What is the area of the figure ?

This table models a linear function. x −8 −4 4 8 y −3 0 6 9 Enter the coordinates of the y-intercept in the boxes.

adell [148]

Answer:

y-intercept is 3

Step-by-step explanation:

We are given table

x: -8 -4 4 8

y: -3 0 6 9

We can select any two points

$x_1=-8,y_1=-3$

$x_2=-4,y_2=0$

Firstly, we will find slope

$m=\frac{y_2-y_1}{x_2-x_1}$

now, we can plug values

$m=\frac{0+3}{-4+8}$

$m=\frac{3}{4}\quad$

now, we can use point slope form of line

$y-y_1=m(x-x_1)$

we can plug values

$y+3=\frac{3}{4}(x+8)$

now, we can solve for y

$y=\frac{3}{4}x+3$

For finding y-intercept , we can plug x=0

$y=\frac{3}{4}\times 0+3$

$y=0+3$

$y=3$

So,

y-intercept is 3

8 0

3 years ago

In the expansion of (3a + 4b)8, which of the following are possible variable terms? Explain your reasoning. a2b3; a5b3; ab8; b8;

Fiesta28 [93]

We have to find the expansion of $(3a+4b)^{8}$

We will use binomial expansion to expand the given expression, which states that the expression $(a+b)^{n}$ is expanded as :

$(a+b)^{n}=^{n}C_{0}a^{n}+^{n}C_{1}a^{n-1}b+^{n}C_{2}a^{n-2}b^{2}+........^{n}C_{n}b^{n}$

Now expanding $(3a+4b)^{8}$ we get,

$(3a+4b)^{8}=^{8}C_{0}(3a)^{8}+^{8}C_{1}(3a)^{7}(4b)+^{8}C_{2}(3a)^{6}(4b)^{2}+^{8}C_{3}(3a)^{5}(4b)^{3}+^{8}C_{4}(3a)^{4}(4b)^{4}+^{8}C_{5}(3a)^{3}(4b)^{5}+^{8}C_{6}(3a)^{2}(4b)^{6}+^{8}C_{7}(3a)(4b)^{7}+^{8}C_{8}(4b)^{8}$

$(3a+4b)^{8}=^{8}C_{0}(3)^{8}a^{8}+^{8}C_{1}(3)^{7}(4)(a^{7}b)+^{8}C_{2}(3)^{6}(4)^{2}(a^{6}b^{2})+^{8}C_{3}(3)^{5}(4)^{3}(a^{5}b^{3})+^{8}C_{4}(3)^{4}(4)^{4}(a^{4}b^{4})+^{8}C_{5}(3)^{3}(4)^{5}(a^{3}b^{5})+^{8}C_{6}(3)^{2}(4)^{6}(a^{2}b^{6})+^{8}C_{7}(3)(4)^{7}(ab^{7})+^{8}C_{8}(4)^{8}(b^{8})$

So, the variables are $a^{5}b^{3}$ , $b^{8}$ , $a^{4}b^{4}$ , $a^{8} , [tex] ab^{7}$

5 0

3 years ago

Which of the binomials below is a factor of this trinomial? -3x^2-21x+24 x-4 x+1 x+4 x-1

OleMash [197]

Answer:

-3x^2-21x+24

Step-by-step explanation:

Kindly separate the answer choices: (x - 4), (x + 1), (x + 4) , (x - 1). The trinomial is thus -3x^2-21x+24, which can be factored as follows: -3(x^2 + 7x - 8)

Then we have -3x^2-21x+24 = -3(x^2 + 7x - 8), which factors further into:

-3(x + 8)(x -1) and so we conclude that the only binomial that is a factor of

-3x^2-21x+24 is (x - 1).

5 0

3 years ago

Find the area of the shaded region. Express your answer in terms of pi

Likurg_2 [28]

Area of the shaded region is 540 – 65.25π.

Solution:

Length of the rectangle = 12 + 9 + 6 + 3 = 30 in

Width of the rectangle = 18 in

Radius of the larger circle ( $r_1$ ) = 12 ÷ 2 = 6 in