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3 years ago

What is the best way to classify each equation? 22-3x+7x=4(x+5) ,6(2x-3=3(3-5), 6x-14=2(3x-7), 6x+3(x-4)=8(x-3)

1 answer:

8 0

1. 22 - 3x + 7x = 4(x + 5)
 22 - 3x + 7x = 4x + 20
 +3x +3x +3x 
 22 + 10x = 7x + 20
 -7x -7x 
 22 + 3x = 20
 -22 -22
 3x = -2
 3 3
 x = -2/3

2. 6(2x - 3) = 3(3 - 5)
 12x - 18 = 3(-2)
 12x - 18 = -6
 +18 +18
 12x = 12
 12 12
 x = 1

3. 6x - 14 = 2(3x - 7)
 6x - 14 = -3x
 6x - 14 = 2(-7)
 6x - 14 = -14
 +14 +14
 6x = 0
 6 6
 x = 0

4. 6x + 3(x - 4) = 8(x - 3)
 6x + 3x - 12 = 8x - 24
 9x - 12 = 8x - 24
 -8x -8x 
 x - 12 = -24
 +12 +12
 x = -12

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A piggy bank contains 3 pennies, 4 nickels, 4 dimes and 9 quarters. Two coins

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1325/10000

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2 years ago

A chef got 7 bags of onions. The red onions came in bags of 8 and the yellow onions came in bags of 3. If the chef got a total o

frutty [35]

Answer:

$\#\text{ of 8-onion bags: }4,\\\#\text{ of 3-onion bags: }3$

Step-by-step explanation:

Let $a$ be the number of bags with 8 onions and let $b$ be the number of bags with 3 onions. We have the following system of equations:

$\begin{cases}a+b=7,\\8a+3b=41\end{cases}$

Subtracting $b$ from both sides of the first equation, we get $a=7-b$ . Substitute this into the second equation:

$8(7-b)+3b=41,\\56-8b+3b=41,\\56-5b=41,\\-5b=-15,\\b=\boxed{3}$

Therefore, the number of 8-onion bags is:

$a=7-b,\\a=7-3,\\a=\boxed{4}$

Thus, the chef got 4 8-onion bags and 3 3-onion bags.

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3 years ago

Is -2 a solution to 4x^(3)-x^(2)+16x-4

sergiy2304 [10]

Answer:

Not a solution

Step-by-step explanation:

In order for $x=-2$ to be a solution, the result after substituting must be 0:

$4(-2)^3-(-2)^2+16(-2)-4\stackrel{?}{=}0$

$4(-8)-4-32-4\stackrel{?}{=}0$

$-32-40\stackrel{?}{=}0$

$-72\neq0$

Therefore, $x=-2$ is not a solution to $4x^3-x^2+16x-4$

3 0

2 years ago

The perimeter of a playing field for a certain sport is 254 ft. The length is 47 ft longer than the width. Find the dimensions.

Vikentia [17]

Answer: the length is 87 feet

The width is 40 feet

Step-by-step explanation:

Let L represent the length of the playing field.

Let W represent the width of the playing field.

The playing field is rectangular. The formula for determining the perimeter of a rectangle is expressed as

Perimeter = 2(L + W)

The perimeter of a playing field for a certain sport is 254 ft. This means that

254 = 2(L + W)

L + W = 254/2

L + W = 127 - - - - - - - - - - - -1

The length is 47 ft longer than the width. This means that

L = W + 47

Substituting L = W + 47 into equation 1, it becomes

W + 47 + W = 127

2W + 47 = 127

2W = 127 - 47 = 80

W = 80/2 = 40

L = W + 47 = 40 + 47

L = 87

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3 years ago

Olve for x. Check each step or answer that is correct. 34(x + 4) = 14(x + 8) (A) Distribute 34 on the left side of the equation.

Fantom [35]

Answer:

x = -1.2

Step-by-step explanation:

Th given equation is :

34(x + 4) = 14(x + 8)

Step (A) Distribute 34 on the left side of the equation such as :

34x + 34(4) = 14(x + 8)

34x + 136 = 14(x + 8)

Step (B) Distribute 14 on the right side of the equation such as :

34x + 136 = 14x + 14(8)

34x + 136 = 14x + 112

Step (C) Subtract 14x from each side of the equation.

34x + 136 - 14x = 14x + 112 -14x

20x + 136 = 112

Step (D) Subtract 136 from each side of the equation.

20x + 136 -136 = 112 -136

20x = -24

Step (E) Divide both side by 20

$\dfrac{20x}{20}=\dfrac{-24}{20}\\\\x=-1.2$

So, the value of x is (-1.2). Hence, steps (D) and (E) are incorrect.

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3 years ago