Answer:
See explanation
Step-by-step explanation:
(i) Consider triangles ABC and ADC. In these triangles:
- given;
- given;
- reflective property.
So,
by SAS postulate.
(ii) Congruent triangles have congruent corresponding parts:
(a) ![\angle ABC=\angle ADC](https://tex.z-dn.net/?f=%5Cangle%20ABC%3D%5Cangle%20ADC)
(b) ![\angle ACD=\angle ACB](https://tex.z-dn.net/?f=%5Cangle%20ACD%3D%5Cangle%20ACB)
(c) Line segment AC bisects
and ![\angle BCD.](https://tex.z-dn.net/?f=%5Cangle%20BCD.)
Answer:
$286.80
Step-by-step explanation:
First, find the price after the 150% markup:
478(1.5)
= 717
Now, calculate the price with the 60% discount:
717(0.4)
= 286.8
= $286.80
Answer:
![A = \int\limits^3__-3}{9}-{x^{2}} \, dx = 36](https://tex.z-dn.net/?f=A%20%3D%20%5Cint%5Climits%5E3__-3%7D%7B9%7D-%7Bx%5E%7B2%7D%7D%20%5C%2C%20dx%20%3D%2036)
Step-by-step explanation:
The equations are:
![y = x^{2} + 2x + 3](https://tex.z-dn.net/?f=y%20%3D%20x%5E%7B2%7D%20%2B%202x%20%2B%203)
![y = 2x + 12](https://tex.z-dn.net/?f=y%20%3D%202x%20%2B%2012)
The two graphs intersect when:
![x^{2} + 2x + 3 = 2x + 12](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B%202x%20%2B%203%20%3D%202x%20%2B%2012)
![x^{2} = 0](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%3D%200)
![x_{1} = 3\\x_{2} = -3](https://tex.z-dn.net/?f=x_%7B1%7D%20%20%3D%203%5C%5Cx_%7B2%7D%20%20%3D%20-3)
To find the area under the curve for the first equation:
![A_{1} = \int\limits^3__-3}{x^{2} + 2x + 3} \, dx](https://tex.z-dn.net/?f=A_%7B1%7D%20%3D%20%5Cint%5Climits%5E3__-3%7D%7Bx%5E%7B2%7D%20%2B%202x%20%2B%203%7D%20%5C%2C%20dx)
To find the area under the curve for the second equation:
![A_{2} = \int\limits^3__-3}{2x + 12} \, dx](https://tex.z-dn.net/?f=A_%7B2%7D%20%3D%20%5Cint%5Climits%5E3__-3%7D%7B2x%20%2B%2012%7D%20%5C%2C%20dx)
To find the total area:
![A = A_{2} -A_{1} = \int\limits^3__-3}{2x + 12} \, dx -\int\limits^3__-3}{x^{2} + 2x + 3} \, dx](https://tex.z-dn.net/?f=A%20%3D%20A_%7B2%7D%20-A_%7B1%7D%20%3D%20%5Cint%5Climits%5E3__-3%7D%7B2x%20%2B%2012%7D%20%5C%2C%20dx%20-%5Cint%5Climits%5E3__-3%7D%7Bx%5E%7B2%7D%20%2B%202x%20%2B%203%7D%20%5C%2C%20dx)
Simplifying the equation:
![A = \int\limits^3__-3}{2x + 12}-({x^{2} + 2x + 3}) \, dx = \int\limits^3__-3}{9}-{x^{2}} \, dx](https://tex.z-dn.net/?f=A%20%3D%20%5Cint%5Climits%5E3__-3%7D%7B2x%20%2B%2012%7D-%28%7Bx%5E%7B2%7D%20%2B%202x%20%2B%203%7D%29%20%5C%2C%20dx%20%3D%20%5Cint%5Climits%5E3__-3%7D%7B9%7D-%7Bx%5E%7B2%7D%7D%20%5C%2C%20dx)
Note: The reason the area is equal to the area two minus area one is that the line, area 2, is above the region of interest (see image).
Answer:
Step-by-step explanation:
- <em>During a mathematics activity, teacher Julieta distributed to each of her students 4 straws measuring 2 cm, 3 cm, 7 cm and 8 cm. In this activity, Julieta's students had to build triangles with these straws, without cutting them.
</em>
- <em>How many different triangles could each of Julieta's students form with these straws?</em>
==========================================================
- <em>Triangle inequality theorem says that no any side of a triangle can be longer or equal to the sum the other two sides</em>
<u>Given measures:</u>
<u>We see that:</u>
Therefore we can't make triangles with the sides of 2 cm, 3 cm and 7 cm or 8 cm
<u>Possible solutions are:</u>
- 2 cm, 7 cm, 8 cm
- 3 cm, 7 cm, 8 cm
So we can make two different triangles