y = -3x+4
y = 3x+4

HELP

Answer:

The solution set of the quadratic function \(x^{2}+6\cdot x +10\) is \(\{-3+i,-3-i\}\) .

Step-by-step explanation:

Let be a second-order polynomial (quadratic function) is standard form and equalized to zero:

\(a\cdot x^{2}+b\cdot x + c = 0\)

Its roots can be determined by the Quadratic Formula in terms of its polynomial coefficients, which states that:

\(x_{1,2} = \frac{-b\pm\sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}\)

Given that \(a = 1\), \(b = 6\) and \(c = 10\), the roots of the polynomial are, respectively:

\(x_{1,2} = \frac{-6\pm \sqrt{6^{2}-4\cdot (1)\cdot (10)}}{2\cdot (1)}\)

\(x_{1,2} = -3\pm i\)

\(x_{1} = -3+i\)

\(x_{2} = -3 -i\)

The solution set of the quadratic function \(x^{2}+6\cdot x +10\) is \(\{-3+i,-3-i\}\) .

Answer:

answer for the first is "Obtuse", answer for the second is "acute", answer for the third is a=right, b=obtuse, c=obtuse, d=acute

Step-by-step explanation:

A basis for the subspace is given by the three vectors consisting of all vectors of the form [x1, -2x1+x2, -9x1+4x2, -5x1-7x2]:

[1, 0, 0, -5], [0, 1, 4, -7], and [0, 0, 0, 1].

To find a basis for the given subspace, we need to determine the linearly independent vectors that span the subspace.

Let's rewrite the given vector as a linear combination of the standard basis vectors in R4:

[x1, -2x1+x2, -9x1+4x2, -5x1-7x2] = x1[1, 0, 0, -5] + x2[0, 1, 4, -7] + 0[0, 0, 0, 1]

Thus, the subspace is spanned by the vectors [1, 0, 0, -5], [0, 1, 4, -7], and [0, 0, 0, 1].

To check for linear independence, we can set up the following augmented matrix and row reduction:

[ 1 0 0 | 0 ]

[ 0 1 4 | 0 ]

[ 0 -2 -9 | 0 ]

[-5 -7 0 | 0 ]

Using row operations, we can reduce this to:

[ 1 0 0 | 0 ]

[ 0 1 0 | 0 ]

[ 0 0 1 | 0 ]

[ 0 0 0 | 0 ]

Since the only solution is the trivial solution, the vectors are linearly independent.

Therefore, a basis for the subspace is given by the three vectors:

[1, 0, 0, -5], [0, 1, 4, -7], and [0, 0, 0, 1].

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The solutions to $Q = np$ are exactly the integers of the form $no + \frac{p+1}{k}s$ where $s$ is relatively prime to $k$.

We have $Q = np$ and $Q = isP$ for some positive integers $n$ and $s$, where $sP = 0$.

By the division algorithm, we can write $n = is + r$ for some non-negative integer $r < s$.

Then we have $Q = np = isp + rp = s(ip) + rp$, which implies that $r$ is also a solution to $Q = np$.

Since $n$ is the smallest positive integer for which $Q = np$, we must have $r = 0$, which implies that $n = is$.

Therefore, every solution to $Q = np$ looks like $no + is$ for some integer $i$.

To see this, note that if $Q = mp$ for some positive integer $m$, then we have $m = nt$ for some integer $t$, and hence $Q = mp = (nt)o + (mt)s = no + (mt)s$.

Since $s$ is the smallest positive integer such that $sP = 0$, we have $s \leq \frac{p+1}{2}$ (by Hasse's theorem).

Therefore, there are at most $\frac{p+1}{2}$ possible values for $is$, and hence at most $\frac{p+1}{2}$ possible solutions to $Q = np$.

Since $Q$ has order $n$, we have $n \mid p+1$ by Lagrange's theorem.

Therefore, $is \mid p+1$ for every solution $is$ to $Q = np$, and hence there are exactly $\frac{p+1}{n}$ solutions to $Q = np$.

Therefore, we have $n = \frac{p+1}{k}$ for some integer $k$, and hence every solution to $Q = np$ looks like $no + \frac{p+1}{k}s$ for some integer $s$.

