Write the formula for the parabola that has x-intercepts (−2,0) and (4. 6,0), and y-intercept (0,1. 5)

{-2 2 22}

a) The characteristic polynomial of A is given by:
$$p_A(\lambda) = \lambda^3 - 5\lambda^2 + 18\lambda + 36$$
b) The two eigenvalues of A are:
$$\lambda_1=2, \lambda_2=-4, \lambda_3=9$$
c) A basis for the eigenspace corresponding to the smallest eigenvalue $\lambda_2=-4$ is given by the set of vectors:
$$\begin{bmatrix} 0\\1\\0 \end{bmatrix}, \begin{bmatrix} 2\\0\\1 \end{bmatrix}$$
d) A basis for the eigenspace corresponding to the largest eigenvalue $\lambda_3=9$ is given by the set of vectors:
$$\begin{bmatrix} 1\\0\\-4 \end{bmatrix}, \begin{bmatrix} -2\\2\\22 \end{bmatrix}$$

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The Simple ratio and the ratio of the perimeters of two regular octagons are approximately 1.472

The formula for the area of the regular polygon is:

Area = (2 + 2[tex]\sqrt{2}[/tex]) × [tex]s^{2}[/tex]

Where, s = length of the side of a polygon

consider two equations for the two octagons,

48 = (2 + 2[tex]\sqrt{2}[/tex]) × [tex](s1)^{2}[/tex]

147 = (2 + 2[tex]\sqrt{2}[/tex]) × [tex](s2)^{2}[/tex]

The length of each polygon is

s1 = [tex]\sqrt{\frac{48}{(2 + 2\sqrt{2} )} }[/tex] ≈ 3.079cm

s2 = [tex]\sqrt{\frac{147}{(2 + 2\sqrt{2} )} } }[/tex] ≈ 4.532cm

The similarity ratio is,

s2 ÷ s1 ≈ 1.472

The ratio of perimeters is,

8s2 ÷ 8s1 = s2 ÷ s1 ≈ 1.472

Therefore, the similarity ratio and the ratio of the perimeters are both approximately 1.472.

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In response to the given query, the result we have is As a result, the expressions following statement may be used to explain how long Interstate 90 is: 2m + 153.5

Multiplying, dividing, adding, and subtracting are all mathematical operations. As an example, consider the following expression: Expression, mathematics, and a numeric value Numbers, parameters, and functions are the components of an expression in mathematics. Using opposing words and phrases is possible. An expression, sometimes referred to as an algebraic expression, is any mathematical statement that includes variables, numbers, and a mathematical action between them. For instance, the expression 4m + 5 is made up of the expressions 4m and 5, as well as the variable m from the previous equation, all of which are separated by the mathematical symbol +.

Let L represent the length of I-90. We are informed that

L = 2m + 153.5

where m is Interstate 15's length.

As a result, the following statement may be used to explain how long Interstate 90 is:

2m + 153.5

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Answer:

To find the x-intercepts of the equation y = -(x+7)(x+4), we need to set y = 0 and solve for x. So, we have:

0 = -(x+7)(x+4)

This equation will be true if either (x+7) = 0 or (x+4) = 0. Solving each of these equations, we get:

x+7 = 0 => x = -7

x+4 = 0 => x = -4

Therefore, the x-intercepts of the equation y = -(x+7)(x+4) are x = -7 and x = -4.

Now, we know that the equations y = -(x+7)(x+4) and y = -(x-3) are equivalent. This means that they have the same solutions, or the same x-intercepts. So, we can use the x-intercepts we found for the first equation to determine the x-intercepts of the second equation.

To find the x-intercepts of the equation y = -(x-3), we set y = 0 and solve for x:

0 = -(x-3)

This equation will be true if (x-3) = 0, which gives us:

x-3 = 0 => x = 3

Therefore, the x-intercept of the equation y = -(x-3) is x = 3, which is different from the x-intercepts of the equation y = -(x+7)(x+4). This means that the two equations are not equivalent.

