If one of the roots of the equation x² – 4x + k = 0 exceeds the other by 2, then find the roots and determine the value of k.
​

The rule for given translation is (x,y)→(x + 3, y - 4).

In mathematics, the phrases translation, rotation, and reflection are all used to describe the change of forms. This refers to a form moving beyond a mirror line or a fixed point. While being translated, rotated, or reflected, the shape doesn't change. The constant rotation of a shape around a fixed point or across the mirror line is known as translation. Rotation defines the way a form moves about a central axis. Shapes can be rotated by a specific number of degrees either clockwise or counterclockwise.

The rule for translation of given figure will be,

We need to move x for 3 units to left and y for 4 units downwards to get the translation, so the rule is:

(x,y)→(x + 3, y - 4).

Therefore, the rule for given translation is (x,y)→(x + 3, y - 4).

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The turtle's average velocity in the x-direction is approximately 0.00707 m/s, while in the y-direction it is approximately -0.00650 m/s. The magnitude of its average velocity, which represents the overall speed, is approximately 0.00955 m/s.

To find the components and magnitude of the turtle's average velocity, we can use the following formulas:

Average velocity components:

\(v_{av,x}\) = Δx / Δt

\(v_{av,y}\) = Δy / Δt

Magnitude of average velocity:

|\(v_{av}\)| = √(\((v_{av,x})^2\) + \((v_{av,y})^2\))

where:

Δx is the change in the x-coordinate (r2,x - r1,x)

Δy is the change in the y-coordinate (r2,y - r1,y)

Δt is the time taken for the excursion (323 s)

Given the position vectors:

r1,x = 1.07 m

r1,y = -2.69 m

r2,x = 3.35 m

r2,y = -4.79 m

Δt = 323 s

We can calculate the average velocity components and magnitude as follows:

Δx = r2,x - r1,x = 3.35 m - 1.07 m = 2.28 m

Δy = r2,y - r1,y = -4.79 m - (-2.69 m) = -2.10 m

\(v_{av,x}\) = Δx / Δt = 2.28 m / 323 s ≈ 0.00707 m/s

\(v_{av,y}\) = Δy / Δt = -2.10 m / 323 s ≈ -0.00650 m/s

|\(v_{av}\)| = √(\((v_{av,x})^2\) + \((v_{av,y})^2\)) = √\(((0.00707 m/s)^2 + (-0.00650 m/s)^2\)) ≈ 0.00955 m/s

Therefore, the components of the turtle's average velocity are approximately:

\(v_{av,x}\)≈ 0.00707 m/s

\(v_{av,y}\) ≈ -0.00650 m/s

And the magnitude of the turtle's average velocity is approximately:

|\(v_{av}\)| ≈ 0.00955 m/s

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Answer

(-4,3)

Step-by-step explanation:

The z-score of 2 for a sample has a mean of 100 and a standard deviation of 6 is 112.

The value that would correspond to the z-score of 2 for a sample with a mean of 100 and standard deviation of 6 can be calculated using the formula for z-score:
z = (x - mean) / standard deviation

In this case, we want to find the value of x that corresponds to a z-score of 2. We can rearrange the formula to solve for x:
x = (z * standard deviation) + mean

Substituting the values given in the question:
x = (2 * 6) + 100
x = 12 + 100
x = 112

Therefore, the value that corresponds to the z-score of 2 for this sample is 112.

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Answer:

Matt is a lawyer who used to charge his clients $330 per hour. Matt recently reconsidered his rates and ultimately decided to charge $231 per hour. What was the percent of decrease in the billing rate?

Step-by-step explanation:

c is the ansswer

Answer:

241.44  maybe the number 572 is wrong? is strange you get decimals for such a simple problem

Step-by-step explanation:

chair=c

lamp=l

table=a

we know everything costs 572 dollars

a+l+c=572

c=4*l so the next equations is a+l+4l=572 or a+5l=572

but a=4*l-23

next equation will be

4l-23+5l=572

9l=572+23

9l=595

lamp=66.11  chair=264.44

table=264.44-23=241.44

Answer:

Step-by-step explanation:

Since there are 985 square feet to cover, and it costs 12.50 per square foot, you multiply 12.50 by 985 to get 12,312.50, the total cost and answer.

Answer:

A

Step-by-step explanation:

A

The correct options are (b) f(x)=-3x⁵+5x-2

                                        (d) f(x)=x³-8x²

The function are written in standard form by writing the highest degree term at first and then writting other term according to decreasing order of degree of the variable.

for example f(x)=x⁴+x³+x²+x+1

So according to the question

the function should be written in standard form

so by checking every option,

(a) f(x)=8-x⁵ here highest power is 5 but that term is present at second term. so option A is incorrect.

