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9.4 Deriving and Using Formulae

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  • use the formula v= u + at to work out the value of v when u=7, a=10, t=8
    v=87
  • Hiếu Minh already has 18 plants in her backyard, and she can also grow 7 plants with every seed packet she uses. How many seed packets does Hiếu Minh need to have a total of 53 plants in her backyard?
    5
  • Aldi buys and sells paintings. he uses the formula shown to work out the percentage profit he makes. work out Aldi 's percentage profit if the cost price is $250 and the selling price is $300
    16,67%
  • Make x the subject of this formula; 49x = 7y + 1
    x = 7y +1 /49
  • Rearrange the formula to make the variable inside the bracket as subject
    (a - 3) / 7
  • Rearrange the formula to make the variable inside the bracket as subject
    (y - c) / x
  • Make x the subject of this formula; x - y = 6
    x = 6 + y
  • A hot-air balloon is at a height of 2,250 feet. It begins to descend at a rate of 150 feet per minute. Write an expression to model its height after m minutes. Then evaluate the expression for 2, 4, 6, 8, and 10 minutes.
    1950, 1650, 1350, 1050, 750
  • A hiking club charges an initial fee of $60 and then $12 for each hiker. Write an expression to model the total cost and then evaluate the expression for 1 to 6 hikers.
    72, 84, 96, 108, 120, 132
  • Make y the subject of this formula; x =18y − 6
    y = x + 6 /18
  • Here is the price list of some stationery in a stationery store. (The price is only for one item) Pencil (P) = $2 Ruler (R) = $3 Pencil Case (C) = $6. If Trúc gives this note to the cashier: 3R + 2C,    what is the total price she
    $21
  • Phương Anh already knew 16 appetizer recipes before starting culinary school, and she will learn 3 new appetizer recipes each week of school. After how many weeks of culinary school will Phương Anh know a total of 37 recipes?
    7
  • use the formula v= u + at to work out the value of u when v=75, a=4, t=12
    u=27
  • Rearrange the formula to make the variable inside the bracket as subject
    (y - c) / x
  • Rearrange the formula BMI=m/h^2 to make "m" the subject.
    m = BMI × h^2
  • Rearrange the formula to make the variable inside the bracket as subject
    (a - 3) / 7
  • Autumn buys an item which normally sells for a certain price, x. Today the item is selling for 25% off the regular price. A sale tax of 6% is added to the equation to find the final price, f.
    0.06 (x * 0.25) = f
  • Make y the subject of this formula; ; x=4y−3
    y = 3 + x /4
  • Joe thinks of a number, n, triples it, and subtracts 3. The result is 42. Write this as an equation in terms of n, and solve the equation.
    see the picture
  • Đăng scores 21 points per coin. In all, how many coins does Đăng have to collect to score 42 points?
    2
  • Hùng's graduation picnic costs $9 for every attendee. At most, how many attendees can there be if Hùng budgets a total of $36 for his graduation picnic?
    $4
  • A person can pay $12.64 for a membership to the science museum and then go the museum for $1.07 per visit. What is the maximum number of visits a member of the science museum can make for a total cost of $14.78?
    2
  • Make x the subject of this formula; x - 10y = −7
    x = 10y - 7
  • Make y the subject of this formula; 6x =18y − 6
    y = x + 1 / 3
  • Jennie thinks of a number, p, double it, and add with 5. The result is 27. Write this as an equation in terms of p, and solve the equation.
    see the picture
  • Given v = u + at, make "t" the subject of the formula.
    t=(v-u)/a
  • make t the subject of the formula: k= t/5-m
    t= (k+m) x 5
  • Nguyên's office recycled 63 kg of paper this year before starting the new recycling plan; the new plan will have the office recycling 5 kg of paper/week. How many weeks will it take Nguyên's office to recycle a total of 83 kg of paper?
