Answer: x = 6
(WORK SHOWN BELOW)
(WORK SHOWN BELOW)
Solve the inequality. Graph the solution on a number line. 7 ≥ t/-2
1 answer:
The graph is shown in the figure attached.
Step-by-step explanation:
We need to solve the inequality and graph the solution.
Solving the inequality:
Switch sides and reverse the inequality:
Multiplying both sides by -2 and reverse the inequality
The graph is shown in the figure attached.
Keywords: Graph the inequality
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Answer:
a)
y = 0.3035 + 0.0082x
b)
0.6315 mm
c)
x = 23.9634 °C
Step-by-step explanation:
a. Compute the least-squares line for predicting warping from temperature. Round the answers to four decimal places.
We need to find an equation of the form
y = b + mx
where m is the slope and b the Y-intercept.
The slope m can be computed with the formula
Replacing the values in our formula (we will round at the end of the calculations)
the Y-intercept b is computed with the formula
therefore we have
and the least-squares line rounded to 4 decimals would be
y = 0.3035 + 0.0082x
b. Predict the warping at a temperature of 40°C. Round the answer to three decimal places.
We simply replace x with 40 to get
y = 0.3035 + 0.0082*40 = 0.6315 mm
c. At what temperature will we predict the warping to be 0.5 mm? Round the answer to two decimal places
Here, we replace y with 0.5 and solve for x
0.5 = 0.3035 + 0.0082x ===> x = (0.5-0.3035)/0.0082 ===>
x = 23.9634 °C
Given:
The vertex of a quadratic function is (4,-7).
To find:
The equation of the quadratic function.
Solution:
The vertex form of a quadratic function is:
...(i)
Where a is a constant and (h,k) is vertex.
The vertex is at point (4,-7).
Putting h=4 and k=-7 in (i), we get
The required equation of the quadratic function is where, a is a constant.
Putting a=1, we get
Therefore, the required quadratic function is .