In Problems 9–24, find a general linear equation (Ax + By + C = 0) of the straight line that has the indicated properties, and sketch each line. %3D 9. Passes through (-1,7) and has slope -5
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- In Problems 7 & 8, Find an equation in point-slope form, y-y1=m(x-x1), of the line through the given points. 7. (2,7) and (4, -5) 8. (3, 20) and (-5,4) Can Explain to me Step by StepSuppose that the market research found the following relationships for Apple's iPhone 14 in 2022 Supply equation: 2q-1/4p=100, where q (supply in millions) is the number of iPhone 14s that apple would produce if they could sell them for $p each demand equation: 15q+p=4200, where q (demand in millions) is the number of iPhone 14s consumers would buy if they were sold for $p each Find the equhibrium price p and supply demand using gauss-Jordan elimination4. Suppose for a company manufacturing flash drives, the cost and revenue equations are given by C= 6,000 + 3x and R = 20x − 0.002x , where the production output in 1 week is x flash drives. a. Find the profit function. b. Find the marginal profit function c. If production is increasing at a rate of 500 flash drives per week when production is 2,000 flash drives, find the rate of increase in profit .
- A value of r close to _______ suggests at most a weak linear relationship between the variables.As a result of urbanization, the temperatures in Paris have increased. In 1891 the average daily minimum and maximum temperatures were 5.8°C and 15.1°C, respectively. Between 1891 and 1968, these average temperatures rose 0.019°C/yr and 0.011°C/yr, respectively. Assuming the increases were linear, find the year when the difference between the minimum and maximum temperatures was 9C, and determine the corresponding average maximum temperature.A value of r close to −1 suggests a strong _______ linear relationship between the variables.
- If the equation of the regression line for hours xx spent cycling in the summer and hours yy spent working in the summer is ˆy=−0.7x+42y^=-0.7x+42 , then as the number of cycling hours increases, the number of work hours tends to decrease. false trueIf the slope of the regression line is calculated to be 3.33 and the y' intercept is 13.25 then the approximated value of y when x is 6 is __________. Only the final answer should be rounded-off to TWO decimal places.The properties in Problem 83 provide us with another way to write the equation of a line parallel or perpendicular to a given line that contains a given point not on the line. For example, suppose that we want the equation of the line perpendicular to 3x + 4y = 6 that contains the point (1, 2). The form 4x - 3y = k, where k is a constant, represents a family of lines perpendicular to 3x + 4y = 6 because we have satisfied the condition AA' = -BB'. Therefore, to find what specific line of the family contains (1, 2), we substitute 1 for x and 2 for y to determine k.4x - 3y = k4(1) - 3(2) = k-2 = k Thus the equation of the desired line is 4x - 3y = -2. Use the properties from Problem 83 to help write the equation of each of the following lines.(a) Contains (1, 8) and is parallel to 2x + 3y = 6(b) Contains (-1, 4) and is parallel to x - 2y = 4(c) Contains (2, -7) and is perpendicular to 3x - 5y = 10(d) Contains (-1, -4) and is perpendicular to 2x + 5y = 12
- Your customer states that when the price of your product is $103.6 a unit, they will purchase 150 units. If you firm charged $70.4 a unit, however, your customer says that they would purchase 153 units. Recalling that price is on the y-axis of the demand curve and quantity demanded is on the x-axis of the demand curve and assuming that your customer's demand is a linear function over this range, what is the slope of your customer's demand curve?Since the founding of the Equal EmploymentOpportunity Commission and the passage ofequal-pay laws, the gulf between men’s andwomen’s earning has continued to closegradually. At the beginning of 1990 (t = 0),women’s wages were 68% of men’s wages,and then by beginning of 2000 (t = 10),women’s wages were 80% of men’s wages. Ifthis gap between women’s and men’s wagescontinued to narrow linearly, then women’swages were what percentage of men’s wagesat the beginning of 2004?So the solution to this problem was supposed to be -3: "Since the slope of the line is 4, we know that the rise over run is 4/1. Therefore, for every increase of 1 in x, there is an increase of 4 in y. Starting from (-3, 5), we can move 2 units to the left and 8 units down to get to the x-axis. Therefore, the y-coordinate of the point where the line intersects the x-axis is 5 – 8 = -3." I don't see how they got -3 and not 0...what am I not understanding? p.s. this is a "hard" GRE quantitative reasoning ques