Answer:
C. Student 3
E. Student 5
Step-by-step explanation:
we know that
The formula to calculate the midpoint between two points is equal to
<u><em>Verify the midpoint of each student</em></u>
student 1
we have the endpoints
(-9,0) and (11,-8)
substitute in the formula
so
The midpoint is not (-1,4)
student 2
we have the endpoints
(-6,-1) and (4,-7)
substitute in the formula
so
The midpoint is not (-1,4)
student 3
we have the endpoints
(-5,2) and (3,6)
substitute in the formula
so
<u>The midpoint is equal to (-1,4)</u>
student 4
we have the endpoints
(-3,10) and (5,-2)
substitute in the formula
so
The midpoint is not (-1,4)
student 5
we have the endpoints
(0,-3) and (-2,11)
substitute in the formula
so
<u>The midpoint is equal to (-1,4)</u>
therefore
Student 3 and student 5
Answer:
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
−9b2−18b=0
Step 2: Factor left side of equation.
(−9b)(b+2)=0
Step 3: Set factors equal to 0.
−9b=0 or b+2=0
b=0 or b=−2
If Ms. Callahan has 24 feet of fencing, and she is building a pen, the PERIMETER of the pen must be 24 feet. The perimeter is basically the distance around a figure. The perimeter of a rectangle is equal to length plus width plus length plus width, AKA l+w+l+w, or P=2l+2w. In a rectangle, two pairs of sides are of equal length--so the two lengths and the two widths must be equal.
So, the formula is P=2l+2w. P, the perimeter, is 24, so 24=2l+2w. Let's try some values for l and see what we get for w. If the length is 1, l=1. 24=(2*1)+2w. 24=2+2w. 22=2w. w=11. So if length is 1 foot, width is 11 feet.
What if l=2? 24=(2*2)+2w. 24=4+2w. 2w=20. w=10. If l=2, w=10. And l=3? 24=(2*3)+2w. 24=6+2w. 18=2w. w=9. If l=3, w=9. Do you see a pattern? Every time we add 1 to l, we subtract 1 from w. So if l=4, w=8. If l=5, w=7. If l=6, w=6. Here, we start getting similar answers: if l=7, w=5. If l=8, w=4. Since we already know these values work, it doesn't matter whether we call it length or width. So, our answers are below.
Answer: Ms Callahan can make a pen with a length of 1 foot and a width of 11 feet, a length of 2 feet and a width of 10 feet, a length of 3 feet and a width of 9 feet, a length of 4 feet and a width of 8 feet, a length of 5 feet and a width of 7 feet, or a length of 6 feet and a width of 6 feet.
Answer: In the exact order up to down: 80, 74, 110, 96, 80
Step-by-step explanation:
Do the equation
360=(x-6)+(x+30)+1.2x+x
we can simplify by doing
360=(x-6)+(x+30)+2.2x
=360=x-6+x+30+2.2x
=360=4.2x+24
=336=4.2x
=80=x
x=80
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Answer:
3x+75=180
3x=180-75
3x=105
x=105/3
x=35
