MATHEMATICS MIDDLE SCHOOL

Nautical flags are used to represent letters of alphabets. The flag for the letter O consists of a yellow right triangle and a red right triangle joined together along their hypotenuse to form a square. The joint hypotenuse of the two triangles is three inches longer than a side of the square. Find the length of a side of the flag. Round your answer to the nearest tenth.

Answers

Answer 1

Answer:

Answer:

The length of a side of the flag is 7.2inches

Step-by-step explanation:

Let length = x

Let hypotenuse = x+3

UsingPythagoras'Theorem:

x^2 + x^2 = (x+3)^2

x^2 + x^2 = x^2 + 6x + 9

2x^2 = x^2 + 6x + 9

×^2 - 6x - 9 = 0

$x = \frac{ - b + - \sqrt{ {b}^(2) - 4ac } }{2a}$

x=[-(-6)+sqrt.(-6)^2-4(1)(-9)]/2(1)

×=[6+sqrt.72]/2

×=7.2inches

×=[-(-6)+sqrt.(-6)^2-4(1)(-9)]/2(1)

x=[6-sqrt.72]/2

×=-1.2(rej)

(PS.sqrt is square root)

(Correctmeifiamwrong)

Answer 2

Answer:

Answer:

7.2 in

Step-by-step explanation:

Let length of side of flag=x

Hypotenuse of right triangle=x+3

According to question information

$(x+3)^2=x^2+x^2$

Using Pythagoras theorem

$(hypotenuse)^2=(base)^2+(perpendicular\;side)^2$

$x^2+6x+9=2x^2$

Using identity: $(x+y)^2=x^2+y^2+2xy$

$2x^2-x^2-6x-9=0$

$x^2-6x-9=0$

Using quadratic formula : $x=(-b\pm√(b^2-4ac))/(2a)$

$x=(6\pm√((-6)^2-4(1)(-9)))/(2(1))$

$x=(6\pm√(36+36))/(2)$

$x=(6\pm√(72))/(2)$

$x=(6\pm6\sqrt2)/(2)$

$x=(6+6\sqrt2)/(2)=3+3\sqrt2=7.2$

$x=(6-6\sqrt2)/(2)=3-3\sqrt2$

$x=-1.24$

It is not possible because the length of side is always positive.

Hence, the side of flag=7.2 in

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Answers

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Answers

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if 3 shirts and 4 caps cost $96, and 2 shirts and 5 caps cost $99, how much did each cap and each shirt cost?

Answers

hmmm..... let us try again...but this time with a different strategy,.... by the graph method.

The system is

3x + 4y =96
2x + 5y = 99.

We find solutions of each system and then plot them on a graph.

Solutions for equation 1 = (2, 22.5) and (30, 0)
Solutions for equation 2 = (49.5 , 0) and (1, 19.4)

Now, we plot both the equations on a graph paper and note its intersecting point.

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$x-cost\ of\ one\ shirt\ny-cost\ of\ one\ cap\n \n3x+4y=\$96\ \ \ and\ \ \ 2x+5y=\$99\n \n \left \{ {{3x+4y=96\ /\cdot(-2)} \atop {2x+5y=99\ /\cdot(3)}} \right. \n \n \left \{ {{-6x-8y=-192} \atop {6x+15y=297} \right. \n --------\n7y=105\ /:7\n\ny=15\ \ \Rightarrow\ \ 3x+4\cdot15=96\ \ \Rightarrow\ \ 3x=36\ /:3\ \ \Rightarrow\ \ x=12\n \nAns.\ one\ shirt\ cost\ \$12,\ \ one\ cap\ cost\ \$15$

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