The difference between two numbers is 4. Three times the larger is 2 more than five times the smaller. Find the numbers.

2 answers:

8 0

Let x represent the larger number.
Let y represent the smaller number.
x-y=4 Given
3x=5y-2 Given
Now we can just substitute; let x=4+y
Substitute 4+y for x in the second equation:
3(4+y)=5y-2
12+3y=5y-2
-2y=-14
y=7
Substitute back (into BOTH equations to double check work).
x, the larger number, is 11

Anon25 [30]3 years ago

7 0

Da numbers are x and y

lets say x>y
differebec between x and y is 4
x-y=4

3 times the larger is 2 more than 5 times the smaller
3 times x is 2 more than 5 times y
3x=2+5y

ok so we gots
x-y=4 and
3x=2+5y

hmm
in the first one we can solve for x and subsitute
x-y=4
add y to both sides
x=y+4
subsitute y+4 for x

3x=2+5y
3(y+4)=2+5y
distribute
3y+12=2+5y
minus 3y both sides
12=2+2y
minus 2 both sides
10=2y
divide 2 both sides
5=y

subsitute back

x=y+4
x=5+4
x=9

the numbers are 9 and 5

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The polynomial of minimum degree is $p(x) = x^{4}-3\cdot x^{3}-44\cdot x^{2}+292\cdot x-480$ .

Step-by-step explanation:

According to the statement, we appreciate that polynomial pass through the following points:

(i) $(4 + 2\,i,0)$ , (ii) $(4 - 2\,i, 0)$ , (iii) $(-8, 0)$ , (iv) $(0, -480)$

From Algebra we know that any n-th grade polynomial can be constructed by knowing n+1 different points. Hence, the polynomial of minimum degree is a quartic function. The polynomial has the following form:

$p(x) = (x-4-2\,i)\cdot (x-4+2\,i)\cdot (x+8)\cdot (x-r_{1})$