Answer:
37 is prime number
Step-by-step explanation:
To prove whether a number is a prime number, first try dividing it by 2, and see if you get a whole number. If you do, it can't be a prime number. If you don't get a whole number, next try dividing it by prime numbers: 3, 5, 7, 11 (9 is divisible by 3) and so on, always dividing by a prime number
Answer:
k=24
Step-by-step explanation:
The tangent of the function f at x=a, can be found by differentiating f w.r.t. x and then replacing x with a.
f=-x^2+8x+20
Differentiating both sides:
f'=(-x^2+8x+20)'
By sum rule:
f'=(-x^2)'+(8x)'+(20)'
By constant multiple rule:
f'=-(x^2)'+8(x)'+(20)'
By constant rule:
f'=-(x^2)+8(x)'+0
By power rule:
f'=-2x+8
f' at x=a is -2a+8
This is the slope of any tangent line to the curve f.
The slope of g is 4 if you compare it to slope intercept form y=mx+b.
So we gave -2a+8=4.
Subtracr 8 on both sides: -2a=-4
Divide both sides by -2: a=2
The tangent line to the curve at x=2 is y=4x+k.
To tind y we must first know the y-coordinate of the point of tangency.
If x=2, then
f(2)=-(2)^2+8(2)+20=-4+16+20=12+20=32
So the point is (2,32).
g(x)=4x+k and we know g(2)=32.
This gives us:
32=4(2)+k
32=8+k
k=32-8
k=24
Answer: Option 3
Step-by-step explanation: Option (3) is correct.The surface area of a rectangular prism of given dimension is 170 square inches.Step-by-step explanation:Given : a rectangular prism whose base is 5 inches by 6 inches and whose height is 5 inches.We have to find the surface area of a rectangular prism of given dimension.Since a rectangular prism whose base is 5 inches by 6 inchesThat is length (l)= 5 inches Width (w) = 6 inches and height (h) = 5 inches.Also . Substitute, we have,simplify , we have,surface area of a rectangular prism = 170 inches²Thus, the surface area of a rectangular prism of given dimension is 170 square inches
$29 dollars is the overall change in his account. The reason that this is correct is because if you make a number line -4 is exactly 29 units away from 25.
M=-7/18 check photo for answer and work
