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Which situations can be represented by a linear function?

Select each correct answer.

a. Every year, Luisa puts $10 into her savings account.

b. Every day, the number of bacteria in the dish is 3 times what it was the previous day.

c. A country's population increases by 0.8% each year.

d. The barrel leaks 0.5 L of water each day.

The correct initial velocity (v) for the basketball to go through the hoop is approximately 0.0406 ft/s.

To find the initial velocity v, we can use the given information and set up the equation using the height of the hoop and the distance away from the hoop. The equation of the path of the basketball is given by:

y = -16x^2/(0.434v^2) + 1.15x + 8

Given that the hoop is 10 feet high and located 17 feet away, we can substitute these values into the equation:

10 = -16(17)^2/(0.434v^2) + 1.15(17) + 8

Now, we can solve this equation for the initial velocity v. First, simplify the equation:

10 = -16(17)^2/(0.434v^2) + 19.55 + 8

Combine the constant terms on the right side:

10 = -16(17)^2/(0.434v^2) + 27.55

Now, isolate the term with v on one side:

(16(17)^2)/(0.434v^2) = 17.55

Next, multiply both sides by (0.434v^2)/(16(17)^2) to solve for v^2:

v^2 = (16(17)^2)/(0.434 * 17.55)

Now, take the square root of both sides to find v:

v = sqrt((16(17)^2)/(0.434 * 17.55))

Calculating this expression will give you the initial velocity v. Let's calculate:

v ≈ 0.0406 ft/s

The initial velocity v of the basketball should be approximately [tex]\(14.86 \, \text{ft/sec}\)[/tex] for it to go through the hoop.

To find the initial velocity v required for the basketball to go through the hoop, we utilize the parabolic model [tex]\(y = -\frac{16x^2}{0.434v^2} + 1.15x + 8\)[/tex]. Given that the height of the hoop (y) is 10 feet and the distance away from the hoop (x) is 17 feet, we substitute these values into the equation:

[tex]\[10 = -\frac{16 \cdot 17^2}{0.434v^2} + 1.15 \cdot 17 + 8.\][/tex]

First, simplify the equation:

[tex]\[10 = -\frac{16 \cdot 17^2}{0.434v^2} + 1.15 \cdot 17 + 8.\][/tex]

Combine like terms:

[tex]\[10 = -\frac{16 \cdot 17^2}{0.434v^2} + 19.55.\][/tex]

Isolate the fraction:

[tex]\[\frac{16 \cdot 17^2}{0.434v^2} = 9.55.\][/tex]

Now, solve for v²:

[tex]\[v^2 = \frac{16 \cdot 17^2}{0.434 \cdot 9.55}.\][/tex]

Finally, find v by taking the square root:

[tex]\[v \approx \sqrt{\frac{16 \cdot 17^2}{0.434 \cdot 9.55}} \approx 14.86 \, \text{ft/sec}.\][/tex]

The calculation shows that an initial velocity of approximately [tex]\(14.86 \, \text{ft/sec}\)[/tex] is required for the basketball to follow the modeled path and successfully go through the hoop.

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.

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.

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.

Answer:

B. 5p³ - 2p² - 7p + 1

Step-by-step explanation:

Good luck! Hope it was found helpful to you!

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%.

Answer:

[tex]DA=3[/tex]

Step-by-step explanation:

We have been given an image of a circle and we are told that Secant DB intersects secant DZ at point D.    

We will use intersecting secants theorem to solve our given problem.  

Intersecting secants theorem states that if two secants say MN  and KL intersect at a point 'X' outside the circle, then product of XN and MX equals the product of XL and KX.

Using intersecting secants theorem we can set an equation as:

[tex]DA\cdot DB=DY\cdot DZ[/tex]

Upon substituting our given values in above equation we will get,

[tex]3x\cdot (3x+8)=x\cdot (32+x)[/tex]

Upon dividing both sides of our equation by x we will get,

[tex]\frac{3x\cdot (3x+8)}{x}=\frac{x\cdot (32+x)}{x}[/tex]

[tex]3\cdot (3x+8)=32+x[/tex]

Upon using distributive property [tex]a(b+c)=a*b+a*c[/tex] we will get,

[tex]9x+24=32+x[/tex]

[tex]9x-x+24-24=32-24+x-x[/tex]

[tex]8x=8[/tex]

Upon dividing both sides of our equation by 8 we will get,

[tex]\frac{8x}{8}=\frac{8}{8}[/tex]

[tex]x=1[/tex]

Since the length of DA is 3x, so upon multiplying 3 by 1 we will get,

[tex]\text{Length of DA}=3\cdot 1=3[/tex]

Therefore, the length of DA is 3 units.

Answer:

What if it was $32 and $44, 82 and 54?

Step-by-step explanation:

On a certain day, the company took 82 people on whale watching trips. There were 54 children aged 12 and under, of which some children were under three years. If x represents the number of children under three years, which equation can be used to find the value of x, where C represents the total amount of money collected from tickets that day?

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 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 answer is 8 and 2 over 3.

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.

You can factor, that takes almost no effort

Hope this helps

Answer:

inspection method

Step-by-step explanation:

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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