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3 years ago

WILL MARK BRAINLIEST!!!

Mathematics

1 answer:

babymother [125]3 years ago

8 0

Answer: $-2$

Step-by-step explanation:

To find the slope of the line , we will write the equation in the form:

$y = mx + x$

where:

$m =$ slope

$c =$ y - intercept.

To write $4x + 2y = 12$ in this form , we will make y the subject of the formula.

Subtract 4x from both sides

$2y = -4x + 12$

Divide through by 2 $y = -2x + 6$

Therefore :

$slope = -2$

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Quadrilateral ABCD with vertices A(0, 6), B(-3, -6), C(-9, -6), and D(-12, -3): a) dilation with scale factor of 1/3 centered at

Oksanka [162]

a) The points of the new quadrillateral are $A'(x,y) = (0, 2)$ , $B'(x,y) = (-1, -2)$ , $C'(x,y) = \left(-3,-2\right)$ and $D'(x,y) = (-4, -1)$ , respectively.

b) The points of the new quadrillateral are $A'(x,y) = (-5, 5)$ , $B'(x,y) = (-8,-7)$ , $C'(x,y) = (-13, -7)$ and $D'(x,y) = (-17, -4)$ , respectively.

<h3>How to perform transformations with points</h3>

a) A dillation centered at the origin is defined by following operation:

$P'(x,y) = k\cdot P(x,y)$ (1)

Where:

$P(x,y)$ - Original point
$P'(x,y)$ - Dilated point.

If we know that $k = \frac{1}{3}$ , $A(x,y) = (0,6)$ , $B(x,y) = (-3,-6)$ , $C(x,y) = (-9, -6)$ and $D(x,y) = (-12, -3)$ , then the new points of the quadrilateral are:

$A'(x,y) = \frac{1}{3}\cdot (0,6)$

$A'(x,y) = (0, 2)$

$B'(x,y) = \frac{1}{3} \cdot (-3,-6)$

$B'(x,y) = (-1, -2)$

$C'(x,y) = \frac{1}{3}\cdot (-9,-6)$

$C'(x,y) = \left(-3,-2\right)$

$D'(x,y) = \frac{1}{3}\cdot (-12,-3)$

$D'(x,y) = (-4, -1)$

The points of the new quadrillateral are $A'(x,y) = (0, 2)$ , $B'(x,y) = (-1, -2)$ , $C'(x,y) = \left(-3,-2\right)$ and $D'(x,y) = (-4, -1)$ , respectively. $\blacksquare$

b) A translation along a vector is defined by following operation:

$P'(x,y) = P(x,y) +T(x,y)$ (2)

Where $T(x,y)$ is the transformation vector.

If we know that $T(x,y) = (-5,-1)$ , $A(x,y) = (0,6)$ , $B(x,y) = (-3,-6)$ , $C(x,y) = (-9, -6)$ and $D(x,y) = (-12, -3)$ ,

$A'(x,y) = (0,6) + (-5, -1)$

$A'(x,y) = (-5, 5)$

$B'(x,y) = (-3, -6) + (-5, -1)$

$B'(x,y) = (-8,-7)$

$C'(x,y) = (-9, -6) + (-5, -1)$

$C'(x,y) = (-13, -7)$

$D'(x,y) = (-12,-3)+(-5,-1)$

$D'(x,y) = (-17, -4)$

The points of the new quadrillateral are $A'(x,y) = (-5, 5)$ , $B'(x,y) = (-8,-7)$ , $C'(x,y) = (-13, -7)$ and $D'(x,y) = (-17, -4)$ , respectively. $\blacksquare$

To learn more on transformation rules, we kindly invite to check this verified question: brainly.com/question/4801277

7 0

2 years ago

How do you solve 800m 35cm-154m 49cm for the smaller unit?

bearhunter [10]

1 m = 100 cm
800 m = 800 x 100 = 80000 cm
Therefore, 800 m 35 cm = 80000 cm + 35 cm = 80035 cm

Also, 154 m = 154 x 100 = 15400 cm
Therefore, 154 m 49 cm = 15449 cm

Therefore, <span>800m 35cm - 154m 49cm = 80035 cm - 15449 cm = 64586 cm = 645m 86cm</span>

4 0

2 years ago

The length of the rectangle is 5 inches more than the width. The perimeter of the rectangle is 42 inches. Write an equation to m

Sunny_sXe [5.5K]

Answer:

<h2>Length = 13 in. </h2>

Step-by-step explanation:

perimeter of a rectangle (P) = 2L + 2W

where;

P = 42 in.

Length (L) = 5 + W

Find:

length (L) of the rectangle

solution:

P = 2L + 2W

42 = 2(5 + W) + 2W

42 = 10 + 2W + 2W

42 - 10 = 4W

32 = 4W

W = 32/4

W = 8

Length (L) = 5 + W

= 5 + 8

= 13 in

proof:

42 = 2(13) + 2(8)

42 = 42 in

4 0

3 years ago

Find the difference <br> a. 41- 275 <br> b. -15 - 47<br> c. -72 - (-151) <br> d. 612 - (-144)

Gekata [30.6K]

Answer:

41-275=234

15-47=62

-72-{151}=223

612-144=174

Step-by-step explanation:

6 0

3 years ago

Triangle ABC and Triangle DEF are similar. For triangle ABC, AB = 2x , AC = 24 inches and BC = 20. For triangle DEF, EF = 5 and

Norma-Jean [14]

X=8.

Following the similarity statement, we know that AC is to DF as BC is to EF. The ratio would be:

24/(x-2) = 20/5

Cross multiply:
24*5 = 20(x-2)

Use the distributive property:
120 = 20x - 40

Add 40 to both sides:
120+40 = 20x - 40 + 40
160 = 20x

Divide both sides by 20:
160/20 = 20x/20
8 = x

8 0

2 years ago