Which expressions are equivalent to (a^2-16(a+4)? Select the three equivalent expressions
A.) a^3-64
B.) (a-4)^3
C.) (a+4)^3
D.) (a+4)^2(a-4)
E.) (a-4)^2(a+4)
F.) [(a)^2-(4^2)](a+4)
G.) (a-4)(a+4)(a+4)

Answer:

what about you read well and stop cheating

The area of the rectangle is 9 square units

First, we need to know the properties of a rectangle. They are;

From the diagram shown, we have that;

Length of the transformed shape(parallelogram to rectangle) = 3 units

Width = 3 units

The formula for the area of a rectangle is expressed as;

Area = lw

Substitute the values

Area = 3(3)

Area = 9 square units

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Answer:

Let's start by using variables to represent the number of rows containing 20 vines and 25 vines. Let:

x be the number of rows containing 20 vines

3x be the number of rows containing 25 vines (since there are 3 times as many rows containing 25 vines as there are rows containing 20 vines)

We know that Sarah plants a total of 760 vines, and that each row contains either 20 vines or 25 vines. Therefore, we can write an equation based on the total number of vines:

20x + 25(3x) = 760

Simplifying and solving for x:

20x + 75x = 760

95x = 760

x = 8

So there are 8 rows containing 20 vines, and 3 times as many rows containing 25 vines, or 3(8) = 24 rows containing 25 vines.

Therefore, Sarah planted 8 rows with 20 vines and 24 rows with 25 vines.

To summarize, the correct answer is:
"If all features are scaled by the same factor λ∈R>0, i.e., xi is replaced by λxi for all i=1,…,N, then λβ^,β^,ξ^ solves SVM for penalty parameter λ2C."

The correct answer is "If all features are scaled by the same factor λ∈R>0, i.e., xi is replaced by λxi for all i=1,…,N, then λβ^,β^,ξ^ solves SVM for penalty parameter λ2C."

This is because scaling all features by the same factor λ does not change the relative importance of each feature in the classification problem. Therefore, the optimal solution for the scaled features will be the same as the optimal solution for the original features, but scaled by λ. The penalty parameter C will also need to be scaled by λ^2 to account for the scaling of the features.

To summarize, the correct answer is:
"If all features are scaled by the same factor λ∈R>0, i.e., xi is replaced by λxi for all i=1,…,N, then λβ^,β^,ξ^ solves SVM for penalty parameter λ2C."

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Answer:

You forgot the +- part when taking the square roots

Step-by-step explanation:

5 x^2  = -2

x^2 = -2/5

x = +- sqrt ( -2/5)       <==== note sqrt(-2/5)   NOT  sqrt (-2) / 5

x = ± i sqrt(2/5)

x^2 = 8

x = ±sqrt 8

x = ±2 sqrt (2)

Answer: 36

Step-by-step explanation:

The function which represent the distance and time is y=6x-17.5.

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Here according to the given data, let us take to points to find linear function then,

[tex](x_1,y_1)=(0.5,3)[/tex] and [tex](x_2,y_2)=(1,6)[/tex].

Now using slope formula, m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

=> Slope m = [tex]\frac{6-3}{1-0.5} = \frac{3}{0.5}[/tex] = 6

Now using equation formula , [tex]y-y_1=m(x-x_1)[/tex] then,

=> y-0.5=6(x-3)

=> y-0.5=6x-18

=> y=6x-18+0.5

=> y=6x-17.5

Hence the function which represent the distance and time is y=6x-17.5.

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Answer:

Step-by-step explanation:

This expression isn't in simplest form. The terms 3x and 2x can be added, since they are like terms.

In simplest form, this expression would be 5x - 4.

Hope this helps!

Number of years = 4

Hi there! To answer your question, Doug needs to deposit $2226.19 into a savings account that earns 2.9% interest compounded continuously. This amount was calculated using the formula P = Pe^rt, where P is the final amount Doug will have after 4 years, e is the natural logarithm constant (2.71828), r is the interest rate (2.9%), and t is the number of years (4).

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No change is needed. The underlined text is grammatically correct and conveys the intended meaning clearly.

The underlined text "Taking up to six months, hikers who plan to complete the entire journey" means that the journey being referred to may take up to six months to complete, and it is being undertaken by hikers who have planned to complete the entire journey.

The text suggests that the journey is a long and challenging one that requires careful planning and preparation by the hikers.

Therefore, the correct answer is as given above. It could then be concluded that the underlined text does not need to change.

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The step that Jackson made an error when solving the inequality was Step 1 because he did not multiply - 10 by 4.

When solving the inequality, Jackson had the right idea of multiplying the different sides of the equation by 4 in order to get rid of 4 as a denominator.

However, he was to multiply every figure in the equation by 4. He did not do this with the - 10 on the left side of the equation. This meant that Jackson did not convert that number to - 40 which then led to an incorrect inequality.

