Help me please this question is too tricky for me

The roots of equation are 2 , -2, 3i, 1/5 and -5.

We have,

([tex]x^4[/tex] + 5x² -36)(2x² + 9x-5)=0

Now, factories each equation as

([tex]x^4[/tex] + 5x² -36)

= ([tex]x^4[/tex] + 9x² - 4x² -36)

= x²(x² + 9) - 4(x² + 9)

= (x² - 4)(x² + 9)

= (x-2)(x+2)(x²+9)

and, 2x² + 9x-5

= 2x² + 10x - x -5

= 2x(x+5)- (x+5)

= (2x -1)(x+5)

So, the factored form is (x-2)(x+2)(x²+9) (2x -1)(x+5)

and, the roots of equation are 2 , -2, 3i, 1/5 and -5.

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Note that the graph of the function f(x) = a(b)^x is attached accordingly. Here a = 8 and b = 5

f(x) = a(b^x)......1

from the graph we can see that

When x = 0, y = 8

f(0) = 8

8 = a(b^0)
8 = a x 1

a = 8


f(1) = 4

4 = a(b^1)
4 = ab
8b = 4
b = 0.5

Thus a = 8 and b = 5

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Full Question:

Another copy machine also has the ability to reduce image dimensions, but by a different percentage. This graph shows the results found when copying a design x times. Use the graph to write the equation modeling this relationship

Enter the correct answer in the box by replacing the values of a and b.

f(x) = a(b)^x

Answer:

Regarding the conjecture of Serena and Jack:

Serena suggests that they can use the graph of the first rocket and shift it to find the graphs for the other two rockets. This means that the paths of the rockets are similar, and the only difference is the time of launch. Jack suggests that they need to recalculate the graphs for the other two rockets, which means that the paths of the rockets are different.

In this scenario, Serena is correct. Since the rockets are identical, they will follow the same path, but with a different time of launch. Thus, they can use the graph of the first rocket and shift it to the right to get the graph of the second rocket and shift it further to the right and up to get the graph of the third rocket.

Analyzing the equation:

The equation for the first rocket's path is h(t) = -6(t-3.7)^2 + 82.14. Assuming that the graph is a transformation from f(t) = -6t^2, the term -3.7 shifts the graph horizontally to the right by 3.7 seconds. This means that the first rocket was launched 3.7 seconds before the time t in the equation. The value t = 3.7 represents the time when the first rocket was launched.

The term 82.14 shifts the graph vertically up by 82.14 feet. This means that the initial height of the rocket is 82.14 feet above the ground. Therefore, the value h(t) = 82.14 represents the initial height of the rocket.

Equation of the second rocket:

The second rocket is launched 3 seconds after the first rocket. This means that the graph of the second rocket is a horizontal shift of the first rocket's graph by 3 seconds. Therefore, the equation of the second rocket is:

h(t) = -6(t-6.7)^2 + 82.14

This is because the launch time of the second rocket is t = 6.7 seconds (which is 3 seconds after the first rocket's launch).

Description of the third rocket's graph:

The third rocket is launched 3 seconds after the second rocket and from a 20-foot-tall platform. This means that the graph of the third rocket is a horizontal shift of the second rocket's graph by 3 seconds and a vertical shift upwards by 20 feet. Therefore, the equation of the third rocket is:

h(t) = -6(t-9.7)^2 + 102.14

This is because the launch time of the third rocket is t = 9.7 seconds (which is 3 seconds after the second rocket's launch).

Answers to the questions:

a. The third rocket is launched at approximately t = 9.7 seconds.

b. The first rocket lands when h(t) = 0. Solving -6(t-3.7)^2 + 82.14 = 0 gives t = 5.16 seconds (approximate).

c. The approximate interval during which all three rockets are in the air is from t = 6.7 seconds (when the second rocket is launched) to t = 14.46 seconds (when the first rocket lands).

The equation of line perpendicular to "y = (1/2)x - 1" and passing through point (5,6) is y = -2x + 16,

The equation of the line is y = (1/2)x - 1, is in slope-intercept form "y = mx + b", where m is slope,

To find the slope of the given line, we see that it is in the form y = mx + b, where m = 1/2.

