Solve for x/4-x+2/6=x/3

Answers

Answer 1
Answer: (x)/(4) -( x+ 2 )/(6) = (x)/(3) \ \ \cdot 12\n \n3x-2(x+2)=4x\n \n3x-2x-4=4x \n \n3x-2x-4x=4 \n \n-3x =4\ \ / :(-3)\n \nx=-(4)/(3)\n \nx=-1(1)/(3)
Answer 2
Answer: (x)/(4) - (x+2)/(6) = (1)/(3) \ /\cdot12\n\n (x)/(4)\cdot12 - (x+2)/(6)\cdot12 = (1)/(3)\cdot12\n\n3x-2(x+2)=4\n\n3x-2x-4=4\n\nx=8

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Which shows 60^2 − 40^2 being evaluated using the difference of squares method?(A)60^2-40^2=(3600+1600)(3600-1600)=10,400,000 (B)6^2-40^2=3600-1600=2,000 (C)60^2-40^2=(60-40)^2=20^2=400 (D)60^2-40^2=(60+40)(60-40)=(100)(20)=2,000
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Below are two different functions, f(x) and g(x). What can be determined about their slopes?f(x) Alex earns 1600 dollars in 400 hours.
x
g(x)
1
−8
5
12
9
32

Answers

Answer:

As per the statement:

Below are two different functions, f(x) and g(x).

For f(x):

Alex earns 1600 dollars in 400 hours.

\text{unit rate per hour} = (1600)/(400) = 4 dollars.

Slope of f(x) = 4

Now, find the slope of g(x):

Formula for slope is given by:

\text{Slope} = (y_2-y_1)/(x_2-x_1)

From the given tables:

Consider two values  (x, g(x)) i.e,

(1, -8) and (5, 12)

Then;

\text{Slope} = (12-(-8))/(5-1)

\text{Slope} = (20)/(4) =5

⇒Slope of g(x) = 5

\text{Slope of g(x)} > \text{Slope of f(x)}

Therefore, the function g(x) has faster slope.

f(x) = 1600/400 reduces to 4....the slope of f(x) is 4

g(x) :
(1,-8)(5,12)
slope = (12 - (-8) / (5 - 1) = (12 + 8)/4 = 20/4 = 5...slope of g(x) is 5

so g(x) has a greater slope then f(x)

There are 5 performers who will present their comedy acts this weekend at a comedy club. One of the performers insists on being the first stand-up comedy of the evening. If this performer's request is granted, how many different ways are there to schedule the appearances?

Answers

We have to use basic combinatorics to solver his problem. We first have to determine what kind of problem this is. 

Does order matter in this question? Yes it does. So it is a permutation. 

Is is a permutation with repetition? No, because once a performer goes, they cannot perform again. Hence, we have defined this problem as a permutation without repetition. The formula for this kind of question is: 

(n!)/((n-r)!)

Where n is the number of things we choose from, and p is the number of places we want to put them in. 

There are 4 places for 4 performers, because 1st performer, lets call him Joe, has already taken the 1st spot. Hence, we substitute our values: 

(4!)/((4-4)!)

= 4!

=24 

There are 24 different ways to schedule this performance. 

Hope this helped!

Sincerely,

~Cam943, Junior Moderator

The sum of an integer and its square is 72. Find the greatest possible integer.

Answers

x + x^2 = 72

x^2 + x - 72 = 0

(x -8)(x+9) = 0

x = -9, 8

Greatest Possible Integer: 8

Find z

Help me please

Answers

Answer: z=56

Step-by-step explanation:

Based on the figure, we can determine that 3y+8=68 and 4x=2z. With the knowledge that a trapezoid has 360°, we can first find the value of y to get the angle measures of the top angles. We can then subtract that from 360°.

3y+8=68        [subtract both sides by 8]

3y=60            [divide both sides by 3]

y=20

We now know the value of y is 20, but that is not relevant to solving this problem because we already know that the top angles are 68° each. So, we can subtract that from 360.

360-68-68=224

Now, we know that the bottom 2 angles have to add up to 224. Therefore, we can come up with 2 equations.

Equation 1: 4x=2z

Equation 2: 4x+2z=224

We can manipulate Equation 1 to be x=(1)/(2)z. Once we plug that into Equation 2, we can find the value of z.

4((1)/(2) z)+2z=224         [multiply]

2z+2z=224              [add]

4z=224                      [divide both sides by 4]

z=56

Now, we know that z=56.

Which shows one way to determine the factors of x3 – 9x2 + 5x – 45 by grouping?x2(x – 9) – 5(x – 9)
x2(x + 9) – 5(x + 9)
x(x2 + 5) – 9(x2 + 5)
x(x2 – 5) – 9(x2 – 5)

Answers

x³ - 9x² + 5x - 45

x²(x - 9) - 5(x - 9) ⇒ x³ - 9x² - 5x + 45 INCORRECT
x²(x + 9) - 5(x + 9) ⇒ x³ + 9x² - 5x - 45 INCORRECT

x(x² + 5) - 9(x² + 5) ⇒ x³ + 5x - 9x² - 45 CORRECT
It just needs to be rearranged.

x(x² - 5) - 9(x² - 5) ⇒ x³ - 5x - 9x² + 45 INCORRECT

The answer choice which shows a way to determine the factors by grouping is; x(x² + 5)9(x² + 5).

Which shows one way to determine the factors of x3 – 9x2 + 5x – 45 by grouping?

According to the task content, the factors of the expression are to be determined by grouping.

On this note, one way to group the factors would be;

x³ + 5x - 9x² -45

Upon factorisation;

x(x² + 5) – 9(x² + 5).

Read more on factorisation by grouping;

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Chelsea made monthly payments for four years before her $13,440 loan was paid off. The loan had an interest rate of 5.86%, compounded monthly. Chelsea paid $156.60 in service charges. To the nearest tenth, what percentage of the total cost of the loan did her finance charges comprise? Round all dollar values to the nearest cent.

Answers

Given:
PV = 13,440
i = 5.86% , compounded monthly
t = 4 years

13,440(0.0586/12))/(1-(1+0.0586/12)^-48= 15,109.44 
15,109.44 + 156.60 = 15,266.04
15,266.04 - 13,440.00 =  1,826.04 
1,826.04/15,266.04 = 11.96 % Percentage total of Finance Charge of the total loa

Answer: 11.9%

Step-by-step explanation: