Q5 Use variation of parameters to solve 22 y" + 4y + 5y 1+ 2x (15 marks)

a. The graph of the budget line would have hamburgers on the x-axis and bags of figs on the y-axis. b. the budget line equation represents Rachel's affordability based on her income and the prices of hamburgers and figs. Changes in prices, income, or additional resources can affect the slope, position, or rotation of the budget line on a graph.

a) Rachel's budget line equation can be written as follows:

Budget = (Price of Hamburger * Quantity of Hamburgers) + (Price of Figs * Quantity of Figs)

Since the price per hamburger is $3 and the price per bag of figs is $2, the equation becomes:

Budget = 3x + 2y

Where x represents the quantity of hamburgers and y represents the quantity of bags of figs. The graph of the budget line would have hamburgers on the x-axis and bags of figs on the y-axis.

b) If the price of figs increases to $3, the new budget line equation becomes:

Budget = 3x + 3y

The graph of the new budget line would show a steeper slope compared to the original budget line. This indicates that the relative price of figs has increased, making them relatively more expensive compared to hamburgers.

c) In this scenario, Rachel has an income of $50, the price per hamburger is $3, the price per bag of figs is $3, and she receives an additional $10 in cash from a friend. The new budget line equation can be written as:

Budget = (3x + 3y) + 10

The graph of the new budget line would shift upward parallel to the original budget line. The additional cash from Rachel's friend increases her purchasing power, allowing her to afford more hamburgers and/or bags of figs.

d) Now, Rachel's friend gives her a gift basket containing 3 free bags of figs. In this case, the budget line equation remains the same as in part c:

Budget = (3x + 3y) + 10

However, since Rachel receives 3 free bags of figs, she can allocate more of her budget towards purchasing hamburgers. This would cause the budget line to rotate outward from the y-intercept, resulting in a flatter slope. The new budget line would reflect Rachel's ability to purchase more hamburgers with the same income and price of figs.

In summary, the budget line equation represents Rachel's affordability based on her income and the prices of hamburgers and figs. Changes in prices, income, or additional resources can affect the slope, position, or rotation of the budget line on a graph.

Learn more about budget here

https://brainly.com/question/29028797

#SPJ11

Answer:

Step-by-step explanation:

3x^4-25x^2-18=0

X= -3

Answer:

√41

Step-by-step explanation:

Here we want to find the value of AC

A = (-4,0)

C = (1,4)

The distance formula is;

D = √(y2-y1)^2 + (x2-x1)^2

D = √(4-0)^2 + (1-(-4)^2

D = √4^2 + 5^2

D = √(16+25)

D = √41

During a study, he finds that 12 out of 32 deer were affected by parasites. How many of the 1200 deer in the local population would he expect to be affected by parasites?

Answer:

450

For Trigonometric ratios, the values of sin, cos, and tan are defined by the ratio of sides of a right-angled triangle. The cosine of an acute angle in a right triangle is calculated using trigonometry.

By dividing the measurements of the side that it is adjacent to by the hypotenuse of the triangle.

The neighboring  base-to-hypotenuse ratio is known as the cos function. It aids in determining the triangle's side lengths regardless of the provided angle.

If the angle between the neighboring side and the hypotenuse of a right triangle is, we can write this using the cos function.

In a right-angled triangle, We calculate their values by the ratio

Cos = Base of the right-angled triangle/ Hypotenuse of the right-angled triangle.

To learn more about Trigonometric ratios visit:

https://brainly.com/question/29166781

#SPJ4

Answer:

Step-by-step explanation:

There is no answer if the question is as written. If you subtract 2/3 h from 2/3 h you get 0.

That means that 11 = 8 which has no meaning.

F(5) means replace x with 5 then solve:

3x-4 = 3(5)-4 = 15-4 = 11

F(5) = 11

The decimal expansion of the given fraction is 0.0208. Therefore, the correct answer is option D.

The given fraction is 13/625.

Decimals are one of the types of numbers, which has a whole number and the fractional part separated by a decimal point.

Here, the decimal expansion is 13/625 = 0.0208

So, the number of places of decimal are 4.

