Which number in the monomial 125x18y3z25 needs to be changed to make it a perfect cube?

Answers

Answer 1

Answer: To make the monomial 125 x^18 y^3 z^25 a perfect cube, the entire expression should be reduced to a rational number when the cube root is taken. For the constant 125, the cube root is 5, so it doesn't need to be changed. For the variables, the exponents should be divisible by 3. The exponent of z is not divisible by 3. It can be subtracted with 1 or added with 2 to make the expression a perfect cube.

Answer 2

Answer:

The number in the monomial 125x¹⁸y³z²⁵ that needs to be changed to make the expression a perfect cube is 25

Data obtained from the question

Monomial = 125x¹⁸y³z²⁵
Number to be changed =?

How to determine the number to be changed

To determine the number to be changed in order to obtained a perfect cube, we shall determine the cube root of each entity. This is illustrated below

Cube root of 125

³√125 = 5

Cube root of x¹⁸

³√x¹⁸ = x⁶

Cube root of y³

³√y³ = y

Cube root ofz²⁵

³√z²⁵ = z^(25/3)

From the illustration above, we can see that 25 is not a perfect cube.

Thus, 25 needs to be changed in order for the expression 125x¹⁸y³z²⁵to be a perfect cube

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The solutions to the equation 2x^2 + x - 1 = 2 are x = -3/2 or x = _______.

Answers

Answer:

The remaining solution to the equation is x = 1

Step-by-step explanation:

2x^2 + x - 1 = 2

First set the equation to zero by subtracting 2 from each side:

2x^2 + x - 1 - 2 = 2 - 2

2x^2 + x - 3 = 0

Factor the left side of the equation:

2x^2 + x - 3 = 0

(2x + 3)(x - 1) = 0

Now set each factor to zero and solve:

2x+ 3 = 0

2x+ 3 - 3 = 0 - 3

2x= -3

2x/2= -3/2

x= -3/2 (The given expression)

x - 1 = 0

x - 1 + 1 = 0 + 1

x = 1

Since we already knew x = -3/2, the missing solution is x = 1.

X + y = 1,000
0.06x = 0.04y

Answers

If:
x + y = 1000
then:
y = 1000 - x

We can plug that into the other equation to solve for a value of x.
0.06x = 0.04y
0.06x = 0.04(1000-x)
0.06x = 40-0.04x
0.1x = 40
x = 400

We can then solve for y:
y = 1000 - 400
y = 600

Therefore, x = 400 and y = 600.

Widget Wonders produces widgets. They have found that the cost, c(x), of making x widgets is a quadratic function in terms of x. The company also discovered that it costs $16 to produce 2 widgets, $18 to produce 4 widgets, and $48 to produce 10 widgets. Find the total cost of producing 8 widgets. Write your answer in quadratic equation.

Answers

The answer is Incorrect

Four hundred vouchers were sold for a carwash. Vouchers to wash trucks were $4, while vouchers to wash compact cars were $3. If the total sales were $1350, how many of each type of voucher were sold?

Answers

Answer:

150 vouchers to wash trucks were sold

250 vouchers to wash compact cars were sold

Step-by-step explanation:

Here, we are interested in calculating the number of each type of vouchers sold.

Let the number of vouchers to wash trucks be x while the number of vouchers to wash compact trucks be y.

Firstly, we know that both sums up to be 400.

Mathematically;

x + y = 400 •••••••••(i)

Secondly,

since a voucher to wash trucks sell $4, and we sold a total of x, the amount generated from selling is 4 * x = $4x

Same way for the vouchers to wash compact cars, we have a total of $3 * y = $3y

The sum of both gives $1350, which is the total sales.

Mathematically;

4x + 3y = 1350 ••••••(ii)

So we have two equations to solve simultaneously;

x + y = 400

4x + 3y = 1350

Multiply equation i by 4 , we have;

4x + 4y = 1600

4x + 3y = 1350

Subtract equation ii from i, we have 4y-3y = 1600-1350

y = 250

From equation 1, we know that

x + y = 400

This means that;

x = 400 -y

x = 400 -250

x = 150

A football team loses 5 yards on one play and then loses 8 yards on the nezt play. Write an addition expression that represents the change in the position of the team for the two plays. Then find the sum

Answers

-5+-8+-13 yards in would be

2. Justify each step of the proof.Conjecture: If 2(x2 + 5) = 60, then x is 5 or –5.

1. 2(x2 + 5) = 60                 1.

2. 2x2 + 10 = 60                  2.

3. 2x2 = 50                          3.

4. x2 = 25                            4.

5. x = ±5                              5.

Answers

Hello,

2(x²+5)=60
<==>x²+5=30 (divided teh 2 members by the positive 5 :keep the equality)
<==>x²-25=0 (substract 25 from 2 members)
<==>(x-5)(x+5)=0 (remarquable product a²-b²=(a+b)(a-b))
<==> x= 5 or x=-5 (a product if null if one at least of its factor is null)

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