The implication x => y is equivalent to ??

PLEASE HELP!!! Trapezoid ABCD was dilated to create trapezoid A'B'C'D'. Which statements are true about the trapezoids? Check al

hichkok12 [17]

Answer:

Option A , B and D are true.

The statement which are true:

The length of side AD is 4 units

The length of side A'D' is 8 units.

The scale factor is, $\frac{1}{2}$

Step-by-step explanation:

Given in figure trapezoid ABCD;

The coordinates of ABCD are:

A= (-4, 0)

B = (-2, 4)

C = (2,4)

D = (4, 0)

Since, trapezoid ABCD was dilated to create trapezoid A'B'C'D' as shown in figure;

The coordinates of A'B'C'D' are;

A' =(-2, 0)

B'=(-1, 2)

C' = (1, 2)

D' = (2, 0)

First calculate the length of AD

Using Distance formula for any two points i.e,

$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Since, A = (-4, 0) and D = (4, 0)

then;

Length of AD = $\sqrt{(4-(-4))^2+(0-0)^2} = \sqrt{(4+4)^2} =\sqrt{64}=8$ units

Therefore, the length of side AD is, 8 units.

Similarly find the length of A'D'.

Where A' = (-2, 0) and D' =(2,0)

Using distance formula:

Length of A'D' = $\sqrt{(2-(-2))^2+(0-0)^2} =\sqrt{(2+2)^2}= \sqrt{4^2} = 4$

Therefore, the length of side A'D' is, 4 units.

Now, find the slope of CD and C'D'

where C =(2, 4) , D = (4, 0) , C' = (1, 2) and D' =(2,0)

using slope formula for any two points is given by:

$Slope = \frac{y_2-y_1}{x_2-x_1}$

$Slope of CD = \frac{0-4}{4-2} = \frac{-4}{2} = -2$

Similarly,

$Slope of C'D' = \frac{0-2}{2-1} = \frac{-4}{2} = -2$

Since, Sides CD and C'D' have same slope i.e, -2

Scale factor(k) states that every coordinate of the original figure has been multiplied by the scale factor.

If k > 1, then the image is an enlargement.

if 0<k< 1, then the image is a reduction.

If k = 1, then the figure and the image are congruent.

The rule for dilation with scale factor(k) is;

$(x, y) \rightarrow (kx , ky)$

To find the scale factor:

A = (-4, 0) and A' = (-2, 0)

$(-2, 0) \rightarrow (-4k , 0)$

On comparing we ghet;

-4k = -2

Divide -4 both sides we get;

$k = \frac{1}{2}$

∴ The Scale factor is, $k = \frac{1}{2}$

Since, k < 1 which implies the image is a reduction.

Therefore, the statements which are true regarding about trapezoids are;

The length of side AD is 4 units

The length of side A'D' is 8 units.

The scale factor is, $\frac{1}{2}$

6 0

3 years ago

If the null hypothesis of an experiment is “The true mean weight of the piglets is at least 39lbs” what is the alternate hypothe

AlexFokin [52]

Answer:

“The true mean weight of the piglets is at most 39lbs”would be the alternate hypothesis.

Step-by-step explanation:

Given that the null hypothesis of an experiment is “The true mean weight of the piglets is at least 39lbs”

We have to find the alternate hypothesis.

In hypothesis testing, alternate is the opposite of null hypothesis. If null hypothesis supports one statement alternate hypothesis opposes it. In other words, alternate hypothesis would be the negative of the claim of null hypothesis.

Here the null hypothesis of an experiment is “The true mean weight of the piglets is at least 39lbs”

i.e H0: $x bar\geq 39 lbs$

So alternate hypothesis

Ha: $x bar\leq 39 lbs$

8 0

3 years ago

Can i have help please

galina1969 [7]

Answer:

A

Step-by-step explanation:

8 0

3 years ago

Suppose that farmers grew and unexpectedly large number of tomatoes this year .how would this increase in production affect the

zloy xaker [14]

Answer:

The price would go down as people would be more willing to buy cheaper potatoes and the producers would want to sell them for a lower price to get rid of them easy and fast.

3 0

3 years ago

Read 2 more answers

Two pumps connected in parallel fail independently of one another on any given day. The probability that only the older pump wil

Bogdan [553]

Answer : Probability that the pumping system will fail on any given day = 0.005

Explanation:

Probability that only older pump fail = P(A) = 0.10

Probability that only newer pump fail = P(B) = 0.05

Since they are independent events ,

then the conditions will be

P(A∩B) = P(A). P(B)

= 0.10 ×0.05

= 0.005

Hence, the probability will fail on any given day = 0.005

8 0

3 years ago

The implication x => y is equivalent to ??​

The implication x => y is equivalent to ??