Step-by-step explanation:

Answer:

x-intercepts can be found below

Step-by-step explanation:

The equation:

[tex]y=-(x+7)(x+4)[/tex]

Can also be written as:

[tex]y=-1(x+7)(x+4)[/tex]

In order to find the x-intercepts, we must set each of the factors equal to 0.

[tex]-1=0[/tex]

[tex]x+7=0, x=-7[/tex]

[tex]x+4=0, x=-4[/tex]

The x-intercepts are:

[tex](0,0)[/tex]

[tex](-7,0)[/tex]

[tex](-4,0)[/tex]

The equation:

[tex]y=-(x-3)[/tex]

Can also be written as:

[tex]y=-1(x-3)[/tex]

In order to find the x-intercepts, we must set each of the factors equal to 0.

[tex]-1=0[/tex]

[tex]x-3=0, x=3[/tex]

The x-intercepts are:

[tex](0,0)[/tex]

[tex](3,0)[/tex]

The correct domain for the function f(t)=(5)/(t^(2)+4) is {all reals}.

The domain of a function is the set of all possible inputs or values for the independent variable, t in this case. The function f(t)=(5)/(t^(2)+4) has a denominator of t^(2)+4. To find the domain, we need to determine the values of t that would make the denominator equal to zero, as those values would make the function undefined.

t^(2)+4=0
t^(2)=-4
t=±√(-4)

Since the square root of a negative number is not a real number, there are no real values of t that would make the denominator equal to zero. Therefore, the domain of the function is {all reals}.

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The approximate probability that the total aggregate cost of fighting

The approximate probability that less than 1801800 citizens will get vaccinated can be calculated using the de Moivre-Laplace theorem. This theorem states that the probability distribution of the sum of a large number of independent random variables approaches the normal distribution as the number of variables increases. In this case, the random variable is whether or not a citizen gets vaccinated, and the sum is the total number of citizens who get vaccinated.

To calculate the approximate probability, we need to find the mean and standard deviation of the distribution. The mean is equal to the number of citizens times the probability of getting vaccinated, which is 9.10^6 * (1/5) = 1820000. The standard deviation is equal to the square root of the number of citizens times the probability of getting vaccinated times the probability of not getting vaccinated, which is sqrt(9.10^6 * (1/5) * (4/5)) = 1200.

Using the de Moivre-Laplace theorem, we can approximate the probability that less than 1801800 citizens will get vaccinated as the probability that a normal random variable with mean 1820000 and standard deviation 1200 is less than 1801800. This can be calculated using the standard normal distribution:

P(Z < (1801800 - 1820000)/1200) = P(Z < -1.52) = 0.064

Therefore, the approximate probability that less than 1801800 citizens will get vaccinated is 0.064.

The approximate probability that the total aggregate cost of fighting the virus-inflicted illness for all citizens of the country will surpass 7207200000 dollars can be calculated using the Central Limit Theorem (CLT). The CLT states that the sum of a large number of independent random variables approaches the normal distribution as the number of variables increases. In this case, the random variable is the cost of treating a single non-vaccinated individual, and the sum is the total cost of treating all non-vaccinated individuals.

To calculate the approximate probability, we need to find the mean and standard deviation of the distribution. The mean is equal to the number of citizens times the probability of not getting vaccinated times the expected value of the cost of treating a single non-vaccinated individual, which is 9.10^6 * (4/5) * (2000/2) = 7207200000. The standard deviation is equal to the square root of the number of citizens times the probability of not getting vaccinated times the variance of the cost of treating a single non-vaccinated individual, which is sqrt(9.10^6 * (4/5) * (2000^2/12)) = 1633333.33.

Using the CLT, we can approximate the probability that the total aggregate cost of fighting the virus-inflicted illness for all citizens of the country will surpass 7207200000 dollars as the probability that a normal random variable with mean 7207200000 and standard deviation 1633333.33 is greater than 7207200000. This can be calculated using the standard normal distribution:

P(Z > (7207200000 - 7207200000)/1633333.33) = P(Z > 0) = 0.5

Therefore, the approximate probability that the total aggregate cost of fighting the virus-inflicted illness for all citizens of the country will surpass 7207200000 dollars is 0.5.

