What are the solutions of x2 - 2x +17 - 0?
O A. x = 1+2, or x = 1 - 2
O B. X = 1+4, or x = 1- 47
O c. x = 2, or x = -2
O D. x = 4; or x = -4/

The correct answer is B. $1022.To find out how much of her bonus Amee has left, we need to subtract the total amount she spent from her initial bonus amount.

Amee's initial bonus amount is $1550.

She spent $225 at the department store, $275 at the home furnishing store, and $28 at the card shop.

Total amount spent = $225 + $275 + $28 = $528.

To find the amount she has left, we subtract the total amount spent from her initial bonus amount:

Amount left = Initial bonus amount - Total amount spent = $1550 - $528 = $1022.

Therefore, Amee has $1022 left from her bonus.

The correct answer is B. $1022.

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Answer:

C.

Step-by-step explanation:

Slope-intercept form is described as y=mx+b, where m = the slope, and b = the y-intercept. Since you are given these two numbers, just plug them into the slope-intercept form. This gives you y=5x-3.

"All of the above" is the correct answer, as per the given conditional statements.

Conditional statements are statements that are true or false based on the truth or falsity of another statement. The following are conditional statements:

a) If it is raining, then I'll wear my hat

b) You can come only if you wear your socks

c) You should tell the truth unless you don't care about your conscience

Conditional statements are statements that relate two things together, where one thing relies on the other thing being true or false. There are a few different ways to write conditional statements. The most common format for writing conditional statements is using the “if-then” format.

A conditional statement has two parts:

If the hypothesis is true, then the conclusion must be true.

If the hypothesis is false, then the conclusion can be either true or false.

In the given question, all the options are conditional statements. Therefore, the correct answer is "All of the above".

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Given:

Number of tomatoes Sheldon picks = \(4\dfrac{4}{10}\) kg

Rotten tomatoes = 1.5 kg

To find:

How many kilograms of tomatoes were not rotten?

Solution:

Number of tomatoes Sheldon picks = \(4\dfrac{4}{10}\) kg

                                                            = \(\dfrac{4(10)+4}{10}\) kg

                                                            = \(\dfrac{40+4}{10}\) kg

                                                            = \(\dfrac{44}{10}\) kg

                                                            = \(4.4\) kg

Rotten tomatoes = 1.5 kg

Remaining tomatoes which are not rotten is

Required tomatoes = Tomatoes Sheldon picks - Rotten tomatoes

                                = \(4.4-1.5\)

                                = \(2.9\) kg

Therefore, the tomatoes which were not rotten is 2.9 kg.

The candy store will use 103 grams of sugar in 10 hours.

To find out how many grams of sugar the store will use in 10 hours, we can simply multiply the amount of sugar used in one hour (10.3 grams) by the number of hours (10).

To solve the problem, we use a simple multiplication formula: the amount used per hour (10.3 grams) multiplied by the number of hours (10) to find the total amount of sugar used in 10 hours.

We can interpret this problem using a rate equation: the rate of sugar usage is 10.3 grams/hour, and the time period is 10 hours. Multiplying the rate by the time gives the total amount of sugar used.

So the calculation would be:

10.3 grams/hour x 10 hours = 103 grams

Therefore, the candy store will use 103 grams of sugar in 10 hours.

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Answer:

after a week  7 days

Step-by-step explanation:

1.75+0.75=2.5

17.5/2.5=7

7 days is a week \please mark brailiest if it helped

Answer:

-40

Step-by-step explanation:

you multiply both sides by 10 to get the variable by its self

n = -40

hope this helps

Answer:

n = -40

Step-by-step explanation:

n/10 = -4

n/10 x 10 = -4 x 10

n = -40

Multiply 10 on the side w/ the variable and do the same on the other side of the equal sign (this is a rule while solving for variables: something you do to one side, you do the same to the other).

Then, you got your answer. Hope I helped <3

the shaded segment PQR will be 18.265m².

What is are of triangle?

The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.

The sum of all angle of triangle = 180

the diagram shows a sector OPQR of a circle, centre O and radius 8 cm.

Area of shaded part = Area of quadrant − Area of triangle

=πr²/ 4 - 1/2 bh

= π × 8²/ 4  - 1/ 2 × 8× 8

= 18.265m².

