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3 years ago

Subtract 6 from me. Then multiply by 2. If you subtract 40 and then divide by 4, you get 8. What number am I?

Mathematics

1 answer:

aliina [53]3 years ago

7 0

Answer:

Step-by-step explanation:

Let the number be "x"

We translate the word equation to algebraic equation.

First,

subtract 6 from me, so we have:

x - 6

Now,

Multiply by 2, so we have:

2(x-6)

Now,

Subtract 40, then divide by 4:

$\frac{2(x-6)-40}{4}$

Now, you get "8", so equate this to 8, we get:

$\frac{2(x-6)-40}{4}=8$

We now solve using algebra:

$\frac{2(x-6)-40}{4}=8\\2(x-6)-40=4*8\\2(x-6)-40=32\\2x-12-40=32\\2x-52=32\\2x=32+52\\2x=84\\x=42$

The number is 42

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Find all solutions of the equation in the interval [0,2pi)

irinina [24]

Answer:

{π/4, 5π/4}

Step-by-step explanation:

Tan theta -1=0 could be rewritten as tan Ф = 1. The tangent function is 1 at Ф = π/4. As the period of the tangent function is π,

tan Ф = 1 will be true for Ф = π/4 + π, or (5/4)π.

The solution set is {π/4, 5π/4}.

4 0

2 years ago

3 letters without replacement 4 letters A B C D how many ways can this be done if the order of the choices matters

Veseljchak [2.6K]

Answer:

Since the order of choice matters, we will permute the values. a bit more explanation for this:

If the order of choice did NOT matter, ABC and BCA will be counted as one since order of choice does NOT matter

Since order of choice does matter, ABC , BCA and CAB are all different possibilities for the arrangement of the same 3 letters

Since we have 3 slots:

___ ___ ___

Now, for the first slot. You can out either one if the 4 alphabets in the first slot since no slot has been used as of now

So:

_4_ ___ ___

**Keep in mind that the 4 is the possible number of values this slot can have**

Now that one slot has been used, one of the 4 alphabets has been used and since we are not allowed to repeat the same alphabets, we are left with 3 more alphabets

we can put any one of the 3 alphabets in this second slot, Hence:

_4_ _3_ ___

Now that 2 of the 4 alphabets have been used, we are left with only 2 alphabets, so there are only 2 possible alphabets for slot 3

Therefore:

_4_ _3_ _2_

Now that we know the possible alphabets for all 3 slots, we will multiply them with each other to get the total possible number of 3 - alphabet words we can make with 4 alphabets

Total possible words = 4 * 3 * 2

Total possible words = 24

We could've used the formula for Permutation as well

8 0

3 years ago

Once each day, Erika tracks the depth of the water in her local creek. Her first nine measurements, in inches, are: 16, 15, 13,

solniwko [45]

Answer:

Median = 13

Step-by-step explanation:

We are given the following data:

16, 15, 13, 12, 17, 14, 11, 9, 11

Formula:

$Median:\\\text{If n is odd, then}\\\\Median = \displaystyle\frac{n+1}{2}th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle\frac{\frac{n}{2}th~term + (\frac{n}{2}+1)th~term}{2}$

Sorted data: 9, 11, 11, 12, 13, 14, 15, 16, 17

Median =

$=\dfrac{9+1}{2}^{th} = 5^{th}\text{ term} = 13$

Thus, the median of the given data is 13.

4 0

3 years ago

Suppose U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is the universal set and G = {1, 2, 3, 4, 5, 6, 7}. What is G?

Nesterboy [21]

Your posted question defines G, then asks what G is.
G is the set in the definition you gave.

G = {1, 2, 3, 4, 5, 6, 7}

_____
Perhaps you want to know the complement of G. That is all the elements of U that are not in G.

G' = {8, 9, 10}

3 0

2 years ago

Learning goal: to understand the rules for computing dot products. let vectors a=(2,1,−4), b=(−3,0,1), and c=(−1,−1,2). part a -

miv72 [106K]

For this case we have the following vectors:
$a = (2,1, -4)

b = (- 3,0,1)

c = (- 1, -1,2)$
The dot product of two vectors is a scalar.
The point product consists of multiplying component by component and then adding the result of the multiplication of each component.
For the product point of the vectors a and b we have:
$a.b = (2,1, -4). (- 3,0,1)

a.b = (2) (- 3) + (1) (0) + (-4) (1)

a.b = - 6 + 0 - 4

a.b = - 10$
Answer:
The product point of the vectors a and b is:
$a.b = - 10$

3 0

3 years ago