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2 years ago

Which equation describes a line parallel to y= 4x+ 5 through point (-2, 1)?

Mathematics

1 answer:

Tema [17]2 years ago

8 0

Hi there!

For a line to be PARALLEL, it must contain the same slope.

The given line has a slope of 4, so we can use the point-slope formula to solve:

$\large\boxed{y - y_1 = m(x - x_1)}$

y1 = y-coordinate of given point

x1 = x-coordinate of given point

m = slope

Plug in the values:

$y - 1 = 4(x - (-2))\\\\y - 1 = 4(x + 2)$

Simplify:

$y - 1 = 4x + 8\\\\\boxed{y = 4x + 9}$

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Segment FG begins at point F(-2, 4) and ends at point G (-2, -3). Segment FG is translated by (x, y) → (x – 3, y + 2) and then r

Mariana [72]

Answer:

The length of the segment F'G' is 7.

Step-by-step explanation:

From Linear Algebra we define reflection across the y-axis as follows:

$(x',y')=(-x, y)$ , $\forall\, x, y\in \mathbb{R}$ (Eq. 1)

In addition, we get this translation formula from the statement of the problem:

$(x',y') =(x-3,y+2)$ , $\forall \,x,y\in \mathbb{R}$ (Eq. 2)

Where:

$(x, y)$ - Original point, dimensionless.

$(x', y')$ - Transformed point, dimensionless.

If we know that $F(x,y) = (-2, 4)$ and $G(x,y) = (-2,-3)$ , then we proceed to make all needed operations:

Translation

$F''(x,y) = (-2-3,4+2)$

$F''(x,y) = (-5,6)$

$G''(x,y) = (-2-3,-3+2)$

$G''(x,y) = (-5,-1)$

Reflection

$F'(x,y) = (5, 6)$

$G'(x,y) = (5,-1)$

Lastly, we calculate the length of the segment F'G' by Pythagorean Theorem:

$F'G' = \sqrt{(5-5)^{2}+[(-1)-6]^{2}}$

$F'G' = 7$

The length of the segment F'G' is 7.

8 0

3 years ago

The bearing of Q from P is 150° and the bearing of P from R is 15°.if Q and R are 244metres and 324metres respectively from P.(i

Vedmedyk [2.9K]

CNBC cncncbcbfbfbfncbcbcnvncbbvbvn

5 0

3 years ago

PLEASE HELP!!

beks73 [17]

<span>Let x = the width
:
It says,"The length of a rectangle is 4 less than 3 times the width." write that as:
L = 3x - 4
:
If the perimeter is 40, find the dimensions of the rectangle.
:
We know: 2L + 2W = 40
:
Substitute (3x-4) for L and x for W
2(3x-4) + 2x = 40
:
6x - 8 + 2x = 40; Multiplied what's inside the brackets
:
6x + 2x = 40 + 8; do some basic algebra to find x; (added 8 to both sides)

:
8x = 48
:
x = 48/8
:
x = 6 which is the width
:
It said that L = 3x - 4, therefore:
L = 3(6) - 4
L = 18 - 4
L = 14; is the length
:
Check our solutions in the perimeter:
2(14) + 2(6) =
28 + 12 = 40</span>

8 0

3 years ago

Read 2 more answers

What is the answer to this equation?

Ivan

X < -5 is your answer

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3 years ago

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P= $1,000, t= 6, r= 11%, compounded annually (k = 1)

kobusy [5.1K]

Answer: well if p= $1000 and t=6 and r-11 % then 6k+11=1000 then 11- 1000 is 6k=989 divide 6/ 164.83 i think