Hence the shaded segment PQR will be 18.265m².

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Substituting these values back into equation (4), we can solve for x2. For λ = -1 + 2√5: (3 - (-1 + 2√5)) - (3 + (-1 + 2√5))x2² - x2 = 0

To find the local minimizers of the function f(x1, x2) = x1² - 2x1x2 + 4x1x2, subject to the constraint x1² + x2² - 1 = 0, we can use the Lagrange multiplier method.

Let's set up the Lagrangian function L(x1, x2, λ) = f(x1, x2) + λ(g(x1, x2)), where g(x1, x2) is the constraint equation.

L(x1, x2, λ) = x1² - 2x1x2 + 4x1x2 + λ(x1² + x2² - 1).

To find the critical points, we take the partial derivatives of L with respect to x1, x2, and λ, and set them equal to zero:

∂L/∂x1 = 2x1 - 2x2 + 4x1 + 2λx1 = 0   (1)

∂L/∂x2 = -2x1 + 4x2 + 2λx2 = 0      (2)

∂L/∂λ = x1² + x2² - 1 = 0             (3)

From equation (1), we have:

2x1 - 2x2 + 4x1 + 2λx1 = 0

6x1 - 2x2 + 2λx1 = 0

3x1 - x2 + λx1 = 0

From equation (2), we have:

-2x1 + 4x2 + 2λx2 = 0

-2x1 + (4 + 2λ)x2 = 0

We can solve these equations simultaneously to find the values of x1, x2, and λ.

Solving equations (3) and (4) for x1 and x2:

x1² + x2² = 1   (3)

3x1 - x2 + λx1 = 0   (4)

From equation (3), we can express x1² as 1 - x2².

Substituting this into equation (4):

3(1 - x2²) - x2 + λ(1 - x2²) = 0

3 - 3x2² - x2 + λ - λx2² = 0

(3 - λ) - (3 + λ)x2² - x2 = 0

Now we have a quadratic equation in x2. To find the values of x2, we set the discriminant of the quadratic equation equal to zero:

(3 + λ)² - 4(3 - λ)(-1) = 0

9 + 6λ + λ² + 12 - 4λ = 0

λ² + 2λ + 21 = 0

Solving this quadratic equation, we find the values of λ as follows:

λ = -1 ± 2i√5

Since the Lagrange multiplier λ must be real, we can discard the complex solutions. Therefore, we have two possible values for λ: λ = -1 + 2√5 and λ = -1 - 2√5.

Substituting these values back into equation (4), we can solve for x2.

For λ = -1 + 2√5:

(3 - (-1 + 2√5)) - (3 + (-1 + 2√5))x2² - x2 = 0

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Given data:

The diameter of the cut sphere, D=14 in.

The radius of the cut sphere is,

The cut sphere is called a hemisphere.

The surface area of a sphere is

So, the lateral surface area of a hemisphere is half the surface area of sphere. Therefore, the lateral surface area of a hemisphere is,

The hemisphere has a lateral surface and a circular surface. The area of the circular surface is,

Therefore, the total area of the hemisphere is,

The total surface area of a hemisphere is,

Therefore, the total surface area of the cut sphere is 461.8 square inches.

Answer:

Hello the required image is missing attached below is the missing box

answer : FHGE

Step-by-step explanation:

The plane representing the top surface of the box is FHGE. there are still other planes there but do not represent the entire top surface of the Box and they are : FGE, HGE, FHG and FHE. This is because a plane can be represented by three to four Noncollinear points on a solid like a box.

To construct a confidence interval to estimate the true average tip with 90% confidence, we can use the following formula:
Confidence Interval = mean ± (critical value * standard deviation / sqrt(sample size))

In this case, the sample mean is 11.6% and the standard deviation is 2.5%. The critical value for a 90% confidence level is 1.645 (obtained from the z-table).

Plugging in the values, we have:

Confidence Interval = 11.6 ± (1.645 * 2.5 / sqrt(sample size))

Since the sample size is not mentioned in the question, we cannot calculate the exact confidence interval. However, you can use the formula provided above and substitute the actual sample size to obtain the interval. Remember to round the endpoints to two decimal places, if necessary.

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The equation for traveling x miles in the cab can be written as:

Cost = $0.60 + $0.14 * x. The cab charges $0.88 for a ride of 2 miles. And the cab charges $1.72 for a trip of 8 miles.

a. The equation for traveling x miles in the cab can be written as:

Cost = $0.60 + $0.14 * x

b. To find the number of miles for a cab ride that costs $0.88, we can set up the equation:

$0.88 = $0.60 + $0.14 * x

Subtracting $0.60 from both sides, we get:

$0.88 - $0.60 = $0.14 * x

$0.28 = $0.14 * x

Dividing both sides by $0.14, we find:

x = $0.28 / $0.14

x = 2 miles

Therefore, the cab charges $0.88 for a ride of 2 miles.

c. To calculate the cost of a trip of 8 miles, we can substitute x = 8 into the equation:

Cost = $0.60 + $0.14 * 8

Cost = $0.60 + $1.12

Cost = $1.72

Therefore, the cab charges $1.72 for a trip of 8 miles.

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To complete the joint PMF, we need to fill in the matrix with the appropriate probabilities. These probabilities can be determined using historical data, an experiment, or other statistical methods. Once the matrix is complete, we can analyze the joint distribution of calls and complaints received in a 5-minute period.  

The joint PMF, denoted as P(x, y), gives us the probability of observing a particular pair of values (x, y) for the random variables X and Y. Assuming X and Y are discrete random variables and have known probability distributions, we can calculate the joint PMF using the following formula:
P(x, y) = P(X = x, Y = y)
To construct the joint PMF table, we can list all possible values of X (number of calls) and Y (number of complaints) in a matrix. Each cell of the matrix will represent the probability of observing a specific combination of X and Y values. For example, if X can take on values 0 to 5 (representing 0 to 5 calls) and Y can take on values 0 to 2 (representing 0 to 2 complaints), we will have a 6x3 matrix. The element at the (i, j) position of the matrix will be P(X = i, Y = j).

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The first five terms of the sequence are 27, 22, 17, 12, and 7.

To find the first five terms of the sequence given by a₁=27 and d=-5,

we can use the formula for the nth term of an arithmetic sequence:

\(a_n=a_1+(n-1)d\)

Substituting the given values, we have:

\(a_n=27+(n-1)(-5)\)

Now, we can calculate the first five terms of the sequence by substituting the values of n from 1 to 5:

\(a_1=27+(1-1)(-5)=27\)

\(a_1=27+(2-1)(-5)=22\)

\(a_1=27+(3-1)(-5)=17\)

\(a_1=27+(4-1)(-5)=12\)

\(a_1=27+(5-1)(-5)=7\)

Therefore, the first five terms of the sequence are 27, 22, 17, 12, and 7.

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The speed v[t] is always a positive value, since it's the magnitude of the velocity vector.

The velocity of the motion at time t is given by V[t] = x'[t], which is the derivative of the position function x[t] with respect to time.

To compute v[t], you take the square root of the magnitude of V[t], which is given by:

v[t] = |V[t]| = sqrt(|x'[t]|) = sqrt(sqrt[t] * |V[t]|)

Here, the square root of t is taken as a weighting factor for the velocity, which means that the speed increases with time. The speed v[t] is always a positive value, since it's the magnitude of the velocity vector.

Note that this formula assumes that the motion x[t] is differentiable, which means that the velocity V[t] is well-defined and continuous. If x[t] is not differentiable, then the velocity V[t] may not exist, and this formula wouldn't apply.T

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hi

Sales  taxes  = 390 *0.074 = 28.86  

Total cost :  390+28.86 =  418.86

Answer:

326.73cm²

Step-by-step explanation:

=

2

π

r

h

2

π

r

2

=

2

π

4

9

2

π

4

2

≈

326.72564cm²

Answer:  

Answer:

A

Step-by-step explanation:

It looks like the most reasonable answer, and made the most sense. Sorry if im wrong!!

The volume of the sphere, centered at the origin with a radius of 2, can be calculated using the integrals in Cartesian, cylindrical, and spherical coordinates.

To find the integrals that compute the volume of a sphere centered at the origin with a radius of 2, we'll consider the three coordinate systems: Cartesian, cylindrical, and spherical.

1. Cartesian Coordinates:

The volume element in Cartesian coordinates is given by dV = dx dy dz.

To integrate over the sphere, we need to find the limits for x, y, and z.

Since the sphere is centered at the origin, we have -2 ≤ x ≤ 2, -2 ≤ y ≤ 2, and -sqrt(4 - x² - y²) ≤ z ≤ sqrt(4 - x²- y²).

Therefore, the integral for the volume in Cartesian coordinates is:

∭ dV = ∫∫∫ dx dy dz (over the limits described above).

2. Cylindrical Coordinates:

The volume element in cylindrical coordinates is given by dV = r dr dθ dz.

To integrate over the sphere, we need to find the limits for r, θ, and z.

In cylindrical coordinates, the sphere can be expressed as 0 ≤ r ≤ 2, 0 ≤ θ ≤ 2π, and -sqrt(4 - r²) ≤ z ≤ sqrt(4 - r²).

Therefore, the integral for the volume in cylindrical coordinates is:

∭ dV = ∫∫∫ r dr dθ dz (over the limits described above).

3. Spherical Coordinates:

The volume element in spherical coordinates is given by dV = r² sin(θ) dr dθ dφ.

To integrate over the sphere, we need to find the limits for r, θ, and φ.

In spherical coordinates, the sphere can be expressed as 0 ≤ r ≤ 2, 0 ≤ θ ≤ π, and 0 ≤ φ ≤ 2π.

Therefore, the integral for the volume in spherical coordinates is:

∭ dV = ∫∫∫ r² sin(θ) dr dθ dφ (over the limits described above).

Note: The integral limits for θ and φ are already provided in their respective coordinate systems.

The actual integration process would involve evaluating the integrals based on the given limits, but the exact numerical values will depend on the chosen coordinate system and the specific integration techniques used.

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The measure of angle D is \( 125^{\circ} 88^{\prime} 5^{\prime \prime} \).

The interior angles of a quadrilateral are measured as A \( 51^{\circ} 22^{\prime} 30^{\prime \prime} \), B \( 105^{\circ} 38^{\prime} 48^{\prime \prime} \), C \( 78^{\circ} 10^{\prime} 37^{\prime \prime} \), and D \( 124^{\prime} 46^{\prime \prime} \).

To find the measure of angle D, we can use the fact that the sum of the interior angles of a quadrilateral is 360 degrees.

Add the measures of angles A, B, and C:
\( 51^{\circ} 22^{\prime} 30^{\prime \prime} \) + \( 105^{\circ} 38^{\prime} 48^{\prime \prime} \) + \( 78^{\circ} 10^{\prime} 37^{\prime \prime} \) = \( 234^{\circ} 71^{\prime} 55^{\prime \prime} \)

Subtract the sum of angles A, B, and C from 360 degrees to find the measure of angle D:
360^{\circ} - \( 234^{\circ} 71^{\prime} 55^{\prime \prime} \) = \( 125^{\circ} 88^{\prime} 5^{\prime \prime} \)

Therefore, the measure of angle D is \( 125^{\circ} 88^{\prime} 5^{\prime \prime} \).

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Answer:

The answer is "35.22".

Step-by-step explanation:

Let the given equation:

\(\to 130(x-38) +950 \% \times 38=0\\\\\to 130x- 4940+\frac{950}{100} \times 38=0\\\\\to 130x- 4940+9.5\times 38=0\\\\\to 130x- 4940+361=0\\\\\to 130x- 4579=0\\\\\to 130x= 4579\\\\\to x= \frac{4579}{130}\\\\\to x= 35.22\)

Answer: $25

Step-by-step explanation: took the quiz

When using the Lagrange multiplier method to optimize a function subject to a constraint, focusing on the points where the gradient of the function is perpendicular to the constraint line helps identify potential extremal points that satisfy both the objective function and the constraint simultaneously.

In the context of optimization with a constraint, the Lagrange multiplier method is commonly used. This method introduces Lagrange multipliers to incorporate the constraint into the optimization problem. When considering the points on the line at which the gradient of the function f[x, y, z] (denoted as ∇f[x, y, z]) is perpendicular to the line, we are essentially examining the points where the gradient of the function and the gradient of the constraint (in this case, the line) are parallel.

By introducing a Lagrange multiplier λ, we can form the Lagrangian function L[x, y, z, λ] = f[x, y, z] - λg[x, y, z], where g[x, y, z] represents the equation of the given line. The Lagrange multiplier method seeks to find the values of x, y, z, and λ that simultaneously satisfy the equations:

∇f[x, y, z] - λ∇g[x, y, z] = 0 (1)

g[x, y, z] = 0 (2)

The equation (1) ensures that the gradient of f and the gradient of g are parallel, while equation (2) enforces the constraint that the variables lie on the given line.

At the points where ∇f[x, y, z] is perpendicular to the line, the dot product between ∇f[x, y, z] and the tangent vector of the line is zero. This means that ∇f[x, y, z] and the tangent vector are orthogonal, and thus the gradient of f is parallel to the normal vector of the line.

In the Lagrange multiplier method, finding the points where ∇f[x, y, z] is perpendicular to the line becomes crucial because it helps identify potential extremal points that satisfy both the objective function and the constraint simultaneously.

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Answer:

Step-by-step explanation:perp. 3/2

y + 8 = 3/2(x - 4)

y + 8 = 3/2x - 6

y = 3/2x - 14

Answer:

The solution of the system of equations will be:

\(x=0,\:y=3\)

And the system of equations has ONLY ONE solution.

Step-by-step explanation:

Given the system of the equations

\(\begin{bmatrix}3x+6y=18\\ 3y=-5x+9\end{bmatrix}\)

Arrange equation variables for elimination

\(\begin{bmatrix}3x+6y=18\\ 5x+3y=9\end{bmatrix}\)

\(\mathrm{Multiply\:}3x+6y=18\mathrm{\:by\:}5\:\mathrm{:}\:\quad \:15x+30y=90\)

\(\mathrm{Multiply\:}5x+3y=9\mathrm{\:by\:}3\:\mathrm{:}\:\quad \:15x+9y=27\)

\(\begin{bmatrix}15x+30y=90\\ 15x+9y=27\end{bmatrix}\)

\(15x+9y=27\)

\(-\)

\(\underline{15x+30y=90}\)

\(-21y=-63\)

so the system of the equations becomes

\(\begin{bmatrix}15x+30y=90\\ -21y=-63\end{bmatrix}\)

solve -21y = -63

\(-21y=-63\)

\(\mathrm{Divide\:both\:sides\:by\:}-21\)

\(\frac{-21y}{-21}=\frac{-63}{-21}\)

\(y=3\)

\(\mathrm{For\:}15x+30y=90\mathrm{\:plug\:in\:}y=3\)

\(15x+30\cdot \:3=90\)

\(15x+90=90\)

subtract 90 from both sides

\(15x+90-90=90-90\)

\(15x=0\)

Divide both sides by 15

\(\frac{15x}{15}=\frac{0}{15}\)

\(x = 0\)

as

\(x = 0\), \(y=3\)

so, the system of equations contains only one solution.

Therefore, the solution of the system of equations will be:

\(x=0,\:y=3\)

And the system of equations has ONLY ONE solution.

a.  The clockmaker can produce 21 clocks with 42 hands.

b. The clockmaker can produce four clocks with eight hands.

a. A clock maker can make 21 clocks if he has 42 hands. This is due to the fact that each clock needs one face and two hands, making a total of three pieces for each clock.

As a result, the clockmaker can use the 42 hands to create 21 clocks by dividing them into three pieces for each clock.

b. The clockmaker can construct four clocks even with only eight hands. This is due to the fact that each clock needs one face and two hands, making a total of three pieces for each clock.

As a result, the clockmaker can use the eight hands to create four clocks by dividing them into three pieces for each clock.

Complete Question:

A clock maker has 15 clock faces. Each clock requires one ' face and two hands_

a. If the clock maker has 42 hands, how many clocks are produced? can be

b. If the clock maker has only eight hands, how can it be produced? many clocks

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Answer: 3 \(\leq\) x \(\leq\) 8

3 is the smallest x value, and 8 is the largest.