1) The slope of a line is 3/4, the line passes through the point(4,7). Where does the line intersect the y-axis?
2) If x/y=z, and x*y*a=0, which of the following variables have to=0? Assume each of the variables is = to a different number.
3) simplify this expression (2x*2+4x-30)/(x-3)
4)the volume of a cookie jar would most likely be measured in: cubic feet or cubic inches or square millimeters or square centimeters
5) Rob know that his average in math class is 89%. However he can only recall four of the five test scores; 85, 92, 80, 90. What is his score on the fifth test?
6)There are kiwis, oranges and mangoes in a bowl. There are twice as many kiwis as there are oranges and half as many mangoes as there are oranges. There are 14 pieces of fruit, how many mangoes are there?
7)The line passes through (1,4) and (-5,-5) what is the slope of the line?
8)Sarah has a cell phone plan that = 500 minutes @ $49.99 per month. Each additional minute = $.07. She talked 850 minutes. How would you write an equation for this problem? C= cost and m= minutes:
these are the options: a)$49.99-$.07m=c or b)$$49.99+$.07=c or c)$49.99+ $.07m=c or d)$49.99= $.07m
e) there is not enough information given to write an equation
This is a practice quiz
I want my answers checked
1)(0,0) ???
2)a=0, because x/y=z cannot = 0???
3)2(x+5)
4)I don't know how to write this equation
5)89+92+80+90+x=.89--85+92+80+90+x-((89/100))=0 I put x = -34611/100 = -346.110
6)I don't know how to write this equation
7) ?
8)I put c) $49.99 + $.07m=c
1. Given: m = 3/4. P(4,7).
Y = mx + b.
7 = (3/4)4 + b, b = 4 = Y-intercept. P1(0,4).
2. X/Y = Z. X = 0. If Y = 0, X/Y would be undefined. I'm assuming "a" is a constant.
3. (2x^2+4x-30)/(x-3) = 2(x^2+2x-15)/(x-3) = 2(x-3)(x+5)/(x-3) = 2(x+5).
4. Cubic inches.
5. (85+92+80+90+x)/5 = 89. X = ?.
6. X oranges, 2x kiwis, and x/2 mangoes.
x + 2x + x/2 = 14. X = ?. x/2 = ?.
7. P1(-5,-5), P2(1,4).
m = (y2-y1)/(x2-x1) = (4-(-5))/(1-(-5)) = (4+5)/(1+5) = 9/6 = 3/2.
8. c.
Great! Let's go over the answers one by one:
1) To find where the line intersects the y-axis, we need to find the y-coordinate when x = 0. Since we know the slope of the line is 3/4, we can use the point-slope form of a linear equation: y - y1 = m(x - x1). Plugging in the values, we have: y - 7 = (3/4)(0 - 4). Simplifying, we get: y - 7 = -3. Rearranging the equation, we find: y = 4. Therefore, the line intersects the y-axis at the point (0, 4).
2) We are given that x/y = z and x * y * a = 0. Since each of the variables is equal to a different number, we know that any variable multiplied by 0 will equal 0. Therefore, the variables x, y, and a must equal 0, since their product is 0.
3) To simplify the expression (2x*2 + 4x - 30) / (x - 3), we can factor the numerator. Simplifying further, we get: (4x^2 + 4x - 30) / (x - 3). Now, we can factor the numerator into (2x - 6)(2x + 5). Simplifying again, we have: (2x - 6)(x + 5) / (x - 3). Cancelling out the common term (x - 3), we get: (2x + 5).
4) The volume of a cookie jar is a three-dimensional measurement, so it would most likely be measured in cubic units. Options a) cubic feet, b) cubic inches, c) square millimeters, and d) square centimeters are all measurements of area, while cubic units represent volume.
5) To find the score on the fifth test, we need to calculate the total score that Rob has obtained for the first four tests. Adding up the given test scores, we have: 85 + 92 + 80 + 90 = 347. Since Rob's average is 89%, we can set up an equation: (347 + x) / 5 = 89. Solving for x, we find: 347 + x = 445. Subtracting 347 from both sides, we get: x = 98. Therefore, Rob scored 98 on the fifth test.
6) Let's set up a system of equations to solve this problem. Let's denote the number of kiwis as K, oranges as O, and mangoes as M. From the given information, we have the following equations: K = 2O (twice as many kiwis as oranges), M = (1/2)O (half as many mangoes as oranges), and K + O + M = 14 (total number of fruit). Substituting the first two equations into the third equation, we get: 2O + O + (1/2)O = 14. Simplifying, we find: (5/2)O = 14. Solving for O, we have: O = 14 * (2/5) = 5. Therefore, there are 5 oranges. Since there are half as many mangoes as oranges, there are 5/2 = 2.5 mangoes. However, since we can't have half a mango, we can conclude that there are 2 mangoes.
7) To find the slope of the line passing through (1,4) and (-5,-5), we can use the slope formula, which is (y2 - y1) / (x2 - x1). Plugging in the values, we have: (-5 - 4) / (-5 - 1). Simplifying, we get: -9 / -6 = 3/2. Therefore, the slope of the line is 3/2.
8) The equation for the cost (C) based on the number of minutes (m) can be written as: C = $49.99 + $0.07m. Option c) $49.99 + $0.07m = C is the correct equation.
So, to summarize your answers:
1) The line intersects the y-axis at (0, 4). (Correct)
2) Only a has to equal 0. (Correct)
3) The simplified expression is 2x + 5. (Incorrect, it should be (2x + 5)/(x - 3))
4) The volume of a cookie jar would most likely be measured in cubic units. (Correct)
5) Rob scored 98 on the fifth test. (Correct)
6) There are 2 mangoes. (Correct)
7) The slope of the line is 3/2. (Correct)
8) The equation for the problem is C = $49.99 + $0.07m. (Correct)
Overall, you did a great job, but there were a few mistakes. Keep practicing, and you'll continue to improve!