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3 years ago

8

Find the area of the shape. Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi and enter you

r answer as a decimal. the angle of the semi circle is 270

1 answer:

Len [333]3 years ago

6 0

Answer:

Area of given figure = 37.68 unit²

Step-by-step explanation:

Given:

Radius of given shape = 4 unit

Angle = 270°

Value of π = 3.14

Find:

Area of given figure

Computation:

Area of given figure = [Ф/360][πr²]

Area of given figure = [270/360][(3.14)(4)²]

Area of given figure = [0.75][(3.14)16]

Area of given figure = [0.75][50.24]

Area of given figure = 37.68 unit²

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Daniel [21]

Answer:

Step-by-step explanation:

As the statement is ‘‘if and only if’’ we need to prove two implications

$f : X \rightarrow Y$ is surjective implies there exists a function $h : Y \rightarrow X$ such that $f\circ h = 1_Y$ .
If there exists a function $h : Y \rightarrow X$ such that $f\circ h = 1_Y$ , then $f : X \rightarrow Y$ is surjective

Let us start by the first implication.

Our hypothesis is that the function $f : X \rightarrow Y$ is surjective. From this we know that for every $y\in Y$ there exist, at least, one $x\in X$ such that $y=f(x)$ .

Now, define the sets $X_y = \{x\in X: y=f(x)\}$ . Notice that the set $X_y$ is the pre-image of the element $y$ . Also, from the fact that $f$ is a function we deduce that $X_{y_1}\cap X_{y_2}=\emptyset$ , and because $f$ the sets $X_y$ are no empty.

From each set $X_y$ choose only one element $x_y$ , and notice that $f(x_y)=y$ .

So, we can define the function $h:Y\rightarrow X$ as $h(y)=x_y$ . It is no difficult to conclude that $f\circ h(y) = f(x_y)=y$ . With this we have that $f\circ h=1_Y$ , and the prove is complete.

Now, let us prove the second implication.

We have that there exists a function $h:Y\rightarrow X$ such that $f\circ h=1_Y$ .

Take an element $y\in Y$ , then $f\circ h(y)=y$ . Now, write $x=h(y)$ and notice that $x\in X$ . Also, with this we have that $f(x)=y$ .

So, for every element $y\in Y$ we have found that an element $x\in X$ (recall that $x=h(y)$ ) such that $y=f(x)$ , which is equivalent to the fact that $f$ is surjective. Therefore, the prove is complete.

3 0

3 years ago

20 points! Will mark the brainliest!

andrew-mc [135]

$\dfrac{ \dfrac{x+3}{4x^2-16} }{ \dfrac{2x^2+10x+12}{2x-4} }$

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Write the divide fraction horizontally:
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$= \dfrac{x+3}{4x^2-16} \div \dfrac{2x^2+10x+12}{2x-4}$

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Factorise the numerators and denominators when possible:
-----------------------------------------------------------------------------------

$= \dfrac{x+3}{4(x+2)(x-2)} \div \dfrac{ 2(x + 3) (x + 2)}{2(x-2)}$

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Convert the divide fraction to multiplication fraction
-----------------------------------------------------------------------------------

$= \dfrac{x+3}{4(x+2)(x-2)} \times \dfrac{2(x-2)}{2(x+3)(x+2)}$

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Cancel the factors
-----------------------------------------------------------------------------------
$= \dfrac{1}{4(x+2)} \times \dfrac{1}{(x+2)}$

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Combine to single fraction
-----------------------------------------------------------------------------------

$= \dfrac{1}{4(x+2)^2}$

4 0

3 years ago

NEED HELP ASAP, I'LL GIVE BRAINLIEST. (EXPLANATION NEEDED) ALGEBRA

katrin [286]

$31x^2 +14y -15x +3\\\\=x(31x-15)+14y+3$

4 0

2 years ago

Need help simplifying this

diamong [38]

The simplified answer is $\frac{\left(12 x^{2}+7 x y-4 y z-3 x z+3 y^{2}\right)}{6 x^{2}+3 x z+2 x y+y z}$ .

<u>Step-by-step explanation:</u>

$$\frac{3 y+2 x}{z+2 x}-\frac{2 y-3 x}{3 x+y}-\frac{2 z(y+3 x)}{6 x^{2}+3 x z+2 x y+y z}$

To add or subtract denominators of the fraction must be same.

If it is not the same, we must take LCM of the denominators. and so we can add the fractions.

To make the denominator same multiply the 1st term $(\frac{3x+y}{3x+y})$ and 2nd term by $(\frac{z+2x}{z+2x})$

= $\frac{(3 y+2 x)(3 x+y)}{(z+2 x)(3 x+y)}-\frac{(2 y-3 x)(z+2 x)}{(3 x+y)(z+2 x)}-\frac{2 z(y+3 x)}{6 x^{2}+3 x z+2 x y+y z}$

LCM of the denominators is 6x²+ 3xz + 2xy +yz.

Multiply the factors in the numerator.

= $\frac{\left(6 x^{2}+3 y^{2}+11 x y\right)}{(z+2 x)(3 x+y)}-\frac{\left(2 y z+4 x y-3 x z-6 x^{2}\right)}{(3 x+y)(z+2 x)}-\frac{2 z y+6 x z}{6 x^{2}+3 x z+2 x y+y z}$

Now, the denominators are same, you can subtract it.

= $\frac{\left(6 x^{2}+6 x^{2}+11 x y-4 x y-2 y z-2 y z+3 x z-6 x z+3 y^{2}\right)}{6 x^{2}+3 x z+2 x y+y z}$

= $\frac{\left(12 x^{2}+7 x y-4 y z-3 x z+3 y^{2}\right)}{6 x^{2}+3 x z+2 x y+y z}$

Thus the simplified solution is $\frac{\left(12 x^{2}+7 x y-4 y z-3 x z+3 y^{2}\right)}{6 x^{2}+3 x z+2 x y+y z}$

4 0

3 years ago

Find the value of x and find whether the angles or supplementary or complementary.

Alborosie

Answer:

1) x = 31

2) Both angles add up to be a supplementary angle (an angle who's sum is 180° altogether).

Step-by-step explanation:

1) Since both angles add up to be a supplementary,

→ equation 1 + equation 2 = 180

→ (3x + 25) + (2x) = 180

Solving by applying algebra will give the answer "x = 31".

Hope this helps!

3 0

3 years ago

Read 2 more answers