In the figure below, angle y and angle x form vertical angles. Angle y forms a straight line with the 60° angle and the 70° angle. A straight line is shown and is marked with three angles. The first angle measures 60 degrees. The second angle measures 60 degrees. The third angle is labeled y. The line between the 70 degree angle and angle y extends below the straight line. The angle formed is labeled angle x. Write and solve an equation to determine the measure of angle x.

The correct option for the given vector is the third one:

If the initial point is (0, 0), then the component form of the vector is just equal to the terminal point of the vector.

Then we have:

u = (5, -8)

For a vector w = (x, y) the magnitude is:

\(||w|| = \sqrt{x^2 + y^2}\)

In this case, the magnitude will be:

\(||u|| = \sqrt{5^2 + (-8)^2} = \sqrt{89}\)

Then the correct option is the third one.

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The graph of the rational function f(x) = (x^2 - 1)/(x^2 + 5) does not have any vertical asymptotes. The horizontal asymptote is y = 1. The x-intercepts are -1 and 1, and the y-intercept is (0, -1/5). Additional points on the graph include (-2, 1/3), (-1/2, -1/8), and (2, 1/3).

Let's see the step-by-step explanation of finding the intercepts, asymptotes, and plotting points for the rational function f(x) = (x^2 - 1)/(x^2 + 5).

⇒ Determine the domain

The given function is defined for all real numbers, so the domain of f(x) is all real numbers.

⇒ Simplify the function

The given function is already simplified, so we can proceed to the next step.

⇒ Find the vertical asymptotes

Vertical asymptotes occur when the denominator equals zero. Setting the denominator x^2 + 5 equal to zero, we find that there are no real solutions. Therefore, there are no vertical asymptotes for this function.

⇒ Find the horizontal asymptote

To determine the horizontal asymptote, we compare the degrees of the numerator and denominator. Since both have a degree of 2, we divide the leading coefficients. The result is y = 1, so the horizontal asymptote is y = 1.

⇒ Find the x-intercepts

To find the x-intercepts, we set the numerator x^2 - 1 equal to zero and solve for x. The equation x^2 - 1 = 0 can be factored as (x - 1)(x + 1) = 0. Solving this equation, we find two x-intercepts: x = -1 and x = 1.

⇒ Find the y-intercept

To find the y-intercept, we substitute x = 0 into the function. f(0) = (0^2 - 1)/(0^2 + 5) = -1/5. Therefore, the y-intercept is (0, -1/5).

⇒ Plot additional points

Choose values of x between each intercept and values on either side of the vertical asymptotes. Substitute these values into f(x) and simplify to obtain corresponding y-values.

⇒ Plot the intercepts, asymptotes, and points

Plot the intercepts: (-1, 0) and (1, 0).

Plot the y-intercept: (0, -1/5).

Plot the additional points: (-2, 1/3), (-1/2, -1/8), and (2, 1/3).

Draw the horizontal asymptote: y = 1.

⇒ Sketch the graph

Using the plotted intercepts, asymptotes, and points, connect them to obtain a smooth curve. The graph should resemble a hyperbola approaching the horizontal asymptote y = 1.

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False, if an overall F-test in an ANOVA model is significant, it is important to conduct follow-up comparisons to test for differences between pairs of means.

When the overall F-test in an ANOVA model is found to be significant, it indicates that there is evidence of at least one significant difference among the group means. However, it does not provide specific information about which particular group means are different from each other. Therefore, follow-up comparisons, such as post hoc tests or pairwise comparisons, are necessary to determine the specific pairs of means that are significantly different.

These follow-up comparisons allow for a more detailed understanding of the group differences and help identify which specific groups are driving the significant overall F-test result. By conducting these additional tests, researchers can gain insights into the specific pairwise differences and make more accurate and informed interpretations of their data.

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The height of Jeremy is 159 cm.

To find the height of Jeremy:

So,

Then, Jeremy = 135 + 24 = 159 cm.

Therefore, the height of Jeremy is 159 cm.

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The difference between the sample and the population that occurs by chance is known as sampling error. The term "sampling error" refers to the discrepancy that arises between a sample statistic and a population parameter due to chance sampling variation

.A sample is a subset of a population that is chosen to represent the entire population. The population is the complete set of data that the researcher is interested in. It is impossible to collect information from every member of a population, so samples are used instead.Sampling error arises because the sample used to make inferences or generalizations about a population is never an exact representation of the entire population.

Sampling error may also be caused by differences in the measuring instrument used to collect data or the procedures used to collect data.The difference between the sample and the population that occurs by chance is known as sampling error. So, option B is correct.

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The factor is (w-2)(w-12) and the solution of the expression is  w =2 or 12

Given: 2wto power of 2 minus 16w=12w-48.

This expression can be written as 2w² - 16w = 12w-48

2w² - 16w = 12w-48

2w² - 16w-12w = -48

2w² - 28w + 48 = 0

Divide through by 2:

w² - 14w +  24 = 0

w² - 12w-2w +  24 = 0

Factorize:

(w-2)(w-12) = 0

w-2 = 0 or w-12 = 0

w =2 or 12

Therefore, the solution of 2w² - 16w = 12w-48 is w =2 or 12

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Answer:

That's pretty much correct. A continuous function is one that has no breaks or holes. For example, 1/x+5 is not continuous (or discontinuous) because the domain does not include -5. However, I don't think it needs to necessarily have to have curves because all linear functions are continuous. Hope this helps! (I learned about this a few weeks ago in my pre-calc class lol)

Step-by-step explanation:

The second statement is true. It is a reduction because 0 < n < 1.

Dilation means changing the size of an object without changing its shape. The size of the object may be increased or decreased based on the scale factor.

Given: A triangle is dilated by a scale factor of n = 1/3. As n is less than 1 but greater than 0.

A dilation is a rigid transformation that forms an image that is the same shape as of the original figure but with a different size.  A dilation transforms a figure by scalar factor 'n' about the center of dilation is a fixed point in the plane which never changes.

A dilation that forms a larger image is known as enlargement.  A dilation that forms a smaller image is known as reduction.

• If n is greater than 1, then the image is an enlargement.

• If n is between 0 and 1, then the image is a reduction.

• If n is 1, the figure and then the image is exactly the same.

Hence the second statement is true. It is a reduction because 0 < n < 1.

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Answer:

6

Step-by-step explanation:

3(8−6)

=(3)(2)

=6

Answer:

3(8-6)=6

Step-by-step explanation:

8-6

=2

=3*2

=6

Answer:

m= 7/5

Step-by-step explanation:

Use the slope formula to find the slope (m)

Answer: all angles must ad up 20 180

Step-by-step explanation:

I looked it up

Answer:

3

Step-by-step explanation:

Easy pythagorean theorum question.

The law states that "A squared plus B squared, equals C squared."

A and B are the two sides that border the 90 degree mark.

C is the hypotenuse or the longest side/diagonal.

Since we know C and A (I chose to use A because why not) we can fill in the equation with what we know

2^2 + ?^2 = \(\sqrt{13^{2} }\)

So

4 + ?^2 = \(\sqrt{13^{2} }\)

Since the 13 is already squared in side of a root, it stays as 13

4 + x^2 = 13

4 - 4 + x^2 = 13 - 4

x^2 = 9

x^2 root = root of 9

x = 3

The missing side is 3.

Or you could use an online calculator xD

To find the derivatives of the given expressions, we can apply the chain rule, which states that the derivative of a composition of functions is equal to the derivative of the outer function multiplied by the derivative of the inner function.

(a) To find the derivative of f(g(x)), we start by differentiating the outer function f with respect to the inner function g(x), and then multiply it by the derivative of the inner function g(x) with respect to x.

df/dx = df/dg * dg/dx

df/dx = cos(g(x)) * (2x)

(b) To find the derivative of g(f(x)), we differentiate the outer function g with respect to the inner function f(x), and then multiply it by the derivative of the inner function f(x) with respect to x.

dg/dx = dg/df * df/dx

dg/dx = 2f(x) * cos(x)

Hence, the derivatives are:

(a) d/dx(f(g(x))) = cos(g(x)) * (2x)

(b) d/dx(g(f(x))) = 2f(x) * cos(x)

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Part A: The volume of that prism is 12x³ + 71x² + 97x + 20. Part B: The volume of the construction piece shown in the diagram is 10x³ + 54x² + 54x - 8.

A rectangular prism is a three-dimensional shape that is characterized by its six rectangular faces. It is also known as a rectangular parallelepiped or a cuboid. The rectangular prism has three pairs of parallel faces, and each face is perpendicular to the adjacent faces.

The rectangular prism has eight vertices (corners) and 12 edges. The length, width, and height of the rectangular prism are typically denoted as l, w, and h, respectively. The volume V of a rectangular prism is given by the formula:

V = lwh

The surface area S of a rectangular prism is given by the formula:

S = 2lw + 2lh + 2wh

where lw, lh, and wh are the areas of the six rectangular faces.

Some common examples of rectangular prisms in everyday life include boxes, bookshelves, and bricks. Rectangular prisms are used in architecture, engineering, and construction for building structures such as buildings and bridges. They are also used in mathematics and physics to model real-world situations, such as calculating the volume and surface area of a container.

Part A: The formula of volume of rectangular prism= length × width × height

V = (x+4)(4x+1)((3x+5) = 12x³ + 71x² + 97x + 20

The volume of that prism is 12x³ + 71x² + 97x + 20.

Part B:

(x+1)(2x+7)(x+4)= 2x³ + 17x² + 43x + 28
The volume of prism - the missing part

12x³ + 71x² + 97x + 20 - 2x³ + 17x² + 43x + 28 = 10x³ + 54x² + 54x - 8.

The volume of the construction piece shown in the diagram is 10x³ + 54x² + 54x - 8.

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Answer:

87.5%

Step-by-step explanation:

Answer:

7/8 or 87.5%

Step-by-step explanation:

Total= 72

Correct= 63

Fraction of correct marks= 63/72= 7*9/8*9= 7/8 or 87.5%

Answer:

No

Step-by-step explanation:

Probability meaning: "the extent to which something is probable; the likelihood of something happening or being the case."

Probability only is a range from 1-100 %

Probability can also be written as a percentage, which is a number from 0 to 100 percent. ... The probability of a certain event occurring depends on how many possible outcomes the event has. If an event has only one possible outcome, the probability for this outcome is always 1 (or 100 percent).

(credits to scientific american)

Answer:

d Because I just took the test and got it right

Answer:

5(3-9) = y    

15 - 45 = y  

y = -30        

14 = 5k - 31

-5k = -31 - 14

-5k = -45

k = 9

t = -5(9 - 7)

t = -45 + 35

t = -10

v = 13(8-9)

v = 104 - 117

v = -13

13f = 53

f = 4

Answer:

\(\huge{\boxed{\text{ See ~ attached ~ picture.}}}\)

Step-by-step explanation:

Rules for solving an equation :

Hope I helped!

Best regards!

~\(\text{ TheAnimeGirl}\)

The value of the variable is 9

It is important to note that  inequalities are described as non- equal comparison of numbers or expressions.

The signs of inequalities represents;

From the information given, we have that;

7x - 1  is less than or equal to 62

This is represented as;

7x - 1≤ 62

collect the like terms, we have;

7x ≤ 62 + 1

Add the values

7x ≤ 63

Divide both sides by the coefficient, we get;

x ≤ 63/7

x ≤ 9

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Answer:

a) 6:15 or 2:5 (simplified)

b) 9:30 or 3:10 (simplified)

c) For every 30 songs that Juan downloaded, 9 were hip-hop. OR For every 10 songs Juan downloaded, 3 were hip-hop.

Step-by-step explanation:

A ratio compares the relationship of different values in relation to each other.

**I added the non-simplified and simplified answers because I do not know what your teacher is looking for. You should use either of the answers depending on what your teacher asks you for.

Option d) is correct, i.e. a rotation, then a dilation. Transformation will create a pair of similar but not congruent triangles.

Which composition of transformations will create a pair of similar, not congruent triangles?

In congruent geometry, the shapes that are so identical. can be superimposed to themselves.

When triangle is rotated, than position of angles will change. Aftermath the dilation of the triangle would increase the proportion of the sides, but angles remains equal, by which the triangle remain similar but not congruent.

Thus, a rotation, then a dilation transformation will create a pair of siilar but not congruent triangles.

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Answer:

D. a rotation, then a dilation

Step-by-step explanation:

got it right on edge 23

The probability that a used radio will be working after an additional 8 years, given that the number of years a radio functions is exponentially distributed with parameter λ = 1/8, is approximately 0.3679.

To find the probability that the used radio will be working after an additional 8 years, we can utilize the exponential distribution with the given parameter λ = 1/8. The exponential distribution is characterized by the probability density function f(x) = λe^(-λx), where x represents the number of years.

To calculate the probability, we need to find the survival function or complementary cumulative distribution function (CCDF). The survival function is defined as S(x) = 1 - F(x), where F(x) is the cumulative distribution function (CDF).

For the exponential distribution, the CDF is F(x) = 1 - e^(-λx). Substituting the given parameter λ = 1/8 and x = 8 into the CDF, we have F(8) = 1 - e^(-1/8 * 8) = 1 - e^(-1) = 1 - 1/e ≈ 0.6321.

Finally, the survival function or CCDF for x = 8 is S(8) = 1 - F(8) = 1 - 0.6321 ≈ 0.3679. Hence, the probability that the used radio will be working after an additional 8 years is approximately 0.3679.

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Here, we are given two functions and we want to find the difference between the two functions;

Looking at what we have;

(f-g)x

What this mean is that we are to subtract g(x) from f(x);

Mathematically;

As the spacing between joists increases, the maximum span for any board size will B. decrease only. This is because the wider the spacing between joists, the more weight and pressure will be placed on the boards that are spanning the gap between them.

This means that the boards will need to be stronger in order to support the weight without bending or breaking.
If the boards are not strong enough, they may sag or bow under the weight, which can create safety hazards or damage to the structure. Therefore, it is important to use the appropriate board size and spacing between joists for any given application in order to ensure structural integrity and safety.
In summary, increasing the spacing between joists will result in a decrease in the maximum span for any board size, as the boards will need to be stronger in order to support the weight and pressure. It is important to choose the right board size and joist spacing to maintain the structural integrity and safety of the building or structure.

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The given matrix 'a' can be diagonalized. To diagonalize 'a', we need to find a matrix 'P' and a diagonal matrix 'D' such that 'D' is equal to the inverse of 'P' multiplied by 'a' multiplied by 'P'.

A square matrix 'a' is diagonalizable if there exists an invertible matrix 'P' such that 'P^(-1) * a * P' is a diagonal matrix. To determine whether 'a' is diagonalizable, we need to check if 'a' satisfies certain conditions.

Firstly, we check if 'a' has 'n' linearly independent eigenvectors, where 'n' is the size of the matrix. If 'a' has 'n' linearly independent eigenvectors, it is diagonalizable.

Secondly, we need to verify if the geometric multiplicity of each eigenvalue of 'a' matches its algebraic multiplicity. The geometric multiplicity represents the number of linearly independent eigenvectors corresponding to an eigenvalue, while the algebraic multiplicity denotes the number of times an eigenvalue appears in the characteristic equation.

If 'a' satisfies both conditions, it is diagonalizable. To find the diagonal matrix 'D', we place the eigenvalues of 'a' on the diagonal of 'D'. The matrix 'P' is formed by taking the eigenvectors of 'a' as its columns. Finally, 'D' is equal to the inverse of 'P' multiplied by 'a' multiplied by 'P', as stated earlier.

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Answer:

150= price of each Sneaker

10= amount of money you started with

x=Number of Sneakers

Step-by-step explanation:

When a transversal cuts two parallel lines, 8 angles are created.

When two lines do not cross one another, they are said to be parallel. In addition, parallel lines are two lines that cross each other at infinity.

A transversal line is one that crosses two other lines at two different locations. Line l meets a and b in the image below at two different locations, P and Q. Line l is the transversal line as a result.

Corresponding angles are those that are created when two parallel lines and a transversal intersect, also known as matching corners or corresponding corners.

∠1 and ∠6

∠4 and ∠8

∠2 and ∠5

∠3 and ∠7

When a transversal connects two coplanar lines, alternate interior angles are created.

∠4 and ∠5

∠3 and ∠6

However, each pair of alternate interior angles is equal if a transversal meets two parallel lines.

∠4 = ∠5

∠3 = ∠6

The pair of angles that are created on the outer side of two lines but on the other side of the transversal are known as alternate exterior angles.

Consecutive interior angles, related angles, and co-interior angles are other names for interior angles that are on the same side of the transversal.

∠3 and ∠5

∠4 and ∠6

When a transversal cuts two parallel lines, 8 angles are created.

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∠1 and ∠6

∠4 and ∠8

∠2 and ∠5

∠3 and ∠7

When a transversal connects two coplanar lines, alternate interior angles are created.

∠4 and ∠5

∠3 and ∠6

However, each pair of alternate interior angles is equal if a transversal meets two parallel lines.

∠4 = ∠5

∠3 = ∠6

Consecutive interior angles, related angles, and co-interior angles are other names for interior angles that are on the same side of the transversal.

∠3 and ∠5

∠4 and ∠6