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ycow [4]
3 years ago
9

Does anyone know how to solve this?

Mathematics
1 answer:
Lilit [14]3 years ago
4 0

The pattern is that the numbers in the right-most and left-most squares of the diamond add to the bottom square and multiply to reach the number in the top square.


For example, in the first given example, we see that the numbers 5 and 2 add to the number 7 in the bottom square and multiply to the number 10 in the top square.


Another example is how the numbers 2 and 3 in the left-most and right-most squares add up to the number 5 in the bottom square and multiply to the number 6 in the top square.


Using this information, we can solve the five problems on the bottom of the paper.


a) We are given the numbers 3 and 4 in the left-most and right-most squares. We must figure out what they add to and what they multiply to:

3 + 4 = 7

3 x 4 = 12

Using this, we can fill in the top square with the number 12 and the bottom square with the number 7.


b) We are given the numbers -2 and -3 in the left-most and right-most squares, which again means that we must figure out what the numbers add and multiply to.

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

(-2) x (-3) = 6

Using this, we can fill the top square in with the number 6 and the bottom square with the number -5.


c) This time, we are given the numbers which we typically find by adding and multiplying. We will have to use trial and error to find the numbers in the left-most and right-most squares.


We know that 12 has the positive factors of (1, 12), (2,6), and (3,4). Using trial and error we can figure out that 3 and 4 are the numbers that go in the left-most and right-most squares.


d) This time, we are given the number we find by multiplying and a number in the right-most square. First, we can find the number in the left-most square, which we will call x. We know that \frac{1}{2}x = 4, so we can find that x, or the number in the left-most square, is 8. Now we can find the bottom square, which is the sum of the two numbers in the left-most and right-most squares. This would be 8 + \frac{1}{2} = \frac{17}{2}. The number in the bottom square is \boxed{\frac{17}{2}}.


e) Similar to problem c, we are given the numbers in the top and bottom squares. We know that the positive factors of 8 are (1, 8) and (2, 4). However, none of these numbers add to -6, which means we must explore the negative factors of 8, which are (-1, -8), and (-2, -4). We can see that -2 and -4 add to -6. The numbers in the left-most and right-most squares are -2 and -4.

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Can you please help me solve questions 1 and 2
Katyanochek1 [597]

Answer:

see explanation

Step-by-step explanation:

(1)

Given the perimeter then the third side is the perimeter subtract the sum of the 2 given sides, that is

third side

= 4x + 3y - (x - y + x + y)

= 4x + 3y - 2x ← collect like terms

= 2x + 3y

(2)

The area (A) of a triangle is calculated as

A = \frac{1}{2} bh ( b is the base and h the height )

Here b = 2x + 6 and h = x - 2, thus

A = \frac{1}{2}(2x + 6)(x - 2) ← expand factors using FOIL

   = \frac{1}{2}(2x² + 2x - 12) ← distribute

   = x² + x - 6 ← in standard form

7 0
2 years ago
Scenario: Two people in a major city with a population of 450,000 get infected with a rapidly spreading virus. If each day the i
zmey [24]

1) See attachment.

2) See attachment

3) y=2^{x+1}

4) 17.8 days

Step-by-step explanation:

1)

The table is in attachment.

In this problem, we are told that the initial number of people infected ad day zero is two, so the first row is (0,2).

Then, we are told that each day, an infected person infects 2 additional people. Therefore, at day 1, the number of infected people will be 2*2=4.

Then, each of the 4 persons infect 2 additional persons, so the number of infected people at day 2 will be 4*2=8.

Continuing the sequence, the following days the number of infected people will be:

8*2 = 16

16*2 = 32

32*2 = 64

2)

The graph representing the situation is shown in attachment.

On the x-axis, we have represented the day, from zero to 5.

On the y-axis, we have represented the number of infected people.

We see that the points on the graph are:

0, 2

1, 4

2, 8

3, 16

4, 32

5, 64

3)

Here we have to create a mathematics model (so, an equation) representing this scenario.

First of all, we notice that the number of infected people at day 0 is 2:

p(0)=2

To write an equation, we call x the number of the day; this means that at x = 0, the value of y (number of infected people) is 2:

y=2

Then, at day 1 (x=1), the number of infected people is doubled:

y(1)=2y(0)=2\cdot 2 = 4

And so on. This means that for each increase of x of 1 unit, the value of y doubles: so, we can represents the model as

y=2\cdot 2^x

Or

y=2^{x+1}

4)

Here we are told that the entire city has a population of

p = 450,000

people.

In order for the virus to infect the whole population, it means that the value of y must be equal to the total population:

y = 450,000

Substituting into the equation of the model, this means that

450,000 = 2^{x+1}

And solving for x, we find the number of days after which this will happen:

log_2(450,000)=x+1\\x=log_2(450,000)-1=17.8 d

So, after 17.8 days.

8 0
2 years ago
Please identify the common angles and sides or if there are non. Explain all work please!
stepladder [879]

Answers:

Common angles: ΔBGC and ΔGDC

Common sides: ΔGE and ΔAG

A common angle is a triangle that exists in two or both of the triangles.

Here, the common angles should be ΔBGC and ΔGDC.

These two angles are triangles, and they consist in both triangles.

A common side is when two angles have one vertex in the same area.

Here, we see that the common sides are ΔGE, because they intersect.

Another common side we see here is ΔAG, because they also intersect.

Hope this answer helps you!

3 0
2 years ago
Read 2 more answers
What is the median of the data set given below?
Sholpan [36]

Answer:

C. 19

Step-by-step explanation:

If you arrange the numbers in ascending order, the middle number is 19.

5 0
3 years ago
Read 2 more answers
Solve the following equation for x<br> 2x+6=3x−12x+6=3x−1
Rudik [331]

Answer: x=11/22

Step-by-step explanation: 2x+6=3x−12x+6=3x-1                                           2x+6=3x+−12x+6=3x+-1                                                                                       2x+6=(3x+−12x)+(6+-1)=3x                                                                     2x+6+9x=−9x+5+9x=3x+9x                                                                                   11x+6=5=12x                                                                                                 11x+12x=6+5                                                                                             22x/22=11/22                                                                                                       x=11/22                                                                                                                                                                                                                                                                                            

3 0
2 years ago
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