Write the vector u¯=[−4,−8,−12] as a linear combination u¯=λ1v¯1+λ2v¯2+λ3v¯3 where

v¯1=(1,1,0), v¯2=(0,1,1) and v¯3=(1,0,1).

Solutions: λ1=

λ2=

λ3=

Answer:

1 acre is equal to 43,560 square feet.

(hope this help's let me know if not.)

The ordered pair solutions for the system of equations are (-3, 18) and (3, 6).

To find the y-values corresponding to the given x-values in the system of equations, we can substitute the x-values into each equation and solve for y.

For the ordered pair (-3, ?):

Substituting x = -3 into the equations:

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

So, the y-value for the ordered pair (-3, ?) is 18.

For the ordered pair (3, ?):

Substituting x = 3 into the equations:

y = (3)^2 - 2(3) + 3 = 9 - 6 + 3 = 6

So, the y-value for the ordered pair (3, ?) is 6.

Therefore, the ordered pair solutions for the system of equations are:

(-3, 18) and (3, 6).

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Answer:

I think B, AC = 5

Step-by-step explanation:

You can see that the shape, DEF and ABC, both hav a number at the bottom. So We know that there is a scale factor of 2, because 6÷3 is 2. So, if we wanna know what AC is we can divide 10, from DEF, by two, we get 5. So, AC is equal to 5. :)

Answer:

X2 - X1 = 7 - 1 = 6

Y2 - Y1 = 8 - 3 = 5

L = (6^2 + 5^2)^1/2 = 7.81

2/3 L = 5.21      length of segment

Tan θ = 5 / 6 = .833    slope of line

θ = 39.8 deg

5.21 * sin 39.8 = 3.34

5.21 * cos = 39.8 = 4.00        gives length of line segments

x2 = 1 + 4 = 5      

y2 = 3 + 3.34 = 6.34

(5, 6.34) = point 2/3 up the line

Check (length of line)

[(5 - 1)^2 + (6.34 - 3)^2]^1/2 =

l = 5.21      correct length for line segmet

The general solution for the given differential equation is the sum of the complementary function and the particular solution:

\(y = y_h + y_p\\\\= C_1e^{6x} + C_2e^{-6x} + (-1/70)e^{3x} + (-1/70)e^{-3x}\)

where C₁ and C₂ are arbitrary constants determined by the initial or boundary conditions of the problem.

We are given the differential equation: d²y/dx - 36y = cosh(3x).

In this case, the homogeneous equation is d²y/dx - 36y = 0.

The characteristic equation associated with the homogeneous equation is obtained by replacing the derivatives with their corresponding algebraic expressions. In our case, we have r² - 36 = 0. Solving this quadratic equation, we find the roots to be r = ±6.

Since the roots are distinct and real, the general solution for the homogeneous equation is given by:

\(y_h = C_1e^{6x} + C_2e^{-6x}\)

where C₁ and C₂ are arbitrary constants determined by the initial or boundary conditions of the problem.

The term cosh(3x) can be written as a linear combination of exponential functions using the identities:

\(cosh(ax) = (e^{ax} + e^{-ax})/2, \\\\sinh(ax) = (e^{ax} - e^{-ax})/2.\)

Therefore, \(cosh(3x) = (e^{3x} + e^{-3x})/2.\)

Now, we assume the particular solution has the form:

\(y_p = A_1e^{3x} + A_2e^{-3x}\)

where A₁ and A₂ are undetermined coefficients.

Substituting these derivatives into the original differential equation, we get:

\((9A_1e^{3x} + 9A_2e^{-3x}) - 36(A_1e^{3x} + A_2e^{-3x}) = (e^{3x} + e^{-3x})/2.\)

To satisfy this equation, the coefficients of the exponential terms on both sides must be equal. Therefore, we have the following system of equations:

9A₁ - 36A₁ = 1/2,

9A₂ - 36A₂ = 1/2.

Solving these equations, we find A₁ = -1/70 and A₂ = -1/70.

Thus, the particular solution is:

\(y_p = (-1/70)e^{3x} + (-1/70)e^{-3x}\)

Finally, the general solution for the given differential equation is the sum of the complementary function and the particular solution:

\(y = y_h + y_p\\\\= C_1e^{6x} + C_2e^{-6x} + (-1/70)e^{3x} + (-1/70)e^{-3x}\)

where C₁ and C₂ are arbitrary constants determined by the initial or boundary conditions of the problem.

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Answer:

(3, -2)

Step-by-step explanation:

2+4 = 6

3-7 = -4

6/2 = 3

-4/2 = -2

Answer:

164 people

Step-by-step explanation:

100% represents the 150 people who attended last year.

this year , there is an increase of 9% , which will make the total percentage to be 109%.

if ; 100% = 150 people

     109% = ?

cross multiply to get 163.5 the round off to get 164

Answer:

1

Step-by-step explanation:

Step-by-step explanation:

NO and PQ are congruent segments (have the same length), and both have the same midpoint M.

NO ≅ PQ, given.

NM ≅ ½ NO, definition of midpoint.

PM ≅ ½ PQ, definition of midpoint.

PM ≅ ½ NO, substitution.

PM ≅ NM, substitution.

(i) The average values for the variables andre, pri gpa, and act is sum of all the values divided by the total number of values.

(ii) The model atenderte 5 b0 1 b1 prigpa 1 b2act 1 u in equation form  is atenderte = b₀ + b₁ x prigpa + b₂ x act + u

(iii) The slope coefficients is  b₁ and b₂

(iv) The predicted atenderte if prigpa 5 3.65 and act 5 20 is atenderte = b₀ + b₁ x 3.65 + b₂ x 20 + u

(v) if student a has prigpa 5 3.1 and act 5 21 and student b has prigpa 5 2.1 and act 5 26, then the predicted difference in their attendance rates is  0.5

In this exercise, we will be exploring a regression model that predicts the attendance rate of students based on their academic performance variables. We will be using three variables to predict the attendance rate: "andre", "pri gpa", and "act". Here are the answers to the questions:

(i) To obtain the minimum, maximum, and average values for the variables "andre", "pri gpa", and "act", we need to first look at the data. The minimum value is the smallest value for each variable, the maximum value is the largest value for each variable, and the average value is the sum of all the values divided by the total number of values.

(ii) The regression model that predicts the attendance rate is written in equation form as

=> "atenderte = b₀ + b₁ x prigpa + b₂ x act + u".

This equation means that the predicted attendance rate (atenderte) is equal to the intercept (b₀) plus the product of the coefficient for "pri gpa" (b₁) and the value of "pri gpa" plus the product of the coefficient for "act" (b₂) and the value of "act".

(iii) The estimated slope coefficients (b₁ and b₂) tell us the expected change in the attendance rate for each one-unit increase in "pri gpa" or "act". If b₁ is positive, it means that as "pri gpa" increases, the attendance rate is expected to increase. Similarly, if b₂ is positive, it means that as "act" increases, the attendance rate is expected to increase.

(iv) To find the predicted attendance rate if "pri gpa" is 3.65 and "act" is 20, we can substitute these values into the regression equation:

atenderte = b₀ + b₁ x prigpa + b₂ x act + u

atenderte = b₀ + b₁ x 3.65 + b₂ x 20 + u

This will give us the predicted attendance rate for a student with "pri gpa" of 3.65 and "act" of 20. If there are any students in the sample with these values of the explanatory variables, then their actual attendance rate should be close to the predicted value.

