n arrangement for one container needs to have at least 4 flowers in it and the total wholesale cost must be less than $12. At wholesale, lilies cost $2 per flower and roses cost $3 per flower. If x is the number of lilies and y is the number of roses, which graph represents the system of inequalities for this scenario?

Answer:

76

Step-by-step explanation:

Answer:

the answer is 140

Step-by-step explanation:

my delta math said it was right lol

9514 1404 393

Answer:

  (b)  Congruent Figures

Step-by-step explanation:

Reflections, rotations, and translations are called "rigid transformations" because they do not change the size or shape of the figure. The image is always congruent to the original.

On the other hand, dilations change the size of the figure, so the image is not congruent with the original.

Rigid transformations result in congruent figures.

a) The data in ascending Order; -83/4 < -67/4 < -62/4 < -1/4.

b) Sea Grass is the furthest the Surface of water.

Numbers can be arranged in ascending order, from least value to highest value. The arrangement is left to right. Increasing order is another name for ascending order.

Given that -20 3/4, -15 1/2, -14 3/4, -1/4

Now, the above fraction into Normal fraction;

-83/4, -31/2, -67/4, -1/4.

Now, Arranging the data in ascending Order;

-83/4 < -67/4 < -62/4 < -1/4.

b) Since Sea Grass is the furthest below the Surface of water.

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Answer: x = -12/7

Step-by-step explanation:

\(-5x-\left(2x+3\right)=9\\-7x-3=9\\-7x-3+3=9+3\\-7x=12\\x=-\frac{12}{7}\)

Final Answer:

In-depth explanation:

Hi! The question is asking us to solve the equation:

\(\large\textbf{-5x - (2x + 3) = 9}\)

Distribute the minus:

\(\large\textbf{-5x - 2x - 3 = 9}\)

Move -3 to the right side, using the opposite operation:

\(\large\textbf{-5x - 2x = 9 + 3}\)

\(\large\textbf{-5x - 2x = 12}\)

Combine like terms

\(\large\textbf{-7x = 12}\)

Divide both sides by -7:

\(\large\textbf{x = -12/7}\)

\(\rule{350}{1}\)

Answer:

\((x+2)(x+3)\)

Step-by-step explanation:

⭐What does factorisation mean?

⭐What are factors?

Thus, we have to write \(x^2+5x+6\) in terms of its factors.

I have a picture attached to this response to show you how factorisation works, but I will also explain it here.

How to factorise:

The picture of factorisation is attached to this response.

⭐ if this response helped you, please mark it the "brainliest"!⭐

To achieve a 95% confidence interval with a maximum width of 6 years and a known population variance of 95, the newspaper needs a sample size of approximately 41 subscribers.

The formula for the width of a confidence interval for the population mean is given by:

\(\[ \text{Width} = \frac{Z \cdot \sigma}{\sqrt{n}} \]\)

where Z is the critical value corresponding to the desired confidence level (in this case, 95% confidence corresponds to a Z-value of approximately 1.96), σ is the population standard deviation (which is the square root of the known variance, in this case, √95), and n is the sample size.

Rearranging the formula to solve for n:

\(\[ n = \left(\frac{Z \cdot \sigma}{\text{Width}}\right)^2 \]\)

Plugging in the values, we get:

\(\[ n = \left(\frac{1.96 \cdot \sqrt{95}}{6}\right)^2 \]\[ n \approx 41 \]\)

Therefore, the sample size needed to achieve a 95% confidence interval with a maximum width of 6 years, given a known population variance of 95, is approximately 41 subscribers.

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The correct answer is d. 8, as it represents the greatest possible value for the integral of f(x) over the interval [0, 2].

Given that 2 ≤ f(x) ≤ 4 for all x in the interval [0, 2], we know that the function f(x) is bounded between 2 and 4 throughout the interval. To find the greatest possible value of the integral of f(x) over the interval [0, 2], we want to maximize the area bounded by the function and the x-axis.

Since the function is continuous and bounded, we can use the Fundamental Theorem of Calculus to find the integral. The integral of f(x) over the interval [0, 2] represents the area under the curve of f(x) between x = 0 and x = 2.

