Complete the recursive formula of the arithmetic sequence -16, -33, -50, -67,. −16,−33,−50,−67,. Minus, 16, comma, minus, 33, comma, minus, 50, comma, minus, 67, comma, point, point, point. C(1)=c(1)=c, left parenthesis, 1, right parenthesis, equals
c(n)=c(n-1)+c(n)=c(n−1)+c, left parenthesis, n, right parenthesis, equals, c, left parenthesis, n, minus, 1, right parenthesis, plus

The system of inequalities of the company with the better offer is 75 + 20x ≤ y and 15 + 65x ≤ y

Let's use A to represent the total cost (in dollars) of purchasing a pool membership from the Aquatics Club,

Let S represent the total cost of purchasing a pool membership from the Swimming Hole.

Then we can write the following system of inequalities:

A = 75 + 20x (total cost of Aquatics Club membership)

S = 15 + 65x (total cost of Swimming Hole membership)

Alfonso has no more than y dollars to spend

So, we have

75 + 20x ≤ y

15 + 65x ≤ y

Hence, the system is 75 + 20x ≤ y and 15 + 65x ≤ y

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Answer: 72°

Step-by-step explanation:

To find the interior angle of this shape, use the formula 180(n-2)/n, where n is the amount of sides. Plugging 5 in for the interior angle of a pentagon, you get 180(3)/5, or 108°.

Using the statement that PR intersects QS, we can see that triangle QOR is isosceles (to get this, look at triangle PQR, and note that because it has 2 equal side lengths, and its last length is not equivalent to the other 2 sides, it is isosceles). Solving for angle PRQ, we know one angle is 108°, and the other two are equal. The total angle in a triangle is 180°, so (180°-108°)/2 = 36° (angles QPR and PRQ).

Since the angle of R = 108°, we can find angle PRS as 108° - 36°, or 72°. Since triangles PQR and QRS are similar (share the same angles and side lengths), we can see that angle RQS and RSQ are both 36°.

Since ORS is a triangle, its angle total is 180°. Since we know the angles ORS and OSR (respectively) already as 72° and 36°, we can subtract these angles to find angle ROS. 180°-72°-36° = 72°

In conclusion, we can prove that[tex](A -B) U (A C)[/tex] is a superset of[tex]A - (B nC)[/tex] using both the choose-an-element method and the algebra of sets.

To answer this question, let's first draw two Venn diagrams to represent the sets A, B, and C. In the first Venn diagram, shade the region that represents[tex]A - (B nC)[/tex].

This is the region outside of the intersection of B and C and inside of A. In the second Venn diagram, shade the region that represents [tex](A -B) U (A C).[/tex] This is the union of the region outside of B and the region outside of C, both of which are inside of A. Based on these diagrams, we can make the conjecture that (A -B) U (A C) is a superset of A - (B nC).

To prove this conjecture, we can use the choose-an-element method. Let a be an element of A - (B nC). This means that a is in A, but not in B or C. Since a is in A, it is also in (A -B) U (A C), and therefore (A -B) U (A C) is a superset of A - (B n C).

We can also use the algebra of sets to prove this conjecture.[tex]A - (B n C) = (A -B) U (A -C) since A - (B n C)[/tex]is the union of the regions outside of B and outside of C, both of which are inside of A. This implies that (A -B) U (A C) is a superset of A - (B nC).

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Answer: To convert the given equation, √y = (6/p)x - (2/q), into the linear form y = mx + c, we can use the following steps:

Square both sides of the equation to eliminate the square root:

√y = (6/p)x - (2/q)

√y^2 = (6/p)x - (2/q)^2

Simplifying the right-hand side, we get:

y = (36/p^2)x - (4/q) + 4/q^2

Rearrange the equation to the form y = mx + c:

y = (36/p^2)x + (4/q^2 - 4/q)

So the linear form of the given non-linear equation is y = (36/p^2)x + (4/q^2 - 4/q).

Step-by-step explanation:

The system has infinitely many solutions, which can be written as (x, y, z) = (1 - 60s, -10 + 600s, s) where s is a parameter.

