MATHEMATICS HIGH SCHOOL

Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist.x+3y=9
3x-y=7

Answers

Answer 1
Answer: \left \{ {{x+3y=9~(3)} \atop {3x-y=7(-1)}} \right. \n \n \left \{ {{3x+9y=27} \atop {-3x+y=-7}} \right. \n \n10y=20\n \ny= (20)/(10) \ny=2

x+3y=9\nx=9-3y\nx=9-3.2\nx=3

S=\{3,2\}

One solution.
Answer 2
Answer: x+3y=9\n 3x-y=7\ / \cdot 3\n \n x+3y=9\n 9x-3y=21\n \n 10x=30\ /:10\n x=3\n \n x+3y=9\n 3+3y=9\n 3y=6\n y=2\n one\ solution - (3;2)

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If ab = 10 and a2 + b2 = 30, what is the value of
(a + b)^2?

Answers

Answer: (a + b)² = 50

Step-by-step explanation:

(a + b)² = (a + b)(a + b)

= a² + ab + ab + b²

So, (a + b)² = a² + b² + 2ab

Then substitute the value of ab and (a² + b²)

(a + b)² = 30 + 2(10)

= 30 + 20

Therefore, (a + b)² = 50
ab=10
a^2+b^2=30
((a+b)^2=a^2+2ab+b^2=a^2+b^2+2*10=30+20=50

How many real number solutions does the equation have?-8x^2-8x-2=01
2
no solutions
or
infinitely many solutions

solve the equation by completing the square. round to the nearest hundredth. x^2+6x=-7
4.41,1.59
-4.41,1.59
-4.41,-1.59
4.41,-1.59

and the last one is
solve the systems of equations algebraically. show all of your steps.
y=x^2+2x
y=3x+20

Answers

Hello,

I)
1 solution with multiplicity 2
(2x+1)²=0

II) ANSWER C (-4.41, -1.59)
-3-√2 and -3+√2

III)
y=x²+2x
y=3x+20
==>x²+2x=3x+20
==>x²-x-20=

Δ=1+4*20=81=9²

(x=(1-9)/2=-4 and y= 3*(-4)+20=8 ) or (x=(1+9)/2=5 and y=3*5+20=35)

If 6.3% of your salary is deducted for a fund how much would be deducted from a $488.00 weekly salary

Answers

the issue is to find the 6.3% out of $488, that is easy, just multiply them both and remember that 6.3% is 6.3 out of 100, 6.3/100
deduction = 6.3%($488)
= (6.3/100)(488)
= 30.74
hence, will be deducted $30.74 which is 6.3% of $488

Can you do a number line with no solution set.

Answers

yes 
all you do is draw a line and put numbers on it

There are 5/6 as many black pants as blue pants in george's closet. There are 5/9 as many black pants as brown pants in his closet. What is the ratio of the number black pants to the total number of pants in his closet?

Answers

Answer is the ratio   1 : 4

Work Shown

x = number of black pants

y = number of blue pants

z = number of brown pants

x = (5/6)y

x = (5/9)z

z = (9/5)x

x+y+z = total number of pants

x+y+z = (5/6)y + y + (9/5)x

x+y+z = (5/6)y+y+(9/5)*(5/6)y  

x+y+z = (5/6)y+y+(3/2)y

x+y+z = (5/6)y+(6/6)y+(9/6)y

x+y+z = ( (5+6+9)/6 )y

x+y+z = (20/6)y

x+y+z = (10/3)y

numberOfBlackPants : Total

(5/6)y : (10/3)y

6*(5/6)y : 6*(10/3)y

5y : 20y

5 : 20

1 : 4

The ratio of the number of black pants to the total number is 1 : 4

It means the total is 4 times that of the number of black pants.

Tell whether 807 is divisible by 2, 3, 4, 5, 6, 9, and 10.a. Divisible by 2, 3, 4, 6, and 10
c. Divisible by 3
b. Divisible by 5 and 9
d. Divisible by 2, 4, 5, 6, 9, and 10

Answers

c.divisible by three
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