Algebra 1 Semester Exam

The slope-intercept form of a line is given by y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is -2 and the y-intercept is 3. Therefore, the equation of the line in slope-intercept form is y = -2x + 3.

To solve the equation 2(5x) = 2x + 3x + 40, we can simplify the left side by distributing the 2 to the terms inside the parentheses. This gives us 10x = 2x + 3x + 40. Combining like terms on the right side, we get 10x = 5x + 40. Next, we can subtract 5x from both sides to isolate the x term. This gives us 5x = 40. Finally, dividing both sides by 5, we find that x = 8, which is the solution to the equation.

The given expression is 3x + 6(2 + x). Distributing the 6 into the parentheses, we get 3x + 12 + 6x. Combining like terms, we have 9x + 12. Therefore, the expression that is equivalent to 3x + 6(2 + x) is 9x + 12.

The equation given represents the population of the town as a function of the number of years. To find the number of years it will take for the population to reach 15,500, we can set the equation equal to 15,500 and solve for y. By substituting 15,500 for p in the equation, we get 15,500 = 13,000 + 250y. Solving this equation for y, we find that y = 10. Therefore, it will take 10 years for the population of the town to reach 15,500.

In the given expression, x = y (y3), the value of y is given as 2. Therefore, substituting y = 2 into the expression, we get x = 2(23) = 2(8) = 16. Hence, the value of x is 16.

To find the solution to the equation 6x + 2 = 2(2x + 2), we can start by simplifying the equation. Distributing 2 to 2x + 2 gives us 6x + 2 = 4x + 4. Next, we can subtract 4x from both sides to isolate the x term, resulting in 2x + 2 = 4. Subtracting 2 from both sides gives us 2x = 2. Finally, dividing both sides by 2 gives us x = 1. Therefore, the correct answer is x = 1.

George's shadow is 12 feet long and he is 5 feet tall. If we set up a proportion using the lengths of the shadows, we can find the height of the tree. The proportion would be: George's height / George's shadow length = Tree's height / Tree's shadow length. Plugging in the values, we get: 5 / 12 = Tree's height / 60. Solving for the tree's height, we find that it is 25 feet tall.

The given expression is equivalent to 2x + 3c + 2(3c + 3x) = 2x + 3c + 6c + 6x = 8x + 9c.

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To find the number of pairs of earrings the artist must sell to earn a profit of $580, we can set up the equation P = 8n - 140, where P is the profit and n is the number of pairs of earrings sold. We want to find the value of n when P = 580.
So, we can substitute P = 580 into the equation and solve for n:
580 = 8n - 140
Add 140 to both sides:
720 = 8n
Divide both sides by 8:
90 = n
Therefore, the artist must sell 90 pairs of earrings to earn a profit of $580.

Tom can create 9 rolls of sushi every 40 minutes. To find out how many rolls he can make in six hours, we need to convert six hours into minutes. There are 60 minutes in an hour, so six hours is equal to 6 x 60 = 360 minutes. Now we can calculate the number of rolls by dividing the total minutes (360) by the time taken to make each roll (40). 360 divided by 40 equals 9. Therefore, Tom can make 9 rolls every 40 minutes, and in six hours, he can make 9 x 9 = 81 rolls.

The correct way to express the atomic weight of an atom equaling .00000362 in scientific notation is 3.62 x 10^-6. In scientific notation, the number is written in the form of a decimal number between 1 and 10 multiplied by a power of 10. In this case, the decimal number is 3.62 and it is multiplied by 10 raised to the power of -6, which indicates that the decimal point is moved 6 places to the left.

The expression 2(4x - 4) simplifies to 8x - 8, and the expression 4(2x - 2) simplifies to 8x - 8. Therefore, when we add these two simplified expressions together, we get (8x - 8) + (8x - 8) which simplifies to 16x - 16.