To solve the system of equations:

1x + 0y + 60z = 1

1x + 10y + 0z = 0

0x + 0y + 0z = 0

The third equation is an identity, implying that it does not give us any new information. The first two equations can be used to solve for x, y, and z:

From the first equation, we get x = 1 - 60z

From the second equation, we get y = 0 - 10x = -10(1 - 60z) = -10 + 600z

Therefore, the solution to the system can be written as a point in terms of z as:

(x, y, z) = (1 - 60z, -10 + 600z, z)

Since z can take on any value, there are infinitely many solutions to the system, which can be parameterized as:

(x, y, z) = (1 - 60s, -10 + 600s, s) where s is a parameter.

he system has infinitely many solutions, which can be written as (x, y, z) = (1 - 60s, -10 + 600s, s) where s is a parameter.

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When performing a hypothesis test based on a 95% confidence level, the chances of making a type II error are 5%.

The process of hypothesis testing is used to determine whether or not a given statistical hypothesis is valid. The objective of this method is to determine whether the null hypothesis can be accepted or rejected based on the sample data obtained.

Hypothesis testing can be used to evaluate two hypotheses. The null hypothesis is the one that must be accepted or rejected, while the alternative hypothesis is the one that must be supported. In other words, hypothesis testing is a way of determining whether the null hypothesis is reasonable or not.

The Type II error is defined as the error that occurs when the null hypothesis is not rejected even though it is incorrect. In hypothesis testing, this type of error is referred to as a beta error or a false-negative error. The chances of making a Type II error depend on several factors, including the sample size, the level of significance, and the power of the test. When the level of significance is lowered to 0.05, the chances of making a Type II error are 5%.

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P(0 received correctly) = P(0 sent) × P(0 received correctly | 0 sent)= [tex](2/3) × 0.8= 0.5333[/tex] (rounded to 1 decimal place)Thus, the probability that a 0 is received is 0.5333 (rounded to 1 decimal place).

0.5333

A space probe near Neptune communicates with Earth using bit strings. Suppose that in its transmissions it sends a 1 one-third of the time and a 0 two-thirds of the time. When a 0 is sent, the probability that it is received correctly is 0.8 and the probability that it is received incorrectly (as a 1) is 0.2. When a 1 is sent the probability that it is received correctly is 0.8 and the probability that it is received incorrectly (as a 0) is 0.2.The probability that a 0 is received correctly is given in the problem as 0.8, and the probability that a 0 is sent is 2/3. Therefore, the probability that a 0 is received correctly

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The slope between the points (-3, 0) and (0, -1) is -1/3.

The slope of a line serves as a gauge for its steepness. It may be calculated by dividing the difference in y-coordinate by the difference in x-coordinate between any two points on a line. A line's slope might be zero, positive, negative, or undefinable. A line with a positive slope is moving upward from left to right, a negative slope is moving downward from left to right, and a line with a zero slope is level. The line is vertical if the slope is undefinable.

Let us consider the first two points (-3, 0) and (0, -1).

The slope of the line is given as:

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

Substituting the values we have:

m = (-1 - 0) / (0 - (-3)) = -1/3

Hence, the slope between the points (-3, 0) and (0, -1) is -1/3.

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Using  the substitution method, the solution of the system of equations -4x + y = 3 and 5x - 2y = -9 is (x, y) = (1, 7)

We can solve this system of equations using the substitution method by solving for one variable in terms of the other in one equation, and then substituting that expression into the other equation. Here's how:

-4x + y = 3 (Equation 1)

5x - 2y = -9 (Equation 2)

Solving Equation 1 for y, we get:

y = 4x + 3

Now, we substitute this expression for y into Equation 2 and solve for x:

5x - 2(4x + 3) = -9

5x - 8x - 6 = -9

-3x = -3

x = 1

We have found the value of x to be 1. Now, we substitute this value back into Equation 1 to find the value of y:

-4(1) + y = 3

y = 7

Therefore, the solution to the system of equations is (x, y) = (1, 7)

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Parachutist's rate during free fall is 40 meters per second and will fall approximately 490 meters during 10 seconds of free fall.

