Solve the following system of equations:
2x + 3y − z = 1
3x + y + 2z = 12
x + 2y − 3z = −5
PLEASE HELP!! 25 POINTS!!

Using limits the value of k is c √2

The limit of a function is the valuer the function tends to as the dependent variable tends to a particular value.

Given that the limit lim n → ∞ [x√(x + 1)[1 - √(2x + 3)]/(7 - 6x + kx²) = - 1, we desirte to find the value of k.

So, we proceed as follows

lim n → ∞ [x√(x + 1)[1 - √(2x + 3)]/(7 - 6x + kx²) = - 1

Factorizing out √2x, we have that

lim n → ∞ [x√(x + 1)[1 - √(2x√(1 + 3/√(2x)]/(7 - 6x + kx²) = - 1

lim n → ∞ [x√(x + 1)√(2x[1/√(2x - √(1 + 3/√(2x)]/(7 - 6x + kx²) = - 1

Also, factorizing out √x, we have that

lim n → ∞ [x√x√(1 + 1/√x)√2x[1/√(2x - √(1 + 3/√(2x)]/(7 - 6x + kx²) = - 1

lim n → ∞ [x√x√2x√(1 + 1/√x)[1/√(2x - √(1 + 3/√(2x)]/(7 - 6x + kx²) = - 1

lim n → ∞ [x√2x√(1 + 1/√x)[1/√(2x - √(1 + 3/√(2x)]/(7 - 6x + kx²) = - 1

lim n → ∞ [√2x²√(1 + 1/√x)[1/√(2x - √(1 + 3/√(2x)]/(7 - 6x + kx²) = - 1

Factorizing x² from the denominator, we have that

lim n → ∞ [√2x²√(1 + 1/√x)[1/√(2x - √(1 + 3/√(2x)]/x²(7/x² - 6/x + k) = - 1

lim n → ∞ [√2√(1 + 1/√x)[1/√(2x - √(1 + 3/√(2x)]/(7/x² - 6/x + k) = - 1

Now substituting x = ∞ into the equation, we have that

[√2√(1 + 1/√∞)[1/√(2∞ - √(1 + 3/√(2∞)]/(7/∞² - 6/∞ + k) = - 1

[√2√(1 + 0)[0 - √(1 + 0]/(0 - 0 + k) = - 1

[√2√(1)[- √1]/k = - 1

[√2(1)[- 1]/k = - 1

-√2/k = - 1

k = -√2/-1

k = √2

So, the value of k is c √2

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Vector a: start at (1, 3) and end at (-4, -2) in blue.

Vector b: start at (-4, -2) and end at (1, 3) in red.

Vector a+b: start at (1, 3) and end at (2, 7) in green.

To represent a+b using the parallelogram method,

we must draw vectors representing a and b.

The initial point of vector a is (1, 3), and its terminal point is (-4, -2). The initial point of vector b is (-4, -2), and its terminal point is (1, 3).

Using the vector tool, we then  draw the vectors a and b. We start at the initial point of each vector and select the terminal point.

Vector a: start at (1, 3) and end at (-4, -2)

Vector b: start at (-4, -2) and end at (1, 3)

We the diagonal, we start at the initial point of vector a, (1, 3), and draw a line parallel to vector b that passes through the initial point of vector b, (-4, -2). This line intersects the line parallel to vector a that passes through the initial point of vector b at point (2, 7). This point is the terminal point of the diagonal vector, which is a+b.

We use the vector tool, we can draw vector a in blue, vector b in red, and vector a+b in green.

Vector a: start at (1, 3) and end at (-4, -2) in blue.

Vector b: start at (-4, -2) and end at (1, 3) in red.

Vector a+b: start at (1, 3) and end at (2, 7) in green.

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The value of the expression when x = -1 and y = 4 is 41.

Evaluating the expression [tex]x^2[/tex]+7y+12 when x = -1 and y = 4, we get:

[tex]x^2[/tex]+7y+12 = [tex](-1)^2[/tex] + 7(4) + 12 = 1 + 28 + 12 = 41

Therefore, the value of the expression when x = -1 and y = 4 is 41.

Here is the step-by-step solution:

Substitute x = -1 and y = 4 into the expression.

Evaluate the exponent.

Multiply 7 by 4.

Add 1, 28, and 12.

The answer is 41.