We know that, slope of a line perpendicular to this line will be the "negative-reciprocal" of this slope.

So, the slope of the perpendicular line will be -2.

Now we use the point-slope form of the equation of a line to find the equation of the perpendicular line passing through the point (5, 6). The point-slope form is : y - y₁ = m(x - x₁),

where (x₁, y₁) is given point and "m" is slope of the line;

Substituting the values, we get:

⇒ y - 6 = -2(x - 5),

⇒ y = -2x + 16,

Therefore, the equation of perpendicular line is y = -2x + 16.

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Answer: [tex]x_1 = -\frac{3}{2} \\x_2 = \frac{3}{2} \\\\[/tex]

X could equal either -3/2, or 3/2 because x is made into an absolute value

Answer:

[tex]x = 1 \frac{1}{2} \: \\ x = - 1 \frac{1}{2} [/tex]

Step-by-step explanation:

If we're solving for x, then we should divide both sides by 2 and then simplify.

[tex](2 |x| = 3) \div 2[/tex]

[tex] |x| = \frac{3}{2} [/tex]

This gives us the final answer of

[tex]x = ±\frac{3}{2} [/tex]

Which can be simplified into:

[tex]x = 1\frac{1}{2} , \: - 1\frac{1}{2} [/tex]

Answer:x = midpoint_x - (midpoint_x - (-3)) * (sqrt(5)/6) = 19.5 - (22.5 * sqrt(5))/6 = 19.5 - 3.75sqrt(5)

Step-by-step explanation:To find the x-coordinate of the point that is 2/3 of the distance from (-3, 2) to (42, 32), we first need to find the coordinates of that point.

The distance between the two endpoints of the line segment is:

d = sqrt((42 - (-3))^2 + (32 - 2)^2) = sqrt(45^2 + 30^2) = 15sqrt(45)

The distance from (-3, 2) to the desired point is:

(2/3)d = (2/3)sqrt(45^2 + 30^2)

Let's call the desired point (x, y). We can use the midpoint formula to find the coordinates of the midpoint of the line segment:

midpoint = ((-3 + 42)/2, (2 + 32)/2) = (19.5, 17)

The midpoint is halfway between the two endpoints, so the distance from (-3, 2) to the midpoint is:

sqrt((19.5 - (-3))^2 + (17 - 2)^2) = sqrt(22.5^2 + 15^2) = 15sqrt(5)

To find the coordinates of the desired point, we can use similar triangles. The ratio of the distance from (-3, 2) to the midpoint to the distance from (-3, 2) to the desired point is:

15sqrt(5) / (2/3)sqrt(45^2 + 30^2) = 15sqrt(5) / 30sqrt(45) = sqrt(5)/6

The ratio of the distance from (42, 32) to the midpoint to the distance from (42, 32) to the desired point is the same:

15sqrt(5) / (2/3)sqrt(45^2 + 30^2) = sqrt(5)/6

Based on the above, Since Ana bought 3/4 kg of lanzones and 1/2 kg of apples,  Ana bought 1  1/4 kilograms of fruits in all.

To be able to find out how many kilograms of fruits Ana bought in total, you have to add the amount of lanzones and apples she have.

Ana = 3/4 kg of lanzones

Ana = 1/2 kg of apples

So it will be:

3/4 + 2/4 = 5/4

Therefore, Ana will have bought a total of 5/4 kilograms of fruits.

To convert it to a mixed number, you need to divide the numerator by the denominator:

5 ÷ 4 = 1 remainder 1

So, the mixed fraction will  be 1  1/4 kg.

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See full question below

Ana bought 3/4 kg of lanzones and 1/2 kg of apples. How many kilograms of fruits did she buy in all?​

For points A and B in the economy:

x₁ = 2p₂/p₁ and x₂ = p₂/p₁.

x₁ = 2p₁ / p₂ and x₂ = p₁ / p₂.

2 - p₂ / p₁

1 - p₁ / p₂

2 - p₂ / p₁ + 1 - p₁ / p₂

The market clears for both items at the Walrasian equilibrium, and the aggregate excess demands are zero.