First, we need to convert 132 feet per second to meters per second. We know that 1 meter is equal to 3.3 feet, so we can use the following conversion factor:

[tex]$\frac{3meter}{3.3 feet}[/tex]

To convert feet per second to meters per second, we can multiply by the conversion factor:

[tex]132 (\frac{1}{3.3} ) = 40 meters/second[/tex]

Therefore, the parachutist's rate during free fall is 40 meters per second.

Next, we can use the following formula to find the distance the parachutist falls during 10 seconds of free fall:

distance =[tex]\frac{1}{2}[/tex] * acceleration * time²

where acceleration due to gravity is approximately 9.8 meters/second^2.

Substituting the given values, we get:

distance = [tex]\frac{1}{2}[/tex] * 9.8 meters/second² * (10 seconds)²

distance = 490 meters

Therefore, the parachutist will fall approximately 490 meters during 10 seconds of free fall.

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Answer: Yes Sofia will have enough money

=======================================================

Explanation:

Refer to the drawing below. I've split the hexagon into two pieces. The bottom is a rectangle and the top is a trapezoid.

The area of the rectangle is 16*7 = 112 square meters.

The trapezoid has 16 as one of the parallel sides. The other side is x meters. We'll use the perimeter 54 to determine what x must be

sum of the exterior sides = perimeter

6+7+16+7+6+x = 54

42+x = 54

x = 54-42

x = 12

The top most side is 12 meters. This is the missing side of the trapezoid. The hexagon has a height of 12.66 meters, so the trapezoid's height must be 12.66-7 = 5.66 meters. Refer to the blue segment I marked in the drawing below.

area of the trapezoid = 0.5*height*(base1+base2)

area = 0.5*5.66*(16+12)

area = 79.24 square meters

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

Recap so far

The total area of the entire hexagon is therefore 112+79.24 = 191.24 square meters.

Let's convert that to square decimeters.

Recall that 1 decimeter = 10 centimeters

Multiply both sides by 10

1 decimeter = 10 centimeters

10*(1 decimeter) = 10*(10 centimeters)

10 decimeters = 100 centimeters

10 decimeters = 1 meter

Then,

[tex]191.24 \text{ sq m}= 191.24 \text{ sq m} * \frac{10 \text{ dm}}{1 \text{ m}} * \frac{10 \text{ dm}}{1 \text{ m}}\\\\= \frac{191.24*10*10}{1*1} \text{ sq dm}\\\\= 19124 \text{ sq dm}\\\\[/tex]

The entire lawn is 19124 square decimeters.

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

We have one final block of calculations to determine the total price.

x = number of rolls

1 roll covers 90 square decimeters

x rolls cover 90x square decimeters

90x = 19124

x = 19124/90

x = 212.489 approximately

Round up to the nearest integer to get x = 213. It doesn't matter that 212.489 is closer to 212. We round up to clear the hurdle. It means we'll have leftover grass that isn't used (perhaps it could be handy to have some back up grass just in case mistakes are made, and some patches need to be redone).

In short, Sofia needs 213 rolls.

1 roll costs $4.50

213 rolls will cost 213*4.50 = 958.50 dollars.

This is under the $1000 threshold (with 1000-958.50 = 41.50 dollars to spare).

Sofia will have enough money to pay for all of the grass.

Let n be a positive integer. We can use the properties of modular arithmetic to calculate this remainder. Let's start with a = (32n + 4)-1 mod 9. We can rewrite this as a = 9 - (32n + 4)-1 because 9 = 0 mod 9.

We can use Fermat's Little Theorem to calculate (32n + 4)-1. This theorem states that (32n + 4)-1 mod 9 = (32n + 4)8 mod 9.

Using the identity (a + b)n mod m = ((a mod m) + (b mod m))n mod m, we can simplify the equation to (32n mod 9 + 4 mod 9)8 mod 9.

32n mod 9 = 0, so (32n mod 9 + 4 mod 9)8 mod 9 = 48 mod 9 = 1.

