Answer:
100
Step-by-step explanation:
because 100 divided by 5 is 20
Answer:
(x + 3)²
Step-by-step explanation:
Given
x² + 6x + 9
This is a perfect square of the form
(x + a)² = x² + 2ax + a²
Compare like terms
a² = 9 ⇒ a = 3 and 2a = 2 × 3 = 6, thus
x² + 6x + 9 = (x + 3)² → D
Answer:
$67.41
Step-by-step explanation:
We want to find out how much 30% off of $96.30 is. To do that, we need to first multiply $96.30 to find out how much 30% would be. Don't forget to change 30% into its decimal form (30% - > .3).
96.30 x .3 = 28.89
This means that Steve got $28.89 dollars removed from his final bill. To find the actual final bill, subtract 28.89 from 96.30.
96.30 - 28.89 = $67.41
Answer:
![y = -\frac{1}{2}x + 4](https://tex.z-dn.net/?f=%20y%20%3D%20-%5Cfrac%7B1%7D%7B2%7Dx%20%2B%204%20)
Step-by-step explanation:
The equation of the line can be written in slope-intercept form, as y = mx + b.
We need to find the slope (m) and the y-intercept (b) of the line, then plug their values into the slope-intercept equation, to find the equation of the line shown.
y-intercept (b) = the point where the line intercepts the y-axis = 4
Using two points on the line, say, (0, 4) and (2, 3):
![slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 4}{2 - 0} = \frac{-1}{2} = -\frac{1}{2}](https://tex.z-dn.net/?f=%20slope%20%28m%29%20%3D%20%5Cfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D%20%3D%20%5Cfrac%7B3%20-%204%7D%7B2%20-%200%7D%20%3D%20%5Cfrac%7B-1%7D%7B2%7D%20%3D%20-%5Cfrac%7B1%7D%7B2%7D%20)
m = -½.
Substitute m = -½, and b = 4 into y = mx + b.
The equation of the line would be:
![y = -\frac{1}{2}x + 4](https://tex.z-dn.net/?f=%20y%20%3D%20-%5Cfrac%7B1%7D%7B2%7Dx%20%2B%204%20)
Step-by-step explanation:
Let's finish strong! Maybe we'll have some time for some fun activities!
Let's start with angle B.
Remember that the internal angle of a triangle will always equal 180.
We have a rignt angle (90), a known angle (54), and unknown B.
We can establish a simple equation to solve for B. ![B = 180 - 90 - 54](https://tex.z-dn.net/?f=B%20%3D%20180%20-%2090%20-%2054)
33% done!
To solve for the other sides of the triangle, we'll need to use our trig functions! Boo! I know, but they are super handy! Let's see them in action.
Remember that ol' saying - some old hippy caught another hippy tripping on acid. SOH, CAH, TOA.
sin = opposite over hypotenuse, cos = adjacent over hypotenuse, tan = opposite over adjacent. ![tan(54) = a/23](https://tex.z-dn.net/?f=tan%2854%29%20%3D%20a%2F23)
A little fancy calculator work and we're 66% done! whew!
If we know a and the third side as being 23, we can just use the Pythagorean theorem
![c^2 = a^2 + b^2](https://tex.z-dn.net/?f=c%5E2%20%3D%20a%5E2%20%2B%20b%5E2)
Done! Wow! That's feels good. Great job!