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Area of the parallelogram is 15 cm²

Area of the parallelogram:

Given that;

Base of parallelograms = 3 cm

Side of parallelograms = 5.3

Height of parallelograms = 5 cm

Find:

Area of the parallelogram

Computation:

Area of the parallelogram = l × b

Area of the parallelogram = 3 × 5

Area of the parallelogram = 15 cm²

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The mass of the gold bar of the trapezium shape and a density of 19.3g/cm³ is found to be 8.646 KG.

The volume of the trapezoidal prism will be determined first. V = BL, where B is the area of the trapezoidal face and L is the prism's length, is the formula for the volume of the prism.

We are aware that a trapezoid's area is equal to B = 1/2(6+10). (4)

B = 32 m²

When we enter the formula for volume, V = 32 x 14 V = 448 m³, we know that L is 14 cm.

Divide the mass by the volume to get the density, or D = M/V.

According to values,

19.3 = M/448

M = 8646.4 grams, which is equal to 8.646 grams.

The density is stated to be 19.3 kg/m³. Hence, the gold weighs 8.646 kilos.

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Complete question - The gold bar trapezium has cross-sectional area. Gold has a density of 19. 3 per cm3. Work out the mass of the gold bar. Give your answer in kilograms. The dimension of the trapezium are length = 14cm, parallel sides are 6cm and 10cm nd the height is 4cm.

angles of 0°, 30°, 45°, 60°, and 90° are 100 feet, 86.6 feet, 71.4 feet, 50 feet, and 0 feet, respectively.

To answer this question, we need to use a protractor, a straightedge, and the given graph to estimate the height of the blade tip when the blade is at angles of 0°, 30°, 45°, 60°, and 90°. The arc on the graph represents a portion of the blade tip's path. Assume the blade rotates counterclockwise and the blade is at an angle of 0° when the blade tip is directly to the right of the top of the vertical shaft. This position has been labeled as 0° on the graph.

Using the protractor, we can measure the angles on the graph, which is marked in 15° increments. For each angle, we can measure the horizontal position of the blade tip from the graph. The heights of the blade tips for 0°, 30°, 45°, 60°, and 90° can be estimated using the Pythagorean theorem.

At 0°, the height of the blade tip is 100 feet (which is equal to the length of the blade). At 30°, the height of the blade tip is 86.6 feet. At 45°, the height of the blade tip is 71.4 feet. At 60°, the height of the blade tip is 50 feet. At 90°, the height of the blade tip is 0 feet.

Therefore, the estimated heights of the blade tip when the blade is at angles of 0°, 30°, 45°, 60°, and 90° are 100 feet, 86.6 feet, 71.4 feet, 50 feet, and 0 feet, respectively.

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not completely sure but i think you times the x and y numbers then draw a graph of the units

The following are solutions to the given problems given f(x)=x²- 5x+7 and g(x)=3x² + 4x - 2;

(f- g)(x) = -2x² - 9x + 9

(g-f)(x) = 2x² + 9x - 9

(f + g)(x) = 4 x² - x + 5

A function can be defined as a relation between a set of inputs having one output each. In other words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain (range). A function is generally denoted by f(x) where x is the input.

here, we have,

The general mathematical representation of a function is y = f(x).

f(x)=x²- 5x+7

g(x)=3x² + 4x - 2

so, we get,

(f- g)(x) = x²- 5x+7 - (3x² + 4x - 2)

(f- g)(x) = x²- 5x+7 - 3x² - 4x + 2

(f- g)(x) = -2x² - 9x + 9

(g-f)(x) = 3x² + 4x - 2 - (x²- 5x+7)

(g-f)(x) = 3x² + 4x - 2 - x² + 5x - 7

(g-f)(x) = 2x² + 9x - 9

(f + g)(x) = x²- 5x+7 + 3x² + 4x - 2

(f + g)(x) = 4 x² - x + 5

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A correct 2-column proof include the following: B. table B.

In Mathematics, a supplementary angle simply refers to two (2) angles or arc whose sum is equal to 180 degrees.

Since line segment r is parallel to line segment s, the 2-column proof to justify that angle b and angle h are supplementary angles should be written as follows;

Statement                                             Reasons_________________

r║s                                                            Given

∠b ≅ ∠c                                                Vertical angles

∠c and ∠e are supplementary           Same-side interior angles

∠e ≅ ∠h                                                Vertical angles

∠b and ∠h are supplementary            Substitution

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(a) The probability that X = n is 2^n-1 / 2^N - 1.

(b) ɸ(t) = E[2^tx] = ∑_{n=1}^N 2^tx P(X=n) = ∑_{n=1}^N 2^tx (2^n-1 / 2^N - 1) = (2^t / 2^N - 1) ∑_{n=1}^N 2^(n-1)t = (2^t / 2^N - 1) (2^Nt - 1) / (2^t - 1) = 2^Nt / (2^N - 1)

(c) The probability that X = n and Y = m is 2^(n-m-1) / 2^N - 1.