Finally, a = 9 - 1 = 8 mod 9, so the remainder when a is divided by 9 is 8.

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The Area of Bella's garden as required to be determined in the task content is the difference of the area of the rectangular backyard and the right triangular fish pond.

It follows from the task content that the area of Bella's trapezoidal garden is to be determined from the given information.

Since the garden and the fish pond are from the rectangular backyard; the sum of their areas is equal to the area of the backyard.

Ultimately, the area of the garden is the difference of the area of the rectangular backyard and the right triangular fish pond.

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Since both terms are perfect squares, factor using the difference of squares formula, [tex]a^2-b^2=(a+b)(a-b)[/tex] where [tex]a=b[/tex] and [tex]b=3[/tex]

Answer: y is equal to 8

Step-by-step explanation:

by substituting the x for its vale of three we can add the two values to get 8 or y=8

By answering the presented question, we may conclude that I used the following procedures to produce this graph.

Mathematicians use graphs to visually display or chart facts or values in order to express them coherently. A graph point usually represents a connection between two or more items. A graph, a non-linear data structure, is made up of nodes (or vertices) and edges. Glue the nodes, also known as vertices, together. This graph contains vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical graphs (bar graphs, pie graphs, line graphs, and so on) are graphical representations of exponential development. a logarithmic graph shaped like a triangle.

I used the following procedures to produce this graph:

I classified the personnel as full-time, part-time, and temporary.

I estimated the proportion of employees who assessed the company's work-life balance as "very good" or "excellent" for each employee category, as well as the percentage who rated it as "good" or "fair/poor."

I used the following procedures to produce this graph:

I classified the personnel as full-time, part-time, and temporary.

I estimated the proportion of employees who assessed the company's work-life balance as "very good" or "excellent" for each employee category, as well as the percentage who rated it as "good" or "fair/poor."

I made the segmented bar graph using these percentages.

The graph was made using Excel technology. You may make a similar graph with Excel or any other software that supports segmented bar graphs.

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Answer:

b = [tex]\frac{S-2la}{h+l}[/tex]

Step-by-step explanation:

S = bh + lb + 2la ( reversing the equation )

bh + lb + 2la = S ( subtract 2la from both sides )

bh + lb = S - 2la ← factor out b from each term on the left side

b(h + l) = S - 2la ← divide both sides by (h + l)

b = [tex]\frac{S-2la}{h+l}[/tex]

The value of x that makes the average between 3.15 and x equal to 40 is 76.85.

In this problem, we are given two numbers, 3.15 and x, and told that the average between them is 40. We can set up an equation to solve for x as follows:

(3.15 + x) / 2 = 40

To find the average between 3.15 and x, we add the two numbers together and divide by 2, which gives us the equation above.

To solve for x, we can start by multiplying both sides of the equation by 2:

3.15 + x = 80

Next, we can subtract 3.15 from both sides of the equation:

x = 76.85

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Answer:

If the tires on Mavis’ car have to be replaced when they each have 160 000 km of wear, then the total distance Mavis can drive on a set of tires is:

4 tires * 160,000 km = 640,000 km

If Mavis drives 25,000 km in a year, she will need to replace her tires after:

640,000 km ÷ 25,000 km/year = 25.6 years

Since Mavis will need to replace her tires once every 25.6 years, the cost of the wear on her tires for a single year is:

$140.00/tire * 4 tires = $560.00

So the total cost of the wear on Mavis’ tires for a year in which she drives 25,000 km is $560.00.

Step-by-step explanation:

source: trust me bro

To estimate the distance traveled  we need to find the area under the velocity-time graph from 0 to 8 seconds So,The estimate for the distance the car traveled for the first 8 seconds is 4000 meters.

A velocity-time graph is a graphical representation that shows the velocity of an object on the y-axis and time on the x-axis. It is used to depict the change in velocity over time and can provide information about the acceleration or deceleration of an object.

The height of each strip can be estimated by taking the average of the velocities at the beginning and end of the strip.

