Using the quadratic formula to solve x2 = 5-x, what are the values of x?

The ranking of resistors would be, R1 < R3 < R2

The larger the time constant T = RC,  the more time it takes for the capacitor to discharge.

So the more the resistance the more time it takes for the capacitor to discharge.

In the figure, the one with R2 will take the longest time for Vc to be zero. Then R3 will take less time than R2 and R1 will take smallest time to discharge. So R2 is largest followed by R3 and R1 is smalllest.

So the ranking would be, R1 < R3 < R2

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Initial velocity=0

Height=45m

G=10m/s^2

By the 2 nd equation of motion …(Under free fall)-

H = ut + 1/2 g t^2

45 = 0 + {1/2 * 10 * (t^2)} •: [0*t=0]

45 = 5 t^2

45/5 = t^2

9 = t^2

√9=t

3=t

Answer-: The time taken would be 1.3 seconds to reach the ground.

The length of the adult crocodile more than the young crocodile is 5.0 feet.

A young crocodile is 0.4 feet long. An adult crocodile is 13.5 times as long. The length the adult crocodile is more than the young crocodile can be calculated as follows:

Hence,

length of the adult crocodile = 13.5(0.4)

length of the adult crocodile = 13.5 × 0.4

length of the adult crocodile = 5.4 feet

Therefore,

the length of the adult crocodile more than the young crocodile = 5.4 - 0.4 = 5.0 feet

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The potential areas for Franklin's garden are 144ft², 36ft² and 196ft² hence options (b), (e), and (f) are correct.

To find the potential areas for Franklin's square garden, we need to find the perfect squares that can be expressed as the product of two identical whole numbers. These perfect squares will represent the areas of the square gardens with whole number side lengths,

a) 20 ft² = 2 x 2 x 5 = (2 x 2) x 5 = 4 x 5, not a perfect square

b) 144 ft² = 12 x 12 = (12 x 12), a perfect square

c) 1,000 ft² = 10 x 10 x 10 = (10 x 10) x 10 = 100 x 10, not a perfect square

d) 300 ft² = 10 x 10 x 3 = (10 x 10) x 3 = 100 x 3, not a perfect square

e) 36 ft² = 6 x 6 = (6 x 6), a perfect square

f) 196 ft² = 14 x 14 = (14 x 14), a perfect square

Therefore, the potential areas for Franklin's garden are 144 ft², 36 ft², and 196 ft². So, options (b), (e), and (f) are the potential areas for Franklin's square garden with whole number side lengths.

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As per the given options, the following matches are the correct matches of the column A terms to the column B options,1. Independent variable: G. Verbal description of physical attractiveness.2. Number of factors or conditions of the independent variable: H.2.3. Sample based on: D. Random assignment of participants to IV.4. The dependent variable is probably: A. A percentage of all dating site users.

Given that column A consists of four terms while column B consists of eight options. Therefore, two of the options in column B will not be used. The following are the correct matches for the given situation demo question, Column A

1. Independent variable: It is defined as the factor or variable that is being manipulated and changed by the researchers or investigators during an experiment to see its impact on the dependent variable.

2. Number of factors or conditions of the independent variable: It is defined as the number of variations or groups in which the independent variable is tested.

3. Sample based on: It is defined as the selection criteria or criterion upon which the participants for the experiment are chosen.

4. The dependent variable is probably: It is defined as the variable that changes in response to the independent variable.

Therefore, as per the given options, the following matches are the correct matches of the column A terms to the column B options,1. Independent variable: G. Verbal description of physical attractiveness.2. Number of factors or conditions of the independent variable: H.2.3. Sample based on: D. Random assignment of participants to IV.4. The dependent variable is probably: A. A percentage of all dating site users.

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The midpoint of (-6, -9) and (3, -3) is (-1.5, -6).

To find the midpoint of two given points, we calculate the average of their respective x-coordinates and y-coordinates.

In this case, the x-coordinate of the midpoint is obtained by averaging the x-values of -6 and 3, resulting in (-6 + 3) / 2 = -1.5.

Similarly, the y-coordinate is determined by averaging the y-values of -9 and -3, giving us (-9 + (-3)) / 2 = -6.

Thus, the midpoint of (-6, -9) and (3, -3) is (-1.5, -6).

The midpoint represents the exact center point between the two given coordinates along the line segment connecting them, dividing it into two equal parts.

