2x+y-3z by y+3x =x by 2y. Find the value of z when x=1 and y=4

Answer:

\(1. \: \frac{8v {}^{5} }{u} \)

\(2. \: 32 {}^{6} y {}^{8} \)

Step-by-step explanation:

\(2vu {}^{ - 4} .4u {}^{3} v {}^{4} = 8.(v {}^{1} \times v {}^{4} ).(u {}^{ - 4} \times u {}^{3} ) = 8.v {}^{5} .u {}^{ - 1} = 8.v {}^{5} . \frac{1}{u} = \frac{8v {}^{5} }{u} \)

\(4x {}^{3} y {}^{2} .2y {}^{4} .4x {}^{3} = (4 \times 2 \times 4).(x {}^{3} \times x {}^{3} ).(y {}^{2} \times y {}^{4} ) = 32.x {}^{3 + 3}.y {}^{2 + 6} = 32x {}^{6} y {}^{8} \)

Answer:

700

Step-by-step explanation:

70x10 = 700

The total number of free throws she attempted is 700.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Missed free throws = 10%

Total free throws = 100%

10% = 70

Multiply 10 on both sides.

100% = 700

Thus,

Total free throws are 700.

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Answer:

Triangle KLM

Step-by-step explanation:

Firstly, we need to write the coordinates of triangle NPQ

We have this as;

(-7,-6) for N

(-4,-3) for P

(-4,-6) for Q

Now, we are going to use the given translation formula;

(x + 8, y + 1)

N’ will be (-7+ 8, -6 + 1) = (1,-5)

P’ will be (-4+ 8, -3+1) = (4,-2)

Q’ will be (-4+ 8, -6+1) = (4,-5)

Now, we need to find the triangle with the exact given transformation coordinates calculated above;

We have the triangle as;

KLM

With K as (1,-5) ; L as (4,-2) and ; M as (4,-5)

Answer:

Step-by-step explanation:

Making x the subject of the formula;

y=x+z/a-x

Cross multiply

y(a-x) = x+z

ya - yx = x+z

Collect like terms

x+yx = ya - z

x(1+y) = ya - z

x = ya-z/1+y

Hence the value of x is ya-z/1+y

Answer:

\(\frac{ya-z}{1+y} = x\)

Step-by-step explanation:

\(y=\frac{x+z}{a-x}\)

Use cross multiplication

y ( a - x) =  x + z

Solve the brackets.

y a - y x = x + z

y a - y x - z = x

y a - z = x + y x

y a - z = x ( 1 + y )

Divide both sides by ( 1 + y ).

\(\frac{ya-z}{1+y} = x\)

A function to represent the number of pizzas Antonio’s pizza shop can make in x hours using function notation is y = 13x + 5.

A reasonable domain and range for the number of pizzas Antonio’s can make include the following:

In order to write a function to represent the number of pizzas Antonio’s pizza shop can make in x hours using function notation, we would have to determine the slope and y-intercept by using the point-slope form equation;

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

The table representing the number of pizzas Antonio’s pizza shop can make in x hours should be completed as follows;

Hours, x           1      2      3      4     5

# of pizzas, y  18     31    49    67   85

Next, we would determine the linear equation representing the line which passes through the points (1, 18) and (2, 31) by using the point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 18 = (31 - 18)/(2 - 1)(x - 1)

y - 18 = 13/1(x - 1)

y = 13x - 13 + 18

y = 13x + 5

Therefore, a reasonable domain and range for y = 13x + 5 is given by:

Domain = 1 ≤ x ≤ 5 or [1, 5]

Range = 18 ≤ y ≤ 85 or [18, 85]

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Answer:

Step-by-step explanation:

Every 4 cm takes one second so  y = ¹/₄x

and  \(\frac14=\frac{1\cdot5}{4\cdot5}=\frac5{20}\)   so y = ⁵/₂₀x  also apply

and:

    \(y\ =\ \frac14x\\^{\div\, x}\quad\ ^{\div\, x}\\\frac yx = \frac14\)

so the third also apply

Answer:

40

Step-by-step explanation:

140-180= 40

The proportional relationship between the price and quantity of ears of corn can be represented using a table or a graph, showing how the price and quantity vary in a consistent manner.

One way to represent the proportional relationship between the price and quantity of ears of corn is by using a table:

Price (in dollars) Quantity (in ears of corn)

             2             5

             4             10

This table shows the corresponding values of the price and quantity.