    4
  • Make y the subject of this formula; x = 2y+5
    y = x - 5 / 2
  • make t the subject of the formula: m=7t+9
    t=(m-9)/7
  • Using the formula F = ma to work out the value of m when F = 34 and a = 2.5
    13.6
  • When ringing up a customer, a cashier needs 11 seconds to process payment as well as 4 seconds to to scan each item being purchased. If it takes 43 seconds to ring up a customer, how many items are being purchased?
    8
  • Old Navy advertises a 40% off graphic tees for babies. What would the sale price (p) be on a $2530 purchase?
    $2,530 * 0.40 = p
  • Make x the subject of this formula; 2x + 4y = 12
    x = 6 - 2y
  • Make y the subject if this formula; 3x - y = 6
    y = 6 - 3x
  • Khôi learns two new appetizer recipes during each week of culinary school. After how many weeks of culinary school will Khôi know a total of 18 recipes?
    9
  • The charity gala costs a flat fee of $11.89, plus an additional $5.72 per attendee. How many attendees can there be, at most, if the budget for the gala is $91.97?
    14
  • Given v = u + at, make "u" the subject of the formula.
    u = v - at
  • Make x the subject of this formula; 8x -13y = 4
    x = 13y + 4 / 8
  • Dung's birthday party costs $1 plus an additional $8 for every guest she invites. How many guests can there be, at most, if Dung can afford to spend $41 on her birthday party?
    5
  • Make y the subject of this formula; 7x =14y − 5
    y = 7x + 5 /14
  • Rearrange the formula d/s=C to make "s" the subject.
    s = d/C
  • Make y the subject if this formula; x = 3y -1
    y = x +1 / 3
  • Here is the price list of some stationery in a stationery store. (The price is only for one item);    Pencil (P) = $2;  Ruler (R) = $3 Pencil Case (C) = $6. If Khánh buys 3 pencils and 3 rulers, what is the total price she has to pay?
    $15
  • Minh Anh had already read 1 book before joining a book club, and she plans to read 7 books per month now that she has joined. If Minh Anh has read 50 books so far, how many months has she been with her book club?
    7
  • Trân buys x shares of stock in a company at $34.50 per share. She later sells the shares at $40.50 per share. Write an equation to show how much money, m, Trân has made.
    m= x($40.50 - $34.50)
  • Make x the subject of this formula; x + 16y = −11
    x = -16y - 11
  • Rearrange the formula " 12v/11H=5u " to make "v" the subject.
    v = (55Hu)/12
  • Rearrange the formula " -9t^2+12y=11H^2 " to make "y" the subject.
    y = (11H^2+9t^2)/12
  • Yuan sets his watch 20 seconds behind, and it falls behind by another 4 seconds each day. How many days has it been since Yuan last set his watch if the watch is 40 seconds behind?
    5
  • A plumber charges $21.02 to visit a client's home, plus an additional $23.84 per hour. What is the duration, in hours, of a plumber's visit that costs $68.70?
    2
  • Rearrange the formula " 9y-10s=9C+7W " to make "y" the subject.
    y = (9C+7W+10s)/9
  • The formula used in science is: V = I. R where V is the voltage, I is the current, and R is the resistance. Work out the value of V when I = 3 and R = 8
    24
  • The formula used in science is: V = I. R where V is the voltage, I is the current, and R is the resistance. Work out the value of V when I = 5 and R = 12
    60
  • Danh has already baked 2 pies, and he can bake 3 pies with each additional cup of sugar he buys. How many extra cups of sugar does Danh need to bake a total of 38 pies?
    12
  • Make x the subject of this formula; x - 18y = 6
    x = 18y + 6
  • A photographer charges $16.90 to travel to a client's location, plus $25.25 per hour for his services. What is the duration, in hours, of a photography session that costs $92.65?
    3
  • Make x the subject of this formula; x- 6y = −4
    x = 6y - 4
  • use the formula F=ma to work out the value of F when m=12 and a= 5
    F= 60
  • Make x the subject of this formula; y =5x+2
    x = y -2 / 5