1. To derive agent A's demands for goods 1 and 2, maximize her utility subject to her budget constraint:

max ln x₁ + 2ln x₂

s.t. p₁x₁ + p₂x₂ ≤ p₁(1) + p₂(2)

Using Lagrange multiplier method:

1/x₁ = p₁/(2p₂)

1/x₂ = p₁/p₂

Solving for x₁ and x₂:

x₁ = 2p₂/p₁

x₂ = p₂/p₁

So, agent A's demands for goods 1 and 2 are x₁ = 2p₂/p₁ and x₂ = p₂/p₁.

2. To derive agent B's demands for goods 1 and 2, maximize her utility subject to her budget constraint:

max 2ln x₁ + ln x₂

s.t. p₁x₁ + p₂x₂ ≤ p₁(2) + p₂(1)

Using Lagrange multiplier method:

2/x₁ = p₁/p₂

1/x₂ = p₂/p₁

Solving for x₁ and x₂:

x₁ = 2p₁/p₂

x₂ = p₁/p₂

So, agent B's demands for goods 1 and 2 are x₁ = 2p₁ / p₂ and x₂ = p₁ / p₂.

3. Agent A's excess demands for goods 1 and 2 are:

z₁ = 1 - x₁ = 1 - 2p₂ / p₁

z₂ = 2 - x₂ = 2 - p₂ / p₁

4. Agent B's excess demands for goods 1 and 2 are:

z₁ = 2 - x₁ = 2 - 2p₁ / p₂

z₂ = 1 - x₂ = 1 - p₁ / p₂

5. The aggregate excess demands for goods 1 and 2 are:

Z₁ = z₁ᵃ + z₁ᵇ = 1 - 2p₂ / p₁ + 2 - 2p₁ / p₂

Z₂ = z₂ᵃ + z₂ᵇ = 2 - p₂ / p₁ + 1 - p₁ / p₂

6. At Walrasian equilibrium, Z₁ and Z₂ are both equal to zero. So, solve the system of equations:

1 - 2p₂ / p₁ + 2 - 2p₁ / p₂ = 0

2 - p₂ / p₁ + 1 - p₁ / p₂ = 0

Solving for p₁ and p₂:

p₁ = 2

p₂ = 1

So, the Walrasian equilibrium prices for goods 1 and 2 are p₁ = 2 and p₂ = 1.

7. At the Walrasian equilibrium, the market clears for both goods and the aggregate excess demands are zero. This means that the prices are set such that both agents are willing to buy exactly what is being sold in the market.

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Answer: there were 190 children, 140 parents, and 70 grandparents in attendance at the family reunion.

Step-by-step explanation: Let's denote the number of children, parents, and grandparents as "c", "p", and "g", respectively.

We are given three pieces of information:

The total number of people in attendance is 400:

c + p + g = 400

There were twice as many parents as grandparents:

p = 2g

There were 50 more children than parents:

c = p + 50

We can use this system of equations to solve for the unknown variables.

First, we can use equation (2) to express "p" in terms of "g":

p = 2g

Next, we can substitute this expression for "p" into equation (3) to get:

c = 2g + 50

Now, we can use equations (1) and (4) to eliminate "p" and "c" from the system and express "g" in terms of only known quantities:

c + p + g = 400

2g + 50 + p + g = 400 (substituting c=2g+50)

3g + p = 350 (simplifying)

We can then substitute the expression for "p" from equation (2) into this last equation to obtain:

3g + 2g = 350

Simplifying:

5g = 350

Solving for "g", we get:

g = 70

Now, we can use equation (2) to find "p":

p = 2g = 2(70) = 140

Finally, we can use equation (3) to find "c":

c = 2g + 50 = 2(70) + 50 = 190

Therefore, there were 190 children, 140 parents, and 70 grandparents in attendance at the family reunion.

Step-by-step explanation:

(20 - m) + 3

that's it. there is not more to it.

