MATHEMATICS HIGH SCHOOL

The quotient of the difference of a number and 24 divided 8 is the same as the number divided by 6

Answers

Answer 1

Answer:

The number that satisfies the given condition is -72.

Let's break down the given statement step by step:

The difference of a number and 24:

Let's assume the number is represented by 'x'.

The difference of 'x' and 24 can be written as (x - 24).

Divided by 8: We divide the difference of 'x' and 24 by 8, which gives us ((x - 24) / 8).

The quotient of the difference of a number and 24 divided by 8: So, the quotient is ((x - 24) / 8).

The number divided by 6: We divide the number 'x' by 6, which gives us (x / 6).

The given statement says that the quotient obtained in step 3 is equal to the number divided by 6.

Mathematically, we can represent this as:

((x - 24) / 8) = (x / 6)

To solve this equation for 'x', we can cross-multiply:

6(x - 24) = 8x

Now, we can simplify and solve for 'x':

6x - 144 = 8x

Subtracting 6x from both sides:

-144 = 2x

Dividing by 2:

x = -72

Therefore, the number that satisfies the given condition is -72.

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Answer 2

Answer: $x-the\ number\n\n(x-24)/(8)=(x)/(6)\ \ \ \ |multiply\ both\ sides\ by\ 24\n\n3(x-24)=4x\n\n3x-72=4x\ \ \ \ |subtract\ 3x\ from\ both\ sides\n\n\boxed{x=-72}$

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Solve the following equation: (y - 2) - (y + 1) = (y - 3) - 2

Answers

We can rewrite the equation without the brackets:
y - 2 - y - 1 = y - 3 - 2

Now let’s make both sides simpler:
-3 = y - 5

Let’s leave y on the right side and move 5 to the left:
-3 + 5 = y

So the result is:
y = 2

Answer:

y = 2

Step-by-step explanation:

the formula for finding the volume of a pyramid is v=bh/3. what formula should I use to find altitude h? a. h=3b/v, b. h=3v/b, c. h=v/3b, or d. h=3bv

Answers

solve for h?

v=(bh)/3
mulitply both sides by 3
3v=bh
divide both sides by b
(3v)/b=h

answer is B

A Fair coin is flipped four times. Find: The probability it will land up heads each time.

Answers

If a fair coin is flipped four times, the probability that in all 4 trials, the coin will land up heads is: 1/16. The solution is to multiply the probability of getting a head 4 times. 1/2 * 1/2 * 1/2 * 1/2 = 0.0625 = 1/16

Answer:

1/6

Step-by-step explanation:

Use the method of quadrature to estimate the area under the curve y=-x^2+5 and above the x-axis from x=0 to x=2.

Answers

Answer:

Area = $(22)/(3)$

Step-by-step explanation:

Given is a curve

$y=-x^2+5$

we have to find the area of this curve above x axis from 0 to 2

By method of quadrature we know that area of a curve above x axis is given by,

$\int\limits^a_bf( {x} )\, dx$

Here a= 0 and b =2

Substitute to get

Area = $\int\limits^0_2 {-x^2+5} \, dx \n=(-x^3)/(3) +5x$

Substituting limits

Area = $(-8)/(3) +10 =(22)/(3)$

I'm a calculus teacher at the high school level and I have never heard of quadrature. I teach from an AP approved college-level text so...I'll do it using the antiderivative! Setting that up to integrate we have $- \int\limits^2_0 { (x^2-5)} \, dx$ . If you notice, I pulled the negative out in front of the integral and changed the signs in the function. So it could really be rewritten as $-1 \int\limits^2_0 {(x^2-5)} \, dx$ . Integrating we have $-1[ (x^3)/(3) -5x]$ from 0 to 2. Subbing in those bounds, we have $-1[( (2^3)/(3)-5(2))-( (0^3)/(3)-5(0))]$ which simplifies to $-1( (8)/(3)-10)$ . Distributing the -1 in gives us $10- (8)/(3)= (22)/(3)$

Find the product of 1/6 x 3

Answers

Answer: 0.5 or 3/6 or 1/2

Step-by-step explanation:

1/6 x 3 = 1/6 + 1/6+ 1/6 = 3/6 = 1/2

The amount in a savings account increased from 200 to 216. What was the percent of increase?

Answers

216/200=%
1.08 which equals 108%

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