MATHEMATICS COLLEGE

Baby Unicorns have a weekly training schedule, flying for 4 hours per day on some days and 2 hours per day on the other days. They fly a total of 24 hours in a seven-day week. On how many days do they fly for 4 hours?

Answers

Answer 1
Answer:

The Baby unicorns fly 4 hours for 5 days and 2 hours for 2 days.

Let x represent the number of days flown 4 hours and y represent the number of days flown 2 hours

Since they worked a total of 7 days, hence:

x + y = 7     (1)

Also, they flew for 24 hours hence:

4x + 2y = 24   (2)

Solving equations 1 and 2 simultaneously gives:

x = 5, y = 2

Therefore they fly 4 hours for 5 days and 2 hours for 2 days.

Find out more at: brainly.com/question/16763389

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A house and a lot are appraised at 212,400. If the value of the house is five times the value of the lot, how much Is the house worth

Answers

Answer:

$177,000

Step-by-step explanation:

Let x represent value of lot.

We have been given that the value of the house is five times the value of the lot. The value of house would be 5x.

We have been given that a house and a lot are appraised at 212,400. We can represent this information in an equation as:

x+5x=212,400

6x=212,400

(6x)/(6)=(212,400)/(6)

x=35,400

Now, we will substitute x=35,400 in expression 5x.

5x=5(35,400)=177,000

Therefore, the house is worth $177,000.
If the lot is 5 times more than there are 6 amounts that are the same that add up to be 212,400. so 212,400/6 is 35,400. since the house is 5 times more than the lot we take 35,400 and multiply it by 5 which is 177,000 the value of the house. We can check our answer by adding 35,400 to our 177,000 and we get 212400

Area of Composite Figures.

Answers

The area is 21

The area of a triangle is base*hight/2
Take the area of each triangle and divide them. Hope this helped!

Answer:

21

Step-by-step explanation:

Two - way frequency tables

Answers

Answer: Two-way frequency tables are especially important because they are often used to analyze survey results. Two-way frequency tables are also called contingency tables. Two-way frequency tables are a visual representation of the possible relationships between two sets of categorical data.

Step-by-step explanation:

I'LL MARK THE BRAINLIEST
What is the exact circumference of the circle?

Answers

Answer:    c=2πr

Step-by-step explanation:

because im just that guy

Answer:

c=62.8

Step-by-step explanation:

diameter=20

radius=10

c=2πr

c=2×22/7×10

c=62.8

WHAT IS THE SLOPE OF THE LINE6X + 3Y = 18?
Can anyone actually help me work it out please

Answers

Answer:

6x + 3y = 18 \n \n y = - 2x + 6 \n \n x = 3

3y=6x=18 the equation must look like this y=mx+b where m is the slope in this case it is 2 and b is the y-intercept 18 hope it helps

just divide every term by 3 to isolate y

GraceRosalia

Show that W is a subspace of R^3.

Answers

Answer:

Check the two conditions of Subspace.

Step-by-step explanation:

If W is a Subspace of a vector space, V then it should satisft the following conditions.

1) The zero element should be in W.

Zero element can be different for different vector spaces. For examples, zero vector in $ \math{R^2} $ is (0, 0) whereas, zero element in $ \math{R^3} $ is (0, 0 ,0).

2) For any two vectors, $ w_1 $ and $ w_2 $ in W, $ w_1 + w_2 $ should also be in W.

That is, it should be closed under addition.

3) For any vector $ w_1 $ in W and for any scalar, $ k $ in V, $ kw_1 $ should be in W.

That is it should be closed in scalar multiplication.

The conditions are mathematically represented as follows:

1) 0$ \in $ W.

2) If $ w_1 \in W; w_2 \in W $ then $ w_1 + w_2 \in W $.

3) $ \forall k \in V, and \hspace{2mm} \forall w_1 \in W \implies kw_1 \in W

Here V = $ \math{R^3} $ and W = Set of all (x, y, z) such that $ x - 2y + 5z = 0 $

We check for the conditions one by one.

1) The zero vector belongs to the subspace, W. Because (0, 0, 0) satisfies the given equation.

i.e., 0 - 2(0) + 5(0) = 0

2) Let us assume $ w_1 = (x_1, y_1, z_1) $ and $ w_2 = (x_2, y_2, z_2) $ are in W.

That means: $ x_1 - 2y_1 + 5z_1 = 0 $ and

$ x_2 - 2y_2 + 5z_2 = 0 $

We should check if the vectors are closed under addition.

Adding the two vectors we get:

$ w_1 + w_2 = x_1 + x_2 - 2(y_1 + y_2) + 5(z_1 + z_2) $

$ = x_1 + x_2 - 2y_1 - 2y_2 + 5z_1 + 5z_2 $

Rearranging these terms we get:

$ x_1 - 2y_1 + 5z_1 + x_2 - 2y_2 + 5z_2 $

So, the equation becomes, 0 + 0 = 0

So, it s closed under addition.

3) Let k be any scalar in V. And $ w_1 = (x, y, z) \in W $

This means $ x - 2y + 5z = 0 $

$ kw_1 = kx - 2ky + 5kz $

Taking k common outside, we get:

$ kw_1 = k(x - 2y + 5z) = 0 $

The equation becomes k(0) = 0.

So, it is closed under scalar multiplication.

Hence, W is a subspace of $ \math{R^3} $.
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