Answers:
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Explanation:
Part (a)
Lines LN and PN have the point N in common. This is the intersection point.
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Part (b)
To name a plane, pick any three non-collinear points that are inside it. We cannot pick points H, J, K together because infinitely many planes pass through it. Imagine the piece of flat paper able to rotate around this axis (like a propeller). Having the points not all on the same line guarantees we form exactly one unique plane.
I'll pick the non-collinear points P, H and J to get the name Plane PHJ. Other answers are possible.
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Part (c)
Points H, J and K are collinear as they are on the same line. Pick either H or K to fill out the answer box. I'll go with point K
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Part (d)
Point P and line HK are coplanar. They exist in the same flat plane, or on the same sheet of flat paper together.
We can think of that flat plane as the ground level while something like point N is underground somewhere. So point N and anything on that ground plane wouldn't be coplanar.
Note: there are other possible names for line HK such as line JH or line JK. The order doesn't matter when it comes to naming lines.
Any number above 1 gets greater, below 1 smaller (when above 0), while 1 itself remains the same. Negative numbers are more unpredictable.
Answer:
<em>y = - x - 10 </em>
Step-by-step explanation:
y - (- 3) = - (x + 7)
<em>y = - x - 10</em>
Answer: You need a grade of 78 on the final exam to earn a final grade average of at least 87 in each grading system.
Step-by-step explanation:
(85 + 90 + 95 + x)÷ 4 =87
Simplify:
(270 + x) ÷ 4 = 87
Rearrange:
(x + 270) ÷ 4 = 87
Multiply terms to Reduce:
4((x + 270) ÷ 4) = 4 * 87
Cancel Multiplied terms in Denominator:
x + 270 = 4 * 87
Multiply:
x + 270 = 348
Subtract 270 on both sides of the equation:
x + 270 - 270 = 348 - 270
Simplify:
x = 78
Answer:
50 cents
Step-by-step explanation:
Let's set up a system of equations. Let x be a cookie and y be a brownie then...
x+2y=2x+y
x+y=1
We can solve this using substitution
x=1-y
1-y+2y=2(1-y)+y
1+y=2-2y+y
1+y=2-y
-1=-2y
y=1/2
One brownie costs 50 cents and one cookie costs...
x+1/2=1
x=1/2
One cookie costs 50 cents