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Answer:

7.99912744cm

Step-by-step explanation:

Answer: 16

Step-by-step explanation:

Circumference is 50.26 = pi*d d = 50.26/3.14 = 16

For  given point (21, 28), the exact values of the trigonometric functions for θ are: sinθ = 4/5, cosθ = 3/5, tanθ = 4/3

Let the length of the hypotenuse be h, the length of the adjacent side be x, and the length of the opposite side be y.

Using the Pythagorean theorem, we have:

h² = x² + y²

Substituting the values, we get:

h² = 21² + 28²

h² = 441 + 784

h² = 1225

h = √1225

h = 35

So, the length of the hypotenuse is 35.

Now, we can determine the values of the trigonometric functions for θ using the given lengths of the sides:

sinθ = opposite/hypotenuse = y/35

cosθ = adjacent/hypotenuse = x/35

tanθ = opposite/adjacent = y/x

Let's calculate the values:

sinθ = y/35 = 28/35 = 4/5

cosθ = x/35 = 21/35 = 3/5

tanθ = y/x = 28/21 = 4/3

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Answer:3

Step-by-step explanation:

Answer: n^2+5n+4r+7

Step-by-step explanation:

The amount of Gatorade that Marcus would drink while walking 12 miles depends on several factors such as his personal preference, level of exertion, and the weather conditions.

However, a general rule of thumb is to drink about 8 ounces of fluid (water or sports drink) for every 20 minutes of exercise. If we assume that Marcus takes about 2 hours to walk 12 miles, he would be walking for 120 minutes, and he would need to drink about 48 ounces (8 ounces x 6 cycles of 20 minutes) of fluid during his walk. Therefore, Marcus would drink about 48 ounces of Gatorade (or any other fluid) during his 12-mile walk.

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The system of equations that models this scenario is 45x+45y = 2505

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =

The given parameters that will help us to form the equation are

Number of players = 45

Each hoodie costs $60 and

Each long sleeve performance shirt costs $45.

The entire order totaled $2,400.

This implies that

45(x) = 60 and 45(y) =45

and 45x-60 + 45y -45 = 2400

Collecting like terms

45x+45y =2400+105

45x+45y = 2505 becomes the system of equation

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Answer: 63 Stickers

Step-by-step explanation:

Given information:

Ratio = Slade : Corbett = 5 : 2

Corbett has 27 fewer stickers

Set variables:

Let x be the number of stickers Corbett has

Let x + 27 be the number of stickers Slade has

Set proportional equation:

\(\frac{2}{5}~ =~\frac{x}{x~+~27}\)

Cross multiply the system

\(2~(x~+~27)~=~5~*~x\)

Simplify by distributive property

\(2~*~x~+~2~*~27~=~5x\)

\(2x~+~54~=~5x\)

Subtract 2x on both sides

\(2x~+~54~-~2x~=~5x~-~2x\)

\(54~=~3x\)

Divide 3 on both sides

\(54~/~3~=~3x~/~3\)

\({x=18}\)

Add Corbett's and Slade's amounts together

Corbett = x = 18 stickers

Slade = x + 27 = 18 + 27 = 45 stickers

Total = 18 + 45 = \(\Large\boxed{63~Stickers}\)

Hope this helps!! :)

Please let me know if you have any questions

Answer:

63 stickers

Step-by-step explanation:

Define the variables:

Given ratio:

Slade : Corbett = 5 : 2

Substitute the defined variables:

\(\implies \sf x : x - 27 = 5 : 2\)

\(\implies \sf \dfrac{x}{x-27}=\dfrac{5}{2}\)

Cross multiply:

\(\implies \sf 2x=5(x-27)\)

Expand:

\(\implies \sf 2x=5x-135\)

Subtract 5x from both sides:

\(\implies \sf -3x=-135\)

Multiply both sides by -1:

\(\implies \sf 3x=135\)

Divide both sides by 3:

\(\implies \sf x=45\)

Therefore, Slade had 45 stickers.

Substitute the found value of x into the expression for the number of stickers Corbett had:

\(\implies \sf 45-27=18\)

Therefore, Corbett had 18 stickers.

Total number of stickers = 45 + 18 = 63

Answer:

265

Step-by-step explanation:

9+(8x8x8/2) = 9+(512/2) = 9+256 = 265

The questions that could be used to challenge each claim goes as follows.

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Answer: 50 km

Step-by-step explanation: So the map has a scale of 1 cm: 20 km. Next, you look at how far they are apart and see if the scale and the distance on the map are the same measurement. In this case, they are both centimeters so they stay the same. Then, all you do is multiple the real size, 20 km, by  

2.5 /1 . Then, 20 x 2.5=50. So the answer is 50 km

Answer: y-3= 5/4(x-1) is the point slope form answer, y = 1.25x + 1.75 is the slope intercept form answer.