(b) f(x)=-3x⁵+5x-2 here highest power is 5 and that term is present at first term. then all the terms are arranged in decrreasing order of power.

(c) f(x)=2x⁵+2x+x³ here highest power is 5 and that term is present at first term. then the second highest powered term is 3 and that term is present at third position which should be present at second position.

(d) f(x)=x³-8x² here here highest power is 3 and that term is present at first term. then all the terms are arranged in decrreasing order of power.

Therefore, The correct options are

(b) f(x)=-3x⁵+5x-2

(d) f(x)=x³-8x²

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Answer: The first answers are B. and D.

The second answer is 5

Step-by-step explanation: The third answer is -3

A. Using the given information, we can standardize the value 203.4 using the formula \(z = (X - μ) / σ\), where X is the value of interest, μ is the mean, and σ is the standard deviation.

Thus, we get: \(z = (203.4 - 208.5) / 35.4 = -0.14407\)

Using a standard normal distribution table or calculator, we can find the probability that a randomly selected value is greater than \(203.4\):

\(P(X > 203.4)\) = \(P(Z > -0.14407)\) = \(0.5563\) (rounded to 4 decimal places)

To find the probability that the sample mean is greater than 203.4, we need to use the central limit theorem, which states that the sample mean of a large enough sample size (n >= 30) from a population with any distribution has a normal distribution with mean μ and standard deviation σ / sqrt(n). Thus, we get:

\(z = (203.4 - 208.5) / (35.4 / sqrt(236))\)\(= -1.3573\)

Using a standard normal distribution table or calculator, we can find the probability that the sample mean is greater than 203.4:

\(P(X¯¯¯ > 203.4) = P(Z > -1.3573)\)= \(0.0867\) (rounded to 4 decimal places)

B. Using the given information, we can standardize the values \(217.5\) and \(234.6\) using the same formula as before. Thus, we get:

\(z1 = (217.5 - 223.7) / 56.9\) \(= -0.10915\)

\(z2 = (234.6 - 223.7) / 56.9 = 0.19235\)

Using a standard normal distribution table or calculator, we can find the probability that a randomly selected value is between 217.5 and 234.6:

\(P(217.5 < X < 234.6) = P(-0.10915 < Z < 0.19235) = 0.2397\) (rounded to 4 decimal places)

To find the probability that the sample mean is between 217.5 and 234.6, we can use the same formula as before, but with the sample size and population parameters given in part B. Thus, we get:

\(z1 = (217.5 - 223.7) / (56.9 / sqrt(244)) = -1.0784\)

\(z2 = (234.6 - 223.7) / (56.9 / sqrt(244)) = 1.7256\)

Using a standard normal distribution table or calculator, we can find the probability that the sample mean is between 217.5 and 234.6:

\(P(217.5 < X¯¯¯ < 234.6) = P(-1.0784 < Z < 1.7256)\)= \(0.8414\)(rounded to 4 decimal places)

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The 11th term of this geometric sequence 7 -28, 112, ....​ include the following: 7,340,032.

In Mathematics, the nth term of a geometric sequence can be calculated by using this mathematical equation (formula):

aₙ = a₁rⁿ⁻¹

Where:

Next, we would determine the common ratio as follows;

Common ratio, r = a₂/a₁

Common ratio, r = -28/7

Common ratio, r = -4

For the 11th term, we have:

a₁₁ = 7(-4)¹¹⁻¹

a₁₁ = 7,340,032.

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Answer:

To calculate the distance around the outside of the circular fire pit, also known as the circumference:

Exact distance:

Circumference = pi x diameter

C = pi x 3 feet

C = 3.14 x 3 feet

C = 9.42 feet

Approximate distance:

Circumference = 2 x radius x pi

Radius = diameter / 2 = 1.5 feet

C = 2 x 1.5 feet x 3.14

C = 9.42 feet

Therefore, the exact distance around the outside of the circular fire pit is 9.42 feet, and the approximate distance is also 9.42 feet.

To calculate the area inside the circular fire pit:

Exact area:

Area = pi x (radius)^2

Area = 3.14 x (1.5 feet)^2

Area = 7.07 square feet

Approximate area:

Area = (diameter / 2)^2 x pi

Area = (1.5 feet)^2 x 3.14

Area = 7.065 square feet

Therefore, the exact area inside the circular fire pit is 7.07 square feet, and the approximate area is 7.065 square feet.

Answer:

\((y+2)=\frac{2}{3} (x-5)\)

Step-by-step explanation:

Point slope form is shown below:

\((y-y_1)=m(x-x_1)\)

We are given the slope m = 2/3 and the point x1 = 5, y1 = -2

Simply plug in these numbers into the above equation.

