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2 years ago

Express 10500 in terms of its prime factors

Mathematics

1 answer:

8_murik_8 [283]2 years ago

7 0

Step-by-step explanation:

$10500 = 3 \times 5 \times 5 \times 5 \times 7 \times 2 \times 2 \\ \\ 10500 = 2 \times 2 \times 3 \times 5 \times 5 \times 5 \times 7 \\ 10500 = {2}^{2} \times 3 \times {5}^{3} \times 7$

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Based on the table below, evaluate f(1).

Jobisdone [24]

Answer:

f(1) = 24

Step-by-step explanation:

f(1) is the value of f(x) when x = 1, that is from the table

f(1) = 24

3 0

2 years ago

Write a quadratic equation given the roots -1/3 and 5, show your work

Travka [436]

$\boxed{(x - a)(x - b) = 0}$

The equation above is the intercept form. Both a-term and b-term are the roots of equation.

$x = - \frac{1}{3} \\ x = 5$

These are the roots of equation. Therefore we substitute a = - 1/3 and b = 5 in the equation.

$(x + \frac{1}{3} )(x - 5) = 0$

Here we can convert the expression x+1/3 to this.

$x + \frac{1}{3} = 0 \\ 3x + 1 = 0$

Rewrite the equation.

$(3x + 1)(x - 5) = 0$

Simplify by multiplying both expressions.

$3 {x}^{2} - 15x + x - 5 = 0 \\ 3 {x}^{2} - 14x - 5 = 0$

Answer Check

Substitute the given roots in the equation.

$3 {(5)}^{2} - 14(5) - 5 = 0 \\ 75 - 70 - 5 = 0 \\ 75 - 75 = 0 \\ 0 = 0$

$3( - \frac{1}{3} )^{2} - 14( - \frac{1}{3}) - 5 = 0 \\ 3( \frac{1}{9} ) + \frac{14}{3} - 5 = 0 \\ \frac{1}{3} + \frac{14}{3} - \frac{15}{3} = 0 \\ \frac{15}{3} - \frac{15}{3} = 0 \\ 0 = 0$

The equation is true for both roots.

Answer

$\large \boxed {3 {x}^{2} - 14x - 5 = 0}$

8 0

2 years ago

What is the sign of the product (–5)(–3)(–8)(–6)? Positive, because the products (–5)(–3) and (–8)(–6) are negative, and the pro

chubhunter [2.5K]

Answer:

The product (–5)(–3)(–8)(–6) should be Positive.

Step-by-step explanation:

The product of 2 negative numbers equal a positive product.

N * N = P

-5*-3=15

-8*-6=48

The product of 2 positive numbers is positive.

P * P = P

15 * 48 = 720

Your answer should be: Positive because the products (–5)(–3) and (–8)(–6) are positive, and the product of two positive numbers is positive.

6 0

3 years ago

Read 2 more answers

Find the common ratio and an explicit form in each of the following geometric sequences.

Margaret [11]

Answer:

The explicit form is $a_{n}=162(2/3)^{n-1}$

Step-by-step explanation:

The explicit form of a geometric sequence is given by:

$a_{n}=ar^{n-1}$

where an is the nth term, a is the first term of the sequence and r is the common ratio.

In this case:

a=162

The value of the common ratio is obtained by dividing one term by the previous term.

For the first and second terms:

108/162=2/3

For the second and third terms (In order to prove that 2/3 is the common ratio)

72/108=2/3

Therefore:

r=2/3

Replacing a and r in the formula:

$a_{n}=162(2/3)^{n-1}$

7 0

2 years ago

Please help I with give Brainiest if correct

padilas [110]

Answer:

Perimeter of the rectangle = 6 x +20

Perimeter of the rectangle = 0 x² + 6 x + 20

Step-by-step explanation:

Step(i):-

Given that the length of the rectangle = 2x +3

Given that the width of the rectangle = x +7

Perimeter of the rectangle = 2(length + width)

Step(ii):-

Perimeter of the rectangle = 2(length + width)

= 2(2 x +3 + x+7)

= 4x +6+2x+14

= 6 x +20

Final answer:-

Perimeter of the rectangle = 6 x +20

Perimeter of the rectangle = o x² + 6 x + 20

7 0

2 years ago

Express 10500 in terms of its prime factors​

Express 10500 in terms of its prime factors