MATHEMATICS HIGH SCHOOL

The price of gravel is $24 for every 3/8 ton. kate wants to know the price of 2 tons of gravel

Answers

Answer 1

Answer:

The price of 2 tons of gravel is $128.

Given:

The price of gravel is $24 for every $(3)/(8)$ ton.

To find:

The price of 2 tons of gravel.

Explanation:

Let $x$ be the price of 1 ton of gravel.

Then the price of $(3)/(8)$ ton is $(3)/(8)x$ and the price of 2 tons of gravel is $2x$ .

It is given that the price of gravel is $24 for every $(3)/(8)$ ton.

$(3)/(8)x=24$

$x=(8)/(3)* 24$

$x=8* 8$

$x=64$

Now, the price of 2 tons of gravel is:

$2x=2(64)$

$2x=128$

Therefore, the price of 2 tons of gravel is $128.

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Answer 2

Answer:

Answer:

$128

Step-by-step explanation:

your looking for 16/8, divide 16 by 3, leaving you with 5.333...

now times that by $24, and you have your answer hope this helps

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What is the nth term in the sequence:
4, 7, 12, 19, 28
Please show working out

Answers

4, 7, 12, 19, 28
1st difference +3 +5 +7 +9
2nd difference +2 +2 +2

This is a geometric sequence

The form is:
an² + bn + c
2a is always = to the second difference
2a = 2
a = 1

3a + b = 2nd term - 1st term
3(1) + b = 3
3 + b = 3
b = 0

a + b + c = 1st term
1 + 0 + c = 4
1 +c = 4
c = 3

nth term of sequence {substitute all we have found}
1n² + 0 + 3
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How many hours in 6am to 4 pm

Answers

i believe that it would be 10 hours

a box with no top is constructed from a 10 inch x 12 inch piece of cardboard by cutting out congruent squares from each corner of the cardboard and then folding the resulting tabs. We determined the volume of that box (in cubic inches) is given by V(x) = 4x³ - 44x² + 120x where x denotes the length of the side of the square which is removed from each corner (in inches), 0 < x < 5. Solve the inequality V(x)≥80 analytically and interpret your answer in the context of that example.

Answers

Answer:

$To solve the inequality $V(x) \geq 80$, we'll first set up the inequality and then find the values of $x$ that satisfy it.The inequality is $4x^3 - 44x^2 + 120x \geq 80$.Let's simplify it further:$4x^3 - 44x^2 + 120x - 80 \geq 0$.Now, we need to find the values of $x$ that make this inequality true.We can start by factoring the expression:$4(x^3 - 11x^2 + 30x - 20) \geq 0$.$

$Now, let's factor the cubic polynomial inside the parentheses:$x^3 - 11x^2 + 30x - 20 = (x - 2)(x - 5)(x - 2)$.Now, the inequality becomes:$4(x - 2)(x - 5)(x - 2) \geq 0$.To determine the intervals where this inequality is satisfied, we can use a sign chart. We'll consider the values of $x$ that make each factor and the whole expression positive or negative.$

$1. $x - 2$ is positive for $x > 2$ and negative for $x < 2$.\n2. $x - 5$ is positive for $x > 5$ and negative for $x < 5$.\n3. $x - 2$ is positive for $x > 2$ and negative for $x < 2$.Now, consider the overall sign of the expression $4(x - 2)(x - 5)(x - 2)$:- Positive when all three factors are positive (i.e., $x > 5$).- Negative when exactly one factor is negative (i.e., $2 < x < 5$).- Positive when all three factors are negative (i.e., $x < 2$).$

$So, the solution to the inequality $V(x) \geq 80$ is:\[x < 2 \text{ or } 2 < x < 5.\]$

Step-by-step explanation:

In the context of the example, this means that the side length of the square removed from each corner must be less than 2 inches or between 2 and 5 inches for the volume of the box to be greater than or equal to 80 cubic inches. This helps determine the range of valid values for

x to achieve the desired volume for the box.

Final Answer:

The solution to the inequality V(x) ≥ 80 is x ≥ 3.5 inches.

Explanation:

To solve the inequality V(x) ≥ 80, we set the equation 4x³ - 44x² + 120x ≥ 80 and simplify. This simplifies to x³ - 11x² + 30x - 20 ≥ 0, which can be factored as (x - 3.5)(x - 2)(x - 2.857) ≥ 0. Since x represents the side length of the squares removed from the corners, it cannot be negative, so we focus on the values of x that make the expression on the left side of the inequality greater than or equal to zero. This leads us to the solution x ≥ 3.5 inches.

In the context of the example, when the side length of the squares removed from each corner is 3.5 inches or larger, the resulting box has a volume greater than or equal to 80 cubic inches. This means that to achieve a box with a volume of at least 80 cubic inches, you need to remove squares with sides of at least 3.5 inches.

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If g(x) = 4 square root of x then g(45) is

Answers

Hi,

So we have g(x) = 4√(x). We're looking for g(45). Think of it like this: whatever number is in the place of x in g(x), just place that number AS x.

Therefore, we have :
g(45) = 4√(45) ⇒ (4) × (√(45)) ⇒ (4)(3√(5)) = 12√(5).

-Hope this helps!

What does a straight line on a distance time graph mean

Answers

It means the speed (velocity) was constant - the object traveled the same distance per time period throughout the graph.

What is the LCD of 8 5/12 and 3 5/8?
A.24
B.96
D.48
C.16

Answers

Answer:

Step-by-step explanation:

12, 24

8, 16, 24

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20 pointsA large amount of peanuts was divided equally into 6 small bags. The total number of peanuts, p, was 342. Whichstatements can be used to write an expression and then find the number of peanuts that ended up in each bag?Check all that apply.The operation is division.The operation is multiplication.The variable is the number of bags.342 divided by 6 equals 57.Write the division expression as a fraction,To evaluate, substitute 342 for the variable.Each bag will have 57 peanuts.The constant is 342.