The algebra expression can be expressed as: 3 + (20 - m)

Algebraic word problems are defined as questions that require translating sentences to equations, and then solving those equations. The equations we need to write will only involve basic arithmetic operations. and a single variable. Normally, the variable represents an unknown quantity in a real-life scenario.

We are told that 3 more than the difference of 20 and a number m.

This can be expressed as:

3 + (20 - m)

That is the literal expression of the algebra word problem.

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Answer:

Value-Added Tax

Step-by-step explanation:

Value-added tax (VAT) is a consumption tax on goods and services that is levied at each stage of the supply chain where value is added, from initial production to the point of sale.

Tessa's cumulative GPA for all four semesters is 3.44.

To find Tessa's cumulative GPA, we first need to calculate the total number of course units she has taken. For the first three semesters, she took 46 course units. For the fourth semester, she took 12 course units. So, in total, she has taken 46 + 12 = 58 course units.

Next, we need to calculate her total grade points. To do this, we multiply her GPA for each semester by the number of course units she took in that semester, and then add up the results. For the first three semesters, her total grade points are:

3.35 x 46 = 154.1

For the fourth semester, her total grade points are:

3.74 x 12 = 44.88

So her total grade points for all four semesters are:

154.1 + 44.88 = 198.98

Finally, we divide her total grade points by the total number of course units she has taken:

198.98 / 58 = 3.44

Therefore, Tessa's cumulative GPA for all four semesters is 3.44.

Answer:

2 2/3 cups flour

Step-by-step explanation:

32 cookies

by my calculations

Answer:

23 apple pies and 13 cherry pies were sold.

Step-by-step explanation:

Let's use the variables a and c to represent the number of apple and cherry pies sold, respectively.

From the problem, we know that:

The total number of pies sold is 36: a + c = 36

The total revenue from pie sales is $304.00: 7a + 11c = 304

We now have two equations with two unknowns. We can use substitution or elimination to solve for a and c. Here's one way to use substitution:

Solve the first equation for a: a = 36 - c

Substitute a = 36 - c into the second equation: 7(36 - c) + 11c = 304

Simplify: 252 - 7c + 11c = 304

Simplify further: 4c = 52

Solve for c: c = 13

Substitute c = 13 into the first equation to solve for a: a + 13 = 36

Simplify: a = 23

Therefore, 23 apple pies and 13 cherry pies were sold.

The ratio of science teachers to math teachers is 1:5.

The ratio of science teachers to math teachers can be found by dividing the number of science teachers by the number of math teachers.

The ratio of science teachers to math teachers = (Number of science teachers) / (Number of math teachers)

Here, the number of science teachers is 9 and the number of math teachers is 45.

The ratio of science teachers to math teachers = 9 / 45

Simplifying this ratio by dividing both the numerator and denominator by 9, we get:

The ratio of science teachers to math teachers = 1 / 5

Therefore, the ratio of science teachers to math teachers is 1:5.

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Option A correctly matches the data set.

First, by looking at the numbers and description of the numbers; I notice that it starts at 10, ending at 48.

Second, I see that the first quartile (Q1) is 20, eliminating option D

Third, I see the third quartile (Q3) is 45, eliminating option C.

Lastly, I look at the median (Q2) is 30, eliminating option B.

Since I have eliminated option B, C, and D; only option A remains.

—————

Please remember to revise this and make it in your own words if you want! I hope this helps you. -Doodle

—————

The solution is the number in polar form 4 - 4i is

4 Root(2) (cos(-45) + i sin(-45)).

We know that,

Polar form of a complex number is r( cos(theta) + i sin(theta) )

r is equal to the total distance created by the rectangular coordinates of the complex number

r = Root(4^2 + (-4)^2) = Root(32) = 4 Root(2)

To find theta, if a > 0, use arctan(b/a), where:

a = the first number

b = the second number

arctan (-4/4) = -45 degrees (-0.7854 radians)

The answer is 4 Root(2) (cos(-45) + i sin(-45))

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complete question;

Express the number in polar form 4 - 4i

Answer:

Let's assume that the smaller number is x and the larger number is y.

From the problem, we can write:

y = 2x + 2 (since the quotient and remainder when y is divided by x are both equal to 2)

5x = 2(y - 2) (since the quotient and remainder when 5x is divided by y are both equal to 2)

Substituting the first equation into the second equation, we get:

5x = 2((2x + 2) - 2)

5x = 4x + 4

x = 4

Substituting x = 4 into the first equation, we get:

y = 2x + 2 = 10

Therefore, the two numbers are 4 and 10

Answer:

Charles Baudelaire recommended that artists paint scenes of modern life.

Charles Baudelaire was the one who recommended that artists paint scenes of modern life.

a) To calculate SSTr, we need to first find the overall mean of the samples and then use it to calculate the sum of squares due to treatments (SSTr).

The overall mean of the samples can be found by adding up all the sample means and dividing by the number of samples:

Overall mean = (650 + 750 + 700 + 650) / 4 = 687.5

Next, we can calculate SSTr using the formula:

SSTr = n * (sample mean - overall mean)^2

where n is the number of observations in each sample. In this case, n = 5 for each sample.

So for the first sample, SSTr = 5 * (650 - 687.5)^2 = 5362.5

For the second sample, SSTr = 5 * (750 - 687.5)^2 = 14062.5

For the third sample, SSTr = 5 * (700 - 687.5)^2 = 3062.5

For the fourth sample, SSTr = 5 * (650 - 687.5)^2 = 5362.5

Therefore, the total SSTr is:

SSTr = 5362.5 + 14062.5 + 3062.5 + 5362.5 = 27750

b) The degrees of freedom (df) for SSTr is k-1 where k is the number of groups/populations, and df for SSE is N-k where N is the total number of observations.

df(SSTr) = k - 1 = 5 - 1 = 4

df(SSE) = N - k = 20 - 5 = 15

The mean square for treatments (MSTr) is calculated as:

MSTr = SSTr / df(SSTr) = 12 / 4 = 3

The mean square for error (MSE) is calculated as:

MSE = SSE / df(SSE) = (20 - 5) / 15 = 1

Finally, we can calculate the F-test statistic as:

F = MSTr / MSE = 3 / 1 = 3

Therefore, the MSTr is 3, the MSE is 1, and the F-test statistic is 3.

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The Venn diagram is attached in the solution.

Given that, a Venn Diagram with sets B, D, and the universal set U, we need to Shade (BUD)’ on the Venn diagram,

We know that, the complement of a set is the set that includes all the elements of the universal set that are not present in the given set.

Therefore, (BUD)’ = U - (BUD)

therefore, we will shade all the portion except (BUD),

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Answer:

To calculate the monthly deposit required, we can use the formula for future value of an annuity, which is:

FV = Pmt x (((1 + r)^n - 1) / r)

where FV is the future value, Pmt is the monthly payment, r is the monthly interest rate, and n is the number of months.

In this case, we want to find the monthly payment required to achieve a future value of $12,000 in 6 years, or 72 months. The monthly interest rate is the annual percentage rate (APR) divided by 12, so:

r = 6.5% / 12 = 0.00541666667

Substituting these values into the formula, we get:

12,000 = Pmt x (((1 + 0.00541666667)^72 - 1) / 0.00541666667)

Solving for Pmt, we get:

Pmt = 12,000 / (((1 + 0.00541666667)^72 - 1) / 0.00541666667)

≈ $164.41

Therefore, you should deposit $164.41 each month to end up with $12,000 in 6 years

The required graph shows the x-intercepts and the minimum value.

To find the x-intercepts of the function y = 3x² - 12x + 9, we set y = 0 and solve for x:

3x² - 12x + 9 = 0

Dividing both sides by 3 gives:

x² - 4x + 3 = 0

(x - 1)(x - 3) = 0

So, the x-intercepts are x = 1 and x = 3.

To find the minimum value of the function, we can use the formula:

x = -b / 2a

Here a = 3 and b = -12.

Substitute these values gives:

x = -(-12) / 2(3) = 2

So the minimum value occurs at x = 2.

To find the corresponding y-value, we can plug in x = 2 into the original function:

y = 3(2)² - 12(2) + 9 = -3

So the minimum value is y = -3.

