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Morgarella [4.7K]
2 years ago
15

a board 35 feet long is cut into two pieces such that the length of one piece is two-thirds of the length of the other piece. Fi

nd the length of the shorter piece of board.
Mathematics
1 answer:
Ghella [55]2 years ago
5 0

9514 1404 393

Answer:

  14 ft

Step-by-step explanation:

The ratio of lengths is ...

  shortest : longest = (2/3) : 1 = 2 : 3

Then the ratio of the shortest to the total is ...

  shortest : (shortest +longest) = 2 : (2 +3) = 2/5

The shortest piece length is ...

  (2/5)×(35 ft) = 14 ft

The shorter piece of the board is 14 ft long.

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Write a compound inequality that each graph could represent for the following questions.
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Answer:

Part 67) x > -2  and x < 3

Part 68) x\leq -1  or  x\geq 1

Step-by-step explanation:

Part 67) we know that

The solution of the number line is the interval -------> (-2,3)

All real numbers greater than -2 and less than 3

so

The compound inequality could be

x > -2  and x < 3

"And” indicates that, both statements must be true at the same time

Part 68) we know that

The solution of the number line is the interval (-∞,-1] ∪ [1,∞)

All real numbers less than or equal to -1 or all real numbers greater than or equal to 1    

The compound inequality could be

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"Or” indicates that, as long as either statement is true, the entire compound sentence is true

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The line $y = 3$ intersects the graph of $y = 4x^2 + x - 1$ at the points $A$ and $B$. The distance between $A$ and $B$ can be w
raketka [301]

Answer:

61

Step-by-step explanation:

Let's find the points A and B.

We know that the y-coordinates of both are 3.

So let's first solve:

3=4x^2+x-1

Subtract 3 on both sides:

0=4x^2+x-1-3

Simplify:

0=4x^2+x-4

I'm going to use the quadratic formula, x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}, to solve.

We must first compare to the quadratic equation, ax^2+bx+c=0.

a=4

b=1

c=-4

\frac{-1 \pm \sqrt{1^2-4(4)(-4)}}{2(4)}

\frac{-1 \pm \sqrt{1+64}}{8}

\frac{-1 \pm \sqrt{65}}{8}

Since the distance between the points A and B is horizontal. We know this because they share the same y-coordinate.This means we just need to find the positive difference between the x-values we found for the points of A and B.

So that is, the distance between A and B is:

\frac{-1+\sqrt{65}}{8}-\frac{-1-\sqrt{65}}{8}

\frac{-1+\sqrt{65}+1+\sqrt{65}}{8}

\frac{2\sqrt{65}}{8}

\frac{\sqrt{65}}{4}

If we compare this to \frac{\sqrt{m}}{n}, we should see that:

m=65 \text{ and } n=4.

So m-n=65-4=61.

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Answer:

For 1 club it is 120 students

Step-by-step explanation:

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