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2 years ago

ΔABC is dilated using a scale factor of 12 to produce ΔA'B'C'. Select all of the statements that apply to the transformation.

Mathematics

1 answer:

GalinKa [24]2 years ago

3 0

Answer:

Options (3) and (6)

Step-by-step explanation:

ΔABC is a dilated using a scale factor of $\frac{1}{2}$ to produce image triangle ΔA'B'C'.

Since, dilation is a rigid transformation,

Angles of both the triangles will be unchanged or congruent.

m∠A = m∠A' and m∠B = m∠B'

Since, sides of ΔA'B'C' = $\frac{1}{2}$ of the sides of ΔABC

Area of ΔA'B'C' = $\frac{1}{2}(\text{Area of triangle ABC})$

Area of ΔABC > Area of ΔA'B'C'

Since, angles of ΔABC and ΔA'B'C' are congruent, both the triangles will be similar.

ΔABC ~ ΔA'B'C'

Therefore, Option (3) and Option (6) are the correct options.

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You are given rectangle ABCD on the grid shown and are told that the figure is to be dilated from the origin, but you are not to

Alenkinab [10]

Answer:

The new coordinates of point D(-4, -4) after the dilation by a scale factor of 1/2 will be: D'(-2, -2)

Step-by-step explanation:

The rectangle ABCD on the grid shown is attached below.

From the grid, it is clear that the coordinates of point D are (-4, -4)

i.e. D(-4, -4)

As we are told that the figure is to be dilated from the origin.

A dilation tends to stretch or shrink the original figure, depending upon scale factor.

If scale factor > 1, then the image gets enlarged

If the scale factor < 1, the image gets reduction

When we dilate a figure from the origin by any scale factor, the new coordinates of the image can be obtained by multiplying the scale factor with the coordinates of the original object/figure.

As the the coordinates of point D are (-4, -4). If we dilate the figure by a scale factor of 1/2, the new new coordinates of point D would be:

P(x, y) → P'(1/2x, 1/2y)

D(-4, -4) → D'(-4/2, -4/2) or D'(-2, -2)

Therefore, the new coordinates of point D(-4, -4) after the dilation by a scale factor of 1/2 will be: D'(-2, -2)

7 0

2 years ago

Which shows one way to determine the factors of 12x3 – 2x2 + 18x – 3 by grouping?

Debora [2.8K]

Option A

$2x^2(6x-1) + 3(6x-1)$ is one way to determine the factors of $12x^3-2x^2+18x-3$ by grouping

Solution:

Factoring by grouping means that you will group terms with common factors before factoring

Given expression is:

$12x^3-2x^2+18x-3$

Group the first two terms together and then the last two terms together.

$(12x^3-2x^2)+(18x-3)$

We can see that $2x^2$ is common in first two terms

And 3 is common in last two terms

Factor them out

$(12x^3-2x^2)+(18x-3) = 2x^2(6x-1) + 3(6x-1)$

$2x^2(6x-1) + 3(6x-1)$

Thus option A is correct

6 0

2 years ago

Read 2 more answers

Three highways connect city A with city B. Two highways connect city B with city C.

QveST [7]

(a) The probability that there is no open route from A to B is (0.2)^3 = 0.008.
Therefore the probability that at least one route is open from A to B is given by: 1 - 0.008 = 0.992.
The probability that there is no open route from B to C is (0.2)^2 = 0.04.
Therefore the probability that at least one route is open from B to C is given by:
1 - 0.04 = 0.96.
The probability that at least one route is open from A to C is:
$0.992\times0.96=0.9523$

(b)
α The probability that at least one route is open from A to B would become 0.9984. The probability in (a) will become: $0.9984\times0.96=0.95846$

β The probability that at least one route is open from B to C would become 0.992. The probability in (a) will become:
$0.992\times0.992=0.9841$

Gamma: The probability that a highway between A and C will not be blocked in rush hour is 0.8. We need to find the probability that there is at least one route open from A to C using either a route A to B to C, or the route A to C direct. This is found by using the formula:
$P(A\cup B)=P(A)+P(B)-P(A\cap B)$
$0.9523+0.8-(0.9523\times0.8)=0.99$
Therefore building a highway direct from A to C gives the highest probability that there is at least one route open from A to C.

4 0

2 years ago

Aldo invested in a savings bond for 6 years and was paid simple interest at an annual rate of 4% the total interest that he earn

bonufazy [111]

Answer:

$723.66

Step-by-step explanation:

$x(1 + 4 {)}^{6} = x + 192$