(v) To find the predicted difference in attendance rates between student A (with "pri gpa" of 3.1 and "act" of 21) and student B (with "pri gpa" of 2.1 and "act" of 26), we can first use the regression equation to predict the attendance rates for each student:

Student A:

atenderteA = b0 + b1 x 3.1 + b2 x 21 + u

Student B:

atenderteB = b0 + b1 x 2.1 + b2 x 26 + u

Then, we can take the difference between the predicted attendance rates for each student:

=> atenderteA - atenderteB

=> 52.6 - 52.1 = 0.5

This will give us the predicted difference in attendance rates between the two students.

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The area of the rectangle will be 2,348.3824 cm² as "A rectangle has a length of 26 inches and a width of 14 inches and 1 inch=2.54 cm".

The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina. Area is the total amount of space occupied by a flat (2-D) surface or an object's shape. On a piece of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies. Consider your square as being composed of smaller unit squares.

Here,

Length in inches=26

Width in inches=14

area in inches=26*14

=364 inch²

Now,

1 inch=2.54 cm

area in cm,

=364*2.54*2.54

=2,348.3824 cm²

Since "a rectangle has a length of 26 inches and a width of 14 inches and 1 inch=2.54 cm," the area of the rectangle will be 2,348.3824 cm².

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In a case whereby the slide part of a water slide is 89 feet long and makes a 42 angle of depression with the ground, the lenght or how high up in the air  is 73.6 feet

We know that the length of the slide AB is 89 feet, and the angle of depression from A to B is 42 degrees. We want to find the height h of point A above the ground.

The tangent of an angle is defined as the ratio of the opposite side to the adjacent side. In this case, the opposite side is h (the height we're looking for), and the adjacent side is AB (the length of the slide). So we can write base on trigonometery as ;

tan(42) = h / 89

h = 89 * tan(42)

h ≈ 73.6 feet

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After solving the given  logarithmic expression we get

1. \(log_5 k + log_5 2 = log_5 (k\times2)\)

2. \(2 log_5 k = log_5 k^2\)

3. \(log_5 k - log_5 7 = log_5 (k/7)\)

4. \(log_3 k/log_3 5 = log_5 k/log_5 3\)

5. \(log_5 k + log_25 k = log_5 k^3\)

6.  \(log_3 k^2\)/\(log_3\) 25 = \(2 log_3 (k/5)\)

The power to which a number must be increased in order to obtain another number is known as a logarithm.

Following are the Four Basic Properties of Logs by using which we can solve the given expressions.

\(log_b(xy) = log_bx + log_by\\log_b(x/y) = log_bx - log_by\\log_b(xn) = n log_bx\\log_bx = log_ax / log_ab\)

Using logarithmic properties, we can rewrite each expression as follows:

1. \(log_5 k + log_5 2 = log_5 (k\times2)\)

2. \(2 log_5 k = log_5 k^2\)

3. \(log_5 k - log_5 7 = log_5 (k/7)\)

4. \(log_3 k/log_3 5 = log_5 k/log_5 3\)

5. \(log_5 k + log_25 k = log_5 k + 2 log_5 k\)

\(log_5 k + log_25 k = 3 log_5 k\)
\(log_5 k + log_25 k = log_5 k^3\)

6.  \(log_3 k^2\)/\(log_3\) 25 = \(2 log_3 k - 2 log_3 5\)

 \(log_3 k^2\)/\(log_3\) 25 = \(2 log_3 (k/5)\)

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Question

For each expression, give an equivalent expression that is of the form \(log_5(*)\), where * is an expression with numbers and possibly the variable k.

1. \(log_5\) k + \(log_5\) 2 =          2. 2 \(log_5\) k =

3. \(log_5\) k - \(log_5\) 7 =          4. \(log_3\)k / \(log_3\) 5 =

5. \(log_5\) k + \(log_{25}\) k =       6. \(log_3 k^2\)/\(log_3\) 25 =

Answer:where is the question

Step-by-step explanation:

Answer:

17 cents

Step-by-step explanation:

4250/250

Answer:

(-2, 3)

Step-by-step explanation:

not sure

Answer:

2. 8 1/4

3.8 1/4

5. 5 1/10

6. 6 1/3

8. 10 1/6

9. 10 1/10

11. 3 1/8

12. 5 1/6

Step-by-step explanation:

Hope this helped :)

Answer:

The sum of a and b is a+b.

Step-by-step explanation:

5 divided by the sum of a and b is 5/ (a+b).

The final answer is 5/ (a+b)~

Answer:

The sum of a and b is a+b.

Step-by-step explanation:

5 divided by the sum of a and b is 5/ (a+b).

The final answer is 5/ (a+b)

hope that helps:)

Answer:

The number of different ways the car can be built is 31 different ways

Step-by-step explanation:

The given options are'

1), Leather seats, 2) Heated seats, 3) Sunroof, 4) Tinted windows, 5), back up camera

Therefore, the number of different ways the car can be built, n, is given as follows;

n = ₅C₁  + ₅C₂ + ₅C₃ + ₅C₄ + ₅C₅

n = 5 + 10 + 10 + 5 + 1 = 31 different ways

The number of different ways the car can be built = n = 31 different ways

Answer: it would be -125 but because it's |-125| feet then it's the absolute value making it positive so your answer is -140 feet. if you're walking -140 then that's either the amount of distance left behind or a distance needed to walk

Step-by-step explanation:

The one-variable inequality that represents the number of years, x, it would take for the autographed baseball's value to reach at least $650 is $300 * (1.05)^x ≥ $650.

1. Let's represent the number of years after 2017 as x.

2. The value of the autographed baseball exponentially increases by 5% each year. Therefore, the value after x years would be $300 * (1 + 0.05)^x.

3. We want to find the number of years, x, it would take for the value to reach at least $650.

4. To represent this in an inequality, we can write $300 * (1.05)^x ≥ $650.

5. However, to remove the dollar signs and write the inequality in standard form, we can divide both sides of the inequality by $300 to get (1.05)^x ≥ $650 / $300.

6. Simplifying further, we have (1.05)^x ≥ 2.1667.

7. The inequality is now in standard form, representing that the value of the autographed baseball, after x years, must be greater than or equal to 2.1667.

8. By solving this inequality for x, we can determine the number of years it would take for the baseball's value to reach at least $650.

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1) Doesn't factor

2) Doesn't factor

3) (x + 5) and (x + 5)

4) 4(9x^2 + 25)

5) Can not factor

6) (x + 2) (x + 3)

7) Can not factor

We can factorize the expression as follows;

Write the quadratic expression in the form ax^2 + bx + c, where a, b, and c are coefficients. Find two numbers, m and n, whose product is equal to a times c.

Use the two numbers found in to write the quadratic expression as a product of two linear expressions.

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Answer:

10

Step-by-step explanation:

To find the median in a set of data, organize the data from least to greatest.

Here, our data is the homework scores, those being:

10, 7, 8, 12, 9, 11, 13

Let's organize them in ascending order, like so:

7, 8, 9, 10, 11, 12, 13

The next step in finding the median is figuring out which number is in the middle. Since the amount of data we have is an odd number (7), there will be only one number in the middle.

We can find that the number in the middle is 10.

Thus, the median of the scores is 10.

Answer:

8

Step-by-step explanation:

2+14=16

Divide 16 by 2 because there is only 2 numbers added together.

Tou Will Get  8

I think

it should be 200 as it's the first common multiple of 20 40 and 25

Answer:

x^2

Step-by-step explanation:

=(x^3/x^2)^2

=(x^3/x^2)*(x^3/x^2)

=x^3*x^3/x^2*x^2

Step-by-step explanation:

Hey there!

Please see attached picture for your answer!

Hope it helps!

Answer is in the attachment.

note:

make a slight change in question 1;

An attachment would help. Assuming this is the Pythagorean theorem, c would be 10 feet. (6)^2 + (8)^2 = 100 -----> √100 = 10