Therefore, the correct answer is option D.

To learn more about the decimal numbers visit:

https://brainly.com/question/1578006.

#SPJ1

The Scale factor was used to enlarge the picture is 7/ 31.5.

A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure. It should be remembered that the scale factor only affects how big a figure is, not how it looks.

Given:

A picture is 7 inches wide and 9 inches long.

A photographer enlarges it so it is 31.5 inches wide and 40.5 inches long.

So, scale factor is

= Original dimension / Enlarged dimension

= 9/ 40.5

= 90/ 405

= 10/45

= 2/9

Now, simplifying the scale factor 7/31.5 because it has Nr < Dr.

= 7/ 3.15

= 70/31.5

= 2/9

Learn more about Scale Factor here:

https://brainly.com/question/30051525

#SPJ2

Answer:

x=9°

∡EFG=25°

Step-by-step explanation:

Answer:

isolate the variable by dividing each side by factors that doesn't contain the variable. x=35degrees - 7/2.

Step-by-step explanation:

Hope this helped a little :)

The equation of the line, in the form ax+by=c where a,b, and c are integers, with no common factor, and a≥0, is -x + y = -4.

To find the equation of a line perpendicular to x+y=5 and passing through the point (1, -3), we need to determine the slope of the given line and then find the negative reciprocal of that slope to obtain the slope of the perpendicular line. The equation x+y=5 can be rewritten as y=-x+5. Comparing this equation to the standard form y=mx+b, we see that the slope of the line is -1. The negative reciprocal of -1 is 1, so the perpendicular line will have a slope of 1. Now, we can use the point-slope form of a line to find the equation. Using the point (1, -3) and the slope 1:

y - y₁ = m(x - x₁)

y - (-3) = 1(x - 1)

y + 3 = x - 1

Rearranging the equation:

x - y = 4

Now, we can multiply the equation by -1 to have the coefficient of x as a positive integer:

-(x - y) = -4

-x + y = -4

To know more about equation,

https://brainly.com/question/33661237

#SPJ11

The new coordinates of each of the triangle coordinates are;

1) A'(-12, 6), B'(3, 9), C'(-9, 18)

2) A'(-2, 1), B'(1/2, 3/2), C'(-3/2, 3)

3) X'(-8, 2), Y'(2, 14), Z'(8, 8)

4) X'(-1, 1/4), Y'(1/4, 7/4), Z'(1, 1)

5) A'(-8, 4), B'(2, 6), C'(-6, 12)

6) X'(-4/3, 1/3), Y'(1/3, 7/3), Z'(4/3, 4/3)

7) X'(-20, 5), Y'(5, 35), Z'(20, 20)

8) A'(-1, 1/2), B'(1/4, 3/4), C'(-3/4, 3/2)

Dilation is defined as a type of transformation where an image size either increases or decreases but then has the same shape as the original one. Thus, we will just multiply each coordinate by the scale factor;

We are given the coordinates of both triangles as;

Triangle ABC = A(-4, 2), B(1, 3), C(-3, 6)

Triangle XYZ = X(-4, 1), Y(1, 7), Z(4, 4)

1) Dilate triangle ABC by a scale factor of 3 means we multiply each ABC coordinate by 3 to get;

A'(-12, 6), B'(3, 9), C'(-9, 18)

2) Dilate triangle ABC by a scale factor of 1/2 means we multiply each ABC coordinate by 1/2 to get;

A'(-2, 1), B'(1/2, 3/2), C'(-3/2, 3)

3) Dilate triangle XYZ by a scale factor of 2 means we multiply each XYZ coordinate by 2 to get;

X'(-8, 2), Y'(2, 14), Z'(8, 8)

4) Dilate triangle XYZ by a scale factor of 1/4 means we multiply each XYZ coordinate by 1/4 to get;

X'(-1, 1/4), Y'(1/4, 7/4), Z'(1, 1)

5) Dilate triangle ABC by a scale factor of 2 means we multiply each ABC coordinate by 2 to get;

A'(-8, 4), B'(2, 6), C'(-6, 12)

