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Alina [70]
3 years ago
13

Please help me out :)

Mathematics
1 answer:
Katarina [22]3 years ago
3 0

Answer:

A  = 25√3 cm²

Step-by-step explanation:

View 5√3 cm as being the height of an equilateral triangle whose base is at the bottom of the purple figure.  To find the area of one such triangle, we use the area-of-a-triangle formula A = (1/2)(b)(h).  

                                                     opp

Using the sine function sin Ф = --------

                                                      hyp

we find the length of the hypotenuse, which is also the radius of the octagon, and because this is an equilateral triangle, is also the length of the base:

                √3       5√3 cm

sin 60° = -------- = ------------- , which produces the value of hyp:

                  2             hyp

                √3       5√3 cm

              -------- = ------------- , which produces the value of hyp:

                  2             hyp

√3·hyp = 10√3, or hyp = 10 cm

Then the area of this one triangle is A = (1/2)(b)(h), or

A = (1/2) (10 cm)(5√3 cm) = 25√3 cm²

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32% as a fraction in lowest terms
TiliK225 [7]
32% means 32/100

32/100 = 16/50 = 8/25, which is the lowest you can get because you can no longer divide it to get a whole number.

A; 8/25.
3 0
2 years ago
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
KiRa [710]

Answer:

1863 meters^{2}

Step-by-step explanation:

( 23 x 12 ) x 2 = 552

69 x 19 = 1311

 1311

<u>+552</u>

= 1863 meters^{2}

8 0
3 years ago
Verify that 2,-1 and 1⁄2 are the zeroes of the cubic polynomial
Mariulka [41]

Answer:

i) Since P(2), P(-1) and P(½) gives 0, then it's true that 2,-1 and 1⁄2 are the zeroes of the cubic polynomial.

ii) - the sum of the zeros and the corresponding coefficients are the same

-the Sum of the products of roots where 2 are taken at the same time is same as the corresponding coefficient.

-the product of the zeros of the polynomial is same as the corresponding coefficient

Step-by-step explanation:

We are given the cubic polynomial;

p(x) = 2x³ - 3x² - 3x + 2

For us to verify that 2,-1 and 1⁄2 are the zeroes of the cubic polynomial, we will plug them into the equation and they must give a value of zero.

Thus;

P(2) = 2(2)³ - 3(2)² - 3(2) + 2 = 16 - 12 - 6 + 2 = 0

P(-1) = 2(-1)³ - 3(-1)² - 3(-1) + 2 = -2 - 3 + 3 + 2 = 0

P(½) = 2(½)³ - 3(½)² - 3(½) + 2 = ¼ - ¾ - 3/2 + 2 = -½ + ½ = 0

Since, P(2), P(-1) and P(½) gives 0,then it's true that 2,-1 and 1⁄2 are the zeroes of the cubic polynomial.

Now, let's verify the relationship between the zeros and the coefficients.

Let the zeros be as follows;

α = 2

β = -1

γ = ½

The coefficients are;

a = 2

b = -3

c = -3

d = 2

So, the relationships are;

α + β + γ = -b/a

αβ + βγ + γα = c/a

αβγ = -d/a

Thus,

First relationship α + β + γ = -b/a gives;

2 - 1 + ½ = -(-3/2)

1½ = 3/2

3/2 = 3/2

LHS = RHS; So, the sum of the zeros and the coefficients are the same

For the second relationship, αβ + βγ + γα = c/a it gives;

2(-1) + (-1)(½) + (½)(2) = -3/2

-2 - 1½ + 1 = -3/2

-1½ - 1½ = -3/2

-3/2 = - 3/2

LHS = RHS, so the Sum of the products of roots where 2 are taken at the same time is same as the coefficient

For the third relationship, αβγ = -d/a gives;

2 * -1 * ½ = -2/2

-1 = - 1

LHS = RHS, so the product of the zeros(roots) is same as the corresponding coefficient

7 0
3 years ago
5t^2 - 5.5 - 3.5t + 1.5t^2 +4t
RideAnS [48]
The answer is 6.5t2+0.5t−5.5 , it’s simplified
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Answer:

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Step-by-step explanation:

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