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3 years ago

14

X^2+15x=-45 solve by factoring

2 answers:

Julli [10]3 years ago

6 0

1 Move all terms to one side.

{x}^{2}+15x+45=0

x

2

+15x+45=0

2 Use the Quadratic Formula.

x=\frac{-15+3\sqrt{5}}{2},\frac{-15-3\sqrt{5}}{2}

x=

2

−15+3

5

,

2

−15−3

5

3 Simplify solutions.

x=-\frac{3(5-\sqrt{5})}{2},-\frac{3(5+\sqrt{5})}{2}

x=−

2

3(5−

5

)

,−

2

3(5+

5

)

harina [27]3 years ago

4 0

Answer:

x = - $\frac{15-3\sqrt{5} }{2}$ ; - $\frac{15+3\sqrt{5} }{2}$

Step-by-step explanation:

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Triangle TRI has a base of m centimeters and a height of n centimeters. Rectangle RECT has a length of n centimeters and a width

hram777 [196]

The area of the triangle is
a=( m x n) /2 in cm² , implies 2xa = m xn
the area of the rectanglle
A= n x m in cm²
but we know <span> 2xa = m xn = A, </span>
that means the surface of the rectangle is 2 times of the area of the triangle

7 0

3 years ago

Read 2 more answers

2. In how many ways can 3 different novels, 2 different mathematics books and 5 different chemistry books be arranged on a books

insens350 [35]

The number of ways of the books can be arranged are illustrations of permutations.

When the books are arranged in any order, the number of arrangements is 3628800
When the mathematics book must not be together, the number of arrangements is 2903040
When the novels must be together, and the chemistry books must be together, the number of arrangements is 17280
When the mathematics books must be together, and the novels must not be together, the number of arrangements is 302400

The given parameters are:

$\mathbf{Novels = 3}$

$\mathbf{Mathematics = 2}$

$\mathbf{Chemistry = 5}$

<u />

<u>(a) The books in any order</u>

First, we calculate the total number of books

$\mathbf{n = Novels + Mathematics + Chemistry}$

$\mathbf{n = 3 + 2 + 5}$

$\mathbf{n = 10}$

The number of arrangement is n!:

So, we have:

$\mathbf{n! = 10!}$

$\mathbf{n! = 3628800}$

<u>(b) The mathematics book, not together</u>

There are 2 mathematics books.

If the mathematics books, must be together

The number of arrangements is:

$\mathbf{Maths\ together = 2 \times 9!}$

Using the complement rule, we have:

$\mathbf{Maths\ not\ together = Total - Maths\ together}$

This gives

$\mathbf{Maths\ not\ together = 3628800 - 2 \times 9!}$

$\mathbf{Maths\ not\ together = 2903040}$

<u>(c) The novels must be together and the chemistry books, together</u>

We have:

$\mathbf{Novels = 3}$

$\mathbf{Chemistry = 5}$

First, arrange the novels in:

$\mathbf{Novels = 3!\ ways}$

Next, arrange the chemistry books in:

$\mathbf{Chemistry = 5!\ ways}$

Now, the 5 chemistry books will be taken as 1; the novels will also be taken as 1.

Literally, the number of books now is:

$\mathbf{n =Mathematics + 1 + 1}$

$\mathbf{n =2 + 1 + 1}$

$\mathbf{n =4}$

So, the number of arrangements is:

$\mathbf{Arrangements = n! \times 3! \times 5!}$

$\mathbf{Arrangements = 4! \times 3! \times 5!}$

$\mathbf{Arrangements = 17280}$

<u>(d) The mathematics must be together and the chemistry books, not together</u>

We have:

$\mathbf{Mathematics = 2}$

$\mathbf{Novels = 3}$

$\mathbf{Chemistry = 5}$

First, arrange the mathematics in:

$\mathbf{Mathematics = 2!}$

Literally, the number of chemistry and mathematics now is:

$\mathbf{n =Chemistry + 1}$

$\mathbf{n =5 + 1}$

$\mathbf{n =6}$

So, the number of arrangements of these books is:

$\mathbf{Arrangements = n! \times 2!}$

$\mathbf{Arrangements = 6! \times 2!}$

Now, there are 7 spaces between the chemistry and mathematics books.

For the 3 novels not to be together, the number of arrangement is:

$\mathbf{Arrangements = ^7P_3}$

So, the total arrangement is:

$\mathbf{Total = 6! \times 2!\times ^7P_3}$

$\mathbf{Total = 6! \times 2!\times 210}$

$\mathbf{Total = 302400}$

Read more about permutations at:

brainly.com/question/1216161

8 0

2 years ago

Jeanne Crawford had $9,675.95 deposited in an account paying

Anni [7]

Answer:

a. $10,943.30

b. $1,267.35

Step-by-step explanation:

P = $9,675.95

r = 6.25% = 0.0625

t = Compounded Semiannually = 2

a. Amount after 2 Years

n = 2

A = P [1 + (r / n)]^nt

A = $9,675.95 [1 + (0.0625 / 2)]² ˣ ²

A = $9,675.95 [1 + 0.03125]⁴

A = $9,675.95 [1.03125]⁴

A = $9,675.95 x 1.130982

A = $10,943.30

b. Compound Interest

Compound Interest = Final Amount - Principal Amount

Compound Interest = $10,943.30 - $9,675.95

Compound Interest = $1,267.35

8 0

2 years ago

For all values of x, which expression is equivalent to 2x + 5 − x + 3x + x − 2?

koban [17]

Answer:

5x + 3

Step-by-step explanation:

1) Collect like terms.

(2x − x + 3x + x) + (5 − 2)

2) Simplify

5 x + 3

4 0

3 years ago

Read 2 more answers

Find the sum 34+(-96)

Liula [17]

Answer: -62

Step-by-step explanation:

Hope this helps!!

4 0

3 years ago