6) Dilate triangle XYZ by a scale factor of 1/3 means we multiply each XYZ coordinate by 1/3 to get;

X'(-4/3, 1/3), Y'(1/3, 7/3), Z'(4/3, 4/3)

7) Dilate triangle XYZ by a scale factor of 5 means we multiply each XYZ coordinate by 5 to get;

X'(-20, 5), Y'(5, 35), Z'(20, 20)

8) Dilate triangle ABC by a scale factor of 1/4 means we multiply each ABC coordinate by 1/4 to get;

A'(-1, 1/2), B'(1/4, 3/4), C'(-3/4, 3/2)

Read more about dilation transformation at; https://brainly.com/question/3457976

#SPJ1

The expected value of y is (D.) 35.5.

The expected value of a discrete random variable is found by multiplying each value of the variable by its corresponding probability and then summing these products. In this case, the probability distribution of y is given in the table.

To find the expected value of y, we need to calculate the sum of the products of each value of y and its corresponding probability.

y * probability = y * P(y)

The expected value of y is E(y) = 100.10 + 200.25 + 300.05 + 400.30 + 500.20 + 600.10

= 2 + 5 + 1.5 + 12 + 10 + 6 = 37.

Read more about Probability:

https://brainly.com/question/25870256

#SPJ4

The expression (xmynzp)q can be written as xq * yq * zq * p*q, where each base is raised to the power of q.

To simplify the expression (xmynzp)q, we can apply the exponent rules. According to the rule (ab)c = aᶜ * bᶜ, we can distribute the exponent q to each term inside the parentheses.

Starting with the expression (xmynzp), we raise each variable to the power of q:

(xmynzp)q = xq * yq * zq * p*q

This means that each base, x, y, z, and p, is raised to the power of q.

The result of simplifying the expression (xmynzp)q is xq * yq * zq * p*q. Each base is raised to the power of q, and the product of these terms gives the final simplified expression.

Therefore, we have simplified the expression (xmynzp)q to xq * yq * zq * p*q.

To know more about exponent rules, visit:

https://brainly.com/question/29134756

#SPJ11

Answer:

\(x=±\sqrt[]{4}+9\)

We can conclude that w is in Col(A) but w is not in Nul(A).

To determine if w is in Col(A) and if w is in Nul(A), we must use the matrix A = [ -4 8 ] and W = [ 2 ] and solve the problem.

Let's first determine whether w is in Col(A) or not. A matrix is said to have a column space if there are any linear combinations of the columns of the matrix.

We can create the matrix [ -4 8 ] as a linear combination of its columns as -2[2] + 1[1]

Thus, we can see that w is in Col(A).

Now, let's find out if w is in Nul(A) or not. A matrix is said to have a null space if there are any non-zero vectors that will produce the zero vector when multiplied by the matrix.

In order to find if w is in the null space or not, we can multiply the matrix A with the given vector w.

The multiplication of matrix A with w is as follows;

[ -4 8 ][ 2 ] = [ -8 16 ]

Now we can see that the resulting matrix is not the zero matrix.

Hence, w is not in Nul(A).

Thus, we can conclude that w is in Col(A) but w is not in Nul(A).

Learn more about linear combination at

https://brainly.com/question/30888143

#SPJ11

a) The circle crosses the y-axis at the points (0, 6) and (0, -2). b) the radius of the circle is 5. c) (i) The length of CP is √34. (ii) The length of PQ is 10.

(a) To find the y-coordinates of the points where the circle crosses the y-axis, we substitute x = 0 into the equation of the circle:

0² + y² + 6(0) - 4y = 12

y² - 4y = 12

y² - 4y - 12 = 0

To solve this quadratic equation, we can factor it:

(y - 6)(y + 2) = 0

Setting each factor to zero, we find two possible values for y:

y - 6 = 0 => y = 6

y + 2 = 0 => y = -2

Therefore, the circle crosses the y-axis at the points (0, 6) and (0, -2).

(b) To find the radius of the circle, we can complete the square to rewrite the equation of the circle in standard form:

x² + y² + 6x - 4y = 12

(x² + 6x) + (y² - 4y) = 12

(x² + 6x + 9) + (y² - 4y + 4) = 12 + 9 + 4

(x + 3)² + (y - 2)² = 25

Comparing this equation with the standard form of a circle, (x - h)² + (y - k)² = r², we can see that the center of the circle is at (-3, 2) and the radius is √25 = 5.

Therefore, the radius of the circle is 5.

(c) (i) To find the length of CP, we can use the distance formula between two points. The coordinates of C are (-3, 2), and the coordinates of P are (2, 5).

The distance formula is given by:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Substituting the coordinates into the formula, we have:

CP = √((2 - (-3))² + (5 - 2)²)

= √(5² + 3²)

= √(25 + 9)

= √34

Therefore, the length of CP is √34.

(ii) To find the length of PQ, we can use the fact that PQ is a tangent to the circle. The radius of the circle is 5, and the line segment CP is perpendicular to PQ.

Since CP is perpendicular to PQ, CP is the radius of the circle. Therefore, CP = 5.

Therefore, the length of PQ is equal to 2 times the length of CP:

PQ = 2 * CP

= 2 * 5

= 10

Therefore, the length of PQ is 10.

To learn more about circle here:

https://brainly.com/question/31831831

#SPJ4

Answer:

4+34i

Hope this helps!!!!!!

The given fractions have equal value, so Liam is correct.

Equivalent fractions are defined as fractions that have different numerators and denominators but the same value. For example, 2/4 and 3/6 are equivalent fractions because they are both equal to 1/2. A fraction is part of a whole. Equivalent fractions represent the same part of a whole.  

Liam is claiming that the fraction -(5/12) is equivalent to 5/-12.

Thus, we can say that:

The fraction  -(5/12) can be described as the opposite of a positive number divided by a positive number. A positive number divided by a positive number always results in a positive quotient and its' opposite is always negative.

The fraction 5/-12 can be described as a positive number divided by a negative number which always results in a negative quotient

The fractions have equal value, so Liam is correct

Read more about Equivalent fractions at: https://brainly.com/question/17220365

#SPJ1

The fraction of the pitcher each type of juice are 1/3 and 2/3

From the question, we have the following parameters that can be used in our computation:

Parts = 6

Orange juice = 1

Peach juice = 2

using the above as a guide, we have the following:

Orange juice  : Peach juice = 1 : 2

Multiply by 2

So, we have

Orange juice  : Peach juice = 2 : 4

When represented as a fraction, we have

Orange juice = 1/3

Peach juice = 2/3

Hence, the fractions are 1/3 and 2/3

Read more about proportions at

https://brainly.com/question/1781657

#SPJ1

Answer:

64

Step-by-step explanation:

For a set of \(x\) elements, there are \(2^x\) subsets, including a full and empty subset.

In the set \(\displaystyle \{1, 2, 3, 4, 5, 6\}\), there are 6 elements and therefore \(2^6=\boxed{64}\) subsets

          - - - - - -- - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - -

\(\blue\textsf{\textbf{\underline{\underline{Question:-}}}}\)

What is the volume of a sphere with a radius of 12 units?

\(\blue\textsf{\textbf{\underline{\underline{Answer and How to Solve:-}}}}\)

\(\sf{Formula \ for \ Volume \ of \ a \ sphere \ :\) \(\bigstar\boxed{\bold{V=\displaystyle\frac{4}{3} \pi r^3}}\)

Where

\(\tt{V=Volume}\\\tt{\pi =pi}\\\tt{r=radius}\)

Provided Information:-

\(\tt{r=12\:units}\)

Plug in:-

\(\bold{V=\displaystyle\frac{4}{3} \pi (12)^3}\)

\(\bold{V=\displaystyle\frac{4}{3} \pi (1,728)}\)

On further simplification,

\(\dashrightarrow\boxed{\boxed{\underline{\bold{V=2304\pi\:m^3}}}}\dashleftarrow\)

         -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - -

Answer:

D. Jacob rode a 45-kilometer race in 3 hours.

Step-by-step explanation:

1h = 15km

A. : 30m = \(\frac{30}{60}\) × 15km

              = 7.5km (not 2km)

B. : 15m = \(\frac{15}{60}\) × 15km

             = 3.75km (not 4km)

C. : 5h = 5 × 15km

             = 75km (not 20km)

D. : 3h = 3 × 15km

             = 45km (Yep, 45km)

Pr[E∪F∪G], Pr[E∩F∩G], Pr[E∪F], Pr[F∪G], Pr[E∩G], and Pr[F∩G] can be calculated using the given probabilities.