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Step-by-step explanation:

Refer to pic...........

Answer:6

Step-by-step explanation:

N=6

⇒6=6  

∴LHS=RHS

A performance task is any educational activity or assessment that calls for students to perform in order to demonstrate their comprehension, competency, and knowledge.

Mathematical activity includes the search for patterns as well as experimentation, description, fiddling, invention, picturing, conjecture, and guesswork.

A series of recurrent numbers, symbols, or shapes is referred to in mathematics as a pattern. Every kind of event or thing has a pattern that can be connected to it. A rule that distinguishes between items that are a part of a pattern and those that are not is known as a pattern.

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Complete question:

What is Performance task?

The quadrilateral with the specified value for x has a 45° angle.

A polygon with four sides, four angles, and four vertices is called a quadrilateral.

The Latin words quadri, which means four, and latus, which means side, were combined to create the English word quadrilateral.

A quadrilateral is a four-sided polygon with four edges and four corners that is used in geometry.

The Latin words quadri, a variation of four, and latus, meaning "side," are the source of the name.

The exterior angles of the given quadrilateral are x°, 3x°, x°, and 3x°.

We are aware that a quadrilateral's total exterior angles are 360°.

Now, x°+3x°+x°+3x°=360°

8x°=360°

x°=45°

Therefore, the quadrilateral with the specified value for x has a 45° angle.

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There are 15 blue counters in the bag.

Two quantities are compared to form a ratio. An equality of two ratios is a proportion.

We know that the initial ratio of red counters to blue counters was 4:5. Therefore, we can write:

4x : 5x

We also know that 10 more red counters were added to the bag. Therefore, the new number of red counters in the bag is:

4x + 10

The ratio of red counters to blue counters then became 6:5. Therefore, we can write:

(4x + 10) : y = 6 : 5

We can simplify this equation by cross-multiplying:

5(4x + 10) = 6y

20x + 50 = 6y

Dividing both sides by 6, we get:

y = (20x + 50)/6

Simplifying, we get:

y = (10x + 25)/3

Since y has to be a whole number, 10x + 25 has to be divisible by 3. The only value of x that satisfies this condition is x = 2.

Therefore, the initial number of red counters was 4x = 8, and the initial number of blue counters was 5x = 10.

After adding 10 more red counters, the new number of red counters was 18, and the new ratio of red counters to blue counters was 6:5.

To find the new number of blue counters, we can use the equation we derived earlier:

y = (10x + 25)/3

Substituting x = 2, we get:

y = (10(2) + 25)/3 = 15

Therefore, there are 15 blue counters in the bag.

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Answer:

151 tables

Step-by-step explanation:

If 1 table is used for 6 guests then for 901 guest we need to divide 901 by 6

901÷6= 150.15

Rounding of the answer 151 tables needed

The cost of producing 2000 bagels is $796.8.

To determine the cost of producing 2000 bagels, we need to plug in the value of x into the given equation and solve for C(x).
C(x) = 300 + 0.25x - 0.4(x/1000)^3
C(2000) = 300 + 0.25(2000) - 0.4(2000/1000)^3
C(2000) = 300 + 500 - 0.4(2)^3
C(2000) = 300 + 500 - 0.4(8)
C(2000) = 300 + 500 - 3.2
C(2000) = 796.8

Therefore, the cost of producing 2000 bagels is $796.8.

In general terms, profit is nothing more than revenues minus costs. This mathematically expressed is:

Profit = Revenues - Costs

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The measure of the angle N to the nearest degree for the given triangle is 23 degrees.

Degree and radian both serve as angles' units of measurement in geometry. Two radians (in radians) or 360° can be used to symbolise one whole anticlockwise rotation (in degrees). As a result, degree and radian can be compared as follows:

2π = 360°

The given triangle is an right triangle.

Using the trigonometric functions we can write the relation between the segments as:

Sin (N) = 1.5 / 3.9 = opposite/hypotenuse

N = arcsin (1.5 / 3.9)

N = 22.61 = 23 degrees.

Hence, the measure of the angle N to the nearest degree for the given triangle is 23 degrees.

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As per the perimeter, the length of the rectangular floor is 72 meters, and the breadth is 36 meters.

Now we can use the formula for the perimeter of a rectangle to write an equation in terms of x and solve for x.

Perimeter of the rectangle = 2(length + breadth)

Given that the perimeter is 216 m, we can substitute the values of length and breadth in terms of x to get:

216 = 2(2x + x)

Simplifying this equation, we get:

216 = 2(3x)

Dividing both sides by 2, we get:

108 = 3x

Solving for x, we get:

x = 36

Now that we have the value of x, we can use it to find the length and breadth of the rectangular floor.

Length = 2x = 2(36) = 72 m

Breadth = x = 36 m

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Answer:

y=mx+b

It's already in function notation. Unless you need to graph it or show it.

We can write the mean absolute deviation as -

1.63.

Absolute deviation or mean absolute deviation is the measure of how far a given data element is from a given mean value of the data.

Given is that Suzie's Desserts offers its customers 5 dessert options. The prices are: $5.00 $9.00 $9.00 $6.00 $6.00 $9.00 $9.00.

The formula for absolute deviation is -

[tex]$\frac {1}{n} \sum \limits_{i=1}^n |x_i-m(X)|[/tex]

We can calculate the mean as -

(5 + 9 + 9 + 6 + 6 + 9 + 9)/7 = 7.57

We can write the  absolute deviation as -

Absolute deviation =

1/7(5 - 7.57 + 9 - 7.57 + 9 - 7.57 + 6 - 7.57 + 6 - 7.57 + 9 - 7.57 + 9 - 7.57) = 1.63

Therefore, we can write the mean absolute deviation as -

1.63.

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Zero is an even number, but neither a prime number nor a composite number.

Prime numbers are numbers that are only divisible by one and itself, while composite numbers are numbers that are divisible by more than one and itself. Since zero is divisible by more than one and itself (zero, one, and two), it is neither prime nor composite.

As for odd and even numbers, odd numbers are any integer that is not divisible by two, while even numbers are any integer that is divisible by two. Since zero is divisible by two, it is an even number.

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The total number of trips between the zone: a. 1 and 6 is 10863 trips. b. 3 and 10 is 12617 trips. c. 5 and 10 is 11215 trips. d. 4 and 9 is 15560 trips.

To determine the total number of trips between the zones, we can simply do addition of the production/generation and attraction values for the two zones in question.  Based on the values in the table:

a. For zones 1 and 6, the total number of trips would be 3643 + 3040 + 2542 + 1638 = 10863 trips.

b. For zones 3 and 10, the total number of trips would be 3156 + 2535 + 3172 + 3754 = 12617 trips.

c. For zones 5 and 10, the total number of trips would be 2167 + 2122 + 3172 + 3754 = 11215 trips.

d. For zones 4 and 9, the total number of trips would be 3204 + 4217 + 3597 + 4542 = 15560 trips.

Therefore, the total number of trips between the zones are: a. 10863 trips between zones 1 and 6 b. 12617 trips between zones 3 and 10 c. 11215 trips between zones 5 and 10 d. 15560 trips between zones 4 and 9.

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Carlota's rate on a bicycle who is 74 miles away is approximately 6.1667 miles per hour.

Carlota's rate can be found by using the formula: rate = distance ÷ time. To find her rate for the first part of the trip, we can plug in the given values:

To find her rate for the second part of the trip, we need to subtract the distance and time she had already traveled from the total distance and time:

Then we can plug these values into the formula:

Since Carlota's rate is the same for both parts of the trip, we can simply use the overall distance and time to find her rate:

Therefore, Carlota's rate is approximately 6.1667 miles per hour.

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The value of the segments DB = 23.32 in, RK = 18.22 in and YK = 6.83 in.

The Pythagorean Theorem states that the square on the hypotenuse of a right triangle is equal to the sum of the squares on the triangle's legs.

The connection between the four edges of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem.

For the given figure we see the right triangle DHB.

Here, DH = 20 in and HB = 12 in.

