Ow many solutions does the system of equations –6a + b = 14 and –12a + 2b = 28 have?

Mathematics

1 answer:

Dmitry [639]3 years ago

3 0

Indefinite amount of solutions.

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Discovery of Trigonometry: #28 What is the length of CA? *

Kamila [148]

Answer:

sqrt(3)

Step-by-step explanation:

Each side (donated by small letter ) is opposite to its angle for example :

Side c is opposite to angle C which is 90

side b is opposite to angle B which is 60

4 0

3 years ago

HELP PLEASE!!! I need help with this question!

AlexFokin [52]

Answer:

$\large\boxed{PS=10\sqrt5}$

Step-by-step explanation:

ΔPQS, ΔRQP and ΔRPS are similar (AA). Therefore the sides are in proportion:

$\dfrac{QR}{RP}=\dfrac{RP}{RS}$

We have:

$QR=5,\ RS=20$

Substitute:

$\dfrac{5}{RP}=\dfrc{RP}{20}$ cross multiply

$RP^2=(5)(20)\\\\RP^2=100\to RP=\sqrt{100}\\\\RP=10$

Use the Pythagorean theorem:

$PS^2=PR^2+RS^2$

Substitute:

$PS^2=10^2+20^2\\\\PS^2=100+400\\\\PS^2=500\to PS=\sqrt{500}\\\\PS=\sqrt{100\cdot5}\\\\PS=\sqrt{100}\cdot\sqrt5\\\\PS=10\sqrt5$

6 0

3 years ago

The area of a regular octagon is 35 cm 2 what is the area of a regular octagon with sides three times as large

Maurinko [17]

The area of a polygon = n*side^2 / (4 * tan(180/n))
where "n" is the number of sides

Let's calculate area for side = 2
area = 8*2^2 / (4 * tan(180/8))
area = 32 / (4 * tan(22.5))
area = 32 / 4*0.41421
 area = 19.3138746047 

Now, let's calculate area for side = 6
area = 8*6^2 / (4 * tan(180/8))
area = 288 / 1.65684 
area = 173.824871442 

 173.824871442 / 19.3138746047 = 9

So, the area would be 9 times larger.

ALSO, looking at the formula
n*side^2 / (4 * tan(180/n))
we can see that the side length appears just once in the formula and we are to square it in the calculation. So, if we increase the side length is increased by 3, then the area increases by 3^2 or 9.