What are the least common factors of 8 and 12

The total impedance of the circuit is 8 + 2i.

The total impedance in a series circuit is the sum of the individual impedances. To find the total impedance of the circuit, add the real parts and imaginary parts separately. In this case, Z1 = 3 + 4i and Z2 = 5 - 2i. So, the total impedance Zt = (3 + 5) + (4 - 2)i. Simplifying this, Zt = 8 + 2i.

The approximate probability of choosing one club followed by one heart from a standard deck of 52 playing cards is 5.9%.

The student's question pertains to the calculation of the probability of choosing one club and one heart from a standard deck of 52 playing cards. We start by recognizing that there are 13 clubs and 13 hearts in the deck, with each of the four suits represented equally.

Firstly, the probability of choosing a club (P(club)) is 13/52. After a club is chosen, there are 51 cards left in the deck. The number of hearts remains the same at 13 (since a club was chosen first). So, the probability of then picking a heart (P(heart)) is 13/51.

The two events, choosing a club and then a heart, are dependent events because the outcome of the second event depends on the outcome of the first. Hence, to find the combined probability, we multiply the probabilities of each event.

The probability of choosing one club followed by one heart is therefore P(club)  imes P(heart) = (13/52)  imes (13/51), which simplifies to approximately 0.059, or 5.9%.

The acceleration (x) is approximately 48 mph/hr, determined by dividing the change in velocity (20 mph) by the change in time (0.41667 hr).

The subject of this problem is acceleration, which in this context refers to the rate at which Sarah increased her speed during a particular period of time. Here, the change in speed was from 20 mph to 40 mph, a difference of 20 mph. The time over which this change occurred was 25 minutes, but since acceleration is usually measured in hours, we need to convert this to 25/60 = 0.4167 hours.

The formula for acceleration is change in speed/ change in time.

Therefore, to calculate the acceleration, we divide the change in speed (20 mph) by the time (0.4167 hr) to get x = 20 mph / 0.4167 hr = 47.99 mph/hr or approximately 48 mph/hr, which is the acceleration.

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Using the sine function and known angle and ladder length, the distance up the building the ladder reaches is \(7\sqrt{2}\) feet.

The correct answer is option C) \(7\sqrt{2}\) feet.

To find how far up the building the ladder reaches, we can use trigonometric functions, specifically the sine function since we have the angle and the length of the ladder.

Given:

- Length of the ladder (hypotenuse) = 14 feet

- Angle with the building = 45 degrees

Let [tex]\(x\)[/tex]be the distance up the building that the ladder reaches.

Using the sine function [tex](\(\sin\))[/tex] in a right triangle:

[tex]\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \][/tex]

Substituting the known values:

[tex]\[ \sin(45^\circ) = \frac{x}{14} \][/tex]

Since [tex]\(\sin(45^\circ) = \frac{\sqrt{2}}{2}\),[/tex] we have:

[tex]\[ \frac{\sqrt{2}}{2} = \frac{x}{14} \][/tex]

To solve for [tex]\(x\),[/tex] multiply both sides by 14:

[tex]\[ x = 14 \times \frac{\sqrt{2}}{2} \][/tex]

[tex]\[ x = 7\sqrt{2} \, \text{feet} \][/tex]

Therefore, the ladder reaches [tex]\(7\sqrt{2}\)[/tex] feet up the building.

Therefore the correct answer is option C) [tex]\(7\sqrt{2}\)[/tex]feet.

The question probable may be:

A 14 foot ladder is leaning against a building. The ladder makes a 45 degree angle with the building. How far up the building does the ladder reach?

A. 7 feet

B. 28sqrt(2) feet

c. 7sqrt(2) feet

D. 14sqrt(2) feet.

the correct answer is x+5 :DDD it was also the correct answer on the test !

Final answer:

To determine which of the given options is a factor of the expression 2x⁴ + 22x³ + 60x², we can use synthetic division. The only option that is a factor of the given expression is x⁴.

Explanation:

To determine which of the given options is a factor of the expression  2x⁴ + 22x³ + 60x², we can use synthetic division. Let's test each option:

2x³: When we divide 2x⁴ + 22x³ + 60x² by 2x3, the remainder is not zero. Therefore, 2x3 is not a factor.

x⁴: When we divide  2x⁴ + 22x³ + 60x²by x4, the remainder is zero. Therefore, x4 is a factor.

x + 4: When we divide  2x⁴ + 22x³ + 60x² by x + 4, the remainder is not zero. Therefore, x + 4 is not a factor.

x + 5: When we divide  2x⁴ + 22x³ + 60x² by x + 5, the remainder is not zero. Therefore, x + 5 is not a factor.

Based on the results, the only option that is a factor of the given expression is x⁴.

b: neither arithmetic nor geometric

The given sequence describes the type of sequence that is neither arithmetic nor geometric. which is the correct answer would be an option (B).