The maximum possible value of this integral occurs when the function is at its upper bound of 4 throughout the interval. Therefore, the greatest possible value of the integral is the area of the rectangle with a base of 2 (the width of the interval) and a height of 4, which is 2 * 4 = 8.

Hence, the correct answer is d. 8, as it represents the greatest possible value for the integral of f(x) over the interval [0, 2].

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Answer:

It's quite easy

Step-by-step explanation:

people less than 30 years = frequency of people 0 to 15 + 15 to 30 = 8+15 =23

Therefore there are 23 people less than 30 years old.

pls mark me as brainliest pls.

The number of ways to select 3 pages in ascending index order depends on the total number of pages available.

To find the number of ways to select 3 pages in ascending index order, we can use the concept of combinations . In combinatorics, selecting objects in a specific order is often referred to as permutations. However, since the order does not matter in this case, we need to consider combinations instead.

The number of ways to select 3 pages in ascending index order can be calculated using the combination formula. Since we are selecting from a set of pages, without replacement and order doesn't matter, we can use the formula C(n, k) = n! / (k!  (n-k)!), where n is the total number of pages and k is the number of pages we want to select.

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a) The set {1, 2, 3} does not represent vectors, but rather a collection of scalars. Therefore, there are no vectors in {1, 2, 3}.

b) The number of vectors in "col a" cannot be determined without additional context or information. "Col a" could refer to a column vector or a collection of vectors associated with a variable "a," but without further details, the exact number of vectors in "col a" cannot be determined.

c) Without knowing the specific context of "p" and "col a," it is impossible to determine if "p" is in "col a." The inclusion of "p" in "col a" would depend on the definition and properties of "col a" and the specific value of "p."

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Answer: Part A is (-9, 13) Part B is (9, 13)

Step-by-step explanation:

f(x) = -x² - 4x - 1 is the equation of the parabola in the graph.

From the graph, the parabola passes through point (-1,2) and has a vertex at point (-2,3).

For a parabola with a vertex (h,k), the general equation is expressed as;

y = a( x - h)² + k

First we find 'a', plug in the given coordinates into the equation.

y = a( x - h)² + k

2 = a( -1 - (-2))² + 3

Solve for a

2 = a( -1 + 2 )² + 3

2 = a( 1 )² + 3

2 = a + 3

a = 2 - 3

a = -1

Now substitute the vertex (-2,3 and a ( -1 ) into the general equation.

y = a( x - h)² + k

y = -1( x - (-2))² + 3

Simplify

y = -1( x + 2 )² + 3

Expand using FOIL method

y = -1( (x + 2)(x+2) ) + 3

y = -1( x² + 2x + 2x + 4 ) + 3

y = -1( x² + 4x + 4 ) + 3

Apply distributive property

y = -x² - 4x - 4 + 3

Add like terms

y = -x² - 4x - 1

f(x) = -x² - 4x - 1

Therefore, the equation of the graph is f(x) = -x² - 4x - 1.

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The answer is A: x = 22√3 / 2 and y = 11. We can simplify x by multiplying both the numerator and denominator by 2 to get x = 22√3.

A right-angle triangle is a type of triangle that has one angle that measures exactly 90 degrees (a right angle). This angle is formed where the two shorter sides of the triangle meet. The side opposite to the right angle is called the hypotenuse, while the other two sides are called the legs.

The Pythagorean theorem is a fundamental relationship that applies to right-angle triangles. It states that the sum of the squares of the two shorter sides (legs) of a right-angle triangle is equal to the square of the hypotenuse. In other words, a² + b² = c², where a and b are the lengths of the legs, and c is the length of the hypotenuse.

Right-angle triangles are commonly used in mathematics, physics, engineering, and many other fields. They can be used to solve problems related to distances, heights, and angles, and are a fundamental building block in many geometric constructions.

The special properties of right-angle triangles also make them useful in practical applications, such as in construction, where they can be used to measure angles and distances accurately, and in navigation, where they can be used to calculate distances between two points using trigonometric functions.

