What is the slope of the line y=3x/7 + 4/7

if the probability of getting a 6 on a biased dice is 4/5, and you roll it 500 times, how many 6s would you expect to roll

Tresset [83]

I believe the answer would be 400 you take 4/5 and multiply it by 500

3 0

3 years ago

What is the solution to the equation? 2/3x=10 A. 15 B. 30 C. 6 2/3 D. 6 1/2

Andreyy89

It is A
23x=10Step 1: Multiply both sides by 3/2.(32)*(23x)=(32)*(10)x=15
Answer:x=15

8 0

3 years ago

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a circle has a center (3,5) and a diameter AB. The coordinates of A are (-4,6). what are the coordinates of B?

Kruka [31]

Find the length of the radius.

$r= \sqrt{(3-(-4))^2+(5-6)^2}
\\r = \sqrt{7^2+(-1)^2}
\\r= \sqrt{50} 
\\ r=5 \sqrt{2}$

Find the length of the diameter.

d = 2r = 2 × 5√2 = 10√2

Point B must lie on a line AC, where C is a center of a circle.
Find equation of line AC.
A(–4, 6), C(3, 5)

$y-y_1= \frac{y_2-y_1}{x_2-x_1}(x-x_1)
\\y-6= \frac{5-6}{3-(-4)} (x-(-4))
\\y-6=- \frac{1}{7} (x+4)
\\7y-42=-x-4
\\x+7y-38=0$

The distance from B(x, y) to C(3, 5) is 5√2.
$\sqrt{(x-3)^2+(y-5)^2}=5 \sqrt{2} 
 \\(x-3)^2+(y-5)^2=(5 \sqrt{2})^2 
\\(x-3)^2+(y-5)^2=50$

Solve system of equations.
$x+7y-38=0
\\(x-3)^2+(y-5)^2=50
\\
\\x=38-7y
\\(38-7y-3)^2+(y-5)^2=50
\\(35-7y)^2+(y-5)^2=50
\\1225-490y+49y^2+y^2-10y+25-50=0
\\50y^2-500y+1200=0
\\y^2-10y+24=0
\\y^2-6y-4y+24=0
\\y(y-6)-4(y-6)=0 \\(y-6)(y-4)=0 \\y_1=6,y_2=4
$

$x_1=38-7y_1=38-7 \times 6 = 38-42=-4
\\x_2=38-7y_2=38-7 \times 4 = 38-28=10
$

Point B could have coordinates
$\\
\\(x_1,y_1)=(-4,6),(x_2,y_2)=(10,4)
$

But (–4, 6) are the coordinates of point A.
Therefore, point B has coordinates (10,4).

8 0

4 years ago

Which of the following correctly describes the domain of the function shown

labwork [276]

Option D:

$\{x: x \neq 1\}$ is the domain of the function.

Solution:

Given function is

$$r(x)=\frac{2 x}{x-1}$

To find the domain of the function:

Option A: $\{x: x \neq 0\}$

Substitute x = 0 in r(x).

$$r(0)=\frac{2 \times 0}{0-1}=0$

If x = 0, then r(0) = 0

So that x ≠ 0 is false.

So, $\{x: x \neq 0\}$ is not the domain of the function.

Option B: $\{x: x \neq \pm 1\}$

Substitute x = –1 in r(x).

$$r(-1)=\frac{2 \times (-1)}{-1-1}=1$

If x = –1, then r(–1) = 1

So that x = ± 1 is false.

So, $\{x: x \neq \pm 1\}$ is not the domain of the function.

Option C: $\{x: \text { all real numbers }\}$

Substitute x = 1 in r(x).

$$r(1)=\frac{2 \times 1}{1-1}=\frac{2}{0}$

It is indeterminate.

So, all real numbers are not the domain of the function.

Option D: $\{x: x \neq 1\}$

Substitute x = 1 in r(x).

$$r(1)=\frac{2 \times 1}{1-1}=\frac{2}{0}$

It is indeterminate.

So, $\{x: x \neq 1\}$ is the domain of the function.

4 0

3 years ago

Jamie has 8/10 of a candy bar leftover. He wants to split it into 1/3 pieces. How many 1/3 pieces. How many 1/3 pieces can he ma

valentina_108 [34]

If we change everything to the same denominator it will look like this. 24/30 and he wants to take 10/30. 24/30 - 10/30 is 14/30 so 14/30 - 10/30 is 4/30. *He can take 2 1/3 pieces*

8 0

4 years ago

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