Triangle congruence , how is TVR congruent to SRV? SAS, SSS, ASA, AAS? picture added

The expression for the difference of two linear functions is (f - g)(x) = 4x - 6.

A linear function is a type of function in mathematics that has the form f(x) = mx + b, where x is the independent variable, f(x) is the dependent variable, m is the slope of the line, and b is the y-intercept.

To find the expression for the difference of two linear functions, f(x) and g(x), denoted by (f - g)(x).

The expression for (f - g)(x) can be found by subtracting g(x) from f(x):

(f - g)(x) = f(x) - g(x)

Substituting the given functions f(x) = x - 2 and g(x) = -3x + 4, we get:

(f - g)(x) = f(x) - g(x)

= (x - 2) - (-3x + 4) [Substitute the given values of f(x) and g(x)]

= x - 2 + 3x - 4 [Distribute the negative sign in front of (-3x + 4)]

= 4x - 6 [Combine like terms]

Therefore, (f - g)(x) = 4x - 6.

Option D (-3x² - 2x - 8) is incorrect as it involves squaring a linear expression, which would result in a quadratic expression. Option A (which has no operation between 3 and 22) is not a valid expression. Option B (-3x - 8) and C (3x3x22 or 198) do not take into account the fact that each sundae can be made using one of 3 syrups and one of 3 candy toppings.

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Answer:

y=7

Step-by-step explanation:

log11(y+8) log11 4 = log11 60

log11(4*(y+8))=log11 60

4 * ( y + 8 ) = 60

4 y + 32 = 60

4 y = 60 - 32

4 y = 28

y = 28 : 4

Answer:  y = 7

Answer:

wrong right right wrong right wrong

Step-by-step explanation:

70/ 130= 53.8%

4th row 3rd one to the right

2nd row, 2nd one to the right.

21/156 = 13.4%

70/130 = 53.8% round to get 54%

21/156 = 13.4%

so 2nd 3rd 5th apply

Answer:-22

Step-by-step explanation:

The taxable income for Adela and James is $582,856.

Earnings of Adela last year = $48,500

Earnings of James last year = $549,706

Taxable income can be calculated as follows:

Total Wages of James and Adela

= $48,500 + $549,706 = $598,206

The Additional tax information for the year is follows:

Deductions: Interest earned: $1,200, state and local income taxes paid: $4,200, mortgage interest: $5,200, contributions to charity: $1,400, contributions to retirement plans: $3,350

Total Deductions = $15,350

Taxable income = $598,206 - $15,350 = $582,856

Therefore, the taxable income for Adela and James is $582,856.

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Answer:

15 inches

Step-by-step explanation:

Here, we have a scale of 5 inches to 3 miles

We have 9 miles here, we now want to get the amount of corresponding inches

Let the corresponding inches be x

5 inches to 3 miles

x inches to 9 miles

That means ;

x * 3 = 5.* 9

x = 45/3

x = 15 inches

complement angle meabs 90° so,

90° - 48°

= 42°

hence the complement angle of 48° is 42°

The mailbag released from a helicopter reaches the ground after 2.47 seconds. The boat reaches the two-mile marker in 61.29 seconds and its velocity at that point is -32.33 m/s.

(a) To determine how long after its release the mailbag reaches the ground, we need to find the value of t when h equals zero. Substituting h=0 into the equation h=3.20\(t^3\), we get 0=3.20\(t^3\). Solving for t, we find t ≈ 2.47 seconds. Therefore, it takes approximately 2.47 seconds for the mailbag to reach the ground after its release.

(b) To find the time it takes for the boat to reach the two-mile marker, we can use the equation of motion: x = x0 + v0t + (1/2)\(at^2\), where x is the distance, x0 is the initial distance, v0 is the initial velocity, t is the time, and a is the acceleration. Given x = 100 m, x0 = 0, v0 = 29.5 m/s, and a = -3.10 m/\(s^2\), we can solve for t. Using the quadratic formula, we find t ≈ 61.29 seconds.

To determine the velocity of the boat when it reaches the marker, we can use the equation v = v0 + at, where v is the final velocity. Substituting v0 = 29.5 m/s, a = -3.10 m/\(s^2\), and t ≈ 61.29 seconds, we can calculate the velocity. The negative sign indicates that the boat is moving in the opposite direction, so the velocity is approximately -32.33 m/s. Therefore, the boat reaches the marker with a velocity of approximately -32.33 m/s.