To calculate the probabilities, we can use the basic rules of probability. Given the probabilities Pr[E] = 0.5, Pr[F] = 0.4, Pr[G] = 0.6, Pr[E∩F] = 0.2, Pr[E∩G] = 0.3, and Pr[F∩G] = 0.2, we can find the following probabilities:

Pr[E∪F∪G] - Probability of the union of events E, F, and G. This can be calculated by adding the probabilities of individual events and subtracting the probabilities of their intersections.

Pr[E∩F∩G] - Probability of the intersection of events E, F, and G. This can be calculated using the inclusion-exclusion principle.

Pr[E∪F] - Probability of the union of events E and F. This can be calculated using the addition rule.

Pr[F∪G] - Probability of the union of events F and G. This can also be calculated using the addition rule.

Pr[E∩G] - Probability of the intersection of events E and G.

Pr[F∩G] - Probability of the intersection of events F and G.

By substituting the given probabilities into the appropriate formulas, we can calculate these probabilities.

To learn more about “probabilities” refer to the https://brainly.com/question/13604758

#SPJ11

Answer: B: Exponential

Step-by-step explanation:

lets look at the numbers. he starts from 32 and it gets halved every "interval" of time:

32, 16, 8, 4, 2, 1, 0.5, 0.25 ........

as you can see, at first the time drops quickly, and then it slows down, approaching 0, (but never getting there).

this is the telltale sign of exponential decay!

Answer:

The solution set is (13,− 32). A quadratic equation of the form x 2= k can be solved by factoring with the following sequence of equivalent equations.

Step-by-step explanation:

well, since the y-intercept is at -5, or namely when the line hits the y-axis is at -5, that's when x = 0, so the point is really (0 , -5), and we also know another point on the line, that is (-1 ,6), to get the equation of any straight line, we simply need two points off of it, so let's use those two

\(\stackrel{y-intercept}{(\stackrel{x_1}{0}~,~\stackrel{y_1}{-5})}\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{(-5)}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{0}}} \implies \cfrac{6 +5}{-1} \implies \cfrac{ 11 }{ -1 } \implies - 11\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{- 11}(x-\stackrel{x_1}{0}) \implies y +5 = - 11 ( x -0) \\\\\\ y+5=-11x\implies {\Large \begin{array}{llll} y=-11x-5 \end{array}}\)

Answer:

I45

Step-by-step explanation:

Answer:

I'm assuming that 1 is actually a point with coordinates (1, something) and you meant the point H(25,-16).

To find the equation of the line passing through two points (x1,y1) and (x2,y2), we can use the point-slope form:

y - y1 = m(x - x1)

where m is the slope of the line, which can be calculated as:

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

Using the points H(25, -16) and 1(-2.5, y), we have:

m = (-16 - y) / (25 - (-2.5)) = (-16 - y) / 27.5

Multiplying both sides by 27.5, we get:

-16 - y = -0.58x + b

where x is the x-coordinate and b is the y-intercept of the line. To find b, we plug in one of the points (let's use H) and solve for b:

-16 - (-16) = -0.58(25) + b

b = -16 - (-14.5) = -1.5

Therefore, the equation of the line passing through H(25, -16) and 1(-2.5, y) is:

y + 1.5 = -0.58(x + 2.5)

or:

y = -0.58x - 4.25

Note: I assumed that you meant H(25,-16) and I used -2.5 as the x-coordinate for point 1 because you didn't specify what it was.

Answer: 22( w + 2 ) =77 and the amount of the water bottle would be 1.50

Step-by-step explanation: i dont know what to write??