Solve the system of equations using the combined method <br> 2x-5y=-3<br> 8x-5y=33

Find the point on the line y = 3x + 2 that is closest to the origin.

anzhelika [568]

1.
the slope of the line y=3x+2 is the coefficient of x, that is 3.

2.
the slope of any line perpendicular to the line y=3x+2, is m, such that:

$3*m=-1$

so $m= \frac{-1}{3}$

3.
so any line with equation y=-1/3x+k is perpendicular to y=3x+2.

moreover, the line y=-1/3x (so k=0) is the line passing through the origin
(0, 0) and perpendicular to y=3x+2

4. This means that the closest point of y=3x+2 to the origin is the intersection point of lines y=3x+2 and y=-1/3x

5.
to find this point:

3x+2=(-1/3)x
x(3+1/3)=-2
x(9/3+1/3)=-2

x*10/3=-2

$x= \frac{-2*3}{10} = \frac{-6}{10}=-0.6$

thus y is : (-1/3)(-6/10)=0.2

Answer: (-0.6, 0.2)

3 0

3 years ago

How will the area of the circle change if it is dilated by a scale factor of 3?

Nesterboy [21]

The area would be 1/2 the original

7 0

3 years ago

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While packing for thier cross-country move, the chen family uses a crate that has the shape of a cube. The Chens want to pack a

Brrunno [24]

If the framed picture is shaped like a square and has a 12 square foot surface area, then the answer is yes, it will fit flush against the edge of the crate.

Given Part A:

the volume of the cube = 64 cubic feet

therefore, ∛64 = 4 feet

hence one edge measures 4 feet.

Now for Part B:

the area of the square is 12 square feet.

hence, √12 = 3.36 feet.

we can observe that 3.46<4

which indicates that the area covered by the painting is less than that of the one side of the crate, which makes it easy for the painting to fit in the crate.

Hence the painting will fit a side of crate.

Learn more about Area and Perimeter here:

brainly.com/question/24571594

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Your question was incomplete. Please find the missing content here.

While packing for their cross-country move, the Chen family uses a that has the shape of a cube. PART A PART B If the crate has the volume V = 64 cubic feet, The Chens want to pack a large, framed painting. If an area of 12 square feet , will the painting fit flat what is the length of one edge? the framed painting has the shape of a square with against a side of the crate? Explain.

3 0

2 years ago

Mrs. DeMarco wants to estimate the length of her porch so she knows how much paint to buy. What is the best benchmark for her to

Zigmanuir [339]

The answer c ,I hope I’m right

8 0

3 years ago

2y=-x+9<br>3×-6y=-15 whats the solution to the system

liq [111]

Answer:

Step-by-step explanation:

2y = -x +9

3x - 6y = -15

The solution is the value of x and y that will make the two equations true in the same time.

3x-6y = -15; divide both sides by 3

x-2y = -5; substitute 2y for -x+9 because the first equation tell us they are equal

x-(-x+9) = -5; open parenthesis

x+x-9 = -5 ; add 9 to both sides and combine like terms

2x = -5 +9; 2x = 4; divide both sides by 2

x= 2

Substitute x for 2

2y = -x+9 ; 2y = -2 +9 ; 2y = 7; y = 7/2 = 3.5

Solution is (2, 3.5)

8 0

2 years ago

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Solve the system of equations using the combined method 2x-5y=-3 8x-5y=33