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Questions in mathematics

[Done] The production capacity of factory A is twice as much as that of factory B. The production capacity of factory C is three times as much as that of factory D. The combined production capacities of factory A and factory B is the same as the combined production capacities of factory C and factory D. Write the production capacities of the four factories as a ratio in its simplest form.

[Done] A student is using the following steps to find the area of a parallelogram: | Step 1 | Draw a rectangle around parallelogram ABCD. | | Step 2 | Find the area of the rectangle. | | Step 3 | Find the area of the four right triangles created in the corners of the rectangle. | | Step 4 | Subtract the area of the right triangles from the area of the rectangle. | What are possible dimensions of the rectangle he should draw? A. 2 units by 4 units B. 3 units by 2 units C. 4 units by 4 units D. 5 units by 6 units

[Done] Write the expression $2 x^2 y^4\left(\sqrt[4]{3 x^3 y}\right)$ as an entire radical.

[Done] An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?

[Done] Evaluate the following integral: [tex]$\int 5 e^{3 x} d x$[/tex]

[Done] Suppose an isosceles triangle [tex]A B C[/tex] has [tex]A=\frac{\pi}{4}[/tex] and [tex]b=c=3[/tex]. What is the length of [tex]a^2[/tex] ? A. [tex]3^2 \sqrt{2}[/tex] B. [tex]3^2(\sqrt{2}-2)[/tex] C. [tex]3^2(2-\sqrt{2})[/tex] D. [tex]3^2(2+\sqrt{2})[/tex]

[Done] Simplify. $\sqrt[5]{64 x^3 y^8}$

[Done] Listen Write a factor that you can use to rationalize the denominator of $\frac{3 m}{\sqrt[3]{4}}$. A rationalizing factor is $\square$.

[Done] Each digit lives in a place. Look at the number and find the Place Name (Thousands, Hundreds, Tens, Ones) and Value of the digit. | Number | Digit | Place Name | |---|---|---| | 3,281 | 3 | | | 9,342 | 4 | | | 5,067 | 0 | | | 7,105 | 5 | | | 6,432 | 6 | | | 6,031 | 1 | | | 7,304 | 3 | | | 8,009 | 9 | |

[Done] 3) The sides of a triangle are equal to the sides of another triangle. i) Is the length of the height from each side of one triangle to the opposite vertex equal to the height from the equal side of the other triangle to its opposite vertex? Why? ii) Are the areas of the two triangles equal? Why?