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Ilya
3 months ago
10

Segment GI is congruent to Segment JL and Segment GH is congruent to Segment KL. I have to prove Segment HI is congruent to Segm

ent JK. It has to be done in eight steps with reasons.

Mathematics
1 answer:
Zina [12.3K]3 months ago
3 0

Solution:

Refer to the detailed explanation

Step-by-step process:

1 step: \overline{GI}\cong \overline {JL} - provided

2 step: \overline{GI}\cong \overline{GH}+\overline{HI} - Segments Addition Postulate

3 step: \overline{GH}+\overline{HI}\cong \overline {JL} - Substitution Property

4 step: \overline {JL}\cong \overline {JK}+\overline {KL} - Segments Addition Postulate

5 step: \overline{GH}+\overline{HI}\cong \overline {JK}+\overline {KL} - Substitution Property

6 step: \overline{GH}\cong \overline {KL} - provided

7 step: \overline{GH}+\overline{HI}\cong \overline {JK}+\overline {GH} - Property of Substitution Equality

8 step: \overline{HI}\cong \overline {JK} - Equality Subtraction Property

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The given equation has been solved in the table. In which step was the subtraction property of equality applied?
tester [12383]
The correct answer is Option (D). The subtraction property of equality asserts that whatever is subtracted from one side of an equation must also be subtracted from the other side. In the instance where x + 2 = 2, applying this property leads to: x + 2 - 2 = 2 - 2, simplifying to x = 0. However, the provided question displays the addition property of equality utilized in step 2, indicating that the subtraction property was not applied there. Consequently, Option (D) is the correct response.
5 0
2 months ago
The domain of f(x) is the set of all real values except 7, and the domain of g(x) is the set of all real values except –3. Which
Svet_ta [12734]

Answer: All real numbers except for x ≠ 7 and those x for which f(x)≠-3

Step-by-step explanation:

The domain of function f is defined as R - {7}

In other words, if x belongs to the domain of f,

then, x cannot equal 7

(gof)(x) = g(f(x))

Considering that g has a domain of R - {-3}

Therefore, if f(x) fits within the domain of g,

it follows that f(x)≠ -3

Consequently, the fourth option is the right choice.

8 0
2 months ago
The ground-state wave function for a particle confined to a one-dimensional box of length L is Ψ=(2/L)^1/2 Sin(πx/L). Suppose th
AnnZ [12381]

Respuesta:

(a) 4.98x10⁻⁵

(b) 7.89x10⁻⁶

(c) 1.89x10⁻⁴

(d) 0.5

(e) 2.9x10⁻²

Explicación paso a paso:

La probabilidad (P) de encontrar la partícula está dada por:

P=\int_{x_{1}}^{x_{2}}(\Psi\cdot \Psi) dx = \int_{x_{1}}^{x_{2}} ((2/L)^{1/2} Sin(\pi x/L))^{2}dx  

P = \int_{x_{1}}^{x_{2}} (2/L) Sin^{2}(\pi x/L)dx     (1)

La solución de la integral de la ecuación (1) es:

P=\frac{2}{L} [\frac{X}{2} - \frac{Sin(2\pi x/L)}{4\pi /L}]|_{x_{1}}^{x_{2}}  

(a) La probabilidad de encontrar la partícula entre x = 4.95 nm y 5.05 nm es:

P=\frac{2}{100} [\frac{X}{2} - \frac{Sin(2\pi x/100)}{4\pi /100}]|_{4.95}^{5.05} = 4.98 \cdot 10^{-5}    

(b) La probabilidad de encontrar la partícula entre x = 1.95 nm y 2.05 nm es:

P=\frac{2}{100} [\frac{X}{2} - \frac{Sin(2\pi x/100)}{4\pi /100}]|_{1.95}^{2.05} = 7.89 \cdot 10^{-6}  

(c) La probabilidad de encontrar la partícula entre x = 9.90 nm y 10.00 nm es:

P=\frac{2}{100} [\frac{X}{2} - \frac{Sin(2\pi x/100)}{4\pi /100}]|_{9.90}^{10.00} = 1.89 \cdot 10^{-4}    

(d) La probabilidad de encontrar la partícula en la mitad derecha de la caja, es decir, entre x = 0 nm y 50 nm es:

P=\frac{2}{100} [\frac{X}{2} - \frac{Sin(2\pi x/100)}{4\pi /100}]|_{0}^{50.00} = 0.5

(e) La probabilidad de encontrar la partícula en el tercio central de la caja, es decir, entre x = 0 nm y 100/6 nm es:

P=\frac{2}{100} [\frac{X}{2} - \frac{Sin(2\pi x/100)}{4\pi /100}]|_{0}^{16.7} = 2.9 \cdot 10^{-2}

Espero que te ayude.

3 0
2 months ago
Ralph has budgeted $175 for entertainment. He uses this money to go out on dates for $35 or to go out with his friends for $15.
AnnZ [12381]
If Ralph allocated $180 rather than the intended $175 for entertainment, he spent $35 for each date and let's denote "x" as the number of dates he attended. He also spent $15 when going out with friends, where "y" represents his outings with friends.

The accurate equation is "B" which is 35x + 15y = 180.
8 0
2 months ago
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