Step-by-step explanation:

The equation of the tangent line represents a straight line that passes through the point of tangency and has a slope of -16.

The slope of the tangent line to the graph of the function y = x^4 - 10x^2 + 9 at x = 1 can be found by taking the derivative of the function and evaluating it at x = 1. The equation of the tangent line can then be determined using the point-slope form.

Taking the derivative of the function y = x^4 - 10x^2 + 9 with respect to x, we get:

dy/dx = 4x^3 - 20x

To find the slope of the tangent line at x = 1, we substitute x = 1 into the derivative:

dy/dx (at x = 1) = 4(1)^3 - 20(1) = 4 - 20 = -16

Therefore, the slope of the tangent line is -16.

To find the equation of the tangent line, we use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Given that the point of tangency is (1, y(1)), we substitute x1 = 1 and y1 = y(1) into the equation:

y - y(1) = -16(x - 1)

Expanding the equation and simplifying, we have:

y - y(1) = -16x + 16

Rearranging the equation, we obtain the equation of the tangent line:

y = -16x + (y(1) + 16)

To find the slope of the tangent line, we first need to find the derivative of the given function. The derivative represents the rate of change of the function at any point on its graph. By evaluating the derivative at the specific value of x, we can determine the slope of the tangent line at that point.

In this case, the given function is y = x^4 - 10x^2 + 9. Taking its derivative with respect to x gives us dy/dx = 4x^3 - 20x. To find the slope of the tangent line at x = 1, we substitute x = 1 into the derivative equation, resulting in dy/dx = -16.

The slope of the tangent line is -16. This indicates that for every unit increase in x, the corresponding y-value decreases by 16 units.

To determine the equation of the tangent line, we use the point-slope form of a linear equation, which is y - y1 = m(x - x1). We know the point of tangency is (1, y(1)), where x1 = 1 and y(1) is the value of the function at x = 1.

Substituting these values into the point-slope form, we get y - y(1) = -16(x - 1). Expanding the equation and rearranging it yields the equation of the tangent line, y = -16x + (y(1) + 16).

The equation of the tangent line represents a straight line that passes through the point of tangency and has a slope of -16.

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Answer:

3

Step-by-step explanation:

We know that -3 is on the x axis and 3 is on the y axis.

and the y axis usually determines if you are going to have a positive slope or negative since it would either rise or decrease. In this cause (-3, 3) shows that 3 is going to be our slope.

Answer:

y=3

Step-by-step explanation:

In a normal equation, y=mx+b, m=slope. If slope=0 in this equation, then it is safe to say that the equation is y=b. Since the Y coordinate is 3, then we can safely assume that the equation is equal to y=3

Therefore, it will take about 11 years for the account value to reach 5100 dollars.

Percent is a way of expressing a quantity as a fraction of 100. The symbol "%" is used to represent percent. For example, if we say that an interest rate is 5%, it means that the interest is 5/100 or 0.05 as a decimal. Percentages are commonly used in finance, economics, and everyday life to express rates, proportions, and changes in quantities.

Here,

We can use the formula for compound interest to solve this problem:

A = P(1 + r/n)ⁿˣ

where A is the amount of money in the account after x years, P is the principal amount (initial deposit), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and x is the time (in years).

We are given that P = 2100, r = 0.05, and we want to find the value of x when A = 5100. Let's assume that the interest is compounded annually (n = 1). Substituting the given values into the formula, we get:

5100 = 2100(1 + 0.05)ˣ

Dividing both sides by 2100, we get:

(1 + 0.05)ˣ = 5100/2100

Simplifying the right-hand side, we get:

(1 + 0.05)ˣ = 2.42857

Taking the natural logarithm of both sides, we get:

ln(1 + 0.05)ˣ = ln 2.42857

Using the power rule of logarithms, we can simplify the left-hand side:

x ln(1 + 0.05) = ln 2.42857

Dividing both sides by ln(1 + 0.05), we get:

x= ln 2.42857 / ln(1 + 0.05)

Using a calculator, we get:

x≈ 11.4

Rounding this to the nearest year, we get:

x ≈ 11 years

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Answer:

See below

Step-by-step explanation:

\(2e)15-4x=10x+45\)

Solve:

\(15-4x=10x+45\\-4x-10x=45-15\\-14x=30\\ \boxed {x=-\dfrac{15}{7}}\)\(3(x+1)=21\)

Check:

\(15-4 \left(-\dfrac{15}{7} \right)=10\left(-\dfrac{15}{7} \right)+45\)

\(15+\dfrac{60}{7} \right)=-\dfrac{150}{7} +45\)

\(\dfrac{210}{7} =30\)

\(30=30\)

\(3a) 3(x+1)=21\)

Solve:

\(3(x+1)=21\\3x+3=21\\3x=18\\x=6\)

\(3b) 2+3(x+1)=6x\)

\(2+3x+3=6x\\5=3x\\\)

\(x=\dfrac{5}{3}\)

\(3c) -2(2x-3)=-2\)

Solve:

\(-2(2x-3)=-2\\-4x+6=-2\\-4x=-8\\x=2\)

Answer:

Step-by-step explanation:

The value of the copier after 3 years and 6 months can be found by substituting t = 3.5 into the function and solving for V. The salvage value of the copier can be found by substituting t = 5 into the function and solving for V.

After 3 years and 6 months of use, the copier is worth $5,800. This can be found by substituting t = 3.5 into the function V(t)-3600t+20000: V(3.5) = 3600(3.5) - 20000 + 20000 = $5,800.

The salvage value of the copier after 5 years of use is $4,000. This can be found by substituting t = 5 into the function V(t)-3600t+20000: V(5) = 3600(5) - 20000 + 20000 = $4,000. This is the value of the copier when it is sold or replaced after 5 years of use.

The domain of the function is all real numbers because time and value can take on any real value. However, since the function is only defined for the first 5 years of use, t must be between 0 and 5.

The graph of the function is a downward-sloping line with an intercept of $20,000 on the y-axis and a slope of -3600. This means that the value of the copier decreases by $3,600 each year. At t = 0, the copier is worth $20,000, and after 5 years, it is worth $4,000. The graph is a straight line because the function is linear.

Complete Question:

The function V(t)-3600t+20000, where V is value and t is time in years, can be used to find the value of a large copy machine during the first 5 years of use. a. What is the value of the copier after 3 years and 6 months? After 3 years and 6 months, the copier is worth $ b. What is the salvage value of the copier if it is replaced after 5 years? After 5 years, the salvage value of the copier is ts c. State the domain of this function. d. Sketch the graph of this function. 20000 18000 16000 14000 12000 10000 8000 6000+ 4000 2000 4 .

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Answer:

L = 20 inches

Step-by-step explanation:

w = width

L = length

area = 120

W x L = 120

L - 8 = 2W  then L = 2W + 8

substitute for L:

W x (2W + 8) = 120

2W² + 8W -120 = 0

(2W - 12)(W + 10) = 0

2W-12 = 0

2W = 12

W = 6

L = 20

Answer:

3,15

Step-by-step explanation:

took the test boi

The following data shows the daily production of cell phones. 7, 10, 12, 15, 18, 19, 20. Mean The formula for finding the mean is: mean = (sum of observations) / (number of observations).

Therefore, the mean for the daily production of cell phones is: Mean = (7+10+12+15+18+19+20) / 7

= 101 / 7

Mean = 14.43

Variance The formula for finding the variance is: Variance = (sum of the squares of the deviations) / (number of observations - 1) Where the deviation of each observation from the mean is: deviation = observation - mean First, calculate the deviation for each observation:7 - 14.43

= -7.4310 - 14.43

= -4.4312 - 14.43

= -2.4315 - 14.43

= 0.5718 - 14.43

= 3.5719 - 14.43

= 4.5720 - 14.43

= 5.57

Now, square each of these deviations: 56.25, 19.62, 5.91, 0.33, 12.75, 20.9, 30.96 The sum of these squares of deviations is: 56.25 + 19.62 + 5.91 + 0.33 + 12.75 + 20.9 + 30.96

= 147.72

Therefore, the variance for the daily production of cell phones is: Variance = 147.72 / (7-1) = 24.62 Standard deviation ) Mean = 14.43b) Variance per Day = 24.62c) Standard Deviation = 4.96

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Answer: $27.825

Step-by-step explanation:

From the question, we are informed that Robert want to buy a sports cap that is on sale for 25% off and the original price is 35$. This means the price of the sports car will be:

= Original price - Discount

= $35 - (25% × $35)

= $35 - (0.25 × $35)

= $35 - $8.75

= $26.25

We are further told that there is a sales tax of 6%. The amount that Robert will need to pay for the cap will be:

= $26.25 + (6% × $26.25)

= $26.25 + (0.06 × $26.25)

= $26.25 + $1.575

= $27.825

Answer:

27.83

Step-by-step explanation: