Kevin said that if the index of a radical is even and the radicand is positive, then
the radical has two real roots. Do you agree with Kevin? Explain why or why not.

Answer:

12x -7

Step-by-step explanation:

Answer:

Step-by-step explanation:

A. The data appears to be reported. The heights occur with roughly the same frequency.

A histogram is a graphical representation of a frequency distribution, where the x-axis represents the values of the data, and the y-axis represents the frequency of those values. If the heights are reported, the last digit of the heights should be randomly distributed and the frequency of each digit should be roughly the same, which is the case in a histogram with uniform distribution. This is in contrast to a histogram with non-uniform distribution, where certain heights occur a disproportionate number of times, which is more likely to happen when the heights are measured. Therefore, based on the information provided, it can be concluded that the data appears to be reported.

the answer for the equation is 0

Given:

One of the angle of a triangle is 104°.

The objective is to find the missing angle x.

If two sides of a triangle are equal, then it is an isosceles triangle.

In an isosceles triangle, the angle formed by the equal sides is also equal.

Then, the value of angle x can be calculated angle sum property of triangle.

Hence, option (A) is the correct answer.

Answer:

8/3

Step-by-step explanation:

1. 2 ÷ 3 = .66

.66 · 4 = 2.6

2. 4 × 2/3 =

4/1 × 2/3 = 8/3

good luck, i hope this helps :)

(a) The vector field F = (2x³y² + x)i + (2x¹y³ + y)j is conservative, and its potential function is Φ(x, y) = x²y² + 0.5x² + x²y⁴/2 + 0.5y² + C.

(b) The vector field F(x, y) = (2xe^(ay) + x²y*e^y)i + (x³e^(2ay) + 2y)j is not conservative, and it does not have a potential function.

To determine if a vector field is conservative, we need to check if it satisfies the condition of having a curl of zero. If the vector field is conservative, we can find a potential function for it by integrating the components of the vector field.

(a) Consider the vector field F = (2x³y² + x)i + (2x¹y³ + y)j.

Taking the partial derivative of the x-component with respect to y and the partial derivative of the y-component with respect to x, we get:

∂F₁/∂y = 6x³y,

∂F₂/∂x = 6x²y³.

The curl of the vector field F is given by curl(F) = (∂F₂/∂x - ∂F₁/∂y)k = (6x²y³ - 6x³y)k = 0k.

Since the curl of F is zero, the vector field F is conservative.

To find the potential function for F, we integrate each component with respect to its respective variable:

∫F₁ dx = ∫(2x³y² + x) dx = x²y² + 0.5x² + C₁(y),

∫F₂ dy = ∫(2x¹y³ + y) dy = x²y⁴/2 + 0.5y² + C₂(x).

The potential function Φ(x, y) is the sum of these integrals:

Φ(x, y) = x²y² + 0.5x² + C₁(y) + x²y⁴/2 + 0.5y² + C₂(x).

Therefore, the potential function for the vector field F = (2x³y² + x)i + (2x¹y³ + y)j is Φ(x, y) = x²y² + 0.5x² + x²y⁴/2 + 0.5y² + C, where C = C₁(y) + C₂(x) is a constant.

(b) Consider the vector field F(x, y) = (2xe^(ay) + x²y*e^y)i + (x³e^(2ay) + 2y)j.

Taking the partial derivative of the x-component with respect to y and the partial derivative of the y-component with respect to x, we get:

∂F₁/∂y = 2xe^(ay) + x²e^y + x²ye^y,

∂F₂/∂x = 3x²e^(2ay) + 2.

The curl of the vector field F is given by curl(F) = (∂F₂/∂x - ∂F₁/∂y)k = (3x²e^(2ay) + 2 - 2xe^(ay) - x²e^y - x²ye^y)k ≠ 0k.

Since the curl of F is not zero, the vector field F is not conservative. Therefore, there is no potential function for this vector field.

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Answer: B

Step-by-step explanation:

First you have to do what’s in parentheses so you do 7-3, which is 4. Then you do 4 - 2 = 2. Hope this helped!

The angle that a side of 15 inches makes with the 6-inch side is approximately 78.46 degrees.

c²= a² + b² - 2ab cos(C)

In this case, we know that the lengths of the two congruent sides are both 15 inches, and the length of the remaining side is 6 inches. So we have:

15² = 6² + 15² - 2(6)(15)cos(x)

225 = 261 - 180cos(x)

180cos(x) = 36

cos(x) =\(\frac{36}{180}\)

cos(x) = 0.2

Now we can use the inverse cosine function (\(cos^{-1}\)) to find the value of "x" in degrees:

x = \(cos^{-1}\)(0.2)

x ≈ 78.46 degrees

An angle is a geometric figure formed by two rays with a common endpoint, called the vertex. The rays are known as the sides of the angle. The measure of an angle is usually expressed in degrees, and it represents the amount of rotation needed to rotate one of the sides of the angle onto the other. A full rotation around a point is 360 degrees, so an angle measuring 180 degrees is called a straight angle.

Angles can be classified according to their measure. An acute angle is an angle measuring less than 90 degrees. A right angle is an angle measuring exactly 90 degrees. An obtuse angle measures more than 90 degrees but less than 180 degrees. A reflex angle measures more than 180 degrees but less than 360 degrees.

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The given two-way Frequency table, there are 33 left-handed students who are not in the music program.

The number of left-handed students who are not in the music program, we need to examine the data presented in the two-way frequency table.

From the table, we can see that the number of left-handed students in the music program is 15, and the total number of left-handed students is 48.

the number of left-handed students not in the music program, we subtract the number of left-handed students in the music program from the total number of left-handed students.

Number of left-handed students not in the music program = Total number of left-handed students - Number of left-handed students in the music program

Number of left-handed students not in the music program = 48 - 15

Calculating this, we find that the number of left-handed students not in the music program is 33.

Therefore, there are 33 left-handed students who are not in the music program, based on the data provided in the two-way frequency table.

In conclusion, based on the given two-way frequency table, there are 33 left-handed students who are not in the music program.

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We can conclude after answering the provided question that This expression information can be used to generate a data box plot. Minimum = 55o, Q1 = 61o, Q2 = 69o, Q3 = 76o

Maximum temperature = 79o

In mathematics, an expression is a grouping of representations, digits, and conglomerates that resemble a statistical correlation or regimen. An expression can be a real number, a mutable, or a combination of the two. Addition, subtraction, rapid spread, division, and exponentiation are examples of mathematical operators. Expressions are common in arithmetic, mathematics, and geometry. They are used in mathematical formula representation, equation solution, and mathematical relationship simplification.

To find the five-number summary, we must arrange the data in the following order:

55°, 56°, 59°, 61°, 63°, 67°, 69°, 69°, 71°, 73°, 73°, 78°, 79°

The smallest value in the data set is the minimum value: 55o.

(55o, 56o, 59o, 61o, 63o, 67o, 69o, 69o) = 61o in the lower half data set.

The median (Q2) is the value that separates the data's lowest and highest 50%. To find Q2, we must first calculate the median of the entire data set: (55o, 56o, 59o, 61o, 63o, 67o, 69o, 69o, 71o, 73o, 73o, 78o, 79o) = 69o.

Minimum = 55o, Q1 = 61o, Q2 = 69o, Q3 = 76o

Maximum temperature = 79o

This information can be used to generate a data box plot.

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No, the standard deviation of a data set can never be negative. The standard deviation is a measure of the dispersion or spread of data points from the mean.

It is calculated by taking the square root of the variance, which is the average of the squared differences between each data point and the mean.

Since the variance involves squaring the differences, it ensures that all values are positive. Taking the square root of the positive variance yields a positive value, which is the standard deviation. Thus, the standard deviation is always non-negative.

Similarly, the Interquartile Range (IQR) cannot be negative. The IQR is a measure of statistical dispersion that represents the range between the first quartile (25th percentile) and the third quartile (75th percentile) of a dataset. It provides insights into the spread of the central 50% of the data.

Like the standard deviation, the IQR involves calculating the difference between specific percentiles. Since percentiles represent ordered values in a dataset, the difference between them is non-negative, ensuring that the IQR is also non-negative.

In summary, both the standard deviation and the IQR are measures of dispersion that involve calculating differences between values in a dataset, ensuring that they cannot be negative.

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The component form of a vector refers to breaking the vector into components with unit vectors denoting the direction of each component. The general component form angled vectors in a two-dimensional space is given by:

\(\vec v=|v|cos\theta\hat{x}+|v|sin\theta\hat{y}\)

where |v| is the magnitude of the vector component and theta is the angle of the vector.

Using the magnitude and angle given for vector u we can write its component form :

\(\vec u=|u|cos\theta_u \hat{x}+|u|sin\theta_u \hat{y}\\\vec u=|5|cos(9)\hat{x}+|5|sin\(9) \hat{y}\\\vec v=5cos9_u\hat{x}+5sin9_u\hat{y}\)

Doing the same for v

\(\vec v=|v|cos\theta_u \hat{x}+|v|sin\theta_u \hat{y}\\\vec v=|1|cos5_u \hat{x}+|1|sin5_u \hat{y}\\\vec v=1cos5_u\hat{x}+sin5_u\hat{y}\)

Now adding both vector together

\(\vec u+\vec v=(5cos9_u\hat{x}+5sin9_u\hat{y})+(cos5_u\hat{x}+sin5_u\hat{x})\\\vec u+\vec v=(5cos9_u\hat{x}+cos5_u\hat{x})+(5sin9_u\hat{y}+sin5_u\hat{y})\)

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SC is approximately 73.8 cm, The length of SC can be found using the property of similar triangles.

Since QR is parallel to BC, we have triangle ABC ~ triangle ASR (by the property of corresponding angles). Therefore, the corresponding sides of these triangles are proportional. We can set up the following proportion: |AS| / |AB| = |SR| / |BC|

We are given that |AB| = 5.5 cm and |BC| = 74 cm. To find |AS|, we need to determine the length of |SR|. We know that angle ABC = 120° and triangle ABC is isosceles (|AB| = |BC|),

so angle BAC = angle BCA = (180° - 120°) / 2 = 30°. Since triangle ASR is a right triangle (angle ASR = 90°), we can use trigonometric ratios to find |SR|.

Using the sine ratio, sin(angle BCA) = |SR| / |AB|, we have: sin(30°) = |SR| / 5.5, Solving for |SR|, we get |SR| = 5.5 * sin(30°) = 5.5 * 0.5 = 2.75 cm. Now, we can substitute the values into the proportion: |AS| / 5.5 = 2.75 / 74

Simplifying the equation, we find: |AS| = 5.5 * (2.75 / 74) = 0.2027027 cm

Finally, since SC = |BC| - |AS|, we have: SC = 74 - 0.2027027 = 73.7972973 cm, Therefore, SC is approximately 73.8 cm.

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If t-shirts be t

The expression is

\(\\ \rm\rightarrowtail 12t>100\)

\(\\ \rm\rightarrowtail 12t-100>0\)

The diagonals of the parallelogram intersect at the center. Then the value of the variable 'x' is 38.

It is a polygon with four sides. The total interior angle is 360 degrees. A parallelogram's opposite sides are parallel and equal. Its diagonals intersect in the center.

Given parallelogram A B C D below, DE = 31 If EB = x - 7.

By the definition, then the equation is given as,

EB = DE

x - 7 = 31

Simplify the equation, then we have

x - 7 = 31

x = 31 + 7

x = 38

The value of the variable 'x' is 38.

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Answer:

s=32

Step-by-step explanation:

15x-31 = 9x+11

6x=42

x=7

2(63+11)= 2(74)= 148

180-148=32

Isosceles triangles have equal base angles.

The values of x and S are 7 and 32, respectively.

The base angles are given as: 15x - 31 and 9x + 11

So, we have:

\(\mathbf{15x - 31 = 9x + 11}\)

Collect like terms

\(\mathbf{15x - 9x =31+ 11}\)

\(\mathbf{6x =42}\)

Divide both sides by 6

\(\mathbf{x =7}\)

The measure of S is:

\(\mathbf{S = 180 - (15x - 31) - (9x + 11)}\)

Substitute 7 for x

\(\mathbf{S = 180 - (15\times 7 - 31) - (9\times 7 + 11)}\)

\(\mathbf{S = 180 - (74) - (74)}\)

\(\mathbf{S = 32}\)

Hence, the values of x and S are 7 and 32, respectively.

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The height at time t (in seconds) of a mass, oscillating at the end of a spring, is s(t) = 300 + 16 sin t cm. We have to find the velocity and acceleration at t = π/3 s.

Let's first find the velocity of the mass. The velocity of the mass is given by the derivative of the position of the mass with respect to time.t = π/3 s
s(t) = 300 + 16 sin t cm
Differentiating both sides of the above equation with respect to time
v(t) = s'(t) = 16 cos t cm/s

Now, let's substitute t = π/3 in the above equation,
v(π/3) = 16 cos (π/3) cm/s
v(π/3) = -8√3 cm/s

Now, let's find the acceleration of the mass. The acceleration of the mass is given by the derivative of the velocity of the mass with respect to time.t = π/3 s
v(t) = 16 cos t cm/s
Differentiating both sides of the above equation with respect to time
a(t) = v'(t) = -16 sin t cm/s²
Now, let's substitute t = π/3 in the above equation,
a(π/3) = -16 sin (π/3) cm/s²
a(π/3) = -8 cm/s²
Given, s(t) = 300 + 16 sin t cm, the height of the mass oscillating at the end of a spring. We need to find the velocity and acceleration of the mass at t = π/3 s.
Using the above concept, we can find the velocity and acceleration of the mass. Therefore, the velocity of the mass at t = π/3 s is v(π/3) = -8√3 cm/s, and the acceleration of the mass at t = π/3 s is a(π/3) = -8 cm/s².
At time t = π/3 s, the velocity of the mass is -8√3 cm/s, and the acceleration of the mass is -8 cm/s².

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Diego can make 56 bags with each bag containing 8 brownies and 12 cookies.

To package both items, he can divide the items into groups of 8 brownies and 12 cookies. He will then make 56 of these groups, ensuring each bag contains 8 brownies and 12 cookies.

Diego has 48 brownies and 64 cookies to package. To make the same combination of items in each bag, he needs to group the items into groups of 8 brownies and 12 cookies.

This can be done by dividing the 48 brownies into 6 groups of 8, and the 64 cookies into 5 groups of 12. He then needs to combine these two groups together, making 56 total bags.

Each of these bags will contain 8 brownies and 12 cookies. This is one way of packaging both items so that each bag has the same combination.

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For the given compound inequality  \(x\leq 2 \; and \; x > 4\)

x does not lies between 2  and 4. The shaded region goes left of 2  and right of 4.

The graph is attached below.

Given :

The given compound inequality  \(x\leq 2 \; and \; x > 4\)

We graph the inequalities one by one . because x does not lies between 2  and 4

For graphing x<=2  we put a solid dot at 2  and shade to the left of 2

For graphing x>4, we put a open dot at 4 and shade to the right of 4

so both the shaded region goes left  and right . It does not lies between 2  and 4

The correct graph for the given inequality is attached below.

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Answer:

Step-by-step explanation:

“the center of the ellipse is located below the given co-vertex”

Co-vertex and center are vertically aligned, so the ellipse is horizontal.

Equation for horizontal ellipse:

(x-h)²/a² + (y-k)²/b² = 1

with

a² ≥ b²

center (h,k)

vertices (h±a, k)

co-vertices (h, k±b)

foci (h±c,k), c² = a² -b²

One co-vertex is (-8,9), so h = -8.

One focus is (4,4), so k = 4.

Center (h,k) = (-8,4)

c = distance between center and focus = |-8 - 4| = 12

b = |9-k| = 5

a² = c² + b² = 169

(x+8)²/169 + (y-4)²/25 = 1

Answer:

611 divided by 78

Step-by-step explanation:

7.83333333333 round to 7.83

Answer:

$7,507

Step-by-step explanation:

Divide the length of the longest side of triangle AFB by the longest side of triangle DHG to find the scale factor.

Triangle AFB: A=4 cm, B=5 cm, F=7 cm

Triangle DHG: D=2.8 cm, H=3.5 cm, G=4.9 cm

Scale factor = 7/4.9 = 1.43

Step by explanation

Step 1: Draw triangle AFB on a piece of paper.

Step 2: Measure the side lengths of triangle AFB and record them.

Step 3: Draw a second triangle, DHG, on the paper.

Step 4: Measure the side lengths of triangle DHG and record them.

Step 5: Divide the length of the longest side of triangle AFB by the longest side of triangle DHG to find the scale factor.

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Answer:

3628800 ways if the women are always required to stand together.

To solve this problem, we can consider the number of ways to arrange the women and men separately, and then multiply the results together.

