MATHEMATICS HIGH SCHOOL

Solve for x and y simultaneously:
X-2y=3
4xsquared-5xy+6y=3

Answers

Answer 1
Answer: x - 2y = 3
4x^2 - 5xy + 6y = 3
lets solve for x the first and substitute in the second:
x = 3 + 2y
4(3 + 2y)^2 - 5(3 + 2y)y + 6y = 3
4(9 + 12y + 4y^2) - 15y - 10y^2 = 3
36 + 48y +16y^2 - 15y - 10y^2 = 3
6y^2 + 33y + 33 = 0
we can solve using the general quadratic formula:
y = (-33 +- √(33^2 - 4*6*33))/12
y = (-33 +- √(297))/12
so there are 2 solutions for y:
y1 = (-33 + √(297))/12
y2 = (-33 - √(297))/12
pick one and then substitute the y value in the first equation to find x
Answer 2
Answer: x = 3 + 2y

4(3+2y)^2 - 5(3+2y)y + 6y = 3
4(4y^2 + 12y + 9) - 5(3y + 2y^2) + 6y - 3 = 0
16y^2 + 48y + 36 - 15y - 10y^2 + 6y - 3 = 0
6y^2 + 39y + 33 = 0
6y^2 + 6y + 33y + 33 = 0
6y(y+1) + 33(y+1) = 0
(y+1)(6y+33) = 0
y = -1, -11/2

x = 3 + 2y
x = 3 + 2(-1)
x = 3 + 2(-11/2)
x = 1, -8

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True or false, A function is a relation if and only if the x-values do not repeat in a given set

Answers

Its false because it can't repeat in a set.
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if square root of 405 rounded to the nearest thousandth is 20.125  how do u simplify to get to that answer, thank u.

Answers

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What is the length of the line segment in the x-y plane with end points at (-2,-2) and (2,3)?Can anyone explain me how to make this one step by step?

Answers

You've got a formula. If the two endpoints are A(x_A,y_A) and A(x_B,y_B), then the length is √((x_B-x_A)^2+(y_B-y_A)^2). The result is √(16+25)=√(41).

Please help I will mark you brainliest if you’re right!!

Answers

Answer:

C

Step-by-step explanation:

The two legs (shorter sides ) if a right angle triangle have lengths of 15 cm and 8 cm respectively. Determine the length of the largest third side (to the nearest cm).

Answers

By Pythagoras theorem,
h^2=a^2+o^2
Longest side is the same as the hypotenuse (h)
h^2=8^2+15^2
h^2=64+225
h^2=289
Square root both sides
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A man invests a certain amount of money at 2% interest and $800 more than that amount in another account at 4% interest. At the end of one year, he earned $92 in interest. How much money was invested in each account?A) $1,500 at 2%; $2,300 at 4%
B) $1,400 at 2%; $2,200 at 4%
C) $1,000 at 2%; $1,800 at 4%

Answers

Answer: Option 'C' is correct.

Step-by-step explanation:

Since we have given that

Let the principal amount be 'x'.

First rate of interest = 2%

Second rate of interest = 4%

Number of years = 1

Amount of interest he earned = $92

According to question,

(x* 2)/(100)+((x+800)* 4)/(100)=92\n\n(2)/(100)(x+2(x+800))=92\n\nx+2x+1600=(92* 100)/(2)\n\n3x+1600=4600\n\n3x=4600-1600\n\n3x=3000\n\nx=(3000)/(x)\n\nx=\$1000

So, First investment of $1000 at 2% and Second investment of $1000+$800=$1800 at 4%.

Hence, Option 'C' is correct.
x the first account  interest = x/100*2 = 2x/100 
(x + 800)/100 * 4 =( 4x + 3200)/100 
2x/100 + (4x + 3200)/100 = 92
2x + 4x + 3200 = 9200 
6x = 6000
x = 1000
C is the answer
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