Step-by-step explanation:
we have a function, when for every valid x value we get exactly one y value (not 2 or more, not 0, but exactly 1).
x×7 = y⁴
7x = y⁴
y = 4th root(7x)
the 4th root is the square root of the square root.
so, we know, only positive x-values are valid.
but, even when restricting it to positive x-values, a square root as a 4th root (any even grade root) has a positive and a negative solution for the same x-value.
e.g.
x = 7³ = 343
7×343 = 2,401
the 4th root(2,401) = +7 and -7, as +7⁴ = 2,401, and -7⁴ = 2,401.
so, we have 2 different y-values assigned to most x-values (only exception is x=0), and this is therefore not a function.
<span>6. What is the range of the function f(x) = 6x + 5 for the domain {–1, 0, 1, 2, 3}
x = -1, y = </span>6(-1) + 5 = -1
x = 0, y = 6(0) + 5 = 5
x = 1, y = 6(1) + 5 = 11
x = 2, y = 6(2) + 5 = 17
x = 3, y = 6(3) + 5 = 23
the domain {–1, 5, 11, 17, 23}
<span>7. Find the slope of the graph of the equation 3x + 15y = 25
15y = -3x + 25
y = -1/5(x) + 5/3
slope = -1/5
</span><span>8. What is the slope of the line that would be perpendicular to the graph of y = 6x – 2
</span>y = 6x – 2 has slope = 6
perpendicular lines, slope is opposite and reciprocal so slope = -1/6
answer
-1/6
<span>9. Verify that (-4, 12) is the solution to the system. Show work to justify your answer
2x + y = 5
2(-4) + 12 = 5
-8 + 12 = 5
4 = 5 this is false because 4 < 5
-5x-2y= -6
</span><span>-5(-4)-2(12)= -6
</span>20 - 24 = -6
-4 = -6 this is false because -4 > -6
answer
<span>(-4, 12) is NOT the solution to the system</span>
Step-by-step explanation:
<u>Substitute the point (-9, 2) into the inequality:</u>
<u>Simplify:</u>
False.
-3 isn't greater than or equal to -2.
(-9, 2) is not a solution of
Answer: SA = 644 cm²
Step-by-step explanation:
<u>STEP ONE: Find the surface area of the smaller rectangle (green)</u>
There are in total 5 sides because one of the sides is not shown on the surface level.
Upper base = 3 × 3 = 9 cm²
4 sides = 3 × 8 × 4 = 96 cm²
Total = 9 + 96 = 105 cm²
<u>STEP TWO: Find the surface area of the larger rectangle (orange)</u>
There are in total 5 whole sides with one side covered by the base of the smaller rectangle (green) which should later be subtracted.
Front and back = 7 × 10 × 2 = 140 cm²
Left and right = 7 × 12 × 2 = 168 cm²
Lower base = 10 × 12 = 120 cm²
Upper base = 10 × 12 - 3 × 3 = 111 cm²
Total = 140 + 168 + 120 + 111 = 539 cm²
<u>STEP THREE: Find the total surface area</u>
SA = Green + Orange = 105 + 539 =<u> 644 cm²</u>
Hope this helps!! :)
Please let me know if you have any questions