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3 years ago

(20 Points)

Mathematics

1 answer:

storchak [24]3 years ago

5 0

Answer:

2nd option will be the answer (y=4x²+48x+146)

Step-by-step explanation:

y=4(x+6)²+2

y=4(x²+2*x*6+6²)+2 [(a+b)²=a²+2ab+b²]

y=4(x²+12x+36)+2

y=4(x²)+4(12x)+4(36)+2

y=4x²+48x+144+2

y=4x²+48x+146

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On a coordinate plane, the endpoints of line segment JK are J(−10,12) and K(8,−12). Point L lies on line segment JK and divides

lakkis [162]

Answer:

The coordinates of point L are (4.4 , -7.2) ⇒ answer A

Step-by-step explanation:

Assume that point L is (x , y)

Point L divides the line segment JK into two line segments such that

the ratio of JK to KL is 5 : 1

The coordinates of point J are (-10 , 12)

The coordinates of point K are (8 , -12)

∵ $x=\frac{x_{1}m_{2}+x_{2}m_{1}}{m_{1}+m_{2}}$

∵ $y=\frac{y_{1}m_{2}+y_{2}m_{1}}{m_{1}+m_{2}}$

Let $(x_{1},y_{1})$ = (-10 , 12) and $(x_{2},y_{2})$ = (8 , -12)

and $m_{1}:m_{2}$ = JL : KL

∵ JK : KL = 5 : 1

∵ JK = JL + KL

∴ 5 = JL + 1

Subtract 1 from both sides

∴ JL = 4

∴ JL : LK = 4 : 1

∴ $m_{1}:m_{2}$ = 4 : 1

∵ $x=\frac{(-10)(1)+(8)(4)}{4+1}$

∴ $x=\frac{-10+32}{5}$

∴ $x=\frac{22}{5}=4.4$

∴ <u><em>The x-coordinate of point L is 4.4</em></u>

∵ $y=\frac{(12)(1)+(-12)(4)}{4+1}$

∴ $y=\frac{12+(-48)}{5}$

∴ $y=\frac{-36}{5}=-7.2$

∴ <u><em>The y-coordinate of point L is -7.2</em></u>

* The coordinates of point L are (4.4 , -7.2)

6 0

4 years ago

Problem<br>3x - 12 = 48

Liula [17]

Answer:

x = 20

Step-by-step explanation:

To solve this, your goal should be to get x by itself in front of the equal sign. To do this, first add 12 to both sides of the equal sign. This gets rid of the -12 since -12 + 12 = 0.

3x - 12 + 12 = 48 + 12

3x = 60

The last step is to divide 3 from both sides.

3x / 3 = x.

60 / 3 = 20.

This leaves you with x = 20 which is the answer.

4 0

3 years ago

Read 2 more answers

segment CD has endpoints at C(0, 3) and D(0, 8). If the segment is dilated by a factor of 2 about point C, what is the length of

Julli [10]

The length of the image of segment CD is 10 units

<h3>How to determine the length?</h3>

The given parameters are:

C = (0,3)

D = (0,8)

Because both points are on the same x-coordinate, the length of CD is;

CD = 8 -3

CD = 5

The length of the image is then calculated as:

C'D' = CD * 2

This gives

C'D' = 5 * 2

Evaluate

C'D' = 10

Hence, the length of the image of segment CD is 10 units