Note that if $s$ is not relatively prime to $k$, then $no + \frac{p+1}{k}s$ is not a valid solution.

Therefore, the solutions to $Q = np$ are exactly the integers of the form $no + \frac{p+1}{k}s$ where $s$ is relatively prime to $k$.

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Let's calculate the products and check if they indeed have the same value:

Product of 32 and 46:

32 * 46 = 1,472

Reverse the digits of 23 and 64:

23 * 64 = 1,472

As you mentioned, the products are the same. This phenomenon is not unique to this particular pair of numbers. In fact, it occurs with any pair of two-digit numbers whose digits, when reversed, are the same as the product of the original numbers.

To find two other pairs of two-digit numbers that have this property, we can explore a few examples:

Product of 13 and 62:

13 * 62 = 806

Reversed digits: 31 * 26 = 806

Product of 17 and 83:

17 * 83 = 1,411

Reversed digits: 71 * 38 = 1,411

As for determining if a given pair of two-digit numbers will have this property without actually performing the multiplication, there is a simple rule. For any pair of two-digit numbers (AB and CD), if the sum of A and D equals the sum of B and C, then the products of the original and reversed digits will be the same.

For example, let's consider the pair 25 and 79:

A = 2, B = 5, C = 7, D = 9

The sum of A and D is 2 + 9 = 11, and the sum of B and C is 5 + 7 = 12. Since the sums are not equal (11 ≠ 12), we can determine that the products of the original and reversed digits will not be the same for this pair.

Therefore, by checking the sums of the digits in the two-digit numbers, we can determine whether they will have the property of the products being the same when digits are reversed.

The calculations for the given data set are as follows:

Mean = 75.7

Median = 79

Mode = 80

Standard Deviation ≈ 11.09

Coefficient of Variation ≈ 14.63%

To find the mean, median, mode, standard deviation, and coefficient of variation for the given data set, let's go through each calculation step by step:

Data set: 79, 80, 80, 80, 74, 80, 80, 79, 64, 78, 73, 78, 74, 45, 81, 48, 80, 82, 82, 70

Let's calculate:

Deviation: (-4.7, 4.3, 4.3, 4.3, -1.7, 4.3, 4.3, -4.7, -11.7, 2.3, -2.7, 2.3, -1.7, -30.7, 5.3, -27.7, 4.3, 6.3, 6.3, -5.7)

Squared Deviation: (22.09, 18.49, 18.49, 18.49, 2.89, 18.49, 18.49, 22.09, 136.89, 5.29, 7.29, 5.29, 2.89, 944.49, 28.09, 764.29, 18.49, 39.69, 39.69, 32.49)

Mean of Squared Deviations = (22.09 + 18.49 + 18.49 + 18.49 + 2.89 + 18.49 + 18.49 + 22.09 + 136.89 + 5.29 + 7.29 + 5.29 + 2.89 + 944.49 + 28.09 + 764.29 + 18.49 + 39.69 + 39.69 + 32.49) / 20

Mean of Squared Deviations = 2462.21 / 20

Mean of Squared Deviations = 123.11

Standard Deviation = √(Mean of Squared Deviations)

Standard Deviation = √(123.11)

Standard Deviation ≈ 11.09

Coefficient of Variation:

The coefficient of variation is a measure of relative variability and is calculated by dividing the standard deviation by the mean and multiplying by 100:

Coefficient of Variation = (Standard Deviation / Mean) * 100

Coefficient of Variation = (11.09 / 75.7) * 100

Coefficient of Variation ≈ 14.63%

So, the calculations for the given data set are as follows:

Mean = 75.7

Median = 79

Mode = 80

Standard Deviation ≈ 11.09

Coefficient of Variation ≈ 14.63%

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Answer:

call 911

Step-by-step explanation:

they serve anyone

The equation is e = 62h for the plumber and m = 10h for the runner

An equation is an expression that shows the relationship between two or more numbers and variables.

7) Let e represent the plumber earnings in dollars after h hours of work.