Using the Pythagoras theorem we have:

DB² = DH² + HB²

DB² = 20² + 12²

DB² = 400 + 144

DB = 23.32

For the right triangle RHK we have:

HR = 16 and HK = 8.72

Using the Pythagoras theorem:

RK² = 16² + 8.72²

RK= 18.22

Also, KY = YK = 6.83 in.

Hence, the value of the segments DB = 23.32 in, RK = 18.22 in and YK = 6.83 in.

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The probability that there are not greater than 859 defective products in 359 packages is 0.9999.

We are given that;

Distribution: X 0 3 4 1 2 Р 0.02 0.14 0.34 0.36 0.14 1

0(X) = 0.9635 2

Now,

We need to know the probability of success for each package, which is the probability of having a defective product. Assuming that each product has an equal chance of being defective, we can calculate this probability by dividing the number of defective products by the number of products in a package. In this case, we have:

[tex]p = \frac{0.02 + 0.14 + 0.34 + 0.36 + 0.14}{4} = 0.25[/tex]

This means that each product has a 25% chance of being defective, and each package has a binomial distribution with n=4 and p=0.25.

To find the average and the standard deviation of the number of defective products in a package, we can use these formulas³:

[tex]$$E(X) = np$$$$\sigma(X) = \sqrt{np(1-p)}$$[/tex]

Plugging in the values of $n$ and $p$, we get:

[tex]$$E(X) = 4 \times 0.25 = 1$$$$\sigma(X) = \sqrt{4 \times 0.25 \times (1-0.25)} = \sqrt{0.75} \approx 0.866$$[/tex]

Therefore, the average number of defective products in a package is 1, and the standard deviation is 0.866.

To find the probability that there are not greater than 859 defective products in 359 packages, we need to use the binomial distribution again, but with different values of n and p. In this case, we have:

[tex]$$n = 359 \times 4 = 1436$$$$p = 0.25$$[/tex]

We want to find the probability that [tex]$X \leq 859$[/tex], where [tex]$X$[/tex] is the number of defective products in 1436 trials. We can use this formula:

[tex]$$P(X \leq k) = \sum_{i=0}^{k} \binom{n}{i}p^i(1-p)^{n-i}$$Plugging in the values of $n$, $p$, and $k$, we get:$$P(X \leq 859) = \sum_{i=0}^{859} \binom{1436}{i}0.25^i(1-0.25)^{1436-i}$$[/tex]

Therefore, by probability the answer will be 0.9999.

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The cost of the meal, including the 20% discount, 8% sales tax, and 15% tip, is $43.72.

Suppose a number is 'a'

Suppose another number is 'b'

We want to know how much percent of 'b' is 'a'.

Then, it is calculated as:

[tex]\dfrac{a}{b} \times 100[/tex]

(in percentage)

We are given that;

Items ordered= a 12 piece Grilled Tuscan Chicken Wings, Mozzarella

Fritta and Pan Sauteed Mussels.

Coupon percent off =20%

Sales tax= 8%

Waiter tip= 15%

Now,

Let's start by finding the cost of the appetizers and the pizza before any discounts or taxes are applied:

Grilled Tuscan Chicken Wings: let's assume this is $12

Mozzarella Fritta: let's assume this is $8

Pan Sauteed Mussels: let's assume this is $14

Craft Your Own Pizza: let's assume this is $10 for a small 2-topping pizza

So the total cost of the food before any discounts or taxes is:

$12 + $8 + $14 + $10 = $44

With the 20% coupon, we can apply a discount of:

0.2 x $44 = $8.80

So the new total before taxes is:

$44 - $8.80 = $35.20

Now we can calculate the sales tax on this amount:

0.08 x $35.20 = $2.82

Adding the sales tax to the discounted amount gives:

$35.20 + $2.82 = $38.02

Finally, we can calculate the total cost of the meal after adding the 15% tip:

$38.02 + 0.15 x $38.02 = $43.72

Therefore, by the given percentages the answer will be $43.72.

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The equation that can be used to determine the area of the glass is A = 2 1/2 x 4.

A rectangle is a 2-dimensional quadrilateral with four right angles. A rectangle has two diagonals of equal length which bisect each other. The sum of interior angles is 360 degree and opposite sides are parallel

The area of the rectangle is the product of the length and the width.

