Answer:
129/200
Step-by-step explanation:
To solve the equation using complete square method we proceed:
z^2-19z=66
but
c=(-b/2a)^2
c=(-19/2)^2
c=361/4
thus:
z^2-19z+361/4=66+361/4
factoring the LHS we get:
1/4(2z-19)^2=625/4
(2z-19)^2=625
getting the square root of both sides we get:
2z-19=+/-25
2z=+/-25+19
2z=44 or -6
z=22 or -3
Answer: z=22 or z=-3
Avg. speed Joanna runs: 7.5km/h
how much she runs everyday: 15km
15km/7.5= 2 hours of running time everyday
She leaves at 8:30, comes back at ?
8:30+ 2:00= 10:30
Joanna arrives back at 10:30a.m.
Sum of three numbers is 33 and sum of their cubes is 5049 then three numbers are 7,11,15 or 15,11,7.
As given,
Let a-d, a, a +d be three numbers
Sum =33
⇒a-d + a +a +d =33
⇒ a =11
Sum of cubes= 5049
⇒ (a-d)³ + a +(a +d)³ =5049
⇒ a³ -d³ -3a²d +3ad² + a³ +a³ +d³ +3a²d +3ad² =5049
⇒3a³ + 6ad² = 5049
⇒ d=± 4
Therefore, sum of three numbers is 33 and sum of their cubes is 5049 then three numbers are 7,11,15 or 15,11,7.
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Answer:
The slope of the line given by the linear equation is -2
The slope of the line shown in the graph is -1
Step-by-step explanation:
The form of the linear equation is y = m x + b, where
The rule of the slope of a line is m =
, where
- (x1, y1) and (x2, y2) are two points lie on the line
Let us use these rules to answer the question
∵ The linear equation is y = -2x + 7
→ By comparing it with the form of the linear equation above
∴ m = -2
∵ m is the slope of the line represented by the given equation
∴ The slope of the line given by the linear equation is -2
From the given figure
∵ The line passes through points (6, 0) and (0, 6)
∴ x1 = 6 and y1 = 0
∴ x2 = 0 and y2 = 6
→ Substitute them in the rule of the slope above to find it
∵ m = 
∴ m = -1
∵ m is the slope of the line shown in the graph
∴ The slope of the line shown in the graph is -1