\((y--2)=\frac{2}{3} (x-5)\)

Simplify:

\((y+2)=\frac{2}{3} (x-5)\)

================================================

Work Shown:

M = number of miles

L = cost to rent a luxury car = 1.15M + 16.40

E = cost to rent an economy car = 0.80M+10.95

C = difference in price

C = L - E

C = (1.15M + 16.40) - (0.80M+10.95)

C = 1.15M + 16.40 - 0.80M-10.95

C = 0.35M + 5.45

Don't forget to distribute the negative to each term in the second parenthesis.

-------------------

Optional Section:

Let's say you drove M = 100 miles as an example.

The luxury car would cost L = 1.15M+16.40 = 1.15*100+16.40 = 131.40 dollars to rent.

The economy car would cost E = 0.80M+10.95 = 0.80*100+10.95 = 90.95 dollars to rent.

The difference in rental costs is L-E = 131.40-90.95 = 40.45 dollars.

Or you could say C = 0.35M+5.45 = 0.35*100+5.45 = 40.45

This means you pay $40.45 more if you go for a luxury car instead of an economy car.

Rounding to the nearest tenth, the substance's half-life is approximately 4.7 days.

To find the substance's half-life, we can use the formula N = N0 * e^(-kt), where:

N is the final amount of the substance,

N0 is the initial amount of the substance,

k is the decay constant,

t is the time in days.

In this case, the half-life represents the time it takes for the substance to decay to half of its initial amount. So, we have N = N0/2.

Substituting these values into the formula, we get:

N0/2 = N0 * e^(-k * t)

Dividing both sides by N0 and simplifying, we have:

1/2 = e^(-k * t)

To isolate t, we can take the natural logarithm (ln) of both sides:

ln(1/2) = -k * t

Since ln(1/2) is the natural logarithm of 1/2 (approximately -0.6931), we can rewrite the equation as:

-0.6931 = -k * t

Dividing both sides by -k, we find:

t = -0.6931 / k

Substituting k = 0.1472 (given), we have:

t = -0.6931 / 0.1472 ≈ -4.7121

Since time cannot be negative, we take the absolute value:

t ≈ 4.7121

Rounding to the nearest tenth, the substance's half-life is approximately 4.7 days.

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The length of each side of the box is 10 centimeter.

Volume is the amount of space occupied by a three-dimensional figure as measured in cubic units.

Given,

The volume of the cubic box = 1 liter

We know 1 liter= 1000 cubic centimeter

Volume of the cubic box= \(x^3}\)

Then,

\(x^{3}=1000\\ x=\sqrt[3]{1000}\)

x=10 centimeter

Hence, the length of each side of the box is 10 centimeter.

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Thus, we would expect Maggie to consume 0 scoops of ice cream.

To determine how many scoops of ice cream Maggie is expected to consume, we need to find the value of n that maximizes Maggie's total benefit function, TB(n) = 84n - n^2.

Since the price of ice cream is $27.5 per scoop,

we can equate Maggie's total benefit to the cost of the ice cream: 84n - n^2 = 27.5n.

Simplifying the equation, we have: n^2 - 56.5n = 0.

Factoring out an n, we get: n(n - 56.5) = 0.

Therefore, n = 0 or n = 56.5.

However, since n can only be an integer, Maggie cannot consume 56.5 scoops of ice cream.

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The domain of this relationship would be all possible combinations of values for x and y that satisfy the equation 5x + 9y = 90.

To find the equation:

The domain of the relationship in this scenario is the number of youth and adult tickets that were purchased by the group.

It is given that the cost of a youth ticket is $5 and the cost of an adult ticket is $9. Therefore, the number of youth and adult tickets can be represented by the variables x and y respectively.

We also know that the group spent a total of $90 on tickets, so the equation representing the relationship between the number of youth and adult tickets purchased would be:

5x + 9y = 90

So the domain of this relationship would be all possible combinations of values for x and y that satisfy the equation 5x + 9y = 90.

It's important to note that the domain would be all non-negative integers of x and y as the number of youth and adult tickets cannot be negative numbers.

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Answer: either -65 or -2.6

Hope this helps

It depends on the way you do the math, but Its one of those.

In the triangle below,  m∠K=55°  and  m∠N=75°. KN is the longest side of  △KNT.

We are given a triangle with angles K, N, and T as shown below. We have been given that ∠K = 55° and ∠N = 75°.

We are to find out the side which is the longest among KN, NT, and KT.

Now, we know that in any triangle, the longest side is opposite to the largest angle and the smallest side is opposite to the smallest angle.

We can see that ∠N is the largest angle in this triangle and KN is opposite to it. So, KN is the longest side.

Hence, KN is the longest side of  △KNT. Therefore, option (b) is correct.

