Some people advise that in very cold weather, you should keep the gas tank in your car more than half full. Irene 's car had 5
1 answer:
You might be interested in
Answer:
Step-by-step explanation:
We have the system of equations:
We can convert this to a matrix. In order to convert a triple system of equations to matrix, we can use the following format:
Importantly, make sure the coefficients of each variable align vertically, and that each equation aligns horizontally.
In order to solve this matrix and the system, we will have to convert this to the reduced row-echelon form, namely:
Where the (x, y, z) is our solution set.
Reducing:
With our system, we will have the following matrix:
What we should begin by doing is too see how we can change each row to the reduced-form.
Notice that R₁ and R₂ are rather similar. In fact, we can cancel out the 1s in R₂. To do so, we can add R₂ to -2(R₁). This gives us:
Now, we can multiply R₂ by -1/5. This yields:
From here, we can eliminate the 3 in R₃ by adding it to -3(R₁). This yields:
We can eliminate the -5 in R₃ by adding 5(R₂). This yields:
We can now reduce R₃ by multiply it by -1/4:
Finally, we just have to reduce R₁. Let's eliminate the 2 first. We can do that by adding -2(R₂). So:
And finally, we can eliminate the second 1 by adding -(R₃):
Therefore, our solution set is
And we're done!
In this attached picture according to the conditions of the problem we have an isosceles trapezoid and since we know that legs are equal (AD=BC=5 cm), we have to calculate bases and height in order to find the area. Working with the triangle BCD, we apply Pythagoras theorem and find that CD = = 10 cm. Since BDC is a right triangle, applying theorem for the area of triangles, we find that
and BF=
. Since ABCD is an isosceles trapezoid, triangles ADE and BFC are congruent with Angle Side Angle theorem. Then, DE=FC and with the help of Pythagoras theorem, DE=FC=2.5 cm. Then, AB=EF=5 cm and the area of the trapezoid is
