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3 years ago

The triangles shown are congruent by the SSS congruence theorem.

Mathematics

2 answers:

Keith_Richards [23]3 years ago

6 0

Answer:

B. Rotation, then Translation, then Reflection

Step-by-step explanation:

I got the answer right on Ingenuity.

The site doesn't let me put Ingenuity with an E instead of an I at the front.

denis23 [38]3 years ago

3 0

1. Let's check the problem backwards. So let's map A"B"C" to ABC

2. We first need to reflect A"B"C" to A"B"C' with A"B"" as the axis of rotation.

3. Then we shift a few units up (translation) A"B"C' to A'B'C

4. Finally we rotate A'B'C around C to map the triangle onto ABC

going backwards we get the answer: b

<span>b.rotation, then translation, then reflection</span>

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Calculus Problem

Roman55 [17]

The two parabolas intersect for

$8-x^2 = x^2 \implies 2x^2 = 8 \implies x^2 = 4 \implies x=\pm2$

and so the base of each solid is the set

$B = \left\{(x,y) \,:\, -2\le x\le2 \text{ and } x^2 \le y \le 8-x^2\right\}$

The side length of each cross section that coincides with B is equal to the vertical distance between the two parabolas, $|x^2-(8-x^2)| = 2|x^2-4|$ . But since -2 ≤ x ≤ 2, this reduces to $2(x^2-4)$ .

a. Square cross sections will contribute a volume of

$\left(2(x^2-4)\right)^2 \, \Delta x = 4(x^2-4)^2 \, \Delta x$

where ∆x is the thickness of the section. Then the volume would be

$\displaystyle \int_{-2}^2 4(x^2-4)^2 \, dx = 8 \int_0^2 (x^2-4)^2 \, dx \\\\ = 8 \int_0^2 (x^4-8x^2+16) \, dx \\\\ = 8 \left(\frac{2^5}5 - \frac{8\times2^3}3 + 16\times2\right) = \boxed{\frac{2048}{15}}$

where we take advantage of symmetry in the first line.

b. For a semicircle, the side length we found earlier corresponds to diameter. Each semicircular cross section will contribute a volume of

$\dfrac\pi8 \left(2(x^2-4)\right)^2 \, \Delta x = \dfrac\pi2 (x^2-4)^2 \, \Delta x$

We end up with the same integral as before except for the leading constant:

$\displaystyle \int_{-2}^2 \frac\pi2 (x^2-4)^2 \, dx = \pi \int_0^2 (x^2-4)^2 \, dx$

Using the result of part (a), the volume is

$\displaystyle \frac\pi8 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{256\pi}{15}}}$

c. An equilateral triangle with side length s has area √3/4 s², hence the volume of a given section is

$\dfrac{\sqrt3}4 \left(2(x^2-4)\right)^2 \, \Delta x = \sqrt3 (x^2-4)^2 \, \Delta x$

and using the result of part (a) again, the volume is

$\displaystyle \int_{-2}^2 \sqrt 3(x^2-4)^2 \, dx = \frac{\sqrt3}4 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{512}{5\sqrt3}}$

7 0

2 years ago

Write a paragraph to help Miguel explain to Hannah how to complete the problems. Be sure to explain the process step-by-step (re

Eddi Din [679]

Steps in multiplying fractions. Remember: finding common denominator is not necessary in multiplying fractions.
Common denominators are only needed in adding and subtracting fractions.

14/15 * 5/2

Step 1. Multiply the numerators.
14 * 5 = 70
Step 2. Multiply the denominators
15 * 2 = 30
Step 3. Simplify the fraction.
70/30 = 2 10/30 = 2 1/3

*the fraction 10/30 can still be simplified by dividing both numbers by 10. Hence, 1/3.

Steps in Dividing fractions.

24/60 ÷ 8/15

Step 1. Get the reciprocal of the 2nd fraction. Reciprocal means the reverse of the fraction. Simply swap the places of the numbers.

Reciprocal of 8/15 is 15/8.

Step 2. Multiply the 1st fraction to the reciprocal of the 2nd fraction. Follow steps in multiplying fractions.

24/60 * 15/8 = (24*15) / (60*8) = 360/480

Step 3. Simplify the fraction.
360/480 = 9 / 12 = 3/4

360 ÷ 40 = 9 ; 9 ÷ 3 = 3
480 ÷ 40 = 12 ; 12 ÷ 3 = 4

4 0

3 years ago

Find a better estimate of √2.

Goryan [66]

Answer = 1.414
I used the prime factorization method.
Hope this answers your question.

4 0

2 years ago

In the United States, 40% of the population have brown eyes (based on data from Dr. P. Sorita Soni at Indiana University). If 14

Sav [38]

Answer:

0.0006087 (4 sf)

Step-by-step explanation:

Binomial distribution: X ~ B(n, p)

where n is the number of trials and p is the probability of success

Let the random variable X be the number of people with brown eyes

n = 14

p = 40% = 0.4

Therefore, X ~ B(14, 0.4)

P(X ≥ 12) = 1 - P(X ≤ 11)

= 1 - 0.9993913226...

= 0.000608677...

4 0

2 years ago

Maria sells paintings in an art gallery. She earns $375 each week plus a commission equal to 2.5% of her sales. This week her is

Dennis_Churaev [7]

Answer:

im not 100% sure but i think its 9.375

Step-by-step explanation:

3 0

4 years ago

Read 2 more answers