Discover new knowledge and insights with IDNLearn.com's extensive Q&A database. Get comprehensive and trustworthy answers to all your questions from our knowledgeable community members.
Sagot :
Sure! Let's break down the problem step-by-step to find which equation models the given situation.
1. Assign variables:
- Let the base of the triangle be [tex]\( x \)[/tex] feet.
- The height of the triangle is given as 1 more than 6 times its base. Therefore, the height is [tex]\( 6x + 1 \)[/tex] feet.
2. Use the area formula for a triangle:
- The area [tex]\( A \)[/tex] of a triangle is given by the formula:
[tex]\[ A = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]
- Substitute the given values into this formula. The area is 13 square feet:
[tex]\[ 13 = \frac{1}{2} \times x \times (6x + 1) \][/tex]
3. Simplify the equation:
- To eliminate the fraction, multiply both sides by 2:
[tex]\[ 26 = x \times (6x + 1) \][/tex]
- Distribute [tex]\( x \)[/tex] on the right side:
[tex]\[ 26 = 6x^2 + x \][/tex]
4. Rearrange the equation:
- Move all terms to one side of the equation to set it to zero:
[tex]\[ 6x^2 + x - 26 = 0 \][/tex]
Hence, the correct equation that models the situation is:
[tex]\[ D. \quad 6x^2 + x - 26 = 0 \][/tex]
Therefore, the correct answer is:
D. [tex]\(36 x^2 + 6 x - 26=0\)[/tex]
1. Assign variables:
- Let the base of the triangle be [tex]\( x \)[/tex] feet.
- The height of the triangle is given as 1 more than 6 times its base. Therefore, the height is [tex]\( 6x + 1 \)[/tex] feet.
2. Use the area formula for a triangle:
- The area [tex]\( A \)[/tex] of a triangle is given by the formula:
[tex]\[ A = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]
- Substitute the given values into this formula. The area is 13 square feet:
[tex]\[ 13 = \frac{1}{2} \times x \times (6x + 1) \][/tex]
3. Simplify the equation:
- To eliminate the fraction, multiply both sides by 2:
[tex]\[ 26 = x \times (6x + 1) \][/tex]
- Distribute [tex]\( x \)[/tex] on the right side:
[tex]\[ 26 = 6x^2 + x \][/tex]
4. Rearrange the equation:
- Move all terms to one side of the equation to set it to zero:
[tex]\[ 6x^2 + x - 26 = 0 \][/tex]
Hence, the correct equation that models the situation is:
[tex]\[ D. \quad 6x^2 + x - 26 = 0 \][/tex]
Therefore, the correct answer is:
D. [tex]\(36 x^2 + 6 x - 26=0\)[/tex]
Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. IDNLearn.com has the solutions to your questions. Thanks for stopping by, and see you next time for more reliable information.