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Answer:

We can use the formula for compound interest to calculate the amount of interest Brian will earn:

A = P (1 + r/n)^(nt)

where:

A = the total amount after 7 years

P = the principal amount ($9,411)

r = the annual interest rate (3.48%)

n = the number of times the interest is compounded per year (52 weeks in a year, so n = 52)

t = the number of years (7)

Plugging in the values, we get:

A = $9,411 (1 + 0.0348/52)^(52*7)

A = $9,411 (1.0006692302021135)^364

A = $12,471.36

To find the amount of interest earned, we can subtract the principal amount from the total amount:

Interest = $12,471.36 - $9,411 = $3,060.36

Therefore, Brian will earn $3,060.36 in interest after 7 years. Rounded to the nearest cent, this is $3,060.37.

The correct answer is B) |x| > 6 for the given statement

What is meant by the statement?

A statement is a declarative sentence that can be either true or false. It is a proposition that can be proven using logical reasoning or evidence. Statements are the building blocks of mathematical proofs and are used to establish the truth of mathematical theories and concepts.

According to the given information

The statement “the absolute value of x is greater than 6” can be expressed as an inequality in the following way:

|x| > 6

This means that the distance between x and 0 on the number line is greater than 6 units. In other words, x can be any number that is either less than -6 or greater than 6.

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Answer:

Her rate of mowing lawns per hour is 4 lawns to one hour

Step-by-step explanation:so on a table you divide 4÷4=1 then you do the same thing for the 16÷4=4. So Oliva can mow 4 lawns per hour

Rates of first and second mechanics are 75 and 60 per hour respectively.

A mathematical statement or relation between two or more numeric values, variable and mathematical operations via equal sign is called an Equation.

Elimination method is a kind of method to solve simultaneous equations in two variables. In elimination method we compare coefficient of one of two variables and in next step we eliminate that variable using addition or subtraction and form another relation with only one variable and find the value for that one variable and then substituting that value initial equation we can get the value of another variable.

Let the rate of first mechanic and second mechanic be x and y per hour respectively.

Sum of the two rates is 135 per hour. So the suitable equation will be,

x+y = 135 ............... (i)

Since they charged together 1650 after working 10 hours by first and 15 hours by second mechanics. So the suitable equation this time will be,

10x+15y = 1650

5(2x+3y) = 1650

2x+3y = 1650/5

2x+3y = 330 ............... (ii)

Multiplying 2 with equation (i) and then subtracting it from equation (ii) we get,

(2x+3y) - 2(x+y) = 330 - 2*135

2x+3y-2x-2y = 330-270

y = 60

Substituting y=60 in equation (i) we get,

x+60 = 135

x = 135-60 = 75

Hence, the rates charged per hour are 75 and 60 per hour respectively.

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A linear equation that models the relationship shown in the table is: D. y = 0.8x + 9.75

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (10.55 - 9.75)/(1 - 0)

Slope (m) = 0.8/1

Slope (m) = 0.8

At data point (0, 9.75) and a slope of 0.8, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 9.75 = 0.8(x - 0)  

y = 0.8x + 9.75

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Emilee will spend around $3,726 for her wrist surgery once her insurance company pays 70% and she meets the $371 deductible.

Calculating out-of-pocket costs for a medical expense after insurance coverage and deductibles often requires simple arithmetic.

To begin, deduct the deductible from the overall cost of the surgery: $12,791 - $371 = $12,420.

70% of the remaining cost after the deductible is calculated as follows: 70% of $12,420 = $8,694.

Total cost after insurance coverage: $12,420 - $8,694 = $3,726

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Answer:

To calculate how much is deducted from Scott’s paycheck, we need to first find out how much his employer pays for his health insurance premium.

55% of the annual premium is covered by the employer, so we can calculate this as:

0.55 x $20,969 = $11,532.95

Therefore, Scott’s employer pays $11,532.95 towards his health insurance premium.

To find out how much is deducted from Scott’s paycheck, we need to divide the remaining 45% of the premium by the number of pay periods in a year. Since Scott is paid biweekly, he receives 26 paychecks in a year.

45% of the annual premium is not covered by the employer, so we can calculate this as:

0.45 x $20,969 = $9,437.55

To find out how much is deducted from each biweekly paycheck, we can divide $9,437.55 by 26:

$9,437.55 ÷ 26 = $363.75 (rounded to the nearest cent)

Therefore, Scott’s employer pays $11,532.95 towards his health insurance premium and $363.75 is deducted from each of his biweekly paychecks for health insurance.

