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1 month ago

Select all the lines that have a slope of 5/2.

Mathematics

1 answer:

Leona [12.6K]1 month ago

6 0

A slope of 5/2 signifies that moving 2 units horizontally results in moving 5 units vertically. To visualize this, from any point on the line, shift 2 units right, and from there, move upwards until you intersect the line again. If the vertical movement is 5 units, the slope is confirmed to be 5/2. Option A indicates a slope of 5/2, B specifies a slope of 4/2, while C affirms the slope of 5/2. I can't clearly see the graphs represented in images D and E; however, E might have a slope of 5/2, which should be measured, and D clearly does not match the slope of 5/2, as it can be compared with A, demonstrating a significant difference, thus it can be eliminated.

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Simplify the given expression, using only positive exponents. Then complete the statements that follow. [ (x2y3)−1 (x−2y2z)2 ] 2

AnnZ [12381]

Answer: y²z⁴ / x¹²

The exponent for x is 12

The exponent for y is 2

The exponent for z is 4

Explanation:

1) The expression to simplify:

$((x^2y^3)^{-1}(x^{-2}y^2z)^2)^2$

2) Rule: power of a power:

$(x^{-4}y^{-6})(x^{-8}y^8z^4)$

3) Rule: product of powers with identical bases

$x^{(-2-8)}y^{(-6+8)}z^4$

4) Add up the exponents

$x^{-12}y^2z^4$

5) Transfer the negative exponent to the denominator:

$\frac{y^2z^4}{x^{12}}$

The exponent attached to x is 12, for y it is 2, and for z it is 4.

4 0

2 months ago

Read 2 more answers

What is the logarithm of the equilibrium constant, log K, at 25°C of the voltaic cell constructed from the following two half-re

lawyer [12517]

Answer:

4.0921 reflects the logarithm of the equilibrium constant.

Step-by-step explanation:

$Fe^{2+} (aq) +2e^{-}\rightarrow Fe(s)$ ; E° = - 0.41 V

$Ag^+(aq) + e^-\rightarrow Ag(s)$ ; E° = 0.80 V

Iron has a negative reduction potential, indicating its tendency to lose electrons and undergo oxidation, and thus it will be at the anode.

$E^{o}_{cell}$ =Reduction potential of cathode - Reduction potential of anode

$E^{o}_{cell}=E^{o}_c-E^{o}_a$

$=0.80 V-(-0.41 V)=1.21 V$

$Fe^{2+} (aq) + 2e^{-}\rightarrow Fe(s)$ ; E° = - 0.41 V

$2Ag^+(aq) + 2e^-\rightarrow 2Ag(s)$ ; E° = 0.80 V

Net reaction: $Fe(s)+2Ag^{+}\rightarrow Fe^{2+}+2Ag(s)$

n = 2

To determine the equilibrium constant, we utilize the correlation with Gibbs free energy, as follows:

$\Delta G^o=-nfE^o_{cell}$

and,

$\Delta G^o=-RT\ln K_{eq}$

Aligning these two equations yields:

$nfE^o_{cell}=RT\ln K_{eq}$

where,

n = electrons transferred = 2

F = Faraday's constant = 96500 C

$E^o_{cell}$ = standard electrode potential of the cell = 1.21 V

R = gas constant = 8.314 J/K.mol

T = reaction temperature = $25^oC=[273+25]=298K$

Substituting values into the equation, we arrive at:

$2\times 96500\times 1.21 V=8.314\times 298\times \ln K_{eq}$

$\ln K_{eq}=9.3478$

$\log K_{eq}=\frac{9.3478}{2.303}=4.0921$

4.0921 represents the logarithm of the equilibrium constant.

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2 months ago

Each trapezoid in the figure below is congruent to trapezoid ABDC.

Inessa [12570]

Response:

B: 32 cm

To clarify, one should only sum the external measurements

6+6+4+4+3+3+3+3=32 cm

3 0

1 month ago

Read 2 more answers

Two factories — Factory A and Factory B — design batteries to be used in mobile phones. Factory A produces 60% of all batteries,

tester [12383]

Answer:

The likelihood of a battery being produced by Factory A and being defective is 0.012, which corresponds to 1.2%.

Step-by-step explanation:

We have two manufacturers of batteries for mobile phones: Factory A and Factory B. Factory A is responsible for 60% of the total battery production, while Factory B accounts for the remaining 40%.

Out of the batteries made by Factory A, 2% are found to be defective, whereas 4% of those from Factory B are defective.

Let P(A) denote the probability that a battery comes from Factory A, therefore P(A) = 0.60.

The probability that a battery originates from Factory B can be denoted as P(B) = 0.40.

Furthermore, define D as the event indicating that a battery is defective.

Thus, the probability of a defect given that a battery is from Factory A is P(D/A) = 0.02.

For Factory B, the probability of a defect given it is from there is P(D/B) = 0.04.

The probability for a battery being made at Factory A and also being defective can be calculated as follows:

Probability that Factory A produces batteries $\times$ Probability that a battery from Factory A is defective

= P(A) $\times$ P(D/A)

= 0.60 $\times$ 0.02 = 0.012 or 1.2%

Conclusively, the probability that a battery is both from Factory A and defective is 1.2%.

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2 months ago

A surveyor measures the length of a surveying chain containing 1000 chain links. The length is 0.0533km. What is the length of a

lawyer [12517]

Answer:

The length of each individual chain link is calculated as 5.33 cm.

Step-by-step explanation:

Initial data: the chain consists of 1000 links

the overall length recorded is 0.0533km.

1km = 1000m

1m = 100cm, thus 1km = 100000cm

So, the total length in centimeters = 0.0533* 100000

Total length in cm = 5330 cm

To find out the length of a single chain link, we do:

length of one chain link = 5330/1000

Thus, the length of a single chain link equals 5.33 cm.

7 0

3 months ago