Using the trapezium rule, the estimated area of each strip is:

Strip 1: 0.5 x (0 + 2) x (0 + (-500)) = -500 m/s

Strip 2: 0.5 x (2 + 4) x (-500 + (-1000)) = -1500 m/s

Strip 3: 0.5 x (4 + 6) x (-1000 + (-500)) = -1500 m/s

Strip 4: 0.5 x (6 + 8) x (-500 + 0) = -500 m/s

The total estimated area is the sum of the areas of the 4 strips:

Total estimated area = -500 + (-1500) + (-1500) + (-500) = -4000 m/s

Since the area represents the distance traveled by the car, we can take the absolute value of the area to get the estimated distance traveled:

Estimated distance traveled is = |-4000| = 4000 meters

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The total number of ways of selecting the committee is, therefore,40 x 39 x 38 x 37= 7,903,040

A class of 40 students select a committee from the class that consists of a president, a vice president, a treasurer, and a secretary in the following way:Step-by-step explanation:The number of ways that a class of 40 students can choose a committee consisting of a president, vice president, treasurer, and a secretary can be found by using the permutation formula.If we assume that the positions of the committee members are different, the number of ways can be calculated as follows:The number of ways of selecting the president from 40 students is 40.The number of ways of selecting the vice president from the remaining 39 students is 39.The number of ways of selecting the treasurer from the remaining 38 students is 38.The number of ways of selecting the secretary from the remaining 37 students is 37.The total number of ways of selecting the committee is, therefore,40 x 39 x 38 x 37= 7,903,040Thus, secretary.

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The coordinates of the point P is (-1,2) .

What is translation?

In mathematics, a translation is a geometric transformation that moves every point of a figure or a space by the same amount in a given direction. The amount and direction of the movement can be described using a vector, which is a mathematical object that has both magnitude and direction.

Finding the coordinates of the point P :

The coordinates of point P can be found by subtracting the vector from point Q.

To find the coordinates of point P, we need to subtract the vector [tex]\begin{pmatrix}4\\-3\end{pmatrix}[/tex] from the coordinates of point Q, which are (3, -1).

Subtracting the x-coordinate of the vector from the x-coordinate of point Q gives us:

3 - 4 = -1

Similarly, subtracting the y-coordinate of the vector from the y-coordinate of point Q gives us:

-1 - (-3) = 2

Therefore, the coordinates of point P are (-1, 2).

So, the correct answer is (C) (-1, 2).

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Answer:

y-intercept is (0,3) and the slope is 3

Step-by-step explanation:

Answer: the slope is 3x while 3 is the y-intercept.

Step-by-step explanation:

(a) Point estimate (mean difference): 2.2 tomatoes. (b) The standard deviation of differences: Approximately 3.47. (c) The test statistic: Approximately 1.38.

To perform a t-test for the population mean difference, follow these steps:

(a) Calculate the point estimate (mean difference): The point estimate is the mean difference between the yields of fertilizer A and fertilizer B.

Mean difference = (Sum of differences) / Number of pairs

Using the given data gives:

Mean difference = ((7-4) + (6-7) + (5-6) + (8-5) + (10-3)) / 5

Subtracting gives:

Mean difference = (3 - 1 - 1 + 3 + 7) / 5

Solving gives:

Mean difference = 11 / 5

Dividing gives:

Mean difference = 2.2

(b) Calculate the standard deviation of the differences:

To calculate the standard deviation of the differences, we need to calculate the squared differences, find their sum, divide by (n-1), and then take the square root.

Squared differences:[tex](3 - 2.2)^2, (-1 - 2.2)^2, (-1 - 2.2)^2, (3 - 2.2)^2, (7 - 2.2)^2[/tex]

Solving gives:

Sum of squared differences = (0.64 + 12.96 + 12.96 + 0.64 + 21.16)

Solving gives:

The sum of squared differences = 48.36

The standard deviation of the differences [tex]= \sqrt{48.36 / 4}[/tex]

Solving gives:

The standard deviation of the differences [tex]= \sqrt{2.09}[/tex]

Rounded to three decimal places

The standard deviation of the differences ≈ 3.47

c) Calculate the test statistic:

The test statistic (t) = (Point estimate - Null hypothesis value) / (Standard deviation /√(sample size))

Let's assume the null hypothesis is that there is no difference between the two fertilizers

(i.e., mean difference = 0).