In triangle ABC, we know that angle BAC is 30 degrees, and angle ABC is a right angle. Therefore, angle ACB is 60 degrees (since the angles in a triangle add up to 180 degrees).

We can use the sine and cosine ratios to find the values of x and y. Using the definition of sine and cosine:

sin(30) = opposite / hypotenuse

cos(30) = adjacent / hypotenuse

In this case, AB is the adjacent side to angle BAC, and AC is the hypotenuse. Therefore:

cos(30) = AB / AC

Substituting the given values, we get:

cos(30) = x / y

Solving for x, we get:

x = y cos(30)

Plugging in y = 11, we get:

x = 11 cos(30)

Using a calculator, we can find that cos(30) = √3 / 2, so:

x = 11 × √3 / 2

x = 11√3 / 2

Therefore, the answer is A: x = 22√3 / 2 and y = 11. We can simplify x by multiplying both the numerator and denominator by 2 to get x = 22√3.

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The probability that the customer is a good risk is 0.70 and the probability that the customer is not a poor risk is 0.957.

To calculate the probability of the customer being a good risk, we need to divide the total number of good risk customers (7732) by the total number of customers (11,102). This gives us 7732/11102 = 0.7000. To calculate the probability of the customer not being a poor risk, we can subtract the total number of poor risk customers (949) from the total number of customers (11,102). This gives us 11102-949 = 10,153. We then divide this number by the total number of customers, giving us 10,153/11,102 = 0.9571. Therefore, the probability that the customer is a good risk is 0.70 and the probability that the customer is not a poor risk is 0.9571.

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The domain, range, relative maximum and minimum, the end behavior and the increasing as well as decreasing intervals are all represented below.

In the given function, we need to find the domain, range, relative maximum and minimum, the end behavior and the increasing as well as decreasing intervals.

The function;

f(x) = x⁴ - 4x³ + 3x² + 4x - 4

1. Domain: The domain of the function is all values along the x - axis

Domain = (-∞, ∞)

2. The range is the set of values that corresponds with the domain;

range : [(-9 + 6√3)/4, ∞)

3. The relative maximum of the function is; [(1 + √3)/2, - (9 - 6√3)/4]

4. The relative minimum of the function is  [(1 - √3)/2, - (9 - 6√3)/4]

5. The absolute minimum of the function does not exist

6. The end behavior of the function is "rises to the left and rises to the right"

7. The increasing and decreasing intervals are;  [(1 - √3)/2, (1 + √3)/2)], (2, ∞)

The decreasing interval is ;[-∞,  (1 - √3)/2],  [(1 + √3)/2, 2]

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Solving problems involving normal proportions requires careful attention to detail, as well as a good understanding of statistical concepts such as standardization and probability.

When solving a problem where you want to find normal proportions, you can follow the following steps:

Define the problem: Clearly define the problem you are trying to solve, including any relevant details such as the population, sample size, and the variable of interest.

Check assumptions: Check if the conditions for using normal distributions are met. The data should be continuous, the sample size should be large enough, and the distribution should be approximately normal.

Calculate the sample mean and standard deviation: If you are working with a sample, calculate the sample mean and standard deviation.

Standardize the data: Convert the data into standard normal distribution, by subtracting the mean from each observation and dividing by the standard deviation.

Determine the probability: Once the data has been standardized, you can use a standard normal distribution table or a calculator to determine the probability of the variable falling within a certain range or above/below a certain value.

Interpret the results: After determining the probability, interpret the results in the context of the problem. For example, you might conclude that there is a 95% chance that a randomly selected observation falls within a certain range, or that the variable of interest is higher than a certain value in 5% of cases.

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The linear equation doesn't have a solution.

The linear equation given is illustrated as: 4x-(2x-1) = x+5+x-6

This will be solved thus:

4x - 2x + 1 = x+5+x-6

4x - 2x + 1 = 2x - 1.

2x + 1 = 2x - 1

Collect like terms

2x - 2x = -1 - 1

0 = -2

This illustrates that the equation doesn't have a solution.

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Based on the given information, we know that the 95% confidence interval for the population mean falls between $5938.42 and $6546.32.

