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Katen [24]
3 years ago
11

Consider the addition expression 42 + 2(7) on the number line shown. Explain how you would evaluate the expression on the number

line.
A. Begin at 14 and move seven units to the right six times

B. Begin at 42 and move two units to the left seven times

C. Begin at 42 and move seven units to the right twice

D. Begin at 42 and move seven units to the left twice
Mathematics
1 answer:
ycow [4]3 years ago
3 0

Answer:

  C.  Begin at 42 and move seven units to the right twice

Step-by-step explanation:

Working from left to right, the expression's first term of 42 suggest we want to start at 42 on the number line.

The added term of 2(7) tells us we will be moving <em>farther to the right</em>. The product can be represented by either 2 moves of 7 units each, or 7 moves of 2 units each.

The only description that has the appropriate move in the appropriate direction is that of option C.

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Look at the picture.

The equation:

10x - 15 = 6x + 9       <em>add 15 to both sides</em>

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4x = 24    <em>divide both sides by 4</em>

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4 years ago
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Paul's bathtub is clogged. He has to empty 30 liters of water by hand. Paul has a 3- liter, a 4- liter, and a 5 liter bucket. Of
notka56 [123]
3 and 4 + 3 and 4 + 3 and 4 + 4 and 5 = 30
5 0
3 years ago
Beverly needs to make a container in the shape of a rectangular prism that holds 1000 in3 of liquid. The height of the container
anastassius [24]
Given:
volume = 1,000 in³
height = 10 in

1,000 in³ / 10 in = 100 in² Area.

100 in²

Length     Width        Surface Area of the Rectangular prism
100 in          1 in                       2,220 in²
  50 in          2 in                       1,240 in²
  25 in          4 in                          780 in²
  20 in          5 in                          700 in²
  

Surface area = 2(wl + hl + lw)

The best dimension is 20 inches by 5 inches by 10 inches. It has lesser surface area than other dimensions. Thus, it can save more materials.
7 0
3 years ago
On a citrus farm, the average annual yield of oranges is 124 pounds per tree when the number of trees is 22 per acre. For each a
ELEN [110]

Answer:

Number of orange trees = 3528

Step-by-step explanation:

Given: Average annual orange yield = 124 pounds (lbs) per tree

Number of trees = 22 per acre

Each tree produces 124 pounds, so 22 trees will produce

124*22 = 2728 lbs per acre

For every additional tree over 22, 2 pounds per tree is lost.

So, if you add x trees, you lose 2x pounds.

Thus, we have the function:

f(x) = (124 - 2x)*(22 + x) for the added tree(s)

f(x) = 2728 + 80x - 2x^{2}

For quadratic equations like this, the maximum(or minimum) is obtained by substituting x= -b/2a into the given equation. a and b are obtained from the general form of a quadratic equation:

y =ax^{2} + bx + c

Comparing this with f(x), we have that

a = -2 (coefficient of x2)

b = 80 (coefficient of x)

Using these values in x = -b/2a, we get

x = -\frac{80}{2*(-2)} = 20

So, use x = 20 in the maximum function we got earlier

f(x) = 2728 + 80(20) -2(20^{2}) = 2728 + 1600 - 800\\ \\f(x) = 3528

Therefore, the number of oranges that should be planted in order to maximize the number of pounds of oranges per acre = 3528

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3 years ago
What is the slope of a line perpendicular to the line whose equation is
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