Answer:
-58, -57, -56
Step-by-step explanation:
if the first integer is x,
the second integer must be x + 1 (because it's consecutive)
and the third must be x + 2
Therefore:
3 times the sum of the first and third integers is -342:
3 * (x + (x+2) ) = -342
Combine like terms in parentheses
3 * (2x + 2) = -342
Distribute the 3 to the 2x and the 2:
6x + 6 = -342
Subtract 6 on both sides
6x = -348
Divide by 6 on both sides
x = -58
x + 1 = -57
x + 2 = -56
-58, -57, -56
Check:
3 * (-58 + -56) = 3 * -114 = -342
806 - 44 = 762.
762 divided by 2 = 381.
381 + 44 = 425. Hope it helps! :)
Answer:
If you use 3.14 as an approximation for PI, the answer will be A) 179 sq. feet.
Step-by-step explanation:
The process to determine the area of the sidewalk is computed by figuring the area of the outer circle (Diameter = 16' + 3' + 3') and subtracting the area of the fountain (Diameter = 16') from that.
Area of Circle = PI times Radius squared
Outer circle radius = (22 ft /2) = 11 ft
Area of outer circle (includes fountain area too) = 3.14 x 11 x 11 = 379.94 ~ 380
Inner circle radius = (16 ft / 2) = 8 ft
Area of Fountain = 3.14 x 8 x 8 = 200.96 ~ 201
Area of sidewalk = 380 - 201 = 179
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Answer:
6) y = x^(5/3)
7) B
8) C
10) A
Step-by-step explanation:
6) The fifth root is the same as raising to the 1/5 power, so we can write this in exponent form as:
f(x) = (x^(1/5))³
f(x) = x^(3/5)
To find the inverse, switch x and y and solve for y.
x = y^(3/5)
y = x^(5/3)
7) f(x) = 2√(x − 4) + 8
Switch the x and y and solve for y:
x = 2√(y − 4) + 8
x − 8 = 2√(y − 4)
(x − 8) / 2 = √(y − 4)
(x − 8)² / 4 = y − 4
(x² − 16x + 64) / 4 = y − 4
¼x² − 4x + 16 = y − 4
y = ¼x² − 4x + 20
8) Find the inverse:
x = 5√(y + 3) − 2
x + 2 = 5√(y + 3)
(x + 2) / 5 = √(y + 3)
(x + 2)² / 25 = y + 3
y = -3 + (x + 2)² / 25
The inverse function is an upwards parabola with a vertex at (-2, -3). The best fit is C.
desmos.com/calculator/fbabg5wc8b
10) √(4x − 31) = x − 7
Square both sides:
4x − 31 = (x − 7)²
4x − 31 = x² − 14x + 49
Combine like terms:
0 = x² − 18x + 80
Factor:
0 = (x − 8) (x − 10)
x = 8 or 10
Check for extraneous solutions.
√(4×8 − 31) = 8 − 7
1 = 1
√(4×10 − 31) = 10 − 7
3 = 3
x = 8 and x = 10 are both solutions.
The answer to this problem is B