[tex]t = (2.2 - 0) / (3.47 / \sqrt5)[/tex]

Substituting [tex]\sqrt 5 = 2.236[/tex]

t = 2.2 / (3.47 / 2.236)

Rounded to two decimal places

t ≈ 1.378

So, the test statistic is approximately 1.378.

The gardener can compare this test statistic to critical values from the t-distribution to determine whether the difference between the two fertilizers is statistically significant at a certain significance level. If the calculated test statistic is greater than the critical value, she ma

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When the function d(x) = -x +(-3), then the value of d(0) is -3

In mathematics, a function is a relationship between two sets of numbers, called the domain and range. A function assigns each element of the domain to exactly one element of the range.

In the given problem, we are given a function d(x)=-x-3. The notation d(0) represents the value of the function d(x) when x = 0.

To find d(0), we need to substitute x = 0 in the function d(x)=-x-3, which gives:

d(0) = -(0) - 3

The first term -(0) is equal to zero, and the second term -3 is a constant value that remains the same regardless of the value of x. Therefore, we can simplify the expression as

d(0) = -3

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Probability that X = 5:Since, Joe selects only 4 bags of lettuce. X can't be 5.P(X=5) = 0Hence, the probability that X = 0 is 0.3164 and the probability that X = 5 is 0.

The given problem can be solved using the concept of binomial distribution.

In the given question, there are 48 bags of lettuce out of which 12 bags are contaminated with listeria.

Joe selects 4 bags of lettuce. X is the random variable which represents the number of contaminated bags of lettuce selected by Joe. X can take values from 0 to 4. (as Joe selects only 4 bags).

Part A)Number of ways to select 4 bags of lettuce out of 48:This can be solved using the concept of combinations. The formula to calculate the number of combinations is[tex]:nCr = n! / r!(n-r)![/tex]Here, n = 48 and r = 4.

Number of ways = 48C4 = 194,580

Part B)Probability that X = 0:This can be calculated using the formula for the binomial distribution :

[tex]P(X = r) = nCr * p^r * q^(n-r)[/tex]

Here, p = probability of selecting contaminated bag = 12/48 = 0.25q = probability of selecting non-contaminated bag = 1-0.25 = 0.75Also, n = 4 and r = [tex]0P(X=0) = 4C0 * 0.25^0 * 0.75^4= 0.3164[/tex]

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He bought 4.29 Kilos of fruit.

4+0.29=4.29

Luke bought 4.29 kilograms of fruit in all

Step-by-step explanation:

Simple addition will be used to find the total fruit Luke bought.

Given

Amount of apples he bought  = 4 kilograms

Amount of oranges he bought = 0.29 kilograms

so the total fruit will be:

[tex]\text{total fruit}=\text{Apples}+\text{oranges}[/tex]

[tex]=4+0.29[/tex]

[tex]=4.29[/tex]

So,

Luke bought 4.29 kilograms of fruit in all

Keywords: Measurement, addition

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The zeroes of the function are -12 and 5.

Zeros of a function are the values of the input variables that make the output of the function equal to zero. The zeros are the solutions of equation f(x) = 0.

According to the question:

To find the zeros of the function

f(x) = x² + 7x - 60, we must set f(x) equal to zero and solve for x.

So we start with the equation:

x² + 7x - 60 = 0

Next, we need to factor the left side of the equation. We are looking for two numbers that multiply to -60 and add to 7. After some trial and error, we find that the numbers are 12 and -5:

x² + 7x - 60 = (x + 12)(x - 5) = 0

Now we can apply the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero. Therefore, we set each factor equal to zero and solve for x:

x + 12 = 0 or x - 5 = 0

Solving for x, we get:

x = -12 or x = 5

The zeros of the function f(x) = x² + 7x - 60 are therefore x = -12 and x = 5.

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Answer:153

Step-by-step explanation: