Aubrey says that the product 10x10x10x10 and 10x-10x-10

Mathematics

2 answers:

Sindrei [870]3 years ago

7 0

Answer:

Aubrey says that the product of 104 and 10–2 is 10–8. Is she correct? If not, explain why.

Yes, she is correct.

No, the exponent should be positive 8.

No, she multiplied the exponents instead of adding them.

No, she multiplied the exponents instead of subtracting them.

Step-by-step explanation:

C. No, she multiplied the exponents instead of adding them.

Fed [463]3 years ago

5 0

The third one, because she got -8 for the product's exponent by multiplying 4 and -2 instead of adding them, show the answer should have been 10^2.

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Find the area of a triangle whose vertices are located at (-2,5), (-4, -3), and (3,1). Evaluate the determinant using diagonals.

myrzilka [38]

Answer:

The area of the triangle is 48 unit²

Step-by-step explanation:

The given vertices of the triangle are;

(-2, 5), (-4, -3), and (3, 1)

The formula for finding the area of a triangle with given coordinates of the vertices is as follows;

$\Delta = \dfrac{1}{2}\times \begin{vmatrix}x_1 & y_1 & 1\\ x_2 & y_2 & 1\\ x_3 & y_3 & 1\end{vmatrix} = \dfrac{1}{2}\times \left | x_1\cdot y_2 - x_2\cdot y_1 + x_2\cdot y_3 - x_3\cdot y_2 + x_3\cdot y_1 - x_1\cdot y_3\right |$

Substituting gives;

$\Delta = \dfrac{1}{2}\times \begin{vmatrix}-2& 5 & 1\\ -4 & -3 & 1\\ 3 & 1 & 1\end{vmatrix} \\\Delta = \dfrac{1}{2}\times \left | (-2)\times (-3) - ((-4)\times 5) + (-4)\times 1 - 3\times (-3) + 3 \times 5 - (-2)\times 1\right | \\\Delta = \dfrac{1}{2}\times \left | 6 +20 -4 +9 + 15+2\right | = 48$