This means that if we were to repeat the sampling process many times and construct a confidence interval each time, about 95% of those intervals would contain the true population mean.

As for the hypothesis test with the null hypothesis (which is not specified in the question), we do not have enough information to determine the p-value. The confidence interval and hypothesis test are two different methods of statistical inference, and while they are related, they provide different types of information.

In order to determine the p-value for the hypothesis test, we would need to know the null hypothesis, the sample size, the sample mean, the standard deviation (or a good estimate of it), and the level of significance (alpha). With this information, we could calculate the test statistic and then use a t-distribution or z-distribution (depending on the sample size and whether the standard deviation is known) to find the p-value.

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The function h(0) when evaluated is 3

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

h(n) = 3(2)^n

Given that

h(0)

This means that

n = 0

Substitute the known values in the above equation, so, we have the following representation

h(0) = 3(2)^0

Evaluate

h(0) = 3

Hence, the value is 3

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Step-by-step explanation:

This graph

Have a nice day

Answer:

42,804.35 million people per miles

Step-by-step explanation:

Population density = Number of people / Land area

New York

Population = 8.55 million

Land area = 300 square miles

Manhattan

Population = 1.64 million

Land Area = 23 Square miles

Population density of New York = Number of people / Land area

= 8.55 million / 300 Square miles

= 8,550,000 / 300

= 28,500 people per square miles

Population density of Manhattan = Number of people / Land area

= 1.64 million / 23 miles

= 1,640,000 / 23

= 71,304.35 million people per square miles

Difference between Manhattan and new York City = 71,304.35 - 28,500

= 42,804.35 million people per miles

Therefore,

The population density of Manhattan is greater than that of New York City by 42,804.35 million people per miles

The difference between the population densities of Manhattan and New York is 42,804 people per square mile.

The density of New York is:

= Population / Area

= 8,550,000 / 300

= 28,500 people per square mile

Density of Manhattan:

= 1,640,000 / 23

= 71,304 people per square mile

The difference is:

= 71,304 - 28,500

= 42,804 people per square mile

In conclusion, Manhattan's population density is 42,804 people per square mile higher than New York City's.

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The minimum value of V occurs at x ≈ 0.93, which means that the volume of the box is smallest when the height is about 0.93 units.

To find the extreme values of V, we need to take the derivative of V and set it equal to zero. So, let's begin:

\(V(x) = x(10-2x)(16-2x)\)
Taking the derivative with respect to x:
\(V'(x) = 10x - 4x^2 - 32x + 12x^2 + 320 - 48x\)
Setting V'(x) = 0 and solving for x:
\(10x - 4x^2 - 32x + 12x^2 + 320 - 48x = 0\\8x^2 - 30x + 320 = 0\)
Solving for x using the quadratic formula:
\(x = (30 ± \sqrt{(30^2 - 4(8)(320))) / (2(8))\\x = (30 ± \sqrt{(1680)) / 16\\x = 0.93 or x =5.07\)
So, the extreme values of V occur at x ≈ 0.93 and x ≈ 5.07. To determine whether these are maximum or minimum values, we need to examine the second derivative of V. If the second derivative is positive, then the function has a minimum at that point. If the second derivative is negative, then the function has a maximum at that point. If the second derivative is zero, then we need to use a different method to determine whether it's a maximum or minimum.

Taking the second derivative of V:
V''(x) = 10 - 8x - 24x + 24x + 96
V''(x) = -8x + 106

Plugging in x = 0.93 and x = 5.07:
V''(0.93) ≈ 98.36 > 0, so V has a minimum at x ≈ 0.93.
V''(5.07) ≈ -56.56 < 0, so V has a maximum at x ≈ 5.07.

Now, to interpret these values in terms of the volume of the box, we need to remember that V(x) represents the volume of a box with length 2x, width 2x, and height x. So, the maximum value of V occurs at x ≈ 5.07, which means that the volume of the box is greatest when the height is about 5.07 units. The minimum value of V occurs at x ≈ 0.93, which means that the volume of the box is smallest when the height is about 0.93 units.