(d) This is the same as finding the probability that the difference between the maximum and minimum elements of a subset of {1,...,N} is k. If k = 0, then the only subsets with maximum and minimum elements differing by k are the single-element subsets, so P(W=k) = N / 2^N - 1. If k > 0, then there are (N-k) choices for the minimum element m and 2^(k-1) subsets of {m+1,...,m+k-1}, so P(W=k) = (N-k) 2^(k-1) / 2^N - 1.

To find the probability mass function of X, we need to find the probability that X = n for each n ∈ {1,...,N}. This is the same as finding the probability that the maximum element of a subset of {1,...,N} is n. There are 2^n-1 subsets of {1,...,n-1}, and each of these subsets can be combined with n to form a subset of {1,...,N} with maximum element n. Therefore, the probability that X = n is 2^n-1 / 2^N - 1.

To find the value of ɸ(t) for any t ∈ R, we need to compute the expected value of 2^tx. Using the formula for expected value, we get:

ɸ(t) = E[2^tx] = ∑_{n=1}^N 2^tx P(X=n) = ∑_{n=1}^N 2^tx (2^n-1 / 2^N - 1) = (2^t / 2^N - 1) ∑_{n=1}^N 2^(n-1)t = (2^t / 2^N - 1) (2^Nt - 1) / (2^t - 1) = 2^Nt / (2^N - 1)

To find the joint probability mass function of (X,Y), we need to find the probability that X = n and Y = m for each n,m ∈ {1,...,N}. If n = m, then the only subset of {1,...,N} with maximum element n and minimum element m is {n}, so P(X=n, Y=m) = 1 / 2^N - 1. If n ≠ m, then there are 2^(n-m-1) subsets of {m+1,...,n-1}, and each of these subsets can be combined with m and n to form a subset of {1,...,N} with maximum element n and minimum element m. Therefore, the probability that X = n and Y = m is 2^(n-m-1) / 2^N - 1.

To find the probability mass function of W = X - Y, we need to find the probability that W = k for each k ∈ {0,...,N-1}. This is the same as finding the probability that the difference between the maximum and minimum elements of a subset of {1,...,N} is k. If k = 0, then the only subsets with maximum and minimum elements differing by k are the single-element subsets, so P(W=k) = N / 2^N - 1. If k > 0, then there are (N-k) choices for the minimum element m and 2^(k-1) subsets of {m+1,...,m+k-1}, so P(W=k) = (N-k) 2^(k-1) / 2^N - 1.

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Amount of paint that should be purchased to apply one coat of paint to the side of the building is 12 gallons.

Area is the amount of space occupied by a two-dimensional shape. That is, it is a quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is the square unit, commonly expressed in square inches, square feet, and so on.

Given,

length of the wall  = 105 feet

height of the wall = 35 feet

Area of the wall

= length × height

= 105 × 35

= 3675 square feet

One gallon paints 317 square feet

Number of gallons to paint 3675 square feet

= 3675/317

= 11.59 ≈ 12

Hence, 12 gallons should be purchased to apply one coat of paint to the side of building.

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[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=196\pi \\ r=7 \end{cases}\implies 196\pi =\cfrac{\pi (7)^2 h}{3}\implies 196\pi =\cfrac{49\pi h}{3} \\\\\\ \cfrac{3}{49\pi }\cdot 196\pi =h\implies 12=h[/tex]

Answer:

144

Step-by-step explanation:

6*6=36

36*4=144

The two polygons are similar using the SAS criteria.

A two-dimensional geometric shape with a finite number of sides is called a polygon. A polygon's sides are constructed from segments of straight lines joined end to end. A polygon's line segments are therefore referred to as its sides or edges. The vertex or corners made by two line segments are where an angle is created. A triangle with three sides is an illustration of a polygon. A circle is a planar figure as well, but since it is curved and lacks sides and angles, it is not regarded as a polygon. Hence, we may argue that while all two-dimensional forms are polygons, not all two-dimensional figures are polygons.

For the given polygons we find the scale factor to determine whether the two figures are similar.

The scale factor is given as:

SF = length of original/ length of new image

SF = 4 / 6

SF = 2/3

For the second segment:

SF = 6/9

SF = 2/3

The ratios of the segment are same. Also the angle between the corresponding segments is 86 degrees.

Hence, the two polygons are similar using the SAS criteria.

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Step-by-step explanation:

Inverse of a Function.

To find the inverse of the function f(x) = √(x+7), we need to interchange the roles of x and y and solve for y.

Let y = f(x) = √(x+7)

To find the inverse, we need to solve for x in terms of y.