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Answer:

2 4 6 8 12 14 16 18 20

Step-by-step explanation:

Answer:2 4 6 8 10 12 14 16 18 20

Step-by-step explanation: just add them or count by 2

When Julie divides 98.6 by 12 , So by the rules of significant figures , the number that Julie should write down is  8.3  .

What are Significant Figures ?

The Significant figures can be defined as number of digits in a value, that is often a measurement, which contribute to degree of accuracy of value. The significant figures is counted from first non zero digit .

The Rule of Significant figures says that , when a number "a" that have 3 significant figures is divided by number "b" having 2 significant figures , then the quotient will have the minimum of the two significant figure that is 2 .

Here 98.6 is divided by 12 ,

the number 98.6 has 3 significant figures ; the number 12 has 2 significant figures ,

So , the result can have maximum of 2 significant figures ,

On dividing 98.6 by 12 , we get the result as 8.2166666..  ;

since the result can have at most 2 sig. figure , So , the result is 8.3 .

Therefore , Julie should write down 8.3   .

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Answer:

Answer = 39.25 or 39 if rounded to the nearest whole number

Step-by-step explanation:

The formula for finding the volume of a cone is h(pi)(r^2)/3. We know that the height is 6 and the diameter is 5. Since we know the diameter we know that the radius is 2.5 since it is one half of the diameter. Now that he know the radius and height we can plug the values into the equation to get V=39.25

Hope that helps! :)

Answer:

h=8

Step-by-step explanation:

Fast fast!jjdbdbdjdjdbxjdj

The parametric equations of the line passing through (0,0,4) and parallel to the line passing through (5,5,5) and (3,0,1) are given by:

x = 0 - 2t

y = 0 - 5t

z = 4 - 4t, where t is any real number.

To find the parametric equations of the line passing through (0,0,4) and parallel to the line passing through (5,5,5) and (3,0,1), we can use the following steps:

Step 1: Find the direction vector of the line passing through (5,5,5) and (3,0,1).

Let P1 = (5,5,5) and P2 = (3,0,1)

Then, the direction vector d of the line passing through P1 and P2 is given by:

d = P2 - P1 = (3,0,1) - (5,5,5) = (-2,-5,-4)

Step 2: Use the direction vector and the given point (0,0,4) to find the parametric equations of the line.

Let the point on the line passing through (0,0,4) be given by P = (x,y,z)

Then, since the line is parallel to the line passing through P1 and P2, the direction vector of the line passing through P and (0,0,4) is also d = (-2,-5,-4).

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Answer:

$3000

Step-by-step explanation:

Look at where the x value is equal to 100 and look at what value the purple line intersects with when it reaches 100

you can see that when the purple hits 100 it is also on the 3000 line

hope this helps<3

Answer:

the GCF of the number in the given expression (32+16) is 16.

Step-by-step explanation:

This is your answer

The approximate value of f(1) using Euler's method with two steps of equal size is 6.636. The range of f for t > 0 is 0 < f(t) < 6.

a. The limiting factor in this logistic differential equation is the carrying capacity, which is 6 in this case. As y approaches 6, the growth rate of y slows down, until it eventually levels off at the carrying capacity.

b. To use Euler's method, we first need to calculate the slope of the solution at t=0. Using the given differential equation, we can find that the slope at t=0 is y(0)/8(6-y(0)) = 8/8(6-8) = -1/6.

Using Euler's method with two steps of equal size, we can approximate f(1) as follows:

f(0.5) = f(0) + (1/2)dy/dx|t=0

= 8 - (1/2)(1/6)*8

= 7.333...

f(1) = f(0.5) + (1/2)dy/dx|t=0.5

= 7.333... - (1/2)(7.333.../8)*(6-7.333...)

= 6.636...

Therefore, the approximate value of f(1) using Euler's method with two steps of equal size is 6.636.

c. The range of f for t > 0 is 0 < f(t) < 6, since the carrying capacity of the logistic equation is 6. As t approaches infinity, f(t) will approach 6, but never exceed it. Additionally, f(t) will never be negative, since it represents a population size. Therefore, the range of f for t > 0 is 0 < f(t) < 6.

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Answer:

Hello,

3842

Step-by-step explanation:

\(a=4-\sqrt{15} \\\\\dfrac{1}{a} =\dfrac{1}{4-\sqrt{15}} \\\\=\dfrac{4+\sqrt{15}}{(4-\sqrt{15})*(4+\sqrt{15})}\\\\=\dfrac{4+\sqrt{15}}{16-15} \\\\=4+\sqrt{15}\\\\\)

\(a+\dfrac{1}{a} =4-\sqrt{15}+4+\sqrt{15}=8\\\\\)

\((a+\dfrac{1}{a} )^2=a^2+\dfrac{1}{a^2} +2\\\\a^2+\dfrac{1}{a^2} =8^2-2=62\\\)

\((a+\dfrac{1}{a} )^3=a^3+\dfrac{1}{a^3} +3*\dfrac{a^2}{a} +3*\dfrac{a}{a^2} \\\\8^3=a^3+\dfrac{1}{a^3} +3(a+\dfrac{1}{a} )\\\\a^3+\dfrac{1}{a^3} =8^3-3*8=488\\\)

\((a+\dfrac{1}{a} )^4=a^4+\dfrac{1}{a^4} +4*\dfrac{a^3}{a} +6*\dfrac{a^2}{a^2} +4*\dfrac{a}{a^3}\\\\a^4+\dfrac{1}{a^4}=(a+\dfrac{1}{a} )^4-4*a^2-4*\dfrac{1}{a^2} -6\\a^4+\dfrac{1}{a^4} =8^4-4*62-6\\\\=4096-248-6\\\\=3842\\\boxed{a^4+\dfrac{1}{a^4} =3842}\\\)

Using a calculator:

\(a=4-\sqrt{15}=0,1270166537925831148207346002176....\\\\a^4= 2,6028112122495108436170792979303e-4\\\\\dfrac{1}{a} =4+\sqrt{15} =7,8729833462074168851792653997824...\\\\\dfrac{1}{a^4}=3841,9997397188787750489156382921....\\\\a^4+\dfrac{1}{a^4} \\\\= 2,6028112122495108436170792979303e-4+3841,9997397188787750489156382921....\\\\=3842\\\)

The probability of getting one even and one odd number when rolling two six-sided, fair dice is 1/4.

To calculate the probability of getting one even and one odd number, we can use the following approach:

So the probability of getting one even and one odd number when rolling two six-sided, fair dice is 1/4 or 0.25.

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A. N, B ≥ 0 (non-negativity constraint)

B. The recommended investment portfolio (in dollars) for this client can be found by reading the values in cells A1 and B1.

C.  You can solve for the recommended investment portfolio (in dollars) by reading the values in cells A1 and B1.

D. You can solve for the recommended investment portfolio (in dollars) by reading the values in cells A1 and B1.

(a)

The linear programming model to find the best investment strategy for this client can be formulated as follows:

Maximize: 0.09N + 0.08B

Subject to:

N + B ≤ 85 (maximum investment of $85,000)

N ≤ 55 (maximum investment of $55,000 in the internet fund)

6N + 4B ≤ 410 (maximum risk rating of 410 for a moderate investor)

N, B ≥ 0 (non-negativity constraint)

(b)

To solve the problem using Excel Solver, you can set up the following spreadsheet model:

Cell A1: N (amount invested in the internet fund)

Cell B1: B (amount invested in the Blue Chip fund)

Cell C1: =0.09A1 + 0.08B1 (annual return for the portfolio)

Constraints:

Cell A2: ≤ 85

Cell B2: ≤ 85

Cell C2: ≤ 55

Cell D2: ≤ 410

The objective is to maximize the value in cell C1 by changing the values in cells A1 and B1, subject to the constraints.

Using Excel Solver, set the objective to maximize the value in cell C1 by changing the values in cells A1 and B1, subject to the constraints in cells A2, B2, C2, and D2.

The recommended investment portfolio (in dollars) for this client can be found by reading the values in cells A1 and B1.

(b)

For the aggressive investor with a maximum portfolio risk rating of 450, the linear programming model remains the same, except for the constraint on the maximum risk rating.

The new constraint would be: 6N + 4B ≤ 450

Using the same spreadsheet model as before, with the updated constraint, you can solve for the recommended investment portfolio (in dollars) by reading the values in cells A1 and B1.

(d)

For the conservative investor with a maximum portfolio risk rating of 320, the linear programming model remains the same, except for the constraint on the maximum risk rating.

The new constraint would be: 6N + 4B ≤ 320

Using the same spreadsheet model as before, with the updated constraint, you can solve for the recommended investment portfolio (in dollars) by reading the values in cells A1 and B1.

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Answer:

63 I think

you can find a common denominator by multiplying the denominators together. however keep in mind that what you do to the bottom you must do to the top

1/7 would become 9/63 and 2/9 would become 14/63

The dilated figure is has the vertex

Vertex A: (4, 4)

Vertex B: (8, 4)

Vertex C: (4, 8)

Vertex D: (8, 8)

To begin, let's identify and label the vertices of the original shape, which is a square:

Labeling all the vertices of the original square, we have:

Vertex A: (1, 1)

Vertex B: (2, 1)

Vertex C: (1, 2)

Vertex D: (2, 2)

Now, let's move on to finding the vertices of the dilated shape. If the dilation has a scale factor of k, then each coordinate (x, y) will be transformed to (ka, ky). If k > 1, the dilated shape will be larger, and if 0 < k < 1, the dilated shape will be smaller.

In this case, the scale factor is 4, so we need to multiply each coordinate by 4:

Vertex A: (1, 1) → (4, 4)

Vertex B: (2, 1) → (8, 4)

Vertex C: (1, 2) → (4, 8)

Vertex D: (2, 2) → (8, 8)

Now that we have the vertices of the dilated shape, let's connect them to form the dilated shape. By connecting the dilated vertices, we obtain a larger square.

The original figure had side lengths of 1 unit. The dilated figure, after applying a scale factor of 4, has side lengths of 4 units. It's important to note that the side lengths were also multiplied by the scale factor.

Original Shape:

Vertex A: (1, 1)

Vertex B: (2, 1)

Vertex C: (1, 2)

Vertex D: (2, 2)

Dilated Shape:

Vertex A: (4, 4)

Vertex B: (8, 4)

Vertex C: (4, 8)

Vertex D: (8, 8)

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Complete Question:

For the figure in the image below, perform a dilation centered at the origin with a scale factor of 4. How do the dilated side lengths compare to the original side lengths?

The graph of f(x) = x^3 -6x^2 + 4x +1 hits 3 times to the x-axis

Hence, option (D) is the correct choice.

We have the function:

f(x) = x^3-6x^2+4x+1

The values of the variable in a function that cause the function to equal zero are known as the zeros of the function. The places on the x-axis where the graph crosses the x-axis are known as a function's zeros graphically. In other words, we may say that a function's zeros are the graph's x-intercepts.

The zeros of the function will be:

x^3-6x^2+4x+1 = 0

Since the last term is positive, so (x-1) will be the factor of the above equation.

Factorising, we will get,

(x-1)(x^2-5x-1)=x^3-6x^2+4x+1

So, one factor will be x = 1

Now solving the quadratic equation,

The roots will be: \(x^2 = \frac{( 5 \pm \sqrt 29)}{2}\)

So, the value of both roots will be: (x-5.19)(x+0.192)

Therefore, the graph will hit x-axis at these three points.

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Answer:

3132

Step-by-step explanation:

2.2% of 3500 is 77 which leaves you with 3423 after one year. At this rate you can take 2.2% of 3423. using this formula five times you reach a final answer of 3132.

3500

-77

3423

-75.306

3347.694

-73.649268

3274.044732

-72.028984104

3202.0157479

-70.4443464538

3131.57140145

and rounding up to a whole leaves you with 3132

(a) A nonzero vector orthogonal to the plane through the points P, Q, and R is (9, -17, 35). (b) The area of triangle PQR is \(\sqrt\)(811) / 2.

(a) To determine a nonzero vector orthogonal to the plane through the points P, Q, and R, we can first find two vectors in the plane and then take their cross product. Taking vectors PQ and PR, we have:

PQ = Q - P = (5, 1, -2) - (-4, 0, 0) = (9, 1, -2)

PR = R - P = (6, 4, 1) - (-4, 0, 0) = (10, 4, 1)

Taking the cross product of PQ and PR, we have:

n = PQ x PR = (9, 1, -2) x (10, 4, 1)

Evaluating the cross product gives n = (9, -17, 35). Therefore, (9, -17, 35) is a nonzero vector orthogonal to the plane through points P, Q, and R.

(b) To determine the area of triangle PQR, we can use the magnitude of the cross product of vectors PQ and PR divided by 2. The magnitude of the cross product is given by:

|n| = \(\sqrt\)((9)^2 + (-17)^2 + (35)^2)

Evaluating the magnitude gives |n| = \(\sqrt\)(811).

The area of triangle PQR is then:

Area = |n| / 2 = \(\sqrt\)(811) / 2.

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The  \(1.2742*10^4 km / L\) times longer is the diameter of earth than the piece of wood's length.

The radius of earth is 6371 km.

Let's say the length of the piece of wood is L.

The diameter of the Earth is 2 times its radius

The radius of our planet, The Earth, is the distance from the center of the Earth to a point on or near its surface, and it ranges from nearly 6,378 km to nearly 6,357 km.

The diameter of a circle is the length of the line starting from one point on a circle to another point and passing through the center of the circle. It is equal to twice the radius of the circle. It is usually denoted by ‘d’ or ‘D’.

The diameter of the Earth is 2 times its radius, or 2 x 6371 km = 12742 km.

The diameter of the Earth is 12742 km / L times longer than the length of the piece of wood.

In scientific notation, we can express this as:

12742 km / L = \(1.2742*10^4 km / L\)

The  \(1.2742*10^4 km / L\) times longer is the diameter of earth than the piece of wood's length.

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Answer:

the answer is d. What is the width of the box, in inches, that

produces the maximum volume?

Step-by-step explanation:

length: 120 - 6w >

The leading coefficient of a polynomial is the coefficient of the term with the highest degree. It can tell us a lot about the graph of the polynomial, it can mainly tell us whether the graph is in a downward direction or upward direction.

If the leading coefficient is positive, then the graph will start at the origin and will extend upwards, with the degree of the polynomial determining how steep the graph is. If the leading coefficient is negative, then the graph will start at the origin and extend downwards.

If the leading coefficient is 0, then the graph will be a horizontal line. The leading coefficient can also tell us about the end behavior of the graph. If the degree of the polynomial is even, then the end behavior will be a horizontal line. If the degree of the polynomial is odd, then the end behavior will be a vertical line. Knowing the leading coefficient of a polynomial gives us a basic idea of what the graph of the polynomial will look like.

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There are approximately 27,735 shoppers in the store at the end of the sale (t = 12).

What is a function?

A function is a mathematical concept that relates a set of inputs (called the domain) to a set of outputs (called the range). It is a rule or relationship that assigns a unique output value to each input value. In other words, for every input, there is exactly one corresponding output.

A function is typically denoted by a symbol, such as "f," followed by parentheses containing the input value. The output value is obtained by applying the rule or formula defined by the function to the input value.

To determine the number of shoppers in the store at the end of the sale (t = 12), we need to calculate the net change in the number of shoppers from the beginning of the sale to the end.

The net change in the number of shoppers is obtained by subtracting the number of shoppers leaving the store from the number of shoppers entering the store during the 12-hour sale.

Using the provided functions, we have:

\(S(t) = 0.5t^4 - 16t^3 + 144t^2\) (number of shoppers entering the store)

\(L(t) = -80 + \frac{4400}{t^2 - 14t + 55}\) (number of shoppers leaving the store)

To find the number of shoppers at the end of the sale (t = 12), we can calculate:

\(Number of shoppers =\int\limits^{12}_0(S(12) -L(t) )dt\)

Substituting the values into the equation:

\(Number of shoppers =\int\limits^{12}_0 (S(12) - (-80 + \frac{4400}{t^2 - 14t + 55}))dt\)

Evaluating the integral and substituting t = 12:

\(Number of shoppers =[(0.1t^5-4t^4+t^3 )- (-80t + {ln|t-11|-ln|t-5|})]\) evaluate from 0 to 12.

Calculating further:

\(Number of shoppers = 24883.2 - [-80(12) +\frac{2200}{3}[ {ln|12-11|-ln|12-5|}]] + [-80(0) +\frac{2200}{3} [ {ln|0-11|-ln|0-5|}]]\)

Number of shoppers = 24883.2 - [-2273.95 ] + 578.2

Finally, we need to substitute t = 12 into the S(t) function to obtain the number of shoppers:

Number of shoppers = 24883.2+2852.15

Calculating:

Number of shoppers ≈ 27,735

Therefore, according to the model, there are approximately  27,735 shoppers in the store at the end of the sale (t = 12).

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Answer:

-3/4

Step-by-step explanation:

Point A is at (-4,3) and Point B is at (4,-3)

The slope is at

m = (y2-y1)/(x2-x1)

   = (-3 -3)/(4 - -4)

   = (-3-3)/(4+4)

    = -6/8

     = -3/4

Answer:

9

Step-by-step explanation:

put in order least to greatest

-9 -9 -7 -6 -5 -4 -3  0

9-0=9

range cannot be negative because it is the space between numbers and distance cannot be negative

Answer: The range is 9.