Here is a graph showing the x-intercepts and the minimum value.

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The end behavior of the given function is Both ends of the graph goes down(In the same direction),

The degree and the leading coefficient (The coefficient of the highest degree monomial) of a function shows the end behavior of its graph.

if Degree  is even and leading coefficient is negative then the end behavior of the function f(x) is,

f(x)---> -∞, as x---> -∞

f(x)---> -∞, as x---> + ∞

That is, Both ends of the graph goes down(In the same direction)

Here, the given function is f(x)=-4x⁶+6x²-52

Degree = 6(even), leading coefficient = -4 (negative)

Thus, the end behavior of the given function is Both ends of the graph goes down(In the same direction),

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Answer:

Step-by-step explanation:

Four seconds after the boulder is hurled, it will hit the ground.

When the boulder hits the ground, its height will be 0. So, we need to solve the equation:

[tex]h(t) = -16t^2 + 64t = 0[/tex]

We can factor out -16t from the expression:

h(t) = -16t(t - 4)

Setting each factor to zero, we get:

-16t = 0 or t - 4 = 0

Solving for t, we get:

t = 0 or t = 4

Since t = 0 represents the time when the boulder is launched, we can ignore it. Therefore, the boulder will hit the ground 4 seconds after it is launched.

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The area of the sidewalk is 264 sq. m.

A circle is a figure that is bounded by curved line called its circumference. Its area is the amount of space that he circle will cover on a 2 dimensional plane. It can be determined by:

area of a circle = πr^2

where r is the radius of the circle.

In the given question,

area of the circular flower = πr^2

   r = d/2 (d is the diameter)

      = 17/ 2

r = 8.5 m

area of the circular flower = 3.14*(8.5)^2

                                           = 226.865 sq. m

area of the circular flower with sidewalk = πr^2

d = 4 + 17 + 4 = 25 m

so that,

r = 25/ 2 = 12.5 m

area of the circular flower with sidewalk = 3.14*(12.5)^2

                                              = 490.625 sq. m

Area of the sidewalk = area of the circular flower with sidewalk - area of the circular flower

                                  = 490.625 - 226.865

                                  = 263.76 sq. m

The area of the sidewalk is 264 sq. m.

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The point estimate of the population mean is 25 and the margin of error for the confidence interval is 2.04.

To determine the point estimate of the population mean, we take the midpoint of the interval.

Point estimate of population mean = (Lower bound + Upper bound) / 2 = (20 + 30) / 2 = 25

To calculate the margin of error, we need to know the level of confidence for the interval. Assuming a 95% confidence level, we can use the formula:

The margin of error = (Upper bound - Lower bound) / (2 * z-score)

Where the z-score for a 95% confidence level is 1.96.

Margin of error = (30 - 20) / (2 x 1.96) = 2.04

Hence, the population means point estimate is 25, and the confidence interval's margin of error is 2.04 percent.

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The height of the building, found using the equivalent ratios of the corresponding sides of the similar triangles formed by Rob, the building and the shadows is 90 feet

Similar triangles are triangles that have the same shape but may have different sizes.

The length of the shadow cast by the building = 30 feet

Rob's height = 6 feet

The length of Rob's shadow = 2 feet long

The height of the building can be found from the similar right triangles formed by the building and the building's shadow and the triangle formed by Rob and Rob's shadow as follows;

Let h represent the height of the building, we get;

h/30 = 6/2 = 3

h = 30 × 3 = 90

The height of the building is 90 feet tall

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The value of the given algebraic expression is -2.

To find the value of the expression 2x³ - 2x² + 2x - 8 / 2x² - 5x when x = -2, we simply substitute -2 for every instance of x in the expression:

2(-2)³ - 2(-2)² + 2(-2) - 8 / 2(-2)² - 5(-2)

= 2(-8) - 2(4) - 4 - 8 / 8 + 10

= -16 - 8 - 4 - 8 / 18

= -36 / 18

= -2

Therefore, the value of the expression 2x³ - 2x² + 2x - 8 / 2x² - 5x when x = -2 is -2.

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