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11Alexandr11 [23.1K]
3 years ago
5

Help on 3,4,5 please!

Mathematics
1 answer:
maxonik [38]3 years ago
5 0

Answer:

  3.  DF = 15

  4.  (x +y +2)(x +y +3)

  5. Tuesday

Step-by-step explanation:

3. The angle congruence tells you the triangles are similar. Corresponding sides have a ratio of 5/4:

  DE/AB = 10/8 = 5/4

  EF/BC = 12.5/10 = 5/4

  DF/AC = ?/12 = 5/4

Multiplying by 12, we find ...

  DF = 12(5/4) = 15

__

4. The first three terms look like (x+y)². The next two look like 5(x+y). So we can group terms to make the expression look like ...

  (x+y)² + 5(x+y) +6

We recognize factors of 6 that sum to give 5 as being 2 and 3, so we can factor this as ...

  (x+y +2)(x+y +3)

__

5. Jan 1 falls on a day of the week that is the first of 3 days of which there are 5 in the month.

There are 3 days between Monday and Friday, but only 2 days between Friday and Monday. Hence the 1st of January must fall on Tuesday that year.

There will be 4 of Fri, Sat, Sun, Mon, and 5 of Tue, Wed, Thu in the month.

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8 + x = 25 \\ x = 25 - 8 \\ 17

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7 0
3 years ago
Ed wants to borrow $20,000 from a bank to open a small gym. Three banks charge different interest rates. To help decide the best
Delicious77 [7]

Answer:

First bank = $6792

City bank = $6803

Star bank = $6817  

Step-by-step explanation:

The lists of banks and their annual interests rates are attached.

For first bank, since the interest is 7.5%, The total interest = 7.5% of $20000 = 0.075 × $20000 = $1500

For city bank, since the interest is 8.2%, The total interest = 8.2% of $20000 = 0.082 × $20000 = $1640

For Star bank, since the interest is 9%, The total interest = 9% of $20000 = 0.09 × $20000 = $1800  

The loan plus interest for the banks annually are:

First bank = $20000 + $1500 = $21500

City bank = $20000 + $1640 = $21640

Star bank = $20000 + $1900 = $21900

The monthly payments for the banks are:

First bank = $21500 / 12 months = $1792

City bank = $21640 / 12 months = $1803

Star bank = $21800 / 12 months = $1817

Since The cost to run the gym each month is $5,000. Ed's total monthly expenses for each loan option = monthly payments + cost for each month. It is calculated as:

First bank = $5000 + $1792 = $6792

City bank = $5000 + $1803 = $6803

Star bank = $5000 + $1817 = $6817  

3 0
3 years ago
Ali picked three numbers out of a hat. Use the information in the box to work out what numbers he picked. The lowest number was
IgorC [24]

Answer:

The numbers he picked are 11, 17 and 24

Step-by-step explanation:

To solve this, we will work with the information we are given, interpreting it properly.

From the information given , we can already decode that the first of the three numbers is 11. We can write that number down.

The next piece of information we are given is that the range is 13.

The range of a data set is the difference between the highest and lowest numbers in the data set.

Let us say that our highest number is x

Range =x-11

x= range + 11\\x=13+11=24

Now, we know that the highest number of the data set is 24

Finally, from the information given, we can see that the median number is 17. This is the middle number of the data set. we can simply write that down since the number of figures in our data set is an odd number.

Hence the numbers picked are

11, 17 and 24 arranging them in an ascending order

7 0
2 years ago
What are the coordinates of the point on the directed line segment from (1,-5) to
Black_prince [1.1K]

Answer:

Q (2.5, -4)

Step-by-step explanation:

Let A (1, -5), C = (10, 1), find Q (x, y), so that AQ:QC = 1:5

AQ = (x - 1, y + 5)

QC = (10 - x, 1 - y)

AQ:QC = 1:5

so 5*AQ = QC

5(x - 1) = (10 - x)

5(y + 5) = 1 - y

Solve them:

5x - 5 = 10 - x

6x = 15

x = 15/6 = 2.5

5y + 25 = 1 - y

6y = -24

y = -24/6 = -4

Then answer is Q (2.5, -4)

6 0
2 years ago
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