As we can observe, when the price is $2, the quantity is 5 ears of corn, and when the price is $4, the quantity is 10 ears of corn.

The relationship is proportional because as the price doubles, the quantity also doubles.

Another representation of this proportional relationship is through a graph.

We can plot the points (2, 5) and (4, 10) on a coordinate plane, where the x-axis represents the price and the y-axis represents the quantity.

By connecting these two points with a straight line, we can visualize the proportional relationship.

The line will pass through the origin (0, 0) since zero price corresponds to zero quantity.

The slope of the line will indicate the rate of change between price and quantity.

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Answer:

Step-by-step explanation:

7+6-8x5=

7+6-40=

13-40=

-37

if the x is multiplying

Answer:

A. -1

Multiplicative inverse = -1

Additive inverse = 1

B. 2/5

Multiplicative inverse = -5/2

Additive inverse = -2/5

C. -4/3

Multiplicative inverse = -3/4

Additive inverse = 4/3

D. 3

Multiplicative inverse = 1/3

Additive inverse = -3

Hope this helps :)

The measure of x is 37 degree.

We have the measure of two arc as

m AB = 50 and m CD- 24.

Now, the measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.

So, x= (m AB + m CD) / 2

x= (50 + 24)/2

x = 74 / 2

x= 37 degree

Thus, the measure of x is 37 degree.

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Answer: 2 + 1 = 3      2 x 1 =2

Step-by-step explanation: + 7 = 7

Simplify complex expressions, find matching pairs, determine moduli, identify minimum value and provide an example complex number.

A. Simplifying 4i(1+i)+(6+2i):

4i(1+i) = 4i + 4i\(^2\) = 4i - 4 = -4 + 4i

So the expression becomes: (-4 + 4i) + (6 + 2i) = 2 + 6i

B. Simplifying -3(5i)\(^2\):

(5i)\(^2\) = 5\(^2\) * i\(^2\) = 25 * (-1) = -25

So the expression becomes: -3 * (-25) = 75

C. Simplifying i\(^2\)43(1+3i):

i\(^243\) = i^(4*60 + 3) = (i\(^4\))\(^60\) * i\(^3\) = 1\(^2\) * i\(^3\) = 1 * (-i) = -i

So the expression becomes: -i * (1 + 3i) = -i - 3i^2 = -i - 3(-1) = -i + 3 = 3 - i

D. Simplifying -1/2 (1+i)(2i^10):

(1+i)(2i^10) = (1+i)(2i\(^2\))^5 = (1+i)(-4)^5 = (1+i)(1024) = 1024 + 1024i

So the expression becomes: -1/2 * (1024 + 1024i) = -512 - 512i

E. Simplifying 6(5+5i) / (-2i)(3i\(^5\)):

6(5+5i) = 30 + 30i

(-2i)(3i^5) = -6i * i^5 = -6i * (-i) = -6i * i = 6

So the expression becomes: (30 + 30i) / 6 = 5 + 5i

Matching pairs and their simplified responses:

A → 2 + 6i

B → 75

C → 3 - i

D → -512 - 512i

E → 5 + 5i

The modulus of each complex number:

|2 + 6i| = sqrt(2^2 + 6^2) = sqrt(40) = 2sqrt(10)

|75| = 75

|3 - i| = sqrt(3^2 + (-1)\(^2)\) = sqrt(10)

|-512 - 512i| = sqrt((-512)\(^2\)+ (-512)\(^2\)) = sqrt(2 * 512\(^2\)) = 512sqrt(2)

|5 + 5i| = sqrt(5^2 + 5^2) = sqrt(50) = 5sqrt(2)

Listing the moduli from smallest to largest:

C → sqrt(10)

E → 5sqrt(2)

A → 2sqrt(10)

D → 512sqrt(2)

B → 75

For the complex number n, the minimum value of the modulus is sqrt(10).

One example of the complex number n is n = sqrt(10).

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(a) tangent line to the graph of f(x) = x^3 at the point (4,2).

(b) equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12).

(a) To find the equation of the tangent line to the graph of f(x) = x^3 at the point (4,2), we need to find the slope of the tangent line at that point. We can do this by taking the derivative of f(x) with respect to x and evaluating it at x = 4. The derivative of f(x) = x^3 is f'(x) = 3x^2. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Once we have the slope, we can use the point-slope form of a linear equation to write the equation of the tangent line.

