Answer:
k = - 9
Step-by-step explanation:
h(x) = x² + 3
g(x) = x² - 6
g(x) = h(x) + k
x² - 6 = x² + 3 + k
-6 - 3 = k
k = - 9
The value of y will be 18 or 144.
Given information:
The given expression is ![\sqrt[3]{\frac{144}{y} }](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B%5Cfrac%7B144%7D%7By%7D%20%7D)
.
It is required to find the values of y which are whole numbers.
Now, factorize 144 as,
So, for the value of given expression to be a whole number, the value of y should be,
or 144.
For the above values of y, the given expression will be,
![\sqrt[3]{\frac{144}{y} }=\sqrt[3]{\frac{144}{18} }\\=\sqrt[3]{8} =2\\\sqrt[3]{\frac{144}{y} }=\sqrt[3]{\frac{144}{144} }\\=\sqrt[3]{1} \\=1](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B%5Cfrac%7B144%7D%7By%7D%20%7D%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B144%7D%7B18%7D%20%7D%5C%5C%3D%5Csqrt%5B3%5D%7B8%7D%20%3D2%5C%5C%5Csqrt%5B3%5D%7B%5Cfrac%7B144%7D%7By%7D%20%7D%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B144%7D%7B144%7D%20%7D%5C%5C%3D%5Csqrt%5B3%5D%7B1%7D%20%5C%5C%3D1)
Therefore, the value of y will be 18 or 144.
For more details, refer to the link:
brainly.com/question/17429689
Answer:
x = -1
y = -2
Step-by-step explanation:
To get y by itself:
3x - y = -1
-y = -1 - 3x
y = 1 + 3x
Solve for x with substitution:
2x = 4(1 + 3x) + 6
2x = 4 + 12x + 6
2x = 10 + 12x
-10x = 10
x = -1
Plug the x value into 3x - y = -1
3(-1) - y = -1
-3 - y = -1
-y = 2
y = -2
Answer: P(x > - 0.23) = 0.41
Step-by-step explanation:
Since we are assuming that the readings at freezing on a batch of thermometers are normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = the readings at freezing on a batch of thermometers.
µ = mean temperature reading
σ = standard deviation
From the information given,
µ = 0°C
σ = 1.00°C
the probability of obtaining a reading less than -0.23°C is expressed as
P(x > - 0.23)
For x = - 0.23
z = (- 0.23 - 0)/1 = - 0.23
Looking at the normal distribution table, the probability corresponding to the z score is 0.41