She earns $62 for each hour, therefore:

e = 62h

8) Let m represent the distance in miles run in h hours

The runner averages 10 miles per hour., therefore:

m = 10h

The equation is e = 62h for the plumber and m = 10h for the runner

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Subtract full rotations of 2π until the angle is greater than or equal to 0 and less than 2π

sec(π4) – trigonometry value

The exact value of trigonometry - sec(π4) is 2√2.

Multiply 2√2 by √2.

2⋅√2⋅2

Combine and simplify the denominator.

2√2

Cancel the common factor of 2.

√2

There are various ways to display the outcome.

Exact Form:

√2

Decimal Form:

1.41421356…

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Answer:

For bag C

Step-by-step explanation:

Bag C has more blue marbles than red ones

Answer:

Surface area = 2,160 in²

Step-by-step explanation:

Given:

Length of box = 15 in

Width of box = 30 in

Height of box = 24 in

Find:

Surface area

Computation:

Surface area = 2h[l+b]

Surface area = 2(24)[30 + 15]

Surface area = 48 x 45

Surface area = 2,160 in²

Answer:

Cost of Senior Citizen Ticket: $15

Cost of Student Ticket: $3

Step-by-step explanation:

Let the price of a senior citizen ticket be s.

Let the price of a student ticket be t.

Day 1:

s + 12t = 51

Day 2:

5s + 6t = 93

The system of equations is:

s + 12t = 51

5s + 6t = 93

Let's use the substitution method to solve it. Solve the first equation for s.

s = 51 - 12t

Now substitute s in the second equation with 51 - 12t.

5s + 6t = 93

5(51 - 12t) + 6t = 93

255 - 60t + 6t = 93

Subtract 255 from both sides. Combine -60t and 6t.

-54t = -162

Divide both sides by -54.

t = 3

Now substitute 3 for t in the equation

s = 51 - 12t

s = 51 - 12(3)

s = 51 - 36

s = 15

Answer:

Cost of Senior Citizen Ticket: $15

Cost of Student Ticket: $3

The possible widths of Peggy's garden, in increasing order, are:

40 feet and 60 feet.

Let x be the width of the rectangle.

The length of the rectangle can be determined as: length = (200 - 2x) / 2

We divide by 2 since one side borders an existing fence, so we only need to fence three sides.

Calculate the area of the rectangle:

Area = length * width

Area = [(200 - 2x) / 2] * x

Set up the equation:

[(200 - 2x) / 2] * x = 4800

Simplify the equation:

(200 - 2x) * x = 9600

Expand and rearrange the equation:

\(200x - 2x^2 = 9600\\\\2x^2 - 200x + 9600 = 0\)

Solve the quadratic equation:

We can factor the equation:

(x - 40)(2x - 120) = 0

Setting each factor equal to zero gives us two possible solutions:

x - 40 = 0 => x = 40

2x - 120 = 0 => 2x = 120 => x = 60

Determine the possible widths:

The possible widths are 40 and 60.

Therefore, the possible widths of Peggy's garden, in increasing order, are:

40 feet and 60 feet.

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Using the Poisson distribution, there is a 0.8335 = 83.35% probability that 2 or fewer will be stolen.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

\(P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}\)

The parameters are:

The probability that a rental car will be stolen is 0.0004, hence, for 3500 cars, the mean is:

\(\mu = 3500 \times 0.0004 = 1.4\)

The probability that 2 or fewer cars will be stolen is:

\(P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)\)

In which:

\(P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}\)

\(P(X = 0) = \frac{e^{-1.4}1.4^{0}}{(0)!} = 0.2466\)

\(P(X = 1) = \frac{e^{-1.4}1.4^{1}}{(1)!} = 0.3452\)

\(P(X = 2) = \frac{e^{-1.4}1.4^{2}}{(2)!} = 0.2417\)

Then:

\(P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2466 + 0.3452 + 0.2417 = 0.8335\)

0.8335 = 83.35% probability that 2 or fewer will be stolen.