(b) Similarly, to find the equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12), we differentiate f(x) to find the derivative f'(x). The derivative of f(x) = x^2 - x is f'(x) = 2x - 1. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Using the point-slope form, we can write the equation of the tangent line.

In both cases, the equations of the tangent lines will be in the form y = mx + b, where m is the slope and b is the y-intercept.

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If a matrix is diagonalizable then it is invertible is False.

A matrix can be diagonalizable but not invertible. For example, the zero matrix (a matrix where all entries are 0) is diagonalizable but not invertible.

What is diagonalizable metrix?

A diagonalizable matrix is a square matrix that can be transformed into a diagonal matrix through a similarity transformation. In other words, a matrix A is diagonalizable if there exists an invertible matrix P and a diagonal matrix D such that A = PDP⁻¹.

Geometrically, diagonalizable matrices represent linear transformations that stretch or shrink the space along a set of independent directions, which are called eigenvectors. The diagonal entries of the diagonal matrix D correspond to the eigenvalues of A, which represent the scaling factors along these directions.

Not all matrices are diagonalizable. A matrix is diagonalizable if and only if it has a sufficient number of linearly independent eigenvectors. In particular, symmetric matrices are always diagonalizable, and non-diagonalizable matrices are often associated with non-invertible linear transformations or defective geometric structures.

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Complete question is: If a matrix is diagonalizable then it is invertible is False.

Answer:

=

−

±

2

−

4

√

2

x=\frac{-{\color{#e8710a}{b}} \pm \sqrt{{\color{#e8710a}{b}}^{2}-4{\color{#c92786}{a}}{\color{#129eaf}{c}}}}{2{\color{#c92786}{a}}}

x=2a−b±b2−4ac​​

Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.

5

2

−

7

−

1

8

=

0

5x^{2}-7x-18=0

5x2−7x−18=0

=

5

a={\color{#c92786}{5}}

a=5

=

−

7

b={\color{#e8710a}{-7}}

b=−7

=

−

1

8

c={\color{#129eaf}{-18}}

c=−18

=

−

(

−

7

)

±

(

−

7

)

2

−

4

⋅

5

(

−

1

8

)

Step-by-step explanation:

The solutions to the quadratic equation 5x² - 7x - 18 = 0 are \(\frac{7-\sqrt{ 409} }{10} \ and \ \frac{7+\sqrt{ 409} }{10}\).

Given the quadratic equation in the question:

5x² - 7x - 18 = 0

Compared to the standard form ax² + bx + c = 0:

a = 5, b = -7 and c = -18

To find the solutions to the quadratic equation, we use the quadratic formula:

\(x = \frac{-b\±\sqrt{b^2 - 4(ac)} }{2a}\)

Plug in the values and simplify:

\(x = \frac{-(-7)\±\sqrt{(-7)^2 - 4(5*-18)} }{2*5} \\\\x = \frac{7\±\sqrt{( 49 +360)} }{10} \\\\x = \frac{7\±\sqrt{ 409} }{10} \\\\x = \frac{7-\sqrt{ 409} }{10}, \frac{7+\sqrt{ 409} }{10}\)

Therefore, the values of x are \(\frac{7-\sqrt{ 409} }{10} \ and \ \frac{7+\sqrt{ 409} }{10}\).

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The toy cars Anna must sell for her revenue to equal her expense is 4 toy cars. The result is obtained by using the concept of calculating algebra.

To calculate the algebra with one variable, sum up all the same variable and count the value.

Anna want to sell toy car at a craft fair. Each car is sold at a price of $ 12. The material for each car cost $ 3.50 and the table rental at the fair is 34 dollar for the day.

Find the toy cars must Anna sell for her revenue to equal her expense!

We have

Let's say

Revenue = Expense

a × $12 = (a × $3.5) + $34

12a = 3.5a + 34

12a - 3.5a = 34

8.5a = 34

a = 4 toy cars

Hence, Anna must sell 4 toy cars so that her revenue is equal to expense.

