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geniusboy [140]
3 years ago
5

PLease find attached the question

Mathematics
1 answer:
Jlenok [28]3 years ago
5 0

Answer: 102.9m

Step-by-step explanation: From A to C you can go from the diagonal path and then go around the circular path and then continue the diagonal path. In order to work out the length of the diagonal, you can simply use pythagoras as the triangle is right angled. So to find the length of the whole diameter, you should do 50 squared plus 80 squared and then square root the answer to get 94.34. But then you have to subtract the part of the diagonal line which the circle takes up, so we already know that the diameter of the circle is 15m so we simply do 94.34-15 to get 79.34. This means that we have found the length of the two diagonals, but now we need to find the length of half the circumference of the circle so that the path is complete and to find half the circumference, we'd do Pi multiplied by the diameter (15) and then divide the answer by 2 (because we are only finding the circumference for half of the circle as we have you go around the circle), leaving us with the answer of 23.56. We then add this to the 79.34 to get the answer of 102.9m. We know this is the shortest route as going along the edges of the rectangle would be 130m which is longer than 102.9m.

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20 POINTS !!! <br><br> Find the distance between the points (3,-4) and (5, 4)
jeka57 [31]

Answer:

d=2\sqrt{17}\approx8.2462

Step-by-step explanation:

To find the distance between two points, use the distance formula.

The distance formula is:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2

Let (3,-4) be x₁ and y₁ and let (5,4) be x₂ and y₂. Therefore:

d=\sqrt{(5-3)^2+(4--4)^2

Simplify:

d=\sqrt{(2)^2+(8)^2

Square:

d=\sqrt{4+64}

Add:

d=\sqrt{68}

Simplify:

d=\sqrt{4\cdot17}=\sqrt4\cdot\sqrt{17}

Simplify:

d=2\sqrt{17}\approx8.2462

8 0
3 years ago
Read 2 more answers
If a storm window has an area of 448 square inches, what are the dimensions if the window is 12 inches higher than it is wide (w
pantera1 [17]
Let width = w  then we have the equation:-

w(w + 12) = 448

w^2 + 12w - 448 = 0

(w - 16)(w + 28) = 0

w = 16  

Answer: the dimensions of the window are width 16 by height 28 inches

4 0
3 years ago
If ON = MN, find MN.<br> A 4<br> B. 5<br> C. 4 square root 2<br> D. 4 square root 30
elena-14-01-66 [18.8K]

Answer:

c

Step-by-step explanation:

ON=MN, so triangle onm is a right isosclese triangle, so ON=NM=4 square root 2

4 0
3 years ago
Read 2 more answers
Can someone please help me factor this
Dmitry_Shevchenko [17]

Answer:

\huge\boxed{\bf\:1}

Step-by-step explanation:

\frac{ x  ^ { 2  }  -4x+3  }{ x  ^ { 2  }  -7x+12  }   \times   \frac{ x  ^ { 2  }  +2x-24  }{ x  ^ { 2  }  +5x-6  }    ^ {   }

Take \frac{ x  ^ { 2  }  -4x+3  }{ x  ^ { 2  }  -7x+12  } & factorise it at first.

\frac{ x  ^ { 2  }  -4x+3  }{ x  ^ { 2  }  -7x+12  }   \\= \frac{\left(x-3\right)\left(x-1\right)}{\left(x-4\right)\left(x-3\right)}\\= \frac{x-1}{x-4}

Now factorise the next set : \frac{ x  ^ { 2  }  +2x-24  }{ x  ^ { 2  }  +5x-6  }    ^ {   }.

\frac{ x  ^ { 2  }  +2x-24  }{ x  ^ { 2  }  +5x-6  }    ^ {   }\\= \frac{\left(x-4\right)\left(x+6\right)}{\left(x-1\right)\left(x+6\right)}\\=  \frac{x-4}{x-1}

Now, multiply the two simplified results.

\frac{ x  ^ { 2  }  -4x+3  }{ x  ^ { 2  }  -7x+12  }   \times   \frac{ x  ^ { 2  }  +2x-24  }{ x  ^ { 2  }  +5x-6  }    ^ {   }\\= \frac{x-1}{x-4}\times \frac{x-4}{x-1} \\= \frac{\left(x-1\right)\left(x-4\right)}{\left(x-4\right)\left(x-1\right)} \\= \boxed{\bf\: 1}

\rule{150pt}{2pt}

7 0
2 years ago
A credit union client deposits $3,300 in an account earning 6.5% interest, compounded annually. What will the balance of the acc
astra-53 [7]

Answer:

The balance of account at the end of 36 years is $31,849.29

Step-by-step explanation:

We are given the following in the question:

P = $3,300

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t = 36 years

The compound interest is given by:

A = p\bigg(1+\dfrac{r}{n}\bigg)^{nt}

where A is the amount, p is the principal, r is the interest rate, t is the time in years and n is the nature of compound interest.

Since interest is compounded annualy we use n = 1

A = 3300\bigg(1+\dfrac{0.065}{1}\bigg)^{36}\\\\A = \$31,849.29

Thus, balance of account at the end of 36 years is $31,849.29

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