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2 years ago

What is the value of the expression below? 675 ÷ 3 - (15 - 12)² PLZ HELP-

Mathematics

1 answer:

vodomira [7]2 years ago

5 0

Answer:

675 ÷ 3 - ( 225 - 144)

675 ÷ 3 - (81)

225 - 81

144

I hope it's helps you

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Suppose the roots of the polynomial $x^2 - mx + n$ are positive prime integers (not necessarily distinct). Given that $m < 20

Vsevolod [243]

Answer:

18 values for n are possible.

Step-by-step explanation:

Given the quadratic polynomial:

$x^2 - mx + n$

such that:

Roots are positive prime integers and

$m < 20$

To find:

How many possible values of $n$ are there ?

Solution:

First of all, let us have a look at the sum and product of a quadratic equation.

If the quadratic equation is:

$Ax^{2} +Bx+C$

and the roots are: $\alpha$ and $\beta$

Then sum of roots, $\alpha+\beta = -\frac{B}{A}$

Product of roots, $\alpha \beta = \frac{C}{A}$

Comparing the given equation with standard equation, we get:

A = 1, B = -m and C = n

Sum of roots, $\alpha+\beta = -\frac{-m}{1} = m$

Product of roots, $\alpha \beta = \frac{n}{1} = n$

We are given that $m$

$\alpha$ and $\beta$ are positive prime integers such that their sum is less than 20.

Let us have a look at some of the positive prime integers:

2, 3, 5, 7, 11, 13, 17, 23, 29, .....

Now, we have to choose two such prime integers from above list such that their sum is less than 20 and the roots can be repetitive as well.

So, possible combinations and possible value of $n (= \alpha \times \beta)$ are:

$1.\ 2, 2\Rightarrow n = 2\times 2 = 4\\2.\ 2, 3 \Rightarrow n = 6\\3.\ 2, 5 \Rightarrow n = 10\\4.\ 2, 7\Rightarrow n = 14\\5.\ 2, 11 \Rightarrow n = 22\\6.\ 2, 13 \Rightarrow n = 26\\7.\ 2, 17 \Rightarrow n = 34\\8.\ 3, 3\Rightarrow n = 3\times 3 = 9\\9.\ 3, 5 \Rightarrow n = 15\\10.\ 3, 7 \Rightarrow n = 21\\$

$11.\ 3, 11\Rightarrow n = 33\\12.\ 3, 13 \Rightarrow n = 39\\13.\ 5, 5 \Rightarrow n = 25\\14.\ 5, 7 \Rightarrow n = 35\\15.\ 5, 11 \Rightarrow n = 55\\16.\ 5, 13 \Rightarrow n = 65\\17.\ 7, 7 \Rightarrow n = 49\\18.\ 7, 11 \Rightarrow n = 77$

So,as shown above 18 values for n are possible.

3 0

3 years ago

The first discount on a camera was 18%. The second discount was 20%. After the two discounts the price became $328. What was the

Lelechka [254]

Answer:

500

Step-by-step explanation:

Let x be the original price

Take the first discount

x - 18 percent

x - .18x = new price

x( 1-.18)

x ( .82) = new price

Now we take a 20 percent discount

This is on the discounted price, use .82x

.82x - 20 percent= 2nd discounted price

.82x - .20(.82x)

.82x -.164x

.656x= 2nd discounted price

.656x = 328

Divide each side by.656

.656x/.656 = 328/.656

x =500

The original price was 500

6 0

3 years ago

Read 2 more answers

Find the length of BD and EC. A D 9 8 B с BD = EC =

hammer [34]

I think BD is 16 and EC is 9. hope this helps

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3 years ago

The point(5/13,Y) IS IN THE 4TH quadrant corresponds to angle on the unit circle

shutvik [7]

4th quadrant is positive x (cos) and negative y (sin)

Use the Pythagorean Theorem to calculate the value of y (sin).
x² + y² = c²
5² + y² = 13²
25 + y² = 169
y² = 144
y = 12

Since the y-value is negative in the 4th quadrant, then y = -12

6 0

3 years ago

Sally fills her car with 12 gallons of gas. She goes on a journey and ends up with 7.5 gallons left in the tank. What is the per

melomori [17]

Around 80-75 percent.

5 0

3 years ago