Hey there!
2(x - 3) / y = 5
2(x - 3) / 5 = 5
2(x) + 2(-3) / 5 = 5
(2x - 6) 5 = 5
MULTPLY 5 to BOTH SIDES
(2x - 6)/5 * 5 = 5 * 5
SIMPLIFY IT!
2x - 6 = 5 * 5
2x - 6 = 25
ADD 6 to BOTH SIDES
2x - 6 + 6 = 25 + 6
SIMPLIFY IT!
2x = 25 + 6
2x = 31
DIVIDE 2 to BOTH SIDES
2x/2 = 31/2
SIMPLIFY IT!
x = 31/2
x = 15 1/2
Therefore, the answer should be:
x = 15 1/2
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Remember that the vertex form of a parabola or quadratic equation is:
y=a(x-h)^2+k, where (h,k) is the "vertex" which is the maximum or minimum point of the parabola (and a is half the acceleration of the of the function, but that is maybe too much :P)
In this case we are given that the vertex is (1,1) so we have:
y=a(x-1)^2+1, and then we are told that there is a point (0,-3) so we can say:
-3=a(0-1)^2+1
-3=a+1
-4=a so our complete equation in vertex form is:
y=-4(x-1)^2+1
Now you wish to know where the x-intercepts are. x-intercepts are when the graph touches the x-axis, ie, when y=0 so
0=-4(x-1)^2+1 add 4(x-1)^2 to both sides
4(x-1)^2=1 divide both sides by 4
(x-1)^2=1/4 take the square root of both sides
x-1=±√(1/4) which is equal to
x-1=±1/2 add 1 to both sides
x=1±1/2
So x=0.5 and 1.5, thus the x-intercept points are:
(0.5, 0) and (1.5, 0) or if you like fractions:
(1/2, 0) and (3/2, 0) :P
Answer: x = 2
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Explanation:
Refer to the diagram below.
I've added points D,E,F,G. This helps with labeling the segments and angles, and identifying the proper triangles (to see which are congruent pairs).
Triangle GEA is congruent to triangle GFA. We can prove this using the AAS congruence theorem. We have AG = AG as the pair of congruent sides, and the congruent pairs of angles are marked in the diagram (specifically the blue pairs of angles and the gray right angle markers)
Since triangle GEA is congruent to triangle GFA, this means the corresponding pieces segment GF and GE are the same length.
The diagram shows GF = 3x-4, so this means GE = 3x-4 as well.
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Through similar steps, we can show that triangle GEC is congruent to triangle GDC. We also use AAS here as well.
The congruent triangles lead to GD = GE. So GD = 3x-4. The diagram shows that GD = 6x-10
Since GD is equal to both 3x-4 and 6x-10, this must mean the two expressions are equal.
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Now let's solve for x
6x-10 = 3x-4
6x-3x = -4+10
3x = 6
x = 6/3
x = 2
Answer:
46.56 pounds
Step-by-step explanation:
Given data
4.3 pounds
2 pounds
3.8 pounds, and
5.9 pounds
Let us find the total weight of all the items
=4.3+2+3.8+5.9
=16 pounds
We are told that he is charged $2.91 per pound for shipping
Hence the cost of shipping 16 pounds is
=2.91*16
=46.56 pounds
