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4 years ago

Would do anything for the answer to this question

Mathematics

2 answers:

ss7ja [257]4 years ago

8 0

Answer:

8x² - 10x

Step-by-step explanation:

olga_2 [115]4 years ago

3 0

Given:

The length of the entire rectangle is 10x + 7.

The width of the entire rectangle is 6x.

The length of the unshaded rectangle is 4x - 5.

The width of the unshaded rectangle is 2x.

We need to determine the area of the shaded region of the rectangle.

Area of the entire rectangle:

The area of the entire rectangle can be determined using the formula,

$A=length \times width$

Substituting the values, we have;

$A_1=(10x+7)(6x)$

$A_1=60x^2+42x$

Thus, the area of the entire rectangle is 60x² + 42x

Area of the unshaded rectangle:

The area of the unshaded rectangle can be determined using the formula,

$A=length \times width$

Substituting the values, we have;

$A_2=(4x-5)(2x)$

$A_2=8x^2-10x$

Thus, the area of the unshaded rectangle is 8x² - 10x

Area of the shaded region of the rectangle:

The area of the shaded region of the rectangle can be determined by subtracting the area of the entire rectangle by the area of the unshaded rectangle.

Thus, we have;

$A=A_1-A_2$

Thus, we have;

$A=60x^2+42x-(8x^2-10x)$

$A=60x^2+42x-8x^2+10x$

$A=52x^2+52x$

$A=52x(x+1)$

Thus, the area of the shaded region of the rectangle is 52x(x + 1)

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The following equation involves a trigonometric equation in quadratic form. Solve the equation on the interval [0,2π).

Effectus [21]

Answer:

$\dfrac{\pi}{6}, \dfrac{5\pi}{6}, \dfrac{3\pi}{2}$

Step-by-step explanation:

Given the quadratic equation as:

$2sin^2x+sinx=1\\OR\\2sin^2x+sinx-1=0$

Let us put $sinx=y$ for simplicity of the equation:

Now, the equation becomes:

$2y^2+y-1=0$

Now, let us try to solve the quadratic equation:

$\Rightarrow 2y^2+2y-y-1=0\\\Rightarrow 2y(y+1)-1(y+1)=0\\\Rightarrow (2y-1)(y+1)=0\\\Rightarrow 2y-1 = 0, y+1 = 0\\\Rightarrow y = \dfrac{1}{2}, y = -1$

So, the solution to the given trigonometric quadratic equation is:

$sinx = \dfrac{1}{2}$

and

$sinx=-1$

Let us try to find the values of $x$ in the interval $[0, 2\pi)$ .

$sin\theta$ can have a value equal to $\frac{1}{2}$ in 1st and 2nd quadrant.

So, $x$ can be

$30^\circ, 150^\circ\\OR\\\dfrac{\pi}{6}, \dfrac{5\pi}{6}$

For $sinx=-1$ ,

$x = 270^\circ\ or\ \dfrac{3 \pi}{2}$

So, the answer is:

$\dfrac{\pi}{6}, \dfrac{5\pi}{6}, \dfrac{3\pi}{2}$

7 0

3 years ago

when planning his crops, farmer tim knows that his 7 acres can support peas and carrots. he wants to make $7,000 from his crops.

bixtya [17]

Given:
7 acres planted with peas and carrots.

peas represented by p. carrots represented by c.

p + c = 7

2,000 per acre of peas
1,000 per acre of carrots
goal income: 7,000

2000p + 1000c = 7000

The constraint in his system of equation would be: p + c = 7

4 0

4 years ago

Which equation has a graph that is a parabola with a vertex at (–1, –1)?

Artist 52 [7]

Answer:

$y=(x+1)^2-1$