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Step-by-step explanation:

There are (9+8+7)  = 24 parts  that add up to 144

each part is then 144/24 = 6

then each side is    9 parts =  9*6 = 54

                8 parts = 8 * 6 = 48

       7 parts    7 * 6 = 42

A 10% increase in cigarette prices has been found to result in a 4% decrease of smokers.

An increase in cigarette price will result in a decrease in the demand for cigarettes.

Since more money needs to be spent to but the same product, less consumers can be able to afford it.

Therefore, a 10% increase in cigarette prices has been found to result in a 4% decrease of smokers.

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Answer:

16y+qy  

2

​

+41Y  

2

​

−1140Y

Step-by-step explanation:

Pasos de la solución

8×2y+q×y2+41×Y2−570×2Y

Multiplica 8 y 2 para obtener 16.

16y+qy  

2

​

+41Y  

2

​

−570×2Y

Multiplica 570 y 2 para obtener 1140.

16y+qy  

2

​

+41Y  

2

​

−1140Y

The circumference of the circle to the nearest hundredth is 21.98 inches.

The circumference of a circle is the measure of the boundary or the length of the complete arc of a circle.

The circumference of a circle is the perimeter of the circle. It's the wholes boundary of the circle.

The circumference of the circle can be found as follows:

circumference of a circle = 2πr

where

Therefore,

diameter of the circle = 7 inches

radius of the circle = 7 / 2 = 3.5 inches

Hence,

circumference of a circle = 2 × 3.14 × 3.5

circumference of a circle = 21.98 inches

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The ciphertext for 111000101 when the key is 101 and the initial state is s = 000, using Output Feedback Mode is 101100001 and using Block Chaining is 111011111 is the answer.

Given n = 3. Let K = Z23, and Bk: Z23 → Z23 such that Bk(x) = k + x. Now, we have to encrypt 111000101 using the key 101 and the initial state s = 000, using Output Feedback Mode.

Let us discuss it: Output Feedback Mode Encryption: At first, convert the initial state s to a 3-bit integer. Then, compute the first ciphertext bit c1 as the first bit of the state s XOR with the first bit of the plaintext m1.

Now, compute s1 as (s/2) ⊕ c1  and then compute the second ciphertext bit c2 as the second bit of s1 XOR the second bit of the plaintext m2.

Similarly, compute s2 as (s1/2) ⊕ c2 and then compute the third ciphertext bit c3 as the third bit of s2 XOR the third bit of the plaintext m3.

Continuing in this way, we get the ciphertext, which is 101100001. So, the ciphertext for 111000101 when the key is 101 and the initial state is s = 000, using Output Feedback Mode is 101100001.

Block Chaining Encryption:

In Block Chaining, we use the priming value to generate the ciphertext.

For the given plaintext, we have to start with y0 = 000, the priming value.

Then, compute z1 = Bk(y0) XOR m1.

Similarly, we get the next ciphertext as zi = Bk(yi-1) XOR mi and yi = zi-1, where i = 2,3,...,9.

So, we get the ciphertext as 111011111 for 111000101 when the key is 101 and the priming value is y0 = 000, using Block Chaining.

Hence, the ciphertext for 111000101 when the key is 101 and the initial state is s = 000, using Output Feedback Mode is 101100001 and using Block Chaining is 111011111.

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Given:

Food = 30 pounds of food per hiker.

Food consumption = 12 pounds of food a day.

No. of hikers = 7

To find:

The equation for the given situation.

Solution:

Let x be the number of days and y be the amount of remaining food.

Total amount is the product of number of hikers and food per hiker.

\(\text{Total food}=7\times 30\)

\(\text{Total food}=210\)

Food consumption of one day = 12 pounds

Food consumption of x days = 12x pounds

Now,

Remaining food = Total food - Food consumption of x days

\(y=210-12x\)

\(y=-12x+210\)

Therefore, the required equation is \(y=-12x+210\).

Note: Option C is correct if there is -12 instead of 12.

Answer:

0.134%

Step-by-step explanation:

We have to

sd * P = [p * (1 - p) / n] ^ (1/2)

where p = 0.52 and n = 775, replacing:

sd * P = [0.52 * (1 - 0.52) / 775] ^ (1/2) = 0.0179

Now the probability would be:

P = 1 - P [(- 0.05) /0.0179 <z <(0.05) / 0.0179]

P = 1 - P (-2.79 <z <2.79)

P = 1 - P (z <2.79) - P (z <-2.79)

P = 1 - 0.9974 - 0.00126

P = 1 - 0.99614

P = 0.00134

Therefore the probability is 0.134%

Answer:

Combine Like Terms:

=1728+−9x^2+−4x+3

=(−9x^2)+(−4x)+(1728+3)

= −9x^2+−4x+1731

Answer:

Hello there! I would say the answer is C,

Step-by-step explanation:

I hope this helps!!!