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Answer:

no c

Step-by-step explanation:

Answer:

Step-by-step explanation:

the percentage error: P

Approximate value=a 1.41

Exact = e(1.41421356 or √2)

p=[(e-a)/e]×100

p=[√2-1.41)/√2]×100

p=0.29794385 ≅0.30 or 30 percent when rounded to the nearest hundredth

b: p=[(π-3.14)/π]×100=0.05069573≅0.05 =5 percent when rounded to the nearest hundredth. in the pi case the percentage of error is small 5 % but in the case of square roots the percentage id higher(30%). in this case it is better to round the answer at the end of calculation( math problem)

c) sometimes when rounding square roots or irrational number like pi it is useful to use decimal approximate, in the case of pi the percentage rate was 5 percent which is very low comparing to the square root which is 30 %.

Answer:

1) The image of the line has the same slope as the pre-image but a different y-intercept.

hope this helps ;)

Answer:

13:11

Step-by-step explanation:

325:275

If divided by 5 all through, you get 65:55, then by 5 again you get 13:11

Answer:

13/11 = 1.1818

Step-by-step explanation:

Boys/girls = 325/275 = 13/11 = 1  2/11 = 1.1818

I don't know what simplest form means.

Answer:

Hello!!

The x and y intercepts on the following graph is...

(a) x-intercept \(1\)

(b) y-intercept \(-4\)

Hope this helps!!

Answer: Ramesh has 80,000 100Rs, 120,000 50Rs and 200,000 10Rs.

Step-by-step explanation:

From the question, the ratio of number of 100, 50 and 10Rs notes is 2:3:5respectively and the total cash with ramesh is 400000.

Total ratio = 2+3+5 = 10

100Rs = 2/10 × 400000

= 80,000

50Rs = 3/10 × 400000

= 120,000

10Rs = 5/10 × 400000

= 200,000

Ramesh has 80,000 100Rs, 120,000 50Rs and 200,000 10Rs.

To calculate the amount Briana saved by purchasing a backpack with a sales promotion, we need to find the difference in prices between the two backpacks after applying the respective discounts.

For the first backpack that originally costs $45 with a sales promotion of 20% off:

Discounted price = $45 - (20% * $45) = $45 - $9 = $36

For the second backpack that originally costs $42 with a sales promotion of 10% off:

Discounted price = $42 - (10% * $42) = $42 - $4.2 = $37.8

Now we can calculate the savings:

Amount saved = Original price - Discounted price

Amount saved = $42 - $37.8 = $4.2

Therefore, Briana saved $4.2 by purchasing the backpack that cost $45 with a 20% off promotion instead of the backpack that cost $42 with a 10% off promotion.

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The position of the mass after t seconds is: x(t) = 1.41 * cos(1.77 * t) meters. We can calculate it in the following manner.

The force constant of the spring can be calculated using the formula:

F = -kx

Where F is the force applied, x is the displacement from the equilibrium position, and k is the force constant.

Rearranging the formula, we get:

k = -F/x

Substituting the given values, we get:

k = -10 N / 0.4 m = -25 N/m

The equation of motion for the mass attached to the spring is:

mx'' + kx = 0

Where m is the mass of the object, x'' is the second derivative of displacement with respect to time, and k is the force constant of the spring.

Substituting the given values, we get:

8x'' + (-25)x = 0

This is a second-order homogeneous differential equation with constant coefficients, and its general solution is:

x(t) = A cos(5t) + B sin(5t)

Where A and B are constants determined by the initial conditions.

To find A and B, we use the initial displacement and velocity:

x(0) = 0
x'(0) = 2.5 m/s

Substituting these values into the equation of motion, we get:

x(0) = A cos(0) + B sin(0) = 0
x'(0) = -5A sin(0) + 5B cos(0) = 2.5

From the first equation, we get:

B = 0

Substituting this into the second equation, we get:

A = 0.5

Therefore, the equation of motion for the mass attached to the spring is:

x(t) = 0.5 cos(5t)

The position of the mass after t seconds is given by this equation, so we can substitute any value of t to get the position:

x(t) = 0.5 cos(5t)

For example, after 1 second, the position of the mass is:

x(1) = 0.5 cos(5) = -0.354 meters (rounded to three decimal places)
To find the position of the mass after t seconds, we need to determine the spring constant (k) and the amplitude (A) of the oscillation.

