frac{22}{4}=5.5 \\ \text{Substitute 5.5 for v in equation 1 to get the value of m} \\ 4m+8v=57 \\ 4m+8(5.5)=57 \\ 4m+44=57 \\ 4m=57-44=13 \\ m=\frac{13}{4}=3.25 \\ m=\text{\$}3.25,v=\text{\$}5.50 \end{gathered}$

Rental cost for each movies is $3.25

Rental cost for each video games $5.50

8 0

1 year ago

A box is to be constructed from a sheet of cardboard that is 10 cm by 60 cm by cutting out squares of length x by x from each co

Stells [14]

Volume of a rectangular box = length x width x height

From the problem statement,
length = 60 - 2x
width = 10 - 2x
height = x

where x is the height of the box or the side of the equal squares from each corner and turning up the sides

V = (60-2x) (10-2x) (x)
V = (60 - 2x) (10x - 2x^2)
V = 600x - 120x^2 -20x^2 + 4x^3
V = 4x^3 - 100x^2 + 600x

To maximize the volume, we differentiate the expression of the volume and equate it to zero.

V = 4x^3 - 100x^2 + 600x
dV/dx = 12x^2 - 200x + 600
12x^2 - 200x + 600 = 0

x^2 - 50/3x + 50 = 0

Solving for x,
x1 = 12.74 ; Volume = -315.56 (cannot be negative)
x2 = 3.92 ; Volume = 1056.31

So, the answer would be that the maximum volume would be 1056.31 cm^3.

6 0

3 years ago