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a) The extreme values of V are:

Minimum value: V(0) = 0

Relative maximum value: V(3) = 216

Absolute maximum value: V(4) = 128

b) The absolute maximum value of V at x = 4 represents the case where the box has a square base of side length 4 units, height 2 units, and width 8 units, which has a volume of 128 cubic units.

a) To find the extreme values of V, we first need to find the critical points of the function. This means we need to find where the derivative of the function equals zero or is undefined.

Taking the derivative of V(x), we get:

\(V'(x) = 48x - 36x^2 - 4x^3\)

Setting this equal to zero and solving for x, we get:

\(48x - 36x^2 - 4x^3 = 0\)
4x(4-x)(3-x) = 0

So the critical points are x = 0, x = 4, and x = 3.

We now need to test these critical points to see which ones correspond to maximum or minimum values of V.

We can use the second derivative test to do this. Taking the derivative of V'(x), we get:

\(V''(x) = 48 - 72x - 12x^2\)

Plugging in the critical points, we get:

V''(0) = 48 > 0 (so x = 0 corresponds to a minimum value of V)
V''(4) = -48 < 0 (so x = 4 corresponds to a maximum value of V)
V''(3) = 0 (so we need to do further testing to see what this critical point corresponds to)

To test the critical point x = 3, we can simply plug it into V(x) and compare it to the values at x = 0 and x = 4:

V(0) = 0
V(3) = 216
V(4) = 128

So x = 3 corresponds to a relative maximum value of V.
b) In terms of the volume of the box, the function V(x) represents the volume of a rectangular box with a square base of side length x and height (10-2x) and width (16-2x).
The minimum value of V at x = 0 represents the case where the box has no dimensions (i.e. it's a point), so the volume is zero.
The relative maximum value of V at x = 3 represents the case where the box is a cube with side length 3 units, which has a volume of 216 cubic units.
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Given the system:

y = 3x + 4

y = 2x - 6

3x + 4 = 2x - 6

3x - 2x = -6 - 4

x = - 10

y = 3(-10) + 4

y = -26

(-10, - 26) one solution

Answer:

-5

Step-by-step explanation:

The given Laplace transform is\(:\[F(s)=\frac{9e^{-2s}}{s^2+81}\].\)To find the inverse Laplace transform, we need to convert it to a standard form.

Using partial fraction decomposition:\(\[\frac{9e^{-2s}}{s^2+81}=\frac{A}{s-9i}+\frac{B}{s+9i}\]\)Where \(A\) and \(B\) are constants.

Multiplying both sides by\(\((s-9i)(s+9i)\), we get:\[9e^{-2s}=A(s+9i)+B(s-9i)\]\)

Putting\(\(s=9i\), we have:\[9e^{-18i}=18Bi \Rightarrow B=-\frac{i e^{18i}}{2}\]\)

Putting \(s=-9i\), we have:\[9e^{18i}=-18Ai \Rightarrow A=\frac{i e^{-18i}}{2}\]\(\(s=9i\), we have:\[9e^{-18i}=18Bi \Rightarrow B=-\frac{i e^{18i}}{2}\]\)

Therefore, the Laplace transform becomes:\(\[\begin{aligned} F(s)&=\frac{9e^{-2s}}{s^2+81}\\ &=\frac{\frac{ie^{-18i}}{2}}{s+9i}-\frac{\frac{ie^{18i}}{2}}{s-9i}\\ &=\frac{i}{2}\left[\frac{e^{-18i}}{s+9i}-\frac{e^{18i}}{s-9i}\right]\end{aligned}\]\)

Taking the inverse Laplace transform, we have\(:\[f(t)=\frac{i}{2}\left[u(t-0)\left(e^{-18i}e^{9it}\right)-u(t-0)\left(e^{18i}e^{-9it}\right)\right]\]\)

Simplifying, we get:\(\[f(t)=\sin(9t)u(t)-\sin(9(t-0))u(t-0)\]\)

The inverse Laplace transform of \(\(F(s)\) is \(f(t)=\sin(9t)u(t)-\sin(9(t-0))u(t-0)\).\)

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The 12 months of age) as percentiles of the CDC growth chart reference population.

