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otez555 [7]
3 years ago
9

Point A' is the image of point A when point A is rotated about the origin B. What angle in the counterclockwise direction is

Mathematics
1 answer:
Elza [17]3 years ago
8 0

9514 1404 393

Answer:

  90° CCW

Step-by-step explanation:

The slope of BA is -1/3. The slope of BA' is 3, so the slopes are opposite reciprocals of one another. These segments are perpendicular, meaning the angle between them is 90°.

Point A' has been rotated 90° CCW about point B.

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A dairy company gets milk from two dairies and then blends the milk to get the desired amount of butterfat. Milk from dairy I co
zubka84 [21]

Answer:

a) i The company should buy 40 gallons from dairy I and 60 gallons from dairy

ii) What is the maximum amount of​ butterfat? The total amount of butterfat from Diary I and Diary II = 3.12% + 1.93%

=5.05%

b.The excess capacity of dairy I is 10 ​gallons, and for dairy II it is 30 gallons.

Step-by-step explanation:

a. How much milk from each supplier should the company buy to get at most 100 gallons of milk with the maximum amount of​ butterfat?

From the question, we are told that:

Milk from dairy I costs ​$2.40 per​ gallon, Milk from dairy II costs ​$0.80 per gallon.

Let's represent:

Number of gallons of Milk from dairy I = x

Number of gallons of Milk from dairy II = y

At most ​$144 is available for purchasing milk.

$2.40 × x + $0.80 × y = 144

2.40x + 0.80y = 144........ Equation 1

x + y = 100....... Equation 2

x = 100 - y

2.40(100 - y) + 0.80y = 144

240 - 2.4y + 0.80y = 144

-1.60y = 144 - 240

-1.6y = -96

y = -96/-1.6

y = 60

From Equation 2

x + y = 100....... Equation 2

x + 60 = 100

x = 100 - 60

x = 40

Therefore, since number of gallons of Milk from dairy I = x and number of gallons of Milk from dairy II = y

The company should buy 40 gallons from dairy I and 60 gallons from dairy

II. What is the maximum amount of​ butterfat?

From the question

Dairy I can supply at most 50 gallons averaging 3.9​% ​butterfat,

50 gallons = 3.9% butterfat

40 gallons =

Cross Multiply

= 40 × 3.9/50

= 3.12%

Dairy II can supply at most 90 gallons averaging 2.9​% butterfat.

90 gallons of milk = 2.9% butter fat

60 gallons of milk =

Cross Multiply

= 60 × 2.9%/90

=1.9333333333%

≈ 1.93%

The total amount of butterfat from Diary I and Diary II = 3.12% + 1.93%

=5.05%

b. The solution from part a leaves both dairy I and dairy II with excess capacity. Calculate the amount of additional milk each dairy could produce.

Excess capacity of Diary I =

50 gallons - 40 gallons = 10 gallons

Excess capacity of Diary II =

90 gallons - 60 gallons = 30 gallons

Therefore, the excess capacity of dairy I is 10 ​gallons, and for dairy II it is 30 gallons.

3 0
3 years ago
The pans shown are balanced. Use the SubtractionProperty of Equality to find which shapes are equalto one purple pyramid.
Bad White [126]

According to the Subtraction property of equality, the equality of an expression holds true if the same finite number is subtracted from both sides of the equality,

a=b\Rightarrow a-c=b-c

Now, observe the given figure carefully.

We will use the above-mentioned property to get rid of the common shapes that exist on both sides. Here, the balance represents equality between both sides.

Consider that the pans are initially balanced. And both sides contain a red cube. So we can subtract or eliminate the red cube and the equality will still hold true.

Similarly, we can eliminate the blue sphere.

At this point, we have the purple pyramid and a yellow diamond on the left side, and on the right side, we have 4 pieces of yellow diamond.

Observe that one piece of yellow diamond is common to both sides, so it can also be eliminated from both sides.

After this, the left side will contain only the purple pyramid while the right side contains 3 yellow diamonds. Since we are always using the subtraction property to eliminate the shapes, the balance must be maintained throughout the process.

At last, there must exist a balance between the left side containing the purple pyramid only, and the right side containing 3 yellow diamonds.

Therefore, it can be concluded that one purple pyramid is equal to 3 yellow diamonds.

6 0
1 year ago
Dan invests £6800 into his bank account.
Irina-Kira [14]
£6800 times (1.05)to the power of 6
=£9112.65
6 0
2 years ago
Match each pair of lines to the correct description. Tiles parallel lines and perpendicular lines and neither parallel nor perpe
forsale [732]
From the diagram/figure;
Line EF is perpendicular to both lines AB and CD
Line AB and lines CD are parallel to each other
Line GH is neither parallel nor perpendicular to any line given.
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3 years ago
Help!!!!!!!!!!!!!!!!
Dmitriy789 [7]
The answer is 2/(k+2)

3 0
3 years ago
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