All categories

2 years ago

Find the area of the rectangle or square 19 3 km and 38.4 km.

Mathematics

1 answer:

blagie [28]2 years ago

8 0

Answer:

Area of rectangle is 741.12km^2

Area of square is 1474.56km^2

Step-by-step explanation:

Formula for Area of a rectangle= length x breadth

Area = l x b = 19.3 km x 38.4 km (substitute the numbers)

Area = 741 km^2

Area of square = length x length

Area = l x l = 38.4 x 38.4

Area = 1474.56 km^2

You might be interested in

Refer to the data above. What number represents the slope of the line, if the points on the graph above were joined?

Dmitrij [34]

Answer:

slope = 40

Step-by-step explanation:

Calculate the slope m using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = (2, 80) and (x₂, y₂ ) = (4, 160) ← 2 points on the line

m = $\frac{160-80}{4-2}$ = $\frac{80}{2}$ = $\frac{40}{1}$ = 40

4 0

2 years ago

Which expression is equivalent to (-4y-x)-(y-9x) ?

777dan777 [17]

Answer:

-5y + 8x

Step-by-step explanation:

$(-4y-x)-(y-9x)\\\\-4y-x-(y-9x)\\\\\rightarrow-(y-9x)*-1=-y+9x\\\\-4y-x-y+9x\\\\-4y-y+9x-x\\\\\boxed{-5y+8x}$

7 0

2 years ago

Given the function f(x)=3x+5a / x^2-a^2 find the value of a for which f'(12) = 0

maria [59]

The function, as presented here, is ambiguous in terms of what's being deivded by what. For the sake of example, I will assume that you meant

3x+5a
 f(x)= ------------
 x^2-a^2

You are saying that the derivative of this function is 0 when x=12. Let's differentiate f(x) with respect to x and then let x = 12:

(x^2-a^2)(3) -(3x+5a)(2x)
f '(x) = ------------------------------------- = 0 when x = 12
[x^2-a^2]^2

(144-a^2)(3) - (36+5a)(24)
------------------------------------ = 0
[ ]^2

Simplifying,

(144-a^2) - 8(36+5a) = 0

144 - a^2 - 288 - 40a = 0

This can be rewritten as a quadratic in standard form:

-a^2 - 40a - 144 = 0, or a^2 + 40a + 144 = 0.

Solve for a by completing the square:

a^2 + 40a + 20^2 - 20^2 + 144 = 0
(a+20)^2 = 400 - 144 = 156

Then a+20 = sqrt[6(26)] = sqrt[6(2)(13)] = 4(3)(13)= 2sqrt(39)

Finally, a = -20 plus or minus 2sqrt(39)

You must check both answers by subst. into the original equation. Only if the result(s) is(are) true is your solution (value of a) correct.

6 0

3 years ago

Find the roots of:

Elena-2011 [213]

$\large\displaystyle\text{$\begin{gathered}\sf \pmb{1) \ 2x^3-7x^2+8x-3=0 } \end{gathered}$}$

Synthetic division is used since the equation is of the third degree. The divisors of -3 are 1, -1, 3, +3. So:

| 2 -7 8 -3

1 | 2 -5 3

| 2 -5 3 0

1 | 2 -3

2 -3 0

So the factorization is (x-1)² (2x-3)=0. So:

$\bf{ x_1=x_2=1 \qquad x_2=\dfrac{3}{2} }$

$\large\displaystyle\text{$\begin{gathered}\sf \pmb{2) \ x^3-x^2-4=0 } \end{gathered}$}$

Synthetic division is used since the equation is of the third degree. The divisors of -4 are 1, -1, 2, -2, 4, -4. So:

| 1 -1 0 -4

2 | 2 2

1 2 2 0

So the factorization is (x-2)(x²+x+2)=0 . When calculating the discriminant of the trinomial, it is concluded that it has no roots since the result is negative. So you only have one solution.

$\bf{ 1^2-4(2)(2)=1-16=-15 < 0 \quad \Longrightarrow \quad x=2 }$

$\large\displaystyle\text{$\begin{gathered}\sf \pmb{3) \ 6x^3+7x^2-9x+2=0 } \end{gathered}$}$

Synthetic division is used since the equation is of the third degree. The divisors of 2 are 1, -1, 2, -2. So:

| 6 7 9 2

-2 | -12 10 -2

6 -5 1 0

So the factorization is (x+2)(6x²-5x+1)=0 . The quadratic equation is solved by the general formula:

$\bf{ x_{2, 3}&=\dfrac{5\pm \sqrt{(5)^2-4(6)(1)}}{2(6)}=\dfrac{5\pm \sqrt{25-24}}{12}=\dfrac{5\pm 1}{12} }}$

$\large\displaystyle\text{$\begin{gathered}\sf \begin{matrix} x_1=-2&\ \ \ \ \ \ x_{2}=\dfrac{6}{12} \qquad &\ \ \ x_3=\dfrac{4}{12}\\ &\ \ \ x_2=\dfrac{1}{2} \qquad &x_3=\dfrac{1}{3} \end{matrix} \end{gathered}$}$

6 0

2 years ago

Helpp!!!!!! What is X?

ANEK [815]

Answer:

(6,4)

Step-by-step explanation:

Not sure if that right hope it helps

7 0

2 years ago

Read 2 more answers