The most likely description of Sarah's weights (at 3, 6, 9, and 12 months of age) as percentiles of the CDC growth chart reference population is: 85th percentile at 3 months; 85th percentile at 6 months; 90th percentile at 9 months; 95th percentile at 12 months.What is percentile in statistics?In statistics, a percentile is a value below which a specific percentage of observations in a group falls. It is used to split up data into segments that represent an equal proportion of the entire group, resulting in a data set split into 100 equal portions, with each portion representing one percentage point. Sarah's weight is in the 85th percentile at 3 months, 85th percentile at 6 months, 90th percentile at 9 months, and 95th percentile at 12 months is a most likely description of her weights (at 3, 6, 9, and 12 months of age) as percentiles of the CDC growth chart reference population.

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Answer: A g (x)= [x+4]-2

Step-by-step explanation:

You can see the three points where the result is equal to an integer in the photo below. Good luck!

Answer:

1. a. b = - 8

b. x = 8

c. x = 11

d. x = 5

2. 12 soccer balls and 8 basketballs can be purchased.

Step by step explanation

a. \( - 14 + 6b + 7 - 2b = 1 + 5b\)

Calculate the sum

\( - 7 + 6b - 2b = 1 + 5b\)

Collect like terms

\( 7 + 4b = 1 + 5b\)

Move variable to L.H.S and change it's sign

Similarly, Move constant to R.H.S and change its sign

\(4b - 5b = 1 + 7\)

Collect like terms

\( - b = 8\)

Change the signs on both sides of the equation

\(b = - 8\)

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

b. \( \frac{5x + 10}{ - 6} = - 5\)

Apply cross product property

\(5x + 10 = - 5 \times ( - 6)\)

Multiply the numbers

\(5x + 10 = 30\)

Move constant to R.H.S and change its sign

\(5x = 30 - 10\)

Calculate the difference

\(5x = 20\)

Divide both sides of the equation by 5

\( \frac{5x}{5} = \frac{20}{5} \)

Calculate

\(x = 4\)

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

c. \( - 15 = \frac{ - 8x - 17}{7} \)

Apply cross product property

\( - 15 \times 7 = - 8x - 17\)

Multiply the numbers

\( - 105 = - 8x - 17\)

Swap the sides of the equation

\( - 8x - 17 = - 105\)

Move constant to R.H.S and change its sign

\( - 8x = - 105 + 17\)

Calculate

\( - 8x = - 88\)

Change the signs on both sides of the equation

\(8x = 88\)

Divide both sides of the equation by 8

\( \frac{8x}{8} = \frac{88}{8} \)

Calculate

\(x = 11\)

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

D. \(5 = 6x + 5(x - 10)\)

Distribute 5 through the parentheses

\(5 = 6x + 5x - 50\)

Collect like terms

\(5 = 11x - 50\)

Swap both sides of the equation

\(11x - 50 = 5\)

Move constant to R.H.S and change its sign

\(11x = 5 + 50\)

Calculate the sum

\(11x = 55\)

Divide both sides of the equation by 11

\( \frac{11x}{11} = \frac{55}{11} \)

Calculate

\(x = 5\)

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

2.

Solution,

No.of students in soccer = x

No.of students in basketball = y

Total no.of students = 20

i.e x + y = 20 → equation ( i )

Cost of soccer ball = $ 7

Cost of basketball = $ 10

Total budget = $ 164

i.e 7x + 10 y = 165 → equation ( ii )

In equation ( i ),

x + y = 20

Move 'y' to R.H.S and change its sign

x = 20 - y

Put the value of x in equation ( i )

\(7(20 - y) + 10y = 164\)

\(140 - 7y + 10y = 164\)

\(3y = 164 - 140\)

\(3y = 24\)

\(y = \frac{24}{3} \)

\(y = 8\)

Now, put the value of y in equation ( i ) ,

x + y = 20

\(x + 8 = 20\)

\(x = 20 - 8\)

\(x = 12\)

Hence, 12 soccer balls and 8 basketballs can be purchased.

Hope this helps...

Best regards!!

Answer:

1. b = -8

2. x = 8

3. x = 11

4. x = 5

hope that helpwd