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bezimeni [28]
3 years ago
12

The inner square has sides of 3 inches and the outer square has sides

Mathematics
1 answer:
EastWind [94]3 years ago
7 0
X is the hypotenuse of an isosceles triangle. The length of the sides are the difference of the inner and outer squares divided by 2. Which means that the sides of the triangle is 1.5 inches. Using that information, the length of X can be deduced to be 2.12 inches using Pythagoras theorem
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Given: △ABC, m∠A=60°, m∠C=45°, AB=9 Find: Perimeter of △ABC, Area of △ABC do not rationlize
dexar [7]

Answer:

p = 32.32; A = 47.91  

Step-by-step explanation:

1. Calculate ∠B

∠A + ∠B + ∠C = 180°

60° + ∠B + 45° = 180°

       ∠B + 105° = 180°

                  ∠B =   75°

2. Find sides BC and AC

We can use the Law of Sines

\dfrac{\sin A}{BC} = \dfrac{\sin B}{AC} = \dfrac{\sin C}{AB}

(i) Find BC

\dfrac{\sin 75^{\circ}}{AC} = \dfrac{\sin 45^{\circ}}{9}\\\\\dfrac{0.8660}{BC} = \dfrac{0.7071}{9}\\\\BC = 9 \times \dfrac{0.8661}{0.7071} = 11.02

(ii) Find AC

\dfrac{\sin 75^{\circ}}{AC} = \dfrac{\sin 45^{\circ}}{9}\\\\\dfrac{0.9659}{AC} = \dfrac{0.7071}{9}\\\\BC = 9 \times \dfrac{0.9659}{0.7071} = 12.29

3. Find the perimeter

p = AB + AC + BC = 9 + 12.29 + 11.02 = 32.32

4. Find the area of the triangle

A general formula for the area of a triangle is

A = ½ab sinC

If we use ∠A, the formula becomes

A = ½ × 9 × 12.29 × sin60° = 55.30 × 0.8660 = 47.91

4 0
3 years ago
What is the sum of prime factors of 105
marta [7]
1, 3, 5, 7, 15, 21, 35, 105 these are the factors of 105.
The sum of the prime factors is 3+5+7=15

6 0
3 years ago
Please help answer alll
poizon [28]
A= there are "4"one fourths in one hour and he hikes 2 miles every hour

B= 1, 1 1/2, 2, 4

C= it going to be 1/3 mile for every 1/6hour and she hikes 2 miles every hour.

D= 2/3, 1, 2, 4
7 0
3 years ago
Nadia spent 1/4 of her money on a shirt and 2/5 of her money on new shoes. What fraction of Nadias money was spent?
Ulleksa [173]

Answer:

13/20 of her money was spent.

Step-by-step explanation:

To find the answer you have to add these two fractions together, and to do that you must find a common denominator.

For this problem I chose to use 20 for the denominator since it is the smallest number that both 4 and 5 have in common.

Keep in mind that, whatever you do to the denominator, you must also do to the numerator, so if you multiply 5 by 4, you must also multiply 2 by 4.

5/20 + 8/20 = 13/20

4 0
3 years ago
Help on college algebra, question is on the picture!
kodGreya [7K]
\frac{7x+1}{x-2} + \frac{2}{x} = \frac{-4}{ x^{2} -2x} is given 
here , \frac{7x+1}{x-2} + \frac{2}{x} = \frac{-4}{ x^{2} -2x} 
or, \frac{7x^{2} +x +2x-4 }{x(x-2)} = \frac{-4}{ x^{2} -2x}
or,\frac{7 x^{2} +3x-4}{ x^{2} -2x} = \frac{-4}{ x^{2} -2x}
or,7x²+3x-4=-4
or,7x²+3x=0
or,x(7x+3)=0
Either,x=0| Or,7x+3=0
                |or,7x=-3
                |or,x=\frac{-3}{7}
So , the solution set is S={0,-\frac{3}{7}}
8 0
3 years ago
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