9.
By the Segment Addition Postulate, SAP, we have
XY + YZ = XZ
so
YZ = XZ - XY = 5 cm - 2 cm = 3 cm
10.
M is the midpoint of XZ=5 cm so
XM = 5 cm / 2 = 2.5 cm
11.
XY + YM = XM
YM = XM - XY = 2.5 cm - 2 cm = 0.5 cm
12.
The midpoint is just the average of the coordinate A(-3,2), B(5,-4)
Answer: M is (1,-1)
You'll have to plot it yourself.
13.
For distances we calculate hypotenuses of a right triangle using the distnace formula or the Pythagorean Theorem.
Answer: AB=10
M is the midpoint of AB so
Answer: AM=MB=5
14.
B is the midpoint of AC. We have A(-3,2), B(5,-4)
B = (A+C)/2
2B = A + C
C = 2B - A
C = ( 2(5) - -3, 2(-4) - 2 ) = (13, -10)
Check the midpoint of AC:
(A+C)/2 = ( (-3 + 13)/2, (2 + -10)/2 ) = (5, -4) = B, good
Answer: C is (13, -10)
Again I'll leave the plotting to you.
Answer:
a) y does NOT vary directly with x
b) y = 2.5x -6.5
Step-by-step explanation:
If variation were direct the ratios of y to x would be constant. They are not:
6/5 ≠ 11/7
y does not vary directly with x.
__
y changes by 5 from 6 to 11 when x changes by 2 from 5 to 7. Then the slope of the linear function rule is (change in y)/(change in x) = 5/2. Using a point-slope form of the equation of a line, we can write the rule as ...
y = m(x -h) +k . . . . . . . . for a line of slope m through point (h, k)
y = (5/2)(x -5) +6
y = 2.5x -6.5 . . . . . simplify
Answer:
$185.17
Step-by-step explanation:
The monthly dollar amounts saved here form a geometric progression, since each new amount is derived by multiplying the previous amount by 1.10. This 1.10 is r, the common ratio. The first term is $24 and there will be 5 more terms (June through December is 6 months).
The general formula for individual terms of a geometric series is A(n) = A(1) + r^(n - 1).
Here, with A(1) = $24 (the first term), r =1.10 and n = 6, we'd get $38.65 (the 6th and last term). Following the same procedure, we'd find that the 6 terms will have the values $24, $26.40, $29.04, $31.94, $35.14. $38.65.
Finally, we add these up. We get the sum $185.17.
Fortunately, there's a formula that makes the calculations go much faster: "sum of a geometric sequence." This formula is:
1 - r ^n
a(1)*--------------
1 - r
Here, a(1) = $24 and r = 1.10, and so the sum of the first 6 terms of this geometric sequence is
1 - 1.10^6
$24*---------------- = $185.17
1 - 1.10
(x+7) (x-7)
Because: the difference of two squares.
Answer:
first option _32\21 is the answer