1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
guajiro [1.7K]
3 years ago
11

A farmer needs to mix 12 ounces of fertilizer for every 10 pounds of soil. How many pounds of fertilizer will the farmer need to

make a mix that contains 120 pounds of soil?
Mathematics
1 answer:
9966 [12]3 years ago
5 0
The answer is 9 
     12 ounces x --------------- = ---------------- 10 pounds of soil 120 pounds of soil Set the equation up as a proportion and solve for x: 10x = 1440 ---- ----- 10 10 x = 144 ounces The question asks for the answer in pounds, and 16 ounces = 1 pound. 144/16 = 9
You might be interested in
Graphing polynomial functions?
Leni [432]

NOTES:

Degree: the largest exponent in the polynomial

End Behavior:

  • Coefficient is POSITIVE, then right side goes to POSITIVE infinity
  • Coefficient is NEGATIVE, then right side goes to NEGATIVE infinity
  • Degree is EVEN, then left side is SAME direction as right side
  • Degree is ODD, then left side is OPPOSITE direction as right side

Multiplicity (M): the exponent of the zero. <em>e.g. (x - 3)²  has a multiplicity of 2</em>

Relative max/min: the y-value of the vertices.  

  1. Find the axis of symmetry <em>(the midpoint of two neighboring zeros)</em>
  2. Plug the x-value from 1 (above) into the given equation to find the y-value. <em>(which is the max/min)</em>
  3. Repeat 1 and 2 (above) for each pair of neighboring zeros.

Rate of Change: slope between the two given points.

********************************************************************************************

1. f(x) = (x-1)²(x + 6)

a) Degree = 3

b) end behavior:

  • Coefficient is positive so right side goes to positive infinity
  • Degree is odd so left side goes to negative infinity

c) (x - 1)²(x + 6) = 0

   x - 1 = 0                     x + 6 = 0

       x = 1 (M=2)                   x = -6 (M=1)

d) The midpoint between 1 and -6 is -3.5, so axis of symmetry is at x = -3.5

y = (-3.5 - 1)²(-3.5 + 6)

  =  (-4.5)²(2.5)

  = 50.625

50.625 is the relative max

e) see attachment #1

f) The interval at which the graph increases is: (-∞, -3.5)U(1, ∞)

g) The interval at which the graph decreases is: (-3.5, 1)

h) f(-1) = (-1 - 1)²(-1 + 6)

          = (-2)²(5)

          = 20

    f(0) = (0 - 1)²(0 + 6)

          = (-1)²(6)

          = 6

Find the slope between (-1, 20) and (0, 6)

m = \frac{20-6}{-1-0}

   = \frac{14}{-1}

   = -14

********************************************************************************************

2.    y = x³+3x²-10x

         = x(x² + 3x - 10)      

         = x(x + 5)(x - 2)

a) Degree = 3

b) end behavior:

   Coefficient is positive so right side goes to positive infinity

   Degree is odd so left side goes to negative infinity

c) x(x + 5)(x - 2) = 0

   x = 0                     x + 5 = 0                     x - 2 = 0

   x = 0 (M=1)                   x = -5 (M=1)                x = 2 (M=1)

d) The midpoint between -5 and 0 is -2.5, so axis of symmetry is at x = -2.5

y = -2.5(-2.5 + 5)(-2.5 - 2)

  =  -2.5(2.5)(-4.5)

  = 28.125

28.125 is the relative max

The midpoint between 0 and 2 is 1, so axis of symmetry is at x = 1

y = 1(1 + 5)(1 - 2)

  =  1(6)(-1)

  = -6

-6 is the relative min

e) see attachment #2

f) The interval at which the graph increases is: (-∞, -2.5)U(1, ∞)

g) The interval at which the graph decreases is: (-2.5, 1)

h) f(-1) = -1(-1 + 5)(-1 - 2)

********************************************************************************************

3. y = -x(x + 2)(x - 7)(x - 3)

a) Degree = 4

b) end behavior:

   Coefficient is negative so right side goes to negative infinity

   Degree is even so left side goes to negative infinity

c)  -x(x + 2)(x - 7)(x - 3) = 0

  -x = 0                     x + 2 = 0                     x - 7 = 0             x - 3 = 0

   x = 0 (M=1)                 x = -2 (M=1)                x = 7 (M=1)          x = 3 (M=1)

d) The midpoint between -2 and 0 is -1, so axis of symmetry is at x = -1

y = -(-1)(-1 + 2)(-1 - 7)(-1 - 3)