First, let's consider the arrangement of the women. Since no two men can be seated next to each other, the women must be seated in between the men. We can think of the 5 men as creating 6 "gaps" where the women can be seated (one gap before the first man, one between each pair of men, and one after the last man).

Out of these 6 gaps, we need to choose 7 gaps for the 7 women to sit in. This can be done in "6 choose 7" ways, which is equal to the binomial coefficient C(6, 7) = 6!/[(7!(6-7)!)] = 6.

Next, let's consider the arrangement of the 5 men. Once the women are seated in the chosen gaps, the men can be placed in the remaining gaps. Since there are 5 men, this can be done in "5 factorial" (5!) ways.

Therefore, the total number of ways to seat the 5 men and 7 women is 6 * 5! = 6 * 120 = 720.

There are 720 ways to seat the 5 men and 7 women in a row such that no two men are next to each other.

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Answer:

first option

Step-by-step explanation:

Given

| x + 4 | = 2

The absolute value function always produces a positive value but the expression inside can be positive or negative, thus

x + 4 = 2 ( subtract 4 from both sides )

x = - 2

OR

- (x + 4) = 2, distribute left side

- x - 4 = 2 ( add 4 to both sides )

- x = 6 ( multiply both sides by - 1 )

x = - 6

Thus solutions are x = - 2, x = - 6

These are represented on the graph by solid blue circles at x = - 2, x = - 6

The first option represents the solution

Answer:

is this triangle supposed to be a right triangle?

Step-by-step explanation:

i can't solve unless i know the type of triangle

(a) If f(x) is a convex function with x ∈ ℝⁿ, then all local minima of f(x) are also global minima. In other words, if there exists a point xo such that f(x) ≥ f(xo) for all x in a neighborhood of xo, then f(x) ≥ f(xo) for all x ∈ ℝⁿ.

(b) A graph of a non-convex function can be visualized to understand why the statement in part (a) is not true. It will show a scenario where a local minimum is not a global minimum.

(a) To prove that all local minima of a convex function are also global minima, we can utilize the property of convexity. Suppose there is a point xo such that f(x) ≥ f(xo) for all x in a neighborhood of xo. We assume that xo is a local minimum. Now, consider any arbitrary point x in ℝⁿ. We can express x as a convex combination of xo and another point y in the neighborhood, using the convexity property: x = λxo + (1 - λ)y, where λ is a scalar between 0 and 1. Using this expression, we can apply the convexity property of f(x) to get f(x) ≤ λf(xo) + (1 - λ)f(y). Since f(x) ≥ f(xo) for all x in the neighborhood, we have f(y) ≥ f(xo). Therefore, f(x) ≤ λf(xo) + (1 - λ)f(y) ≤ λf(xo) + (1 - λ)f(xo) = f(xo). This inequality holds for all λ between 0 and 1, implying that f(x) ≥ f(xo) for all x ∈ ℝⁿ, making xo a global minimum.

(b) A graph of a non-convex function can demonstrate a scenario where the statement in part (a) is not true. In such a graph, there may exist multiple local minima, but one or more of these local minima are not global minima. The non-convex nature of the function allows for the presence of multiple valleys and peaks, where one of the valleys may contain a local minimum that is not the overall lowest point on the graph. This occurs because the function may have other regions where the values are lower than the local minimum in consideration. By visually observing the graph, it becomes apparent that there are points outside the neighbourhood of the local minimum that have lower function values, violating the condition for a global minimum.

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PART A) Janet needs only three cups of sugar to make three batches of chocolate chip cookies.

PART B) One cup of sugar will be left over after making three batches of cookies.

What is the unit price?

A unit price is the cost of a single object or unit of measurement, such as a pound, a kilogram, or a pint, and it is used to compare the prices of similar products offered in various weights and quantities. Selling more than one unit of the same product at a discount from its unit price is known as multiple pricing.

Given that Janet needs One cup of sugar to make one batch of chocolate chip cookies.

Part A:

Let The number of cups of sugar Janet needs to make three batches of cookies be 'x'.

Now,

1 batch/ 1 cup = 3 batch/ x cups

x= 3

Therefore, Janet needs only three cups of sugar to make three batches of chocolate chip cookies.

Part B:

Given that Janet has four cups of sugar.

From part A, we found that she only need three cups of sugar.

Available - Needed = Excess

4-3=1

So, one cup of sugar will be left over after making three batches of cookies.

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