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3 years ago

If triangle ABC is dilated using a scale factor of 2, what will be the coordinates of A after the transformation

Mathematics

1 answer:

harkovskaia [24]3 years ago

8 0

Answer:

$A' = (-4,4)$

Step-by-step explanation:

Given

$A = (-2,2)$ $B = (1,3)$ $C = (1,0)$

$k =2$ --- scale factor

Required

Determine A'

This is calculated as:

$A' = A * k$

$A' = (-2,2) * 2$

$A' = (-2 * 2,2 * 2)$

$A' = (-4,4)$

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What is the x-coordinate of the solution of the system? x+y+3 4x-y=-38

steposvetlana [31]

Note: I am assuming the first equation is:

x+y = 3

Answer:

The solution to the system of equations is:

(x, y) = (-2, 36)

Therefore, the x-coordinate of the solution of the system

x = -2

Step-by-step explanation:

Given the system of equations

$\begin{bmatrix}x+y=34\\ x-y=-38\end{bmatrix}$

subtracting the equations

$x-y=-38$

$-$

$\underline{x+y=34}$

$-2y=-72$

solve -2y for y

$-2y=-72$

Divide both sides by -2

$\frac{-2y}{-2}=\frac{-72}{-2}$

$y=36$

For x+y=34 plug in y = 36

$x+36=34$

Subtract 36 from both sides

$x+36-36=34-36$

Simplify

$x=-2$

Thus, the solution to the system of equations is:

(x, y) = (-2, 36)

Therefore, the x-coordinate of the solution of the system

x = -2

6 0

3 years ago

Whats a word problem for (20r -8) ÷4

antoniya [11.8K]

Answer:

5r-2

Step-by-step explanation:

8 0

3 years ago

Find the number b such that the line y = b divides the region bounded by the curves y = 25x2 and y = 1 into two regions with equ

Dennis_Churaev [7]

Answer:

y=1/∛4 divides the area in half

Step-by-step explanation:

since the minimum value of x² is 0 (for x=0 ) and for y=1

1 = 25*x² → x= ±√(1/25) = ±1/5

then the total area between y=1 and y = 25*x² is bounded to x=±1/5 and y=0 . Since there is a direct relationship between x and y , we can find the value of x=a that divides the region in 2 of the same area. thus

Area below x=C = Area above x=C

Area below x=C = Total area - Area below x=C

2*Area below x=C = Total area

Area below x=C = Total area /2

∫ 25*x² dx from x=c to x=-c = 1/2 ∫ 25*x² dx from x=1/5 to x=-1/5

25*[c³/3 - (-c)³/3] = 25/2 * [(1/5)³/3 - (-1/5)³/3]

2*c³/3 = (1/5)³/3

c = 1/(5*∛2)

thus

y=25* x² = 25*[1/(5*∛2)]² = 1/∛4

thus the line y=1/∛4 divides the area in half

4 0

3 years ago

Find the equation of a line that passes through the point (-2,3) and has a gradient of 3.

nadya68 [22]

Answer:

y = 3x+9

Step-by-step explanation:

The standard form of equation of a line is in the form y = mx + c

m is the gradient

c is the y intercept

Get the y-intercept

Substitute m = 3 and the point (-2, 3) into the formula y = mx+c

3 = 3(-2) + c

3 = -6+c

c = 3+6

c = 9

Get the required equation;

y = 3x + 9

Hence the required equation is y = 3x+9

5 0

3 years ago

Write the equation in vertex form and then find the vertex, focus, and directrix of a parabola with equation x=y^2+18y-2

kakasveta [241]

Answer:

Part 1) The vertex is the point (-83,-9)

Part 2) The focus is the point (-82.75,-9)

Part 3) The directrix is $x=-83.25$

Step-by-step explanation:

step 1

Find the vertex

we know that

The equation of a horizontal parabola in the standard form is equal to

$(y - k)^{2}=4p(x - h)$

where

p≠ 0.

(h,k) is the vertex

(h + p, k) is the focus

x=h-p is the directrix

In this problem we have

$x=y^{2} +18y-2$

Convert to standard form

$x+2=y^{2} +18y$

$x+2+81=y^{2} +18y+81$

$x+83=(y+9)^{2}$

This is a horizontal parabola open to the right

(h,k) is the point (-83,-9)

The vertex is the point (-83,-9)

step 2

we have

$x+83=(y+9)^{2}$

Find the value of p

$4p=1$

$p=1/4$

Find the focus

(h + p, k) is the focus

substitute

(-83+1/4,-9)

The focus is the point (-82.75,-9)

step 3

Find the directrix

The directrix of a horizontal parabola is

$x=h-p$

substitute

$x=-83-1/4$

$x=-83.25$

6 0

3 years ago