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To find f(4) - f(2), we first need to find the values of f(4) and f(2).
Substituting x = 4 into the equation f(x) = x^2 - 2x + 2, we get f(4) = 4^2 - 2(4) + 2 = 16 - 8 + 2 = 10.
Substituting x = 2 into the equation, we get f(2) = 2^2 - 2(2) + 2 = 4 - 4 + 2 = 2.
Therefore, f(4) - f(2) = 10 - 2 = 8.

The equation y = -3x+2 best represents the set of data because it is the only equation that produces the correct values of y for each given value of x. When x is -2, y is 8. When x is -1, y is 5. When x is 1, y is -1. When x is 3, y is -7. When x is 4, y is -10. Therefore, y = -3x+2 is the correct equation for this set of data.

The correct answer is 3.1 x 10^7. This is the answer in scientific notation because it represents the number 31,000,000 as a coefficient (3.1) multiplied by 10 raised to the power of 7. Scientific notation is commonly used to express very large or very small numbers in a more compact and convenient form.

Since the two rectangles are similar, their corresponding sides are proportional. The ratio of the length of rectangle A to the length of rectangle B is 15:60, which simplifies to 1:4. Therefore, the width of rectangle B can be found by multiplying the width of rectangle A (12 feet) by the same ratio. 12 feet multiplied by 1 is 12 feet, and 12 feet multiplied by 4 is 48 feet. Hence, the width of rectangle B is 48 feet.

Brian saves money by subtracting his daily expenses (x) from his daily earnings (y). To find out how much he will save in 10 days, we multiply the difference between his earnings and expenses (y - x) by the number of days (10). Therefore, the correct answer is 10(y - x).

The equation c = 6p best describes the relationship between the number of customers who bought Slurpees and the number of boxes of syrup for those Slurpees. This is because for every box of syrup used, there are 6 customers who bought Slurpees. Therefore, the number of customers, c, is equal to 6 times the number of boxes of syrup, p.

The given answer is correct because the problem states that there were 2 fewer boys than twice the number of girls. This can be represented by the equation b = 2g - 2, where b represents the number of boys and g represents the number of girls. Additionally, the problem states that a total of 28 students were present, which can be represented by the equation g + b = 28. Therefore, the correct system of equations to find g and b is g + b = 28 and b = 2g - 2.

The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. To find the slope, we use the formula (y2 - y1) / (x2 - x1) with the given points (4,4) and (2,-1). The slope is (4 - (-1)) / (4 - 2) = 5/2. The y-intercept can be found by substituting one of the points into the equation and solving for b. Using the point (4,4), we have 4 = (5/2)(4) + b, which simplifies to b = -6. Therefore, the equation of the line is y = 5/2x - 6.

The given equation is used to calculate the number of seconds it takes for a chemical reaction to complete based on the temperature in degrees Celsius. Sinbad's reaction took 375 seconds, so we need to find a temperature that satisfies the equation t = 575 - 10C - C^2. By substituting t = 375 into the equation, we can solve for C. The only temperature that satisfies the equation is C = 10. Therefore, 10 is one of the possible temperatures in degrees Celsius at the start of the chemical reaction.

The given equation 4x + 3y = 12 can be rearranged to solve for y in terms of x, which is the slope-intercept form. By isolating the term with y, we get 3y = -4x + 12. Dividing both sides by 3, we have y = -4/3x + 4. Therefore, the correct answer is y = -4/3x + 4.

The equation of a line can be determined using the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. In this case, the line passes through the point (3, 0) and the y-axis at (0, -2). To find the slope, we can use the formula (y2 - y1) / (x2 - x1), which gives us (0 - (-2)) / (3 - 0) = 2/3. Therefore, the slope of the line is 2/3. The y-intercept is given as -2. Plugging these values into the slope-intercept form, we get y = 2/3x - 2.

