Given inequality is ![4x-8y\le9](https://tex.z-dn.net/?f=4x-8y%5Cle9)
Now we need to find the graph of
.
Which can be done into two parts:
First graph the line
then shade the graph for inequality sign ![\le](https://tex.z-dn.net/?f=%5Cle)
Graph the line ![4x-8y=9](https://tex.z-dn.net/?f=4x-8y%3D9)
we can plug any number for x say x=0 to find the y-value
4x-8y=9
4*0-8y=9
0-8y=9
-8y=9
![y=\frac{9}{-8}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B9%7D%7B-8%7D)
y=-1.125
Hence first point is (0,-1.125)
Similarly we can plug y=0 then solve for x
4x-8y=9
4x-8*0=9
4x-0=9
4x=9
![x=\frac{9}{4}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B9%7D%7B4%7D)
x=2.25
hence 2nd point is at (2.25,0)
Now graph both points and join them by a straight line.
Since used inequality is
so we use solid line not the dotted line.
Shading the graph:
we can pick any test point which is not on the line 4x-8y=9 say (0,0) then plug into original problem to see if that point satisfies the original problem or not.
![4x-8y\le9](https://tex.z-dn.net/?f=4x-8y%5Cle9)
![4*0-8*0\le9](https://tex.z-dn.net/?f=4%2A0-8%2A0%5Cle9)
![0-0\le9](https://tex.z-dn.net/?f=0-0%5Cle9)
![0\le9](https://tex.z-dn.net/?f=0%5Cle9)
Which is TRUE.
TRUE means shade in direction of test point otherwise we graph in opposite direction of test point.
Now final graph will look like the graph attached below:
Answer:
<h2>BD = DC</h2>
Step-by-step explanation:
A perpendicular bisector is a line segment that goes form a vertex to its opposite side. The important characteristic is that a perpendicular bisector intersects the opposide at the mid point and with a right angle, that's why is called perpendicular and bisector.
So, Andrew can conclude that side BC is divide equally, that is, BD = DC.
Therefore, the right answer is the second choice.
Answer:
= 4
Step-by-step explanation:
There ar
<h2>
Answer:</h2>
<u>x= 7</u>.
<h2>
Step-by-step explanation:</h2>
<h3>1. Write the expression.</h3>
![\sqrt{4x-3}=5](https://tex.z-dn.net/?f=%5Csqrt%7B4x-3%7D%3D5)
<h3>2. Take the square root of both sides of the equation.</h3>
![(\sqrt{4x-3})^{2} =5^{2} \\ \\4x-3=25](https://tex.z-dn.net/?f=%28%5Csqrt%7B4x-3%7D%29%5E%7B2%7D%20%3D5%5E%7B2%7D%20%5C%5C%20%5C%5C4x-3%3D25)
<h3>3. Sum 3 to both sides of the equation.</h3>
![4x-3+3=25+3\\ \\4x=28](https://tex.z-dn.net/?f=4x-3%2B3%3D25%2B3%5C%5C%20%5C%5C4x%3D28)
<h3>4. Divide by 4 on both sides of the equation.</h3>
![\frac{4x}{4} =\frac{28}{4} \\ \\x=7](https://tex.z-dn.net/?f=%5Cfrac%7B4x%7D%7B4%7D%20%3D%5Cfrac%7B28%7D%7B4%7D%20%5C%5C%20%5C%5Cx%3D7)
<h3>5. Express your result.</h3>
<u>x= 7</u>.
Answer:
Step-by-step explanation:
Let your number be X. To increase X by 40% we can multiply it by 1.4, let's call this new number Y.
So Y = X * 1.4
Now to decrease Y by 40% we can multiply it by 1 - .4 = .6. Lets call this new number C.
So C = Y *.6 = (X * 1.4) * .6 = X * (1.4 * .6) = X * .84.
Therefore, C = .84 * X.
So we can see C is 84% of X, or 16% less than X.
Thus, if you increase a number by 40% then decrease it by 40%, the net percentage is -16% .