An arithmetic sequence is defined as an arrangement of numbers that is a particular order.

The sequence is given in the question following as:

1, 6, 7, 13, ...

We have to identify the type of given sequence

As per the given question, we have

1, 6, 7, 13, ...

For checking as an arithmetic sequence :

Common difference between 1 and 6 is d = 6 - 1 = 5

Common difference between 6 and 7 is d = 7 - 6 = 1

Since the common difference between consecutive terms is not the same, this means it's not an arithmetic sequence.

For checking as a geometric sequence :

Common ratio between 1 and 6 is r = 6/1 = 6

Common ratio between 6 and 7 is r = 7/6

Since the common ratio between consecutive terms is not the same, this means it's not a geometric sequence

Thus, the given sequence describes the type of sequence that is neither arithmetic nor geometric.

Learn more about arithmetic sequence here:

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Final answer:

To solve the equation log2 (x) + log2(x+7) = 3, you can combine the logarithmic terms using the property log(a) + log(b) = log(a*b). By applying this property and solving the resulting quadratic equation, we find that x = 1.

Explanation:

To solve the equation log2 (x) + log2(x+7) = 3, we need to combine the logarithmic terms using the property log(a) + log(b) = log(a*b). Applying this property, we get log2 (x*(x+7)) = 3. Next, we can rewrite this equation in exponential form as 2^3 = x * (x+7). Simplifying further, we have 8 = x^2 + 7x. Rearranging the equation, we get a quadratic equation x^2 + 7x - 8 = 0. Solving this quadratic equation, we find that x = -8 or x = 1. However, since the logarithm of a negative number is undefined, the solution is x = 1.

Answer:

B. 5p³ - 2p² - 7p + 1

Step-by-step explanation:

Good luck! Hope it was found helpful to you!

Final answer:

The rock takes 2 seconds to hit the ground.

Explanation:

In order to find the time it takes for the rock to hit the ground, we can analyze the vertical motion of the rock. Since the rock is kicked horizontally, its initial velocity in the vertical direction is zero. The acceleration due to gravity is -9.8 m/s^2.

Using the equation h = ut + (1/2)gt^2, where h is the height, u is the initial velocity, g is the acceleration due to gravity, and t is the time, we can plug in the values to find the time.

Since the rock is kicked horizontally, the initial velocity in the vertical direction (uy) is zero, so the equation becomes h = (1/2)gt^2. We know that h = 0 since the rock is at the ground, and g = -9.8 m/s^2. Plugging these values into the equation, we get 0 = (1/2)(-9.8)t^2.

Solving for t, we find that t = 0 or t = 2 seconds. Since time cannot be negative, the rock takes 2 seconds to hit the ground.

The tax on an item of price p is calculated as 0.12p and the total price is p + 0.12p. On calculating for an item that costs 75, the total cost with tax is 84. The order of operations (PEMDAS/BODMAS) was used to solve the problem accurately

The tax on the item with a price p can be given by the expression 0.12p, using the operation of multiplication. The total price of the item, including tax would be p + 0.12p. This is done by using both addition and multiplication operations.

To determine the total price, including tax, of an item that costs 75, we substitute 75 for p in the second expression: 75 + 0.12*75 = 75 + 9 = 84. Therefore, an item that costs 75 before tax would cost 84 with tax.

Order of operations is important in this problem to ensure accurate calculations. According to PEMDAS/BODMAS rules (Parentheses/Brackets, Exponents/Orders, Multiplication and Division, Addition and Subtraction), multiplication should be carried out before the addition, hence why 0.12*75 was calculated before adding the result to the initial cost of the item (75).

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The taxation on an item with a price tag of 'p' can be represented as 0.12p. The total cost, counting tax, is depicted as 1.12p. Applying these expressions, an item priced at 75 would cost 84 including the 12% tax.

The tax on an item with a price p can be expressed as 0.12p. This is because 12% is equivalent to 0.12 in decimal form. To find the total price of the item, including tax, you would add the original price (p) to the tax (0.12p). This can be written as p + 0.12p, or simplified further to 1.12p.

The operations involved in these expressions include multiplication and addition. To determine the total price, including tax, of an item that costs 75, you would plug in 75 for p in the total price expression, 1.12p. This works out to 1.12 * 75 = 84. The order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) dictates that you perform multiplication before addition in the total price expression. Since there are no parentheses or exponents, you would multiply 0.12 by p (or the price of the item), and then add that result to p, to find the total price including tax.

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Answer:

Complete Quick Check of...

Lesson 4: Graphing a Function Rule

Algebra 1 A: Unit 5

Step-by-step explanation:

1.C) x,0,1,2,3, y,3,-1,-5,-9

2.A) True

3.D) $698.75

4.C) cant write it out.

5.D) C = 11n; discrete

:) hope this helps!

the answer is B hope it helps

The answer is 8 and 2 over 3.