  =  1(1)(-8)(-4)

  = 32

32 is a relative max

The midpoint between 0 and 3 is 1.5, so axis of symmetry is at x = 1.5

y = -(1.5)(1.5 + 2)(1.5 - 7)(1.5 - 3)

  =  -1.5(3.5)(-5.5)(-1.5)

  = -43.3125

-43.3125 is the relative min

The midpoint between 3 and 7 is 5, so axis of symmetry is at x = 5

y = -(5)(5 + 2)(5 - 7)(5 - 3)

  =  -5(7)(-2)(2)

  = 140

140 is the relative max

e) see attachment #3

f) The interval at which the graph increases is: (-∞, -1)U(1.5, 5)

g) The interval at which the graph decreases is: (-1, 1.5)U(5, ∞)

h) f(-1) = -(-1)(-1 + 2)(-1 - 7)(-1 - 3)

          = 1(1)(-8)(-4)

          = 32

    f(0) = -(0)(0 + 2)(0 - 7)(0 - 3)

          = 0

Find the slope between (-1, 32) and (0, 0)

m = \frac{32-0}{-1-0}

   = \frac{32}{-1}

   = -32



5 0
3 years ago
What is the focus of the parabola?<br><br> y=−14x2−2x−2
nataly862011 [7]
First, we need to transform the equation into its standard form (x - h)²=4p(y - k).
Using completing the square method:

y = -14x² - 2x - 2
y = -14(x² + 2x/14) - 2
y = -14(x² + 2x/14 + (2/28)²) -2 + (2/28)²
y = -14(x + 1/14)² - 391/196
-1/14(y + 391/196) = (x + 1/14)²

This is a vertical parabola and its focus <span>(h, k + p) is (-1/14, -391/196 + 1/56) = (-1/14, -775/392).

Or (-0.071,-1.977).</span>
3 0
3 years ago
What is the area of a rectangle with length 36 cm and width 4 cm?
natita [175]

Answer:

A=144cm²

Length: 36cm

Width: 4cm

Step-by-step explanation:

36 x 4 = 144 cm

3 0
3 years ago
Read 2 more answers
What is the slope of –3x + 5y = 10? A. m = B. m = 5 C. m = – D. m = –3
nika2105 [10]

Answer:

The slope is 3/5

Step-by-step explanation:

–3x + 5y = 10

Rewrite the equation in slope intercept form  y = mx+b where m is the slope and b is the y intercept

Add 3x to each side

5y = 3x+10

Divide by 5

y = 3/5 x + 10/2

The slope is 3/5

7 0
3 years ago
A bag contains 12 red marbles, 10 green marbles, 2 yellow marbles, 19 blue marbles, and 9 purple marbles. What is the probabilit
zheka24 [161]
10/52 or when reduced, is 5 over 26 (5/26) and if they want it as a percent, its 19% (.19)
7 0
3 years ago
Other questions:
  • Sumeet uses 0.4 gallon of gasoline each hour mowing lawns. How much gas does he use in 4.2 hours?
    8·1 answer
  • Use the graph of y=e^x to evaluate e^1.6 to the nearest tenth. A. 4.3. B. 5.0. C. 0.2. D. 2.7
    8·2 answers
  • The Mulraneys hired a contractor to build an addition to their home. The Contractor proposed a rectangular room with an area of
    8·2 answers
  • One acre is equivalent to 43,560 square feet. If an acre is also equivalent 1o 4,840 square yards, how many square yards, how ma
    11·1 answer
  • Need help figuring out this answer
    13·1 answer
  • Can someone answer this
    9·1 answer
  • The Jackson family borrowed $240,000 to purchase a house and, over thirty years they had to repay 250% of what they borrowed. Wh
    13·1 answer
  • Find the area of circle x that has a radius XY¯¯¯¯¯¯¯¯ at coordinates X=(0,3) Y=(-3,-1). Use 3.14 for pi, and round your answer
    13·1 answer
  • A circle with radius r is inscribed inside a square with a side length s. Use 3.14 for TT. Round answers to the nearest hundredt
    7·1 answer
  • Would the sum of two positive integers be positive or negative?
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!