MATHEMATICS HIGH SCHOOL

Solve for x and y in the following set of equation 6x+5xy-5y=8
X+y=3

Please help this is important

Answers

Answer 1
Answer: STEP 1:

6x+5xy-5y=8\n \n 6x+5y\left( x-1 \right) =8\n \n 5y\left( x-1 \right) =8-6x\n \n 5y\left( x-1 \right) =2\left( 4-3x \right) \n \n \frac { 1 }{ 5\left( x-1 \right) } \cdot 5y\left( x-1 \right) =2\left( 4-3x \right) \cdot \frac { 1 }{ 5\left( x-1 \right) } \n \n y=\frac { 2\left( 4-3x \right) }{ 5\left( x-1 \right) }

STEP 2:

x+y=3\n \n y=3-x

STEP 3:

This means that...

3-x=\frac { 2\left( 4-3x \right) }{ 5\left( x-1 \right) } \n \n \left\{ 5\left( x-1 \right) \right\} \left( 3-x \right) =2\left( 4-3x \right) \n \n \left( 5x-5 \right) \left( 3-x \right) =8-6x\n \n 15x-5{ x }^( 2 )-15+5x=8-6x\n \n 20x-5{ x }^( 2 )-15=8-6x\n \n 5{ x }^( 2 )+8-6x+15-20x=0\n \n 5{ x }^( 2 )-26x+23=0

STEP 4:

Which means that...

\n \frac { 1 }{ 5 } \cdot \left( 5{ x }^( 2 )-26x+23 \right) =0\cdot \frac { 1 }{ 5 } \n \n { x }^( 2 )-\frac { 26 }{ 5 } x+\frac { 23 }{ 5 } =0\n \n { x }^( 2 )-\frac { 26 }{ 5 } x=-\frac { 23 }{ 5 }

Which means that...

\ \n { \left( x-\frac { 13 }{ 5 } \right) }^( 2 )-{ \left( \frac { 13 }{ 5 } \right) }^( 2 )=-\frac { 23 }{ 5 } \n \n { \left( x-\frac { 13 }{ 5 } \right) }^( 2 )-\frac { 169 }{ 25 } =-\frac { 23 }{ 5 } \n \n { \left( x-\frac { 13 }{ 5 } \right) }^( 2 )=-\frac { 115 }{ 25 } +\frac { 169 }{ 25 } \n \n { \left( x-\frac { 13 }{ 5 } \right) }^( 2 )=\frac { 54 }{ 25 }

Which means that...

\n \n x-\frac { 13 }{ 5 } =\pm \frac { \sqrt { 54 } }{ 5 } =\pm \frac { 3\sqrt { 6 } }{ 5 } \n \n \therefore \quad x=\frac { 13 }{ 5 } \pm \frac { 3\sqrt { 6 } }{ 5 }

STEP 5:

When:

x=\frac { 13 }{ 5 } +\frac { 3\sqrt { 6 } }{ 5 }

.........

y=3-\left( \frac { 13 }{ 5 } +\frac { 3\sqrt { 6 } }{ 5 } \right) \n \n y=\frac { 15 }{ 5 } -\frac { 13 }{ 5 } -\frac { 3\sqrt { 6 } }{ 5 } \n \n y=\frac { 15-13-3\sqrt { 6 } }{ 5 } \n \n y=\frac { 2-3\sqrt { 6 } }{ 5 }

STEP 6:

When :

x=\frac { 13 }{ 5 } -\frac { 3\sqrt { 6 } }{ 5 }

...........

y=3-\left( \frac { 13 }{ 5 } -\frac { 3\sqrt { 6 } }{ 5 } \right) \n \n y=\frac { 15 }{ 5 } -\frac { 13 }{ 5 } +\frac { 3\sqrt { 6 } }{ 5 } \n \n y=\frac { 15-13+3\sqrt { 6 } }{ 5 } \n \n y=\frac { 2+3\sqrt { 6 } }{ 5 }

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What is the range and domain of the parent function f(x) = |x|

Find the remainder when f(x) is divided by (x - k)
f(x) = 5x4 + 8x3 + 4x2 - 5x + 67; k = 2

Answers

Answer: The remainder when f(x) is divided by (x-2) is 217.

Step-by-step explanation:

Since we have given that

f(x) = 5x^4 + 8x^3 + 4x^2 - 5x + 67

And it is divided by g(x)=(x-k)

Here, k= 2

So, g(x)= x-2

So, we need to find the remainder .

By using "Remainder theorem ":

Put\ g(x)=0\n\nx-2=0\n\nx=2

Now,

f(2)=5(2)^4 + 8(2)^3 + 4(2)^2 - 5(2) + 67\n\nf(2)=80+64+16-10+67\n\nf(2)=217

Hence, the remainder when f(x) is divided by (x-2) is 217.

It is to be solved by reminder thorem
f(x)/(x-k) will have reminder f(k), 
so, f(2) = 5*(2^4) + 8 *(2^3) +4* (2^2) -5(2) +67

             =5*16 + 8*8 +4*4 -5*2 +67
             =80 + 64 + 16 -10 +67

             = 217

What is twenty divided by two, multiplied by the power of three.

Answers

The answer would be 1000. Hope this helps.

Hi is this true or false? Help?

Answers

Answer:

False .

Step-by-step explanation:

On a road map, the distance between 2 cities is 2.5 inches. The map scale is 1 inch: 30 miles. What is the actual distance between the cities?

Answers

Answer:

75 miles.

Step-by-step explanation:

By proportion the actual distance is 2.5 * 30

=    75 miles

Debbie is making an abstract painting with two triangles. The dimensions of the painting are shown below:Two triangles share the same height of 8 inches. One triangle has a base of 6 inches and the other is 10 inches.

The total area of the two triangles is _____ square inches.

Answers

Debbie's abstractpainting are two in numbers both having the same height. since we know the area of a triangle to be

Area = 1/2*Base*Height

Total area =Area of  Triangle A+ Area of  Triangle B

= 24+40

=64 square inches

Given data

Both Triangles share the same height = 8 inches

For Triangle A

Base = 6 inches

Area = 1/2 Base*Height

Area = 1/2*8*6

Area = 24 square inches

For Triangle B

Base = 10 inches

Area = 1/2 Base*Height

Area = 1/2*8*10

Area = 40 square inches

Total = 24+40

Total = 64 square inches

Learn more about area of triangle here

brainly.com/question/2607596
The surface of the triangle count formula
A = b*h*1/2
A - area
b - base
c - height
The first triangle
A₁ = b₁*h = 6in * 8in *1/2= 24in²

The second triangle
A₂ b₂*h = 10in * 8in*1/2 = 40in²

The total area of the two triangles is 24in² + 40in² = 64 square inches

QUESTION 7 of 10: Assuming you sleep eight hours per day, how many hours do you have left for other activities during the week?100 hours
112 hours
118 hours
120 hours

Answers

The CUHrect answer B, 112 hours
-Yours Truly, Super-Cuh
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