A scatter plot containing the point (10,7) has the regression equation yˆ=−x−3

Write the following number as ratios of integers

s2008m [1.1K]

Our goal here is to somehow "surgically remove" the repeating part of the number, so let's start by putting the original value in a variable and messing around with it a bit.

We'll let $x=7.\overline{6}$ . We want to cut the $0.\overline{6}$ bit off completely, so let's create the scalpel that'll let us do that. If $x=7.\overline{6}$ , then we can also say that $10x=76.\overline{6}$ . Maybe I was lying a bit: the $x$ is our real scalpel here, and $10x$ is where we'll be making the cut. Mathematically, a "cut" is almost always shorthand for subtraction, so let's see what our operation (cutting $x$ off of $10x$ ) leaves us with:

$10x-x=76.\overline{6}-7.\overline{6}\\9x=69$

The operation was a success! We can now simply divide either side by 9 to find $x = 69/9$ , which, when reduced by dividing the numerator and denominator by 3, gives us $x=23/3$

7 0

3 years ago

What is 45.67 in expanded form? 40+5+0.6+0.07 or 40+0.5+0.06+0.007 or 40+5+0.6+0.007 or 4+5+0.06+0.007?

polet [3.4K]

It's right .
40+5+0.6+0.07

8 0

3 years ago

Mary borrowed $6000 from a bank for 3 years and was charged simple interest. The total interest that she paid on the loan was $7

daser333 [38]

4.17

Step by step : I don’t know if it’s right but I did $6000 x 3 cause he did it for 3 year and then it came up to $18,000 then I did what is the percentage of 750$ in $18,000 and got 4.17

3 0

3 years ago

1. What is the extraneous solution of √x−3 + x = 9?

Sunny_sXe [5.5K]

Answer:

1. x = 12

2. 3∛4 feet.

Step-by-step explanation:

1. We are given the equation of x as $\sqrt{x - 3} + x = 9$ and we have to find the extraneous solution of the equation.

Now, $\sqrt{x - 3} + x = 9$ ............. (1)

⇒ $\sqrt{x - 3} = 9 - x$

Squaring both sides we get,

⇒ x - 3 = 81 - 18x + x²

⇒ x² - 19x + 84 = 0

⇒ x² - 12x - 7x + 84 = 0

⇒ (x - 12)(x - 7) = 0

⇒ x = 12 or 7.

Now, putting x = 12 in the equation (1) we get,

$\sqrt{12 - 3} + 12 \neq 9$

Again, putting x = 7 in the equation (1) we get,

$\sqrt{7 - 3} + 7 = 9$

Therefore, x = 12 is an extraneous solution of this equation. (Answer)

2. The volume of a cube with side lengths a ft. is given to be 108 ft³.

So, a³ = 108

⇒ a = 3∛4 feet.

Therefore, the length of the sides of the cube are each 3∛4 feet. (Answer)

3 0

3 years ago

A man steps out of a plane at a height of 4,000m above the ground falls 2,000m very quickly and then opens his parachute and slo

Mumz [18]

Answer:

Step-by-step explanation:

A man steps out of a plane at 4,000m of height above the ground.The point at which he jumps out of the plane would make a good reference point. However, if his acceleration is going to change as a result of him opening his parachute 2000m above the ground, a good reference point would be there. Keep in mind though, that his velocity at that instant would need to be known for it to be useful- otherwise the airplane reference point would be just as good with appropriate modeling....

7 0

3 years ago