Find the product. (a^3b)^2 • 4ab3

Mathematics

1 answer:

elena-14-01-66 [18.8K]3 years ago

6 0

(a^3b)^2 • 4ab^3
a^6b • 4ab^3
4a^6b+1b^3

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20% of 57 is what number ? The proportion is ?

Elanso [62]

Answer:

11.4

20/100 = x/57

Step-by-step explanation:

It is perhaps simplest just to translate the given English sentence into a mathematical sentence.

... 20% ... ... of ... 57 ... is ... what number

... 20/100 ... × ... 57 .... = ... what number . . . . . . . . translation to math sentence

... 11.4 = what number . . . . . . . . carry out the multiplication

_____

If you're asked to write this as a proportion, you can write it like this:

$\dfrac{20}{100}=\dfrac{\text{what number}}{57}$

You can solve this proportion by multiplying by 57 (the denominator under "what number"). Doing so gives you the same arithmetic sentence as shown above.

6 0

3 years ago

Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm.

melamori03 [73]

Answer:

$6+2\sqrt{21}\:\mathrm{cm^2}\approx 15.17\:\mathrm{cm^2}$

Step-by-step explanation:

The quadrilateral ABCD consists of two triangles. By adding the area of the two triangles, we get the area of the entire quadrilateral.

Vertices A, B, and C form a right triangle with legs $AB=3$ , $BC=4$ , and $AC=5$ . The two legs, 3 and 4, represent the triangle's height and base, respectively.

The area of a triangle with base $b$ and height $h$ is given by $A=\frac{1}{2}bh$ . Therefore, the area of this right triangle is:

$A=\frac{1}{2}\cdot 3\cdot 4=\frac{1}{2}\cdot 12=6\:\mathrm{cm^2}$

The other triangle is a bit trickier. Triangle $\triangle ADC$ is an isosceles triangles with sides 5, 5, and 4. To find its area, we can use Heron's Formula, given by: