This equation is also equal to 3/4x - 2/3 + 5/6 + 2x since subtracting a negative is the same as adding a positive in the long run. First, simplify the variables to get 2 3/4x - 2/3 + 5/6. -2/3 is also equal to -4/6, so -4/6 + 5/6 is 1/6. The simplified version of this expression is 2 3/4x + 1/6. Hope this helps!
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Answer:
A
Step-by-step explanation:
AA similarity means 2 angles must be similar.
Angle 1: Angle E is the same for both triangles
Angle 2: Angle F and angle G are congruent because they both have right angle markings so they are both 90 degrees.
Answer:
See below.
Step-by-step explanation:
a.
The first figure has 1 square. The second figure has a column of 2 squares added to the left. The third figure has a column of 3 squares added to the left. Each new figure has a column of squares added to the left containing the same number of squares as the number of the figure.
b.
Figure 10 has 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55 squares.
c.
The formula for adding n positive integers starting at 1 is:
1 + 2 + 3 + ... + n = n(n + 1)/2
For figure 55, n = 55.
n(n + 1)/2 = 55(56)/2 = 1540
d.
Let's use the formula set equal to 190 and solve for n. If n is an integer, then we can.
n(n + 1)/2 = 190
n(n + 1) = 380
We know that 380 = 19 * 20, so n = 19.
Answer: yes
e.
Use the formula above,
S = n(n + 1)/2, where S is the sum.
f.
n(n + 1) = 1478
38 * 39 = 1482
37 * 38 = 1406
The total of all the purchases is $73.94. The remaining balance on the card is $26.06. Hope this helps!