Step 1: Square both sides of the equation to eliminate the square root:

y^2 = x + 7

Step 2: Solve for x:

x = y^2 - 7

So the inverse of the function f(x) is:

f^(-1)(y) = y^2 - 7

We can also express the inverse in terms of x:

f^(-1)(x) = x^2 - 7

Note that we changed the variable from x to y, and from y to x, when expressing the inverse function.

The value of the expression is f(g(x)) = f(x^2) = 2(x²) + 1 = 2x² + 1.

A function is composed in mathematics when two functions, f and g, are used to create a new function, h, such that h(x) = g(f(x)). The function of g is being applied to the function of x, in this case. Hence, a function is essentially applied to the output of another function.

Given that,

f(x)=2x+1 and g(x)=x²

To get the composite function we substitute the value of g(x) in the x-value of the function of f(x).

f(g(x)) = f(x^2) = 2(x²) + 1 = 2x² + 1

Hence, the value of the expression is f(g(x)) = f(x^2) = 2(x²) + 1 = 2x² + 1.

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Using composition function , the price of the computer after both discounts are applied is 0.7x - 140.

To find the price of the computer after both discounts are applied, we can use composition function . Specifically, we can find the composition of f and g, denoted as f(g(x)) or (f o g)(x). This will give us the price of the computer after both discounts are applied.

To find f(g(x)), we can substitute the expression for g(x) into the function f(x):

f(g(x)) = f(0.7x) = (0.7x) - 200

So the price of the computer after both discounts are applied is (0.7x) - 200.

Alternatively, we could find the composition of g and f, denoted as g(f(x)) or (g o f)(x). This will give us the same result, since the order of the discounts does not matter.

To find g(f(x)), we can substitute the expression for f(x) into the function g(x):

g(f(x)) = g(x-200) = 0.7(x-200) = 0.7x - 140


Either way, we can see that the price of the computer after both discounts are applied is a function of the original price x, and can be represented by the composition of the functions f and g.

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To find the zeros, set the function equal to 0.  In other words, solve f(x)=0.

             f(x) = 0

x^2 +6x + 8 = 0

 (x+4)(x +2) = 0

x = -4 and x = -2

The vertex will happen when x = -b/2a:

    [tex]x=\dfrac{-6}{2(1)} = -3[/tex]
Then use this x-value of –3 to find the y-value of the vertex:

   y = (-3)^2 + 6(-3) + 8 = 9-18+8 = -1

The vertex is (-3,-1).

Side note: The x-value of the vertex can also be found by finding the average of the two zeros:

    (-4 + (-2)) / 2 = -6/2 = -3

Answer:

First, we need to convert the width of the table from inches to feet to ensure that the units match. There are 12 inches in a foot, so:

42 inches ÷ 12 inches/foot = 3.5 feet

Let the length of the table be L feet. The perimeter is the sum of the lengths of all four sides of the rectangle, so:

2L + 2(3.5 feet) = 18 feet

Simplifying and solving for L:

2L + 7 feet = 18 feet

2L = 11 feet

L = 5.5 feet

Therefore, the length of the table is 5.5 feet.

Answer:

66

Step-by-step explanation:

the problem ask fr it draw out 2 rectangle

The mixed integer would be 2 3/4.

A mixed integer is a number that includes both a whole number and a fraction. For example, 2 1/2 is a mixed integer because it includes the whole number 2 and the fraction 1/2.

To rewrite a fraction as a mixed integer, you need to divide the numerator (the top number) by the denominator (the bottom number) and find the quotient and remainder. The quotient will be the whole number part of the mixed integer and the remainder will be the numerator of the fraction part. The denominator will stay the same.

For example, if you have the fraction 11/4, you can divide 11 by 4 to get a quotient of 2 and a remainder of 3. So the mixed integer would be 2 3/4.

Here are the steps to rewrite a fraction as a mixed integer:
1. Divide the numerator by the denominator.
2. Write the quotient as the whole number part of the mixed integer.
3. Write the remainder as the numerator of the fraction part of the mixed integer.
4. Keep the denominator the same.
5. Simplify the fraction if necessary.

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According to the question the standard deviation is approximately $9,400.

Standard deviation is a measure of variability or dispersion in a data set. It is a measure of how much the individual data points within a set deviate from the mean. The standard deviation is calculated by taking the square root of the variance and is expressed as the same unit of measurement as the data set.

The standard deviation of pre-tax family incomes when the head of the household has a university degree can be computed using the empirical rule. According to the empirical rule, approximately 68% of the data lies within one standard deviation of the mean, 95% of the data lies within two standard deviations of the mean, and 99.7% of the data lies within three standard deviations of the mean.

Given that 70% of the pre-tax family incomes when the head of the household has a university degree are between $76,300 and $95,100,
we can calculate that the standard deviation is approximately ($95,100 - $76,300) / 2.66 ≈ $9,400.

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