The first equation, y = 144 over x, must be solved for y. Then, in the second equation, change 144 over x for y: x + 144 over x = 30. Each side is multiplied by x, so x2 + 144 = 30x. 30x from either side is subtracted, giving x2 - 30x + 144 = 0. By factoring (x - 24)(x - 6) = 0, and then assigning each factor to either zero, x = 24 or x = 6, you could find the solution to this equation. As the issue states that x > y, x = 6 will not be valid. If x = 6, then y = 24. So, x= 24. Reintroducing this x value into either of the initial equations results in y = 6. As a result, x - y = 24 - 6 = 18.
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 answer is 7. 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.
It turns out that the likelihood that the number can be divided by either 2 or 3—but not both—is 7/8.
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 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 right answer is 92 + 122 equals c2 according to the Pythagorean theorem. So c =√9²+12² =√81+144 =√225 = 15.
In the formula, replacing D with 150 results in (1502/25) + 4(150) - 250 =(22500/25) + 600 - 250 = 1,250.
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.
This is the appropriate answer. If you selected this response, you are aware that any two real numbers can be separated by an unlimited amount of irrational integers. For example, 1 and 6 are real numbers.
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)).
The right response is 20, so. 1/8 inch of the screw enters the wood with each full spin. One inch of the screw would thus be in the wood after 8 full revolutions. So, x(⅛) = 2½ . By adding 8, x becomes 8(212) + 8(5/2) = 20.
The right response is this. 2w = length if w = width. With w equal to 5, the perimeter is 2(w + 2w) = 30. The breadth is 5, hence the length is 2(5), which equals 10. The area is then 5(10) = 50.
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.
You may set up the equation 2x + 3x + 5x = 42 if you use 3x as the quantity of secret ingredient B. because B = 3x = 12.6 and 10x = 42, x = 4.2.
The right response is 14, so. When you use the given formulas with x = 3 and y = 5, you get 3x2 - 2y = 3(3)2 - 2(5) = 27 - 10 = 17 and 2x2 - 3y = 2. (3) ² – 3(5) = 18 – 15 = 3. After that, take 3 away from 17 to get 14.
The right answer is 8, thus. A circle with radius r has a circumference calculated as 2r. Therefore, r = 8 or 2r=16.
The distance between (0,0) and (3,4), or (, is the radius of the circle (3–0) ² (4–0) (4–0) ² = 5. (x - h)2+ (y - k)2= r2 is the equation for a circle with (h,k) as the center and r as the radius. Thus, x2 + y2 = 25 or (x - 0)2 + (y - 0)2 = 52.
A number is multiplied by two when written as twice, and a number is deducted by three when written as three less than. When you combine them, you get l = 2w – 3.
(2,2) is the right response. Take the average of each coordinate, ((-3+7/2), (0+4/2)) = to determine the midway (2,2).
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 1/12(360°) = 30°.
