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3 years ago

What series of transformations to quadrilateral ABCD map the quadrilateral onto quadrilateral EFGH to prove that ABCD≅EFGH ?

Mathematics

2 answers:

Alex17521 [72]3 years ago

7 0

B: a reflection across the x-axis followed by a translation 4 units right.

Comparing the points to their mapped images compares A to E, B to F, C to G, and D to H. In each point, the y-coordinate switches signs and the x-coordinate is subtracted by 4.

Reflections across the x-axis will switch the sign of the y-coordinate, and reflections across the y-axis will switch the sign of the x-coordinate. Since the y-coordinates are the ones whose sign changed, the points must have been reflected across the x-axis.

Translations to the left will cause the x-coordinate to increase, and translations to the right will case the x-coordinate to decrease. Since the x-coordinate of every point was subtracted, this means that the translation must have been to the right.

Ratling [72]3 years ago

5 0

Answer: The correct series of transformations is (A) a reflection across x-axis, and then a translation 4 units left.

Step-by-step explanation: We are given to select the correct series of transformations that map quadrilateral ABCD onto the quadrilateral EFGH so that ABCD≅EFGH.

The co-ordinates of the vertices of quadrilateral ABCD are A(2, 4), B(4, 5), C(5, 4) and D(4, 1).

The first transformation will be reflection across the X-axis - Here, the sign before the y-co-ordinate of each vertex will get changed.

After this transformation, the co-ordinates of the vertices become A'(2, -4), B'(4, -5), C'(5, -4) and D'(4, -1). This quadrilateral A'B'C'D' is shown in the attached figure.

The second transformation will be a translation of 4 units left - Here, the x-co-ordinate of each vertex will get decreased by 4 units.

After this transformation, the co-ordinates of the vertices changes to E(-2, -4), F(0, -5), G(1, -4) and H(0, -1).

Since these are the co-ordinates of the vertices of quadrilateral EFGH, so we prove that ABCD≅EFGH.

Thus, the correct transformations is given by option (A) a reflection across x-axis, and then a translation 4 units left.

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Engineers want to design seats in commercial aircraft so that they are wide enough to fit 95%of all males. (Accommodating 100%

Anarel [89]

Answer:

Upper P95 = 16.21in

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

$\mu = 14.4, \sigma = 1.1$

Upper P 95

This is the 95th percentile, which is X when Z has a pvalue of 0.95. So X when Z = 1.645.

Then

$Z = \frac{X - \mu}{\sigma}$

$1.645 = \frac{X - 14.4}{1.1}$

$X - 14.4 = 1.1*1.645$

$X = 16.21$

Upper P95 = 16.21in

3 0

2 years ago

Zoologists are studying two newly discovered species of insects in a previously unexplored section of rain forest. They estimate

salantis [7]

The population Pa of insect A after t years is given by the equation
Pa = 1.3(1-0.038)^t
while the population Pb of insect B after t years is
Pb = 2.1(1-0.046)^t

We equate the above expressions to find the number of years t it will take the two populations to be equal:
Pa = Pb
1.3(1-0.038)^t = 2.1(1-0.046)^t
1.3(0.962)^t = 2.1(0.954)^t
These are the equations that can be used to determine how long it will be before the populations of the two species are equal.

We can now solve for t:
(0.962)^t / (0.954)^t = 2.1/1.3
(0.962/0.954)^t = 2.1/1.3
After taking the log of both sides of our equation, number of years t is
t = log (2.1/1.3) / log (0.962/0.954)
t = 57 years
Therefore, it will take 57 years for the population of insect A to equal the population of insect B.

8 0

3 years ago

Read 2 more answers

Write an expression for the perimeter of the house use the work you completed in parts A and B to guide you (the numbers in the

Bas_tet [7]

Answer:

The total length of Valerie’s walls is (2.5 × 4) + (21.25 × 3) + 32.

The total length of Seth’s walls is 3.5 + (22.75 × 2) + 58.

To find the expression for the perimeter of the house, add Valerie’s expression to Seth’s:

(2.5 × 4) + (21.25 × 3) + 32 + 3.5 + (22.75 × 2) + 58.

Step-by-step explanation:

its the platho answer so change it a bit

8 0

2 years ago

A sled is being pulled across a floor by two ropes such that the angle between them is 40°. If the forces on the ropes are 100 p

Dafna1 [17]

Answer:

option 4 ⇒ 236 lb.

Step-by-step explanation:

Best explanation of the question is as shown in the attached figure.

we will use the parallelogram method to calculate resultant force.

to get the length of the resultant force ⇒ use the cosines law

The cosine law is a² = b² + c² - 2 * b * c * cos (∠A)

Applying at the question where b = F₁ , c = F₂ and ∠A = ∠x

Given that F₁ = 100 pounds , F₂ = 150 pounds and ∠x = 180° - 40° = 140°

∴ (Resultant force)² = 100² + 150² - 2 * 100 * 150 * cos (∠140) = 55481

∴ Resultant force = √55481 = 235.54 ≅ 236 pounds

The answer is option 4 ⇒ 236 lb.

8 0

3 years ago

Use the equation 2,401 = 76 – 2x. What power of 7 is 2,401?

zaharov [31]

Comment
I'm going to take a guess at this and say what you meant is 2401 = 7^(6 - 2x)

Step One
Find out the power of 7 that will equal 2401.
You could do it like this.
7^y = 2401 and just guess at some values.

y 7^y
1 7
2 49
3 7 * 7 * 7 = 343
4 7 * 7 * 7 * 7 = 2401 So the answer is 4

7^4 = 2401

Step 2
Equate the powers.
2401 = 7^(6 - 2x)
7^4 = 7^ (6 - 2x)
4 = 6 - 2x Subtract 6 from both sides.
4 - 6 = - 2x
-2 = - 2x divide by - 2
-2/-2 = x
x = 1 <<<<<<<<<<<<<answer

7 0

3 years ago

Read 2 more answers

What series of transformations to quadrilateral ABCD map the quadrilateral onto ​ quadrilateral EFGH to prove that ABCD≅EFGH ?

What series of transformations to quadrilateral ABCD map the quadrilateral onto quadrilateral EFGH to prove that ABCD≅EFGH ?