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3 years ago

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When a shape is dilated, the _________ of the lengths in the image to the corresponding lengths in the pre-image are equal to th

e scale factor.
A. ratios
B. lengths
C. scale factors
D. proportions

1 answer:

Burka [1]3 years ago

4 0

When a shape is dilated the RATIOS of the lengths in the image to the corresponding lengths in the preimage are equal to the scale factor

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Write the equation of the line shown in point-slope form. (2,1) (3,8)

Ulleksa [173]

<u>Answer:</u>

The line equation that passes through the given points is 7x – y = 13

<u>Explanation:</u>

Given:

Two points are A(2, 1) and B(3, 8).

To find:

The line equation that passes through the given two points.

Solution:

We know that, general equation of a line passing through two points (x1, y1), (x2, y2) in point slope form is given by

$\frac{(y- y1)}{(x-x_1)}= \frac{((y_2- y_1)}{(x_2- x_1 )}$

${(y- y1)= \frac{((y_2- y_1)}{(x_2- x_1 )}\times(x-x_1)$ ..........(1)

here, in our problem x1 = 3, y1 = 8, x2 = 2 and y2 = 1.

Now substitute the values in (1)

$(y-8) = \frac{(1 - 8)}{(2 - 3)}\times(x- 3)$

$(y -8) = \frac{(- 7)}{(-1)}(x-3)$

y – 8 = 7(x – 3)

y – 8 = 7x – 21

7x – y = 21 – 8

7x – y = 13

Hence, the line equation that passes through the given points is 7x – y = 13

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3 years ago

Please help me with this and thank you

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Billy flips the penny ten times in a row. On the first nine flips the penny landed on heads

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2 years ago

A cake manufacturer boxes Swiss chocolate and German chocolate cakes at one site. A box of Swiss chocolate cake contains 0.55 lb

Kobotan [32]

Answer:

2,500 German chocolate cake boxes.

1,500 Swiss chocolate cake boxes.

Step-by-step explanation:

Let 'S' be the number of Swiss chocolate cakes boxed and 'G' the number of German cholocate cakes boxed. If all of the available ingredients are used:

$0.55*S +0.59*G = 2,300\\0.45*S+0.41*G = 1,700$

Solving the linear system above:

$(0.55 *S +0.59*G)- \frac{0.55}{0.45} (0.45*S+0.41*G)= 2,300-\frac{0.55}{0.45}*1,700*\\0.088888*G = 222.222\\G=2,500\\S =\frac{2,300-2,500*0.59}{0.55}\\S=1500$

2,500 German chocolate cake boxes and 1,500 Swiss chocolate cake boxes can be made each day.

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3 years ago

balandron [24]

Answer:

The sequence of transformations that maps triangle XYZ onto triangle X"Y"Z" is <u>translation 5 units to the left, followed by translation 1 unit down, and relfection accross the x-axis</u>.

Explanation:

By inspection (watching the figure), you can tell that to transform the triangle XY onto triangle X"Y"Z", you must slide the former 5 units to the left, 1 unit down, and, finally, reflect it across the x-axys.

You can check that analitically

Departing from the triangle: XYZ

<u>Translation 5 units to the left</u>: (x,y) → (x - 5, y)

Vertex X: (-6,2) → (-6 - 5, 2) = (-11,2)

Vertex Y: (-4, 7) → (-4 - 5, 7) = (-9,7)

Vertex Z: (-2, 2) → (-2 -5, 2) = (-7, 2)

<u>Translation 1 unit down</u>: (x,y) → (x, y-1)

(-11,2) → (-11, 2 - 1) = (-11, 1)

(-9,7) → (-9, 7 - 1) = (-9, 6)

(-7, 2) → (-7, 2 - 1) = (-7, 1)

<u>Reflextion accross the x-axis</u>: (x,y) → (x, -y)

(-11, 1) → (-11, -1), which are the coordinates of vertex X"

(-9, 6) → (-9, -6), which are the coordinates of vertex Y""

(-7, 1) → (-7, -1), which are the coordinates of vertex Z"

Thus, in conclusion, it is proved that the sequence of transformations that maps triangle XYZ onto triangle X"Y"Z" is translation 5 units to the left, followed by translation 1 unit down, and relfection accross the x-axis.

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3 years ago