MATHEMATICS HIGH SCHOOL

Factorise 15x + 35y - 40 z

Answers

Answer 1

Answer:

For this case we have the following expression.

We must find a term of expression that is repeated in all terms.

We then have the number 5.

By doing common factor 5 in all the expression we have:

Answer:

The factored expression is given by:

$5 (3x + 7y - 8z)$

Answer 2

Answer: 15x + 35y - 40 z = 5 (3x + 7y -8z)

hope that helps
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Put these in order of size smallest first 0.8 30% 3/5

Answers

30% , 3/5 , 0.8Checking:30%=30%3/5=60%0.8=80%

Given the arithmetic sequence, find the recursive formula, explicit formula, and the indicated term.8) 1,4,1, 10, ...
7) 12, 7, 2, -3,...

Answers

Answer:

Let's find the recursive formula, explicit formula, and the indicated term for the given arithmetic sequences.

Sequence 1: 1, 4, 1, 10, ...

To find the recursive formula, we need to identify the pattern between consecutive terms. Looking at the sequence, we can see that each term alternates between adding 3 and subtracting 3.

Recursive formula:

a1 = 1 (the first term)

an = an-1 + (-1)^(n+1) * 3

For example, to find the 4th term (a4) using the recursive formula:

a1 = 1 (the first term)

a2 = a1 + (-1)^(2+1) * 3 = 1 + (-1) * 3 = -2

a3 = a2 + (-1)^(3+1) * 3 = -2 + 1 * 3 = 1

a4 = a3 + (-1)^(4+1) * 3 = 1 + (-1) * 3 = -2

Explicit formula:

To find the explicit formula, we need to identify the common difference. In this case, since the terms alternate between adding 3 and subtracting 3, the common difference is not constant.

Indicated term:

To find the indicated term, we need to know which term is being referred to. Please provide the term number or the position of the term in the sequence so that I can assist you further.

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Sequence 2: 12, 7, 2, -3, ...

To find the recursive formula, we need to identify the pattern between consecutive terms. Looking at the sequence, we can see that each term decreases by 5.

Recursive formula:

a1 = 12 (the first term)

an = an-1 - 5

For example, to find the 4th term (a4) using the recursive formula:

a1 = 12 (the first term)

a2 = a1 - 5 = 12 - 5 = 7

a3 = a2 - 5 = 7 - 5 = 2

a4 = a3 - 5 = 2 - 5 = -3

Explicit formula:

To find the explicit formula, we need to identify the common difference. In this case, the common difference is -5.

Explicit formula:

an = 12 + (n - 1)(-5)

Indicated term:

To find the indicated term, we need to know which term is being referred to. Please provide the term number or the position of the term in the sequence so that I can assist you further.

Please provide the term number or the position of the term in the sequence so that I can help you find the indicated term.

Step-by-step explanation:

Solve the following system.
x^2 + y^2 = 25
2x + y = 10
The solution set

Answers

$\begin{cases} x^(2)+y^(2)=25 \n 2x+y=10 \end{cases} \n \n \begin{cases} x^(2)+y^(2)=25 \n y=10 -2x\end{cases} \n \n \begin{cases} x^(2)+(10-2x)^(2)=25 \ny=10-2x \end{cases} \n \n \begin{cases} x^(2)+100-40x+4x^(2)=25 \ny=10-2x \end{cases} \n \n \begin{cases} 5x^(2)-40x+75=0 \ny=10-2x \end{cases}$

$\begin{cases} x^(2)-8x+15=0 \ny=10-2x \end{cases} \n \n \begin{cases} \Delta=(-8)^(2)-4*1*15=64-60=4; \ \ \ √(\Delta) =2 \ny=10-2x \end{cases} \n \n \begin{cases} x_(1)= (8-2)/(2) =3 \ \wedge \ x_(2)= (8+2)/(2)=5 \ny=10-2*3=4 \ \wedge \ y=10-2*5=0 \end{cases}$

PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!!For which intervals is the function increasing?

Select EACH correct answer.

Answers

Answer: B. ( -∞ , 0) and C. (1, 2)

Step-by-step explanation:

The y-value is increasing between x = -∞ and x = 0.

The y-value is decreasing between x = 0 and x = 1.

The y-value is increasing between x = 1 and x = 2.

The y-value is decreasing between x = 2 and x = +∞

So, the y-value is increasing at ( -∞ , 0) ∪ (1, 2)

A rectangular fish tank contains 3,240 cubic inches of water. The dimensions of the base of the fish tank are 12 inches x 18 inches. How tall is the fish tank?