Area of a rectangle = length x width

A = 4 x 2 1/2

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The measure of Angle D in a parallelogram is 88 degrees.

Explain about parallelogram ?

A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length and parallel to each other. The opposite angles are also equal in measure.

Properties of a parallelogram:

According to the question:
Since EFDM is a parallelogram, we know that opposite angles are equal. Therefore,

Angle E = Angle M

Angle D = Angle F

We're given:

Angle E = 16x + 12

Angle D = 18x - 2

So we have:

Angle M = 16x + 12

Angle F = 18x - 2

The sum of the angles in a parallelogram is 360 degrees. Therefore, we have:

Angle E + Angle F + Angle D + Angle M = 360

Substituting the given values, we get:

(16x + 12) + (18x - 2) + (16x + 12) + (18x - 2) = 360

72x + 20 = 360

72x = 340

x = 5

Now we can find the values of Angle E, Angle D, Angle F and Angle M:

Angle E = 16x + 12 = 16(5) + 12 = 92 degrees

Angle D = 18x - 2 = 18(5) - 2 = 88 degrees

Angle F = Angle D = 88 degrees

Angle M = Angle E = 92 degrees

Therefore, the measure of Angle D is 88 degrees.

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The remainder when f(x) is divided by x-1 is 0.

Remainder Theorem states that given a polynomial function and a value for x, the remainder when the polynomial is divided by (x-a) is equal to the value of the polynomial when x=a. This theorem can be used to quickly and accurately find the remainder of a division problem, making it a very useful tool.

The remainder theorem states that if a polynomial f(x) is divided by x-a, then the remainder is f(a). In this case, we want to find the remainder when f(x) is divided by x-1. Therefore, we need to find f(1).

f(1) = 2(1)^(3) + 3(1)^(2) - 12(1) + 7
f(1) = 2 + 3 - 12 + 7
f(1) = 0

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Answer: I remember this question very well. I believe that the correct answer is 99.7%

68% of data falls between 15 and 25.

95% of data falls between 10 and 30.

99.7% of data falls between 5 and 35.

Answer:

Step-by-step explanation:

Here's the long division of (2x³ + 3x² + 4x + 2) ÷ (x + 2):

2x^2 - x + 6

x + 2 | 2x^3 + 3x^2 + 4x + 2

- (2x^3 + 4x^2)

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

- x^2 + 4x

- (- x^2 - 2x)

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

6x + 2

- (6x + 12)

--------

-10

Therefore, the quotient is 2x^2 - x + 6, and the remainder is -10.

The quotient represents the result of the division of the polynomial (2x³ + 3x² + 4x + 2) by the divisor (x + 2). In particular, the quotient 2x^2 - x + 6 represents the quadratic polynomial that, when multiplied by the divisor x + 2, gives the dividend 2x³ + 3x² + 4x + 2.

In other words, we have:

(2x³ + 3x² + 4x + 2) = (x + 2)(2x^2 - x + 6) - 10

The remainder -10 indicates that the division is not exact, and that there is a "leftover" term of -10 when we try to divide the polynomial (2x³ + 3x² + 4x + 2) by (x + 2).

Answer:

Let f be the number of foil balloons Lyla buys, and let t be the number of toy balloons she buys. Then, we can set up a system of linear equations based on the information given:

f + t = 30 (since Lyla buys a total of 30 balloons)

5.49f + 2.29t = 123.10 (since Lyla pays a total of $123.10 for the balloons)

To solve for f and t, we can use the substitution method. From the first equation, we can solve for t in terms of f:

t = 30 - f

Substituting this expression for t into the second equation, we get:

5.49f + 2.29(30 - f) = 123.10

Simplifying and solving for f, we get:

5.49f + 68.70 - 2.29f = 123.10

3.20f = 54.40

f = 17

So Lyla buys 17 foil balloons. We can substitute this value of f back into the first equation to solve for t:

17 + t = 30

t = 13

Therefore, Lyla buys 17 foil balloons and 13 toy balloons.