Answer:
x = -5
Step-by-step explanation:
Since these two triangles are similar, the ratio between the corresponding lengths of each triangle will be the same.
This means the ratio between one side of each triangle (e.g. AD and DC) will be the same as the ratio between a different side of each triangle (e.g. BE and BC).
So, to create an equation for the sides which contain the unknown 'x', we must first find the ratio between the two sides by using a different set of sides.
On the right side we are given 9 for AD, and 18 for DC.
9/18 = 0.5
This means that the extra length of the larger triangle from the smaller one (AD) is half the length of the smaller triangle (DC). We can use this to make an equation for x:
If AD/DC = 0.5, then BE/EC will also = 0.5
BE = x+23
EC = x+41
Therefore:
Now we can solve by multiplying both sides by x+41 to eliminate the fraction:
Now we multiply out the brackets and move the terms to different sides:
And if we substitute the -5 into the equations:
-5+23 = 18
-5 + 41 = 36
We will see that -5 does indeed give us the same ratio between the lengths:
18/36 = 0.5
Hope this helped!
Answer:
C)
The rate of change/slope is constant, when you calculate it for this problem, it doesn't change for any amount of marbles listed in the table
1.8- 3.7x = 4.2x + 0.3
Move 4.2x to the other side
Sign changes from +4.2x to -4.2x
1.8-3.7x-4.2x= 4.2x-4.2x+0.3
1.8-3.7x-4.2x= 0.3
1.8-7.9x= 0.3
Move 1.8 to the other side
Sign changes from +1.8 to -1.8
1.8-1.8-7.9x= 0.3-1.8
-7.9x= 0.3-1.8
-7.9x= -1.5
divide both sides by -7.9
-7.9/-7.9x= -1.5/-7.9
x= 0.18987341
Answer: x= 0.18987341
Answer:
C. one solution
Step-by-step explanation:
The number of solutions can be found from the number of intersection points.
There are 2 lines, a parabola (curve) and a horizontal line that is parallel to the x axis.
We see that there is 1 point of intersection between the 2 lines, at (2,1)-right 2 and up 1. Therefore, this non linear system has 1 solution.
C. one solution is the correct answer.
So, first off it would help if you could define the terms irrational number and integer. Well, an irrational number is basically any real number that can't be expressed as a ratio of integers. They also cannot be represented by terminating or continuing decimals. And an integer is pretty much any number that cannot be written as a fraction or decimal, such as -2, 13, 257. It is not 2 and 1/2, or 4.75. Those would not be integers. Do you think you can figure out the difference?
