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3 years ago

Find the area of the triangle below.

Mathematics

1 answer:

Phoenix [80]3 years ago

5 0

Answer:

20.25

Step-by-step explanation:

Just multiply the base and height then divide the results in half.

Hope this helps!

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In how many ways can 5 different novels, 4 different mathematics books, and 1 biology book be arranged on a bookshelf if

zalisa [80]

Question Continuation:

if (a) the books can be arranged in any order?

(b) the mathematics books must be together and the novels must be together?

Answer:

(a) 3628800 ways

(b) 17280 ways

Step-by-step explanation:

Given

$Novels = 5$

$Mathematics = 4$

$Biology = 1$

Solving (a): In any order

This implies that there is no restriction and the novels, mathematics and biology book are just seen as books.

Total number of books is:

$N = Mathematics + Novel + Biology$

$N = 4+5+1$

$N = 10$

The number of arrangement is:

$10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1$

$10! = 3628800\ ways$

(b):

If the mathematics books are together, there are 4! different arrangements

If the novels are together, there are 5! different arrangements

Now, there are 3 bundles.

The mathematics books as 1
The novels as 1
The biology book

This can be arranged in 3! ways.

Total number of arrangement is:

$Total = 4! * 5! * 3!$

$Total = 4*3*2*1 * 5*4*3*2*1 * 3*2*1$

$Total = 17280\ ways$

6 0

3 years ago

Find two consecutive odd integers such that the square of the first added to 3 times the second, is 24. Part a: Define the varia

fgiga [73]

Given:

There are two consecutive odd integers such that the square of the first added to 3 times the second, is 24.

To find:

Part a: Define the variables.

Part b: Set up an equations that can be solved to find the integers.

Part c: Find the integers.

Solution:

Part a:

Let x be the first odd integers. Then next consecutive odd integer is $x+2$ , because the difference between two consecutive odd integers is 2.

Part b:

Square of first odd integers = $x^2$

Three times of second odd integers = $3(x+2)$

It is given that the sum of square of first odd integers and three times of second odd integers is 24. So, the required equation is:

$x^2+3(x+2)=24$

Part c:

The equation is:

$x^2+3(x+2)=24$

It can be written as:

$x^2+3x+6=24$

$x^2+3x+6-24=0$

$x^2+3x-18=0$

Splitting the middle term, we get

$x^2+6x-3x-18=0$

$x(x+6)-3(x+6)=0$

$(x-3)(x+6)=0$

$x=3,-6$

-6 is not an odd integer, so $x=3$ and the first odd integer is 3.

Second odd integer = $x+2$

= $3+2$

= $5$

Therefore, the two consecutive odd integers are 3 and 5.

8 0

3 years ago

What is the value of x + y(3 − x) when x = −5 and y = 3?

grandymaker [24]

Answer:

Step-by-step explanation:

x + y(3 − x)

Let x = -5 and y = 3

-5 +3(3 - -5)

Subtracting a negative is like adding

-5 +3(3+5)

Parentheses first

-5 +3(8)

Multiply

-5+24

Subtract

6 0

3 years ago

Read 2 more answers

Four friends are creating posters for their presentations, which will be delivered in different locations. Which person should c

Evgen [1.6K]

Answer:

Lindsey, who is delivering her speech in a large auditorium

Step-by-step explanation:

Jin, who is delivering her speech to a small group sitting around a table

Lindsey, who is delivering her speech in a large auditorium

Luke, who is delivering his speech in a typical classroom

Jordan, who is delivering his speech in a small meeting room

8 0

3 years ago

the ratio of green houses to white houses on winthrop street is equal to 2 to 3 . there are 60 white houses on winthrop street.

lord [1]

2/3 = g/60
cross multiply because we have a proportion
3g = 120
g = 120/3
g = 40....so there are 40 green house

8 0

4 years ago

Read 2 more answers