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Answer:

Question 1 y=(1/4)x+8

Step-by-step explanation:

Use  calculator

Answer:

1) y = 1/4x + 8

2) y = -x - 6

3) y = -2x - 1

4) y = -2/5x -3

5) y = 4x + 9

Step-by-step explanation:

1) y = 1/4x + c

6 = -2 + c

c = 8

y = 1/4x + 8

2) y = -x + c

-7 = -1 + c

c = -6

y = - x - 6

3) y = -2x+c

13 = 14 + c

c = -1

y = -2x - 1

4) 5y = -2x + 15

y = -2/5x + 3

Hence,

y = -2/5x + c

-10 = -2/5 + c

c = -3

Therefore,

y = -2/5x -3

5) Slope: (1-(-11))/(-2-(-5))

= (1+11)/(-2+5)

= 12/3

= 4

y = 4x +c

Substituting any one of the points:

1 = -8 + c

c = 9

y = 4x + 9

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The total number of tasks Terrence completed. By substituting the value of 'x' with the number of tasks Terrence completed

The factor 'x' in the expression '90x - 20' represents the total number of tasks that Terrence completed in the game.

To understand why, let's break down the given information. It states that Shelly and Terrence completed a different number of tasks. Shelly earned 90 points on each task, so the total number of tasks she completed is not represented by 'x'.

On the other hand, Terrence's total points were 20 less than Shelly's total. This means that Terrence's total points can be calculated by subtracting 20 from Shelly's total points. Since Shelly earned 90 points on each task, her total points would be 90 multiplied by the number of tasks she completed.

So, the expression '90x - 20' represents Terrence's total points in the game, where 'x' represents the total number of tasks that Terrence completed. By substituting the value of 'x' with the number of tasks Terrence completed, we can calculate his total points.

Therefore, the correct answer is: The total number of tasks Terrence completed.

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Answer:

The equation is y=mx+b in this case the b represents the y int and does not aid in detemining steepness. To determine the steepest, the value of m (or the slope) rise/run must be either the most positive number or the most positive negative. in this case you have 2/1 , 7/1. 5/1.

So y==7x+3 has the steepest (greatest value)  slope

Step-by-step explanation:

The equation has the greatest slope which is 7, hence the equation of the line y = 7x + 3 is the steepest

The formula for finding the equation of a line is expressed as y = mx + b

m is the slope of the line

b is the y-intercept

The line that will be the steepest must have the largest slope.

Looking at the equation y = 7x +3

Get the slope by comparing to have;

mx = 7x

m = 7

Since the equation has the greatest slope which is 7, hence the equation of the line y = 7x + 3 is the steepest

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Answer:

x=-32/5 or -6.4 in decimal form

Step-by-step explanation:

3= 5x+35

-5x=32

x=-32/5

Answer:

Step-by-step explanation:

the anwer  is r=dog y=cat  20r+16y>800-->y>-5/4 r+50 20r-16y<r+80 40 dogs+20 cats 15+55 cats  

Answer:

1/15 pie

Step-by-step explanation:

An easy way to do this is instead of dividing, multiply the denominator by 5. You get 15. You can say Im just making a coincidence, but try it yourself!

(1/3)/5 is basically multiplication. You may have heard the saying, "division with fractions is multiplication". Thats true. Turn 5 into 5/1 and multiply. 5/1x1/3.

you get 1/15. Hope it helps

Also you have to flip 5/1 to 1/5 and then multiply hehe. thats how you get 1/15

Answer:

Its B, 1/15 hope this helps

Step-by-step explanation:

The basic function equivalent to the piecewise-defined function f(x) = x if x ≥ 0 and -x if x < 0 is f(x) = |x|, which represents the absolute value of x.

The given piecewise-defined function f(x) has different expressions for different intervals. For x greater than or equal to zero, f(x) takes the value of x. For x less than zero, f(x) is equal to -x. We need to find a basic function that captures this behavior.

Among the options provided, f(x) = |x| is equivalent to the given piecewise function. The absolute value function, denoted by |x|, returns the positive value of x regardless of its sign. When x is non-negative, |x| equals x, and when x is negative, |x| is equal to -x, mirroring the conditions of the piecewise-defined function.

The function f(x) = |x| represents the absolute value of x and matches the behavior of the given piecewise-defined function, making it the equivalent basic function.

In summary, the basic function equivalent to the piecewise-defined function f(x) = x if x ≥ 0 and -x if x < 0 is f(x) = |x|, which represents the absolute value of x.

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Answer:

128 m^2

Step-by-step explanation:

You have 5 sides of a cube on the bottom with length 4

    5  *    4x4  = 80 m^2

then four triangles on top

   area of triangle = 1/2 base * height     base = 4   height = 6

         4    * 1/2 ( 4)(6)  = 48 m^2

  summed = 128 m^2

Answer:

how old are they im confused

Step-by-step explanation:

Answer:

where are the numbers

(a) By plugging in different values for x1, we can plot the indifference curves passing through the given points (2, 2), (1, 2), and (4, 2).

(b) The shape of the indifference curves shows convexity.

(c) The property used to determine this is the non-satiation property of preferences.

(d) The Walrasian demand may not always be single-valued.

(e) Receiving the voucher makes the consumer better-off .

(f) The cash payment allows the consumer to maximize utility by making trade-offs

For 4x1 + x2 = x1 + 2x2, rearranging the equation gives x2 = 3x1, representing the linear part of the indifference curves.

For x1 + 2x2 = 4x1 + x2, rearranging the equation gives x2 = 3x1, representing the kink in the indifference curves.

By substituting different values for x1, we can plot the indifference curves. They will be upward sloping straight lines with a kink at x2 = 3x1.

(b) Properties of the preferences deduced from the shape of indifference curves and utility function:

Diminishing Marginal Rate of Substitution (MRS): Indifference curves are convex, indicating diminishing MRS. The consumer is willing to give up less of one good as they consume more of it, holding the other good constant.

Non-Satiation: Indifference curves slope upwards, showing that the consumer prefers more of both goods. They always prefer bundles with higher quantities.

Convex Preferences: The kink in the indifference curves indicates convexity, implying risk aversion. The consumer is willing to trade goods at different rates depending on the initial allocation.

(c) UMP does not have a solution when Pk = 0 and X -> R2+. This violates the assumption of finite resources and prices required for utility maximization. The property used is non-satiation, as a consumer will always choose an infinite quantity of goods when they are available at zero price.

(d) Walrasian demand depends on relative prices:

If p1 = p2 > 4, the maximizing bundle lies on the linear portion of indifference curves, where x2 = 3x1.

If 4 < p1 = p2 < 1/2, the maximizing bundle lies on the linear portion of indifference curves but at lower x1 and x2.

If p1 = p2 < 1/2, the maximizing bundle lies at the kink point where x1 = x2.

Walrasian demand may not be single-valued due to the shape of indifference curves and the kink point, allowing for multiple optimal solutions based on relative prices.

(e) Given p1 = p2 = 1 and w = $60, the initial budget set is x1 + x2 = 60. With a $10 voucher for good 1, the new budget set becomes x1 + x2 = 70. Since p1 = 1, the consumer spends the voucher on good 1, resulting in x1 = 20 and x2 = 40. Receiving the voucher improves the consumer's welfare by allowing more consumption of good 1 without reducing good 2.

(f) If given the choice between a $10 cash payment and a $10 voucher for good 1 only, the consumer would choose the cash payment. It provides flexibility to allocate the funds based on individual preferences. The answer remains the same even if the assistance were $30, as the cash payment still allows optimal allocation based on preferences. Cash payment offers greater utility-maximizing options compared to the voucher, which restricts choices.

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Answer:

  False

Step-by-step explanation:

You want to know if it is true that the graph of a rational function cannot cross a horizontal asymptote.

Once a function is on its final approach to an asymptote, it will approach, but not cross, that asymptote.

The function may have a variety of behaviors prior to that point, so may cross the horizontal asymptote one or more times before its final behavior is established.

An example with the asymptote y = 0 is attached.

<95141404393>

Answer:0.52, 0.545, 0.55, 0.6, 0.65

Source:trust me bro

Answer:

O.52 m, 0.545 m, 0.55 m, 0.6 m, 0.65m. :)

Step-by-step explanation:

The expression that could Mr. Jackson use to find the cost of ordering n lunches is 6.25n + 3.50

To find the cost of ordering n lunches, Mr. Jackson can use an expression. An expression is a combination of numbers, variables, and mathematical operations that represents a value. In this case, the expression that Mr. Jackson can use to find the cost of ordering n lunches is:

6.25n + 3.50

In this expression, n represents the number of lunches that Mr. Jackson orders. When Mr. Jackson orders n lunches, he has to pay $6.25 for each lunch, so the cost of the lunches will be 6.25n. In addition, Mr. Jackson has to pay a one-time delivery fee of $3.50, which is represented by the constant term 3.50 in the expression.

To use this expression to find the cost of ordering a specific number of lunches, Mr. Jackson can substitute the value of n into the expression and simplify. For example, if Mr. Jackson orders 10 lunches, the cost would be:

6.25(10) + 3.50 = 62.50 + 3.50 = 66.00

So the cost of ordering 10 lunches would be $66.00.

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