1. Calculate the spring constant (k) using Hooke's Law:
F = k * x
10 N = k * 0.4 m
k = 25 N/m

2. Calculate the angular frequency (ω) using the mass (m) and spring constant (k):
ω = sqrt(k/m)
ω = sqrt(25 N/m / 8 kg)
ω = 1.77 rad/s

3. Calculate the amplitude (A) using the initial velocity (v₀) and angular frequency (ω):
v₀ = ω * A
2.5 m/s = 1.77 rad/s * A
A = 1.41 m

Now, we can find the position of the mass after t seconds using the equation for simple harmonic motion:
x(t) = A * cos(ω * t)

So, the position of the mass after t seconds is:
x(t) = 1.41 * cos(1.77 * t) meters

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Answer:

5n

Step-by-step explanation:

Step one:

Given data

Solve the problem

6n - n

The expression is an algebraic expression, since all the terms are the same, we want to perform a subtraction operation on the terms

so

6n-n= 5n

The answer is clearly no listed in the options

The standard deviation s given z = 3, a desired accuracy of 5%, a mean cycle time of 1.9, a sample size of 17, and (xi+x)2 = 0.1296 is approximately 0.10.

To calculate the standard deviation s, we need to use the formula: s = sqrt((xi+x)2/n-1), where xi is the deviation from the mean, x is the mean, and n is the sample size. First, we need to find xi, which is the square root of 0.1296 divided by n-1, or 0.1296/16 = 0.0081. Next, we find x, which is given as 1.9. Finally, we can use the formula to find s: s = sqrt(0.0081*17) = 0.10 (rounded to two decimal places).

The accuracy of 5% is not directly used in this calculation but is important for determining the confidence level of the standard deviation. The confidence interval is typically expressed as (x-bar ± t(s/√n)), where x-bar is the sample mean, t is the t-distribution value based on the desired confidence level and degrees of freedom, s is the sample standard deviation, and n is the sample size. In this case, we would need to know the desired confidence level and degrees of freedom to calculate the appropriate t-value.

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Answer: 30%

Step-by-step explanation: Solution for 6300 is what percent of 21000: 6300:21000*100 = (6300*100):21000 = 630000:21000 = 30. Now we have: 6300 is what percent of 21000 = 30.

if we take 21000(origin amount) to be the 100%, what's 6300 off of it in percentage?

\(\begin{array}{ccll} Amount&\%\\ \cline{1-2} 21000 & 100\\ 6300& x \end{array} \implies \cfrac{21000}{6300}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{10}{3} ~~=~~ \cfrac{100}{x}\implies 10x=300\implies x=\cfrac{300}{10}\implies x=30\)

Answer:

-4v³ - v² - v - 9

Step-by-step explanation:

1. Subtract the numbers

7v - 4 - 4v³ - v² - 8v - 5

7v - 9 - 4v³ - v² - 8v

2. Combine like terms

7v - 9 - 4v³ - v² - 8v

-v - 9 - 4v³ - v²

3. Rearrange Terms

-v - 9 - 4v³ - v²

-4v³ - v² - v - 9

May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 10 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!

Answer:

X,6,1

Step-by-step explanation:

i mean thats what i think the answer is.

it flips down over the x axis. (x)

then it moves right 6 (x+6)

then it moves up one (y+1)

The correct formula for the revenue generated by the item is Revenue = 200p - 5p^2.

The revenue generated by the item can be calculated by multiplying the price (p) by the unit sales (200 - 5p). Therefore, the correct formula for the revenue generated by the item is:

Revenue = Price x Unit Sales
Revenue = p(200 - 5p)
Revenue = 200p - 5p^2

The revenue generated by the item is a quadratic function of the price (p). To find the maximum revenue, we need to differentiate the function with respect to p and set it equal to zero:

dRevenue/dp = 200 - 10p = 0
10p = 200
p = 20

Therefore, the maximum revenue is generated when the price of the item is $20. Substituting p = 20 in the revenue formula, we get:

Revenue = 200(20) - 5(20^2) = $2000

Hence, the correct formula for the revenue generated by the item is Revenue = 200p - 5p^2, and the maximum revenue is achieved when the price of the item is $20, generating a revenue of $2000.

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