Answer:

[tex]192[/tex] [tex]cm^2[/tex]

Step-by-step explanation:

Recall that the formula for the area of a parallelogram is:

[tex]A=bh[/tex]

Where b is the length of the base, and h is the length of the height.

We are given that the base is 24 cm.

So, b=24.

We are also given that the height is 8 cm.

So, h=8.

Let's plug these values into the formula:

[tex]A=bh=\\A=(24)(8)=\\A=192[/tex]

Since area is a two-dimensional measure, we need to label our answer using units squared.

Thus, the area is [tex]192[/tex] [tex]cm^2[/tex]

Area of a parallelogram => [tex]A=bh[/tex]

Where, b=24 cm and h=8 cm

Plug in the known values and solve.

[tex]\Longrightarrow A=bh \Longrightarrow A=(24 \ cm)(8 \ cm) \Longrightarrow A= \boxed{192 \ cm^2}[/tex]

Therefore, the volume of Prism B is 727/4 ft³ or 181 3/4 ft³ in mixed number form.

Subtract the denominator from the numerator. The quotient should be expressed as a whole number in step 2. Step 3: Enter the denominator and numerator, respectively, as the remainder and the divisor.

We can write: Using the formula for a prism's volume (V = Bh, where B is the base area):

We must determine Prism B's cross-sectional area in order to get the volume of Prism B. By dividing the height equation of prism A by its volume equation, the following result is obtained:

cross-sectional area of Prism A = (Volume of Prism A) / (height of Prism A) = (872/1 ft³) / (6 ft) = 218/3 ft²

Using the scale factor equation for height, we get:

k = (height of Prism A) / (height of Prism B) = (6 ft) / (31/12 ft) = 24/31

Using the scale factor equation for cross-sectional area, we get:

k² = (cross-sectional area of Prism A) / (cross-sectional area of Prism B) = (218/3 ft²) / (cross-sectional area of Prism B)

Solving for the cross-sectional area of Prism B, we get:

cross-sectional area of Prism B = [tex](218/3 ft^2) / k^2 = (218/3 ft^2) / (24/31)^2 = 59/3 ft^2[/tex]

Finally, substituting the height and cross-sectional area of Prism B into the volume equation of Prism B, we get:

Volume of Prism B = (cross-sectional area of Prism B) * (height of Prism B) = [tex](59/3 ft^2) * (31/12 ft) = 727/4 ft^3.[/tex]

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Answer:

We can use the formula for compound interest to solve this problem:

A = P(1 + r/n)^(nt)

where A is the future value, P is the present value, r is the interest rate, n is the number of times the interest is compounded per year, and t is the time period in years.

(a) To find the present value of the money, we need to solve for P in the formula above. We are given that A = $3000 and t = 18/12 = 1.5 years. The interest rate is 6% per year, compounded monthly, which means n = 12. Substituting these values into the formula, we get:

3000 = P(1 + 0.06/12)^(12*1.5)

Simplifying and solving for P, we get:

P = 3000 / (1 + 0.06/12)^(12*1.5)

P = $2,572.39

Therefore, the equivalent value of the money now is $2,572.39.

(b) To find the equivalent value of the money one year from now, we need to calculate the future value of $1 after one year, and then multiply it by the present value we found in part (a). The future value of $1 after one year, at 6% per year, compounded monthly, is:

FV = 1*(1 + 0.06/12)^(12*1)

FV = $1.06168

Multiplying this by the present value we found in part (a), we get:

$2,572.39 * $1.06168 = $2,735.92

Therefore, the equivalent value of the money one year from now is $2,735.92.

(c) To find the equivalent value of the money three years from now, we need to calculate the future value of $1 after three years, and then multiply it by the present value we found in part (a). The future value of $1 after three years, at 6% per year, compounded monthly, is:

FV = 1*(1 + 0.06/12)^(12*3)

FV = $1.19102

Multiplying this by the present value we found in part (a), we get:

$2,572.39 * $1.19102 = $3,066.63

Therefore, the equivalent value of the money three years from now is $3,066.63.

Answer:

B

[tex]6^{-7}[/tex] is equivalent to 1/279936 which is basically [tex]\frac{1}{6^{7}}[/tex]

When 3 is divided by 2/5 , the answer is 7.5

Let's compare our whole number and fraction so that we can see the issue we are attempting to tackle.

3 divided by 2/5

In this case, creating a new numerator just requires multiplying the numerator by the full number. After that, the original numerator becomes the new denominator.

3*5/2 = 15/2

Most people prefer to express results in decimals, and all you have to do to do so is divide the numerator by the denominator:

15/2 = 7.5

The portion written above the horizontal line is referred to as the numerator. Example: 2/5 ,here 2 is numerator.

A decimal number consists of both a whole number and a fractional number. The numerical value of complete and partially whole amounts is expressed using decimal numbers, which are in between integers.

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The complete question is

what happens when 3 divide by 2/5ths in a facrtion?

Generally, it is better to use a Line Graph if your raw data includes non-numeric values. If your raw data only has numeric values, use a Scatter Plot. You can use a Line Graph if you want to label your horizontal axis with text labels. These labels can represent evenly spaced values as days, weeks, and years.

The simplified form of 7 log3x + 4 log3z - 6 log3y is log3(x^7 z^4 / y^6).

We can simplify the expression using the following logarithmic rule:

log a + log b = log ab (product rule)

log a - log b = log(a/b) (quotient rule)

c log a = log a^c (power rule)

Using these rules, we can simplify 7 log3x + 4 log3z - 6 log3y as follows:

7 log3x + 4 log3z - 6 log3y

= log3x^7 + log3z^4 - log3y^6 (using the power rule)

= log3(x^7 z^4 / y^6) (using the quotient rule)

Therefore, the simplified form of 7 log3x + 4 log3z - 6 log3y is log3(x^7 z^4 / y^6).

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Based on the given data, the age of Mr. Wright currently is 30 years

If Micah is 3 years old, then Lilly is twice as old, which means that

Lilly is 2 * 3 = 6 years old.

Now we know that Mr. Wright is five times as old as his daughter, Lilly, so Mr. Wright's age is:

5 * 6 = 30 years old.

Therefore, Mr. Wright is 30 years old.

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The probability that the employee will arrive between 8:05 a.m. and 8:45 a.m. is 0.8, or 80% when expressed as a percentage.

To find the probability that the employee will arrive between 8:05 a.m. and 8:45 a.m., we need to calculate the proportion of the total possible time range between 8:00 a.m. and 8:50 a.m. that falls within the specified time interval.

The total time range between 8:00 a.m. and 8:50 a.m. is 50 minutes (8:50 - 8:00 = 50). The time interval between 8:05 a.m. and 8:45 a.m. is 40 minutes (8:45 - 8:05 = 40).

So, the probability that the employee will arrive between 8:05 a.m. and 8:45 a.m. is:

Probability = (Time interval between 8:05 a.m. and 8:45 a.m.) / (Total time range between 8:00 a.m. and 8:50 a.m.)

Probability = 40 minutes / 50 minutes

Probability = 0.8

Therefore, the probability that the employee will arrive between 8:05 a.m. and 8:45 a.m. is 0.8, or 80% when expressed as a percentage.

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1. A  back-to-back stem-and-leaf plot for the data would be

Mowed by you          stem           mowed by your friend

       8   7   5  4            0              

       7   2   2  0            1                  9

            5   1   0           2                  7    8    9

                      0           3                  0    1     2     2   5   5   8

                                    4                  4

KEY: 3 | 1 ⇒ 31

2.  The mean for you = 14.25 and your friend 31.3. This means that your friend has a higher mean than you. The median for you is 11 and your friend is 30.5. Given that both the mean and median of your friend is higher than yours, it means that your friend mowed more lawns than you

3. The range of data for you is 26 and for your friend is 21.

To find the mean for each data set, add all the number together and divide it by the set number. For example;

4 + 5 + 7 + 8 + 10 + 12 + 12 + 17 + 20 + 21 + 25 + 30

= 171 / 12

= 14.25

To find the range for the data set, simply take the highest number of a set and minus it by the lowest number. For Example;

For your data set, it is 30 - 4 = 26

To find the median for the data sets, simply look for the number in the middle. However, in your data set, there are two middle numbers. take the sum of the two numbers and divide it by 2.

            (10 + 12) / 2 = 11

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When the block is cut into smaller pieces, 512 pieces of cheese remain.

A cube is a solid three-dimensional shape with 6 square faces, 8 vertices and 12 edges. It is also said to be a regular hexahedral.

The volume V of a cube  is given by the formula V = a^3, where a = the length of one side of the cube. V = 4 ^ 3 = 64 cubic meters or inches ^ 3. The volume of a cube is 64 cubic meters

The total volume of the cheese block is obtained as follows:

V = edge length³ = 8³ = 512 cubic meters

Since the volume of each piece is 1 cubic inch, the total number of pieces is obtained by dividing the total volume by the volume of each piece:

Number of pieces = V / volume per piece = 512 / 1 = 512 pieces

Therefore, when the block is cut into smaller pieces, 512 pieces of cheese remain.

