Since 42 is the greatest number that is a factor of all three numbers given, it is the right response. By writing out the prime factorization of all three integers and then raising each of the shared prime factors to the lowest power that results for that factor, you may get the greatest common factor: 42 = 2 × 3 × 7; 126 = 2 × 32 × 7; and 210 = 2 × 3 × 5 × 7. The largest common factor is therefore 2 3 7 = 42.
The right response is 14, so. When you use the given formulas with x = 3 and y = 5, 3x2 - 2y = 3(3)2 - 2(5) = 27 - 10 = 17 and 2x2 - 3y = 2 result (3) 2 – 3(5) = 18 – 15 = 3. After that, take 3 away from 17 to get 14.
A high school student typically eats 67.5 pounds of sugar annually. Each track team member intends to reduce their sugar intake by at least 20% over the course of the upcoming year as part of a new nutrition strategy. What is the maximum amount of sugar that each member of the track team may take in the upcoming year, assuming that they will follow this plan and consume sugar at the same rate as the average high school student?
The right response is A. You may set up the equation 2x + 3x + 5x = 42 if you use 3x as the quantity of secret ingredient A. because A = 3x = 12.6 and 10x = 42, x = 4.2.
The correct response is 54. To consume 20% less sugar than the average high school student, each member of the track team must consume 100% minus 20%, or 80%, less sugar. 80% of 67.5 = 0.80(67.5) = 54.
The right response is D. The median must be the middle number because there will be an odd number of terms. Put the original set of numbers in alphabetical order. You can see that the median will always be 14, regardless of where you place the fifth word. According to Ms. Hernandez, the median is equal to the mean, so the mean will likewise be 14. The mean is 14 if x is the fifth number, which is 14+8+16+14+x/5. Consequently, 14(5) = 52 + x, or x = 18.
The right response is this. 2,727 miles will equal 101 gallons if you split them by the mileage per gallon, which is 27. The number of gallons is then multiplied by the price per gallon, yielding 101 (4.04), or 488.04. The price of gas for this car to travel 2,727 typical miles is given by this.
The right response is this. Sales for the second year are equal to x + 3 if x is the first year's sales. Sales for the third year equal 2(x + 3) since they were twice as high as those for the second year. 38 were the sales for the third year, so 2(x + 3) = 38. You may start by dividing each side of this equation by 2, which would give you x + 3 = 19. x = 16 is then obtained by deducting 3 from both sides.
The appropriate reaction is this. If you selected this response, you are aware that 1 and 6 are real numbers and that any two real numbers can be separated by an unlimited amount of irrational numbers.
C is the appropriate response. Since b > a, changing the relationship between b and a by deducting n from each side will result in b - n > a - n.
The right response is C. The length of the leg opposite the acute angle in a right triangle divided by the length of the hypotenuse is the sine of that angle.
The right answer is C: 100(0.70) = 70 is the amount that would be paid if the DVD was marked down 30%; however, there is a second discount of 20%, so the price will only be 80% of the marked-down price. The cost will be 56 ($70(0.80)).
You were right when you estimated there were 122 11-year-olds. You can solve the system 11e + 12t = 3,238 by setting e = number of 11-year-olds and t = number of 12-year-olds. You might solve the system using a variety of techniques, including substitution, elimination, and matrices. Just keep in mind that you want to find e's value at the end.
A is the appropriate response. To solve this issue, first obtain 3 = x - 4 by deducting 2x from each side of the equation. So that x Equals 7, add 4 to each side.
You're right. There are 12 hourly markers on a clock, and the clock hand rotates 360 degrees in one full rotation. The degree measure of the angle created by the clock hands at precisely one o'clock is one-twelfth of a full rotation, or 1/2 (360°) = thirty degrees.
(2,2) is the right response. Take the average of each of the coordinates, (-3+7/2, 0+4/2) = to determine the midway (2,2).