The distance from where Henry is to Gainesville is 240 miles. On his map, ½ of an inch equals 20 miles. Therefore, we can set up a proportion to find the length in inches. If 20 miles is equal to ½ inch, then 240 miles is equal to x inches. Cross-multiplying, we get 20 * x = 240 * ½. Simplifying, we get 20x = 120. Dividing both sides by 20, we find that x = 6. Therefore, the distance from where Henry is to Gainesville is 6 inches on the map.

The equation that could be used to find the number of seconds it will take Lt. Johnson to reach her cruising altitude of 20,000 feet above sea level is t = (20000 - 90) / 65. This equation subtracts the initial altitude of 90 feet from the target altitude of 20,000 feet and then divides it by the rate of increase in altitude, which is 65 feet per second. This will give the time, in seconds, it will take for Lt. Johnson to reach her cruising altitude.

The equation 3n + (3n +2) + (3n + 4) = 33 would be used to find the three integers if their sum is 33. In this equation, 3n represents the lesser of the three consecutive odd integers. By adding the next two odd integers (3n + 2) and (3n + 4) to the initial integer, we can find the sum of the three integers, which should be equal to 33.

To find f(4) - f(2), we substitute the values of x into the given function.
f(4) = (4^2) + 4(4) + 12 = 16 + 16 + 12 = 44
f(2) = (2^2) + 4(2) + 12 = 4 + 8 + 12 = 24
Therefore, f(4) - f(2) = 44 - 24 = 20.

The slope of a line can be found using the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line. In this case, the coordinates are (2,5) and (-4,-3). Plugging these values into the formula gives (5 - (-3)) / (2 - (-4)), which simplifies to 8 / 6, or 4 / 3. Therefore, the slope of the line is 4/3.

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^ indicates an exponent ie. 3^2 is three squared or three to the second power.

The given equation is in the form of y = mx + b, where m is the slope and b is the y-intercept. By rearranging the equation, we can see that the coefficient of x is the slope and the constant term is the y-intercept. In this case, the coefficient of x is -2/3, so the slope is -2/3. The constant term is 2, so the y-intercept is 2. Therefore, the correct answer is m = -2/3 ; b = 2.

Kevin has a total of 250 marbles, some of which are red and the rest are blue. The question states that he has 24 more blue marbles than red marbles. To find the number of blue marbles, we can set up an equation. Let's assume the number of red marbles is "x". Since Kevin has 24 more blue marbles than red marbles, the number of blue marbles would be "x + 24". The total number of marbles is given as 250, so we can write the equation as "x + (x + 24) = 250". By solving this equation, we find that x = 113, which means Kevin has 113 red marbles. Therefore, the number of blue marbles would be 113 + 24 = 137.

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The equation y = -2/3x + 1 describes the data in the table. This can be determined by observing the pattern in the values of x and y. As x increases by 3, y decreases by 2. This relationship is consistent throughout the table, indicating a linear relationship between x and y. The equation y = -2/3x + 1 represents a line with a slope of -2/3 and a y-intercept of 1, which aligns with the data in the table.

The ship location at noon would be in Quadrant 1 because the ship is at the middle of the segment connecting the lighthouse (located in Quadrant 1) and the buoy (located in Quadrant 3). Since the ship is closer to the lighthouse, it would be in the same quadrant as the lighthouse, which is Quadrant 1.

The equation 12 = (r + c)4.5 can be used to represent the information because it states that the distance traveled, which is 12 miles, is equal to the rate of the boat in still water plus the current's average speed, multiplied by the time it took to travel, which is 4.5 hours.

The correct equation to calculate the length and width of Kat's floor is w(w + 6) = 362. This equation represents the area of the rectangular floor, where w represents the width and (w + 6) represents the length. By multiplying the width and the length, we get the area of the floor, which is equal to 362 square meters.

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The equation 22 = x - 221 could be used to find the total price of the iPhone. This equation represents the tax (22) subtracted from the retail price (x) resulting in the total price of the iPhone.