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The possible rule of the polynomial function is f(x) = 1/2(x + 2)(x + 1)²(x - 1)²

From the question, we have the following zeros and multiplicities that can be used to derive the rule of the function

The possible rule of the function is represented as

f(x) = a(x - zero)^multiplicity

So, we have

f(x) = a(x + 2)(x + 1)²(x - 1)²

The graph passes through (0, 1)

So, we have

a(0 + 2)(0 + 1)²(0 - 1)² = 1

This gives

2a = 1

Divide

a = 1/2

Recall that

f(x) = a(x + 2)(x + 1)²(x - 1)²

So, we have

f(x) = 1/2(x + 2)(x + 1)²(x - 1)²

Hence, the function is f(x) = 1/2(x + 2)(x + 1)²(x - 1)²

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The equation of circle in the standard with given center and radius is  [tex](x+3)^{2} + (y-4)^2[/tex] = 49.

What is equation of circle?

Every point in a plane that is at a certain distance from the center point forms a circle. In order to go around a curve while maintaining a constant distance from another point, a moving point in a plane must follow a specific path.

The following is the typical form for expressing the equation of a circle:

[tex](x-h)^{2} + (y-k)^2 = r^2[/tex]

Here,

(h, k) represents the center and r is the radius.

We are given that the center is (-3, 4) and the radius is 7.

Now, using the standard form, we get

⇒ [tex](x-(-3))^{2} + (y-4)^2 = 7^2[/tex]

⇒ [tex](x+3)^{2} + (y-4)^2[/tex] = 49

Hence, the equation of circle in the standard with given center and radius is  [tex](x+3)^{2} + (y-4)^2[/tex] = 49.

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Since, there are multiple questions so the question answered above is attached below.

Answer:

(m-3)^2

Step-by-step explanation:

(m^2-6m+9) is factored by using this formula:
(a-b)^2=a^2-2ab+b^2.

Therefore, we can substitute the values into this equation.

m^2=a^2,

-6m=-2ab,

9=b^2.

Solving for b in the third equation, b is equal to 3 or -3. However, as this equation is negative, then it must be -3.

(m-3)^2

Answer: there is no solution

Step-by-step explanation:

The solution of the equation is [tex]x=\frac{-7 \pm 3\sqrt{3}i} {2}[/tex]

Quadratics can be defined as a polynomial equation of a second degree, which implies that it comprises a minimum of one term that is squared. It is also called quadratic equations.

The general form of the quadratic equation is: ax² + bx + c = 0

Given that, a quadratic equation (x-5)² + 3(x-5) + 9 = 0, we need to solve it,

So, put x-5 = u

Therefore,

u² + 3u + 9 = 0

Solving using quadratic formula,

[tex]x=\frac{-b \pm \sqrt{b^2-4ac}} {2a}[/tex]

Here a = 1, b = 3 and c = 9

Therefore,

[tex]u=\frac{-3 \pm \sqrt{3^2-4(9)}} {2}[/tex]

[tex]u=\frac{-3 \pm \sqrt{9-36}} {2}[/tex]

[tex]u=\frac{-3 \pm \sqrt{-27}} {2}[/tex]

[tex]u=\frac{-3 \pm 3\sqrt{3}i} {2}[/tex]

Put u = x-5,

Therefore,

[tex]x-5=\frac{-3 \pm 3\sqrt{3}i} {2}[/tex]

[tex]x=\frac{-7 \pm 3\sqrt{3}i} {2}[/tex]

Hence, the solution of the equation is [tex]x=\frac{-7 \pm 3\sqrt{3}i} {2}[/tex]

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Answer:

[tex]\huge\boxed{\sf Yes.}[/tex]

Step-by-step explanation:

In a right angled triangle, the longest side is called hypotenuse.

So,

Hypotenuse = 13 m

The rest are:

Base = 5 m

Perpendicular = 12 m

Using Pythagoras Theorem to verify:

[tex](Hypotenuse)^2=(Base)^2+(Perpendicular)^2[/tex]

Put the given data

(13)² = (12)² + (5)²

169 = 144 + 25

Since, both left hand side and right hand side are equal, this means the triangle is a right-angled triangle.

[tex]\rule[225]{225}{2}[/tex]