Produce an equivalent equation for f(x)=7(x-60)-28 to reveal the y-intercept for the function. What is the y-intercept?

The function  [tex]f(x)=(x-5)(x-2)(x+1)[/tex] represents the graph.

What is graph?

A graph is a visual representation of data or a mathematical function, usually plotted on a coordinate plane. It is a way to display information in a clear and concise manner, making it easier to analyze and interpret.

From the graph, it can be observed that the function intersects the x-axis at three points, namely x=-1, 2, and 5. Therefore, these values are considered to be the zeros of the function.

According to the definition, if c is a zero of a function f(x), then (x-c) is a factor of f(x). Applying this definition, we can infer that (x+1), (x-2), and (x-5) are the factors of the given function.

In summary, the zeros of the function are -1, 2, and 5, and the corresponding factors of the function are (x+1), (x-2), and (x-5).

Therefore the function  [tex]f(x)=(x-5)(x-2)(x+1)[/tex] represents the graph.

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It is not always true that if two fractions have the same numerator, then the fraction with the greater denominator is the greater fraction.

The statement that if two fractions have the same numerator, then the fraction with the greater denominator is the greater fraction is not always correct. This is because the value of a fraction is determined by both its numerator and denominator, and if the denominators of two fractions with the same numerator are different, then the fractions are not directly comparable.

Consider the fractions 3/4 and 3/5. Both have a numerator of 3, but the denominator of the first fraction is greater than the denominator of the second fraction. However, 3/5 is actually the greater fraction because it represents a larger portion of the whole.Consider the fractions 5/7 and 5/9. Both have a numerator of 5, but the denominator of the second fraction is smaller than the denominator of the first fraction. Therefore, 5/7 is the greater fraction because it represents a larger portion of the whole.

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For any value of inequality for t less than or equal to 5 minutes, Routine #1 will burn at most as many calories as Routine #2.

What is inequality?

In mathematics, an inequality is a statement that compares two quantities using symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "!=" (not equal to).

Let's start by calculating the total number of calories burned in each routine as a function of the number of minutes spent running:

Routine #1:

Total calories burned = 24 + 15.5t

Routine #2:

Total calories burned = 52 + 9.9t

To find the point where Routine #1 burns at most as many calories as Routine #2, we need to solve the inequality:

24 + 15.5t ≤ 52 + 9.9t

Simplifying this inequality, we get:

5.6t ≤ 28

Dividing both sides by 5.6, we get:

t ≤ 5

Therefore, for any value of t less than or equal to 5 minutes, Routine #1 will burn at most as many calories as Routine #2.

So the answer is: t ≤ 5.

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Answer:

Yes, I can find the absolute value of -3 2/3.

The absolute value of a number is the distance of the number from zero on the number line. It is always a positive number.

To find the absolute value of -3 2/3, we need to ignore the negative sign and just look at the magnitude of the number.

So, the absolute value of -3 2/3 is:

|-3 2/3| = 3 2/3

Therefore, the absolute value of -3 2/3 is 3 2/3.

Johnny read 30 pages on Monday. On Tuesday he read 1/8 of the book. On Wednesday he read the remaining 1/4. How many pages did he read in total?To find out how many pages Johnny read in total, we need to first determine the total number of pages in the book. We know that he read 1/8 of the book on Tuesday and the remaining 1/4 on Wednesday. So we can add these two fractions to find out the total fraction of the book that he read:1/8 + 1/4 = 3/8Now we know that Johnny read 3/8 of the book. We can use this information to set up a proportion to find out how many pages he read in total:3/8 = x/total number of pagesTo solve for x, we can cross-multiply and simplify:3/8 * total number of pages = xMultiply both sides by 8/3:total number of pages = x * 8/3Now we need to find out what x is. We know that Johnny read 30 pages on Monday, which is 1/8 of the total number of pages. So we can use this information to set up another proportion:1/8 = 30/total number of pagesTo solve for the total number of pages, we can cross-multiply and simplify:1/8 * total number of pages = 30Multiply both sides by 8:total number of pages = 240Now we can substitute this value for the total number of pages in our previous equation to find out how many pages Johnny read in total:total number of pages = x * 8/3240 = x * 8/3Multiply both sides by 3/8:x = 90Therefore, Johnny read a total of 30 + 90 = 120 pages.

The equation used to obtain the probability of a number less than 4 on the spinner is given as follows:

P(less than 4) = number of regions with numbers that are less than 4/ total number of regions in the spinner.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The outcomes for this problem are given as follows:

Hence the probability is calculated as follows:

P(less than 4) = number of regions with numbers that are less than 4/ total number of regions in the spinner.

The problem asks for the probability of spinning a number less than 4 on the spinner.

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Answer:

Answer and Explanation: The symmetric bell shape of the normal curve implies that the skewness of the distribution of the data is 0, and most of the observation is located at the middle of the distribution. The shape of the normal distribution is not positive and negative skewed, the shape seems to be bell-shaped.

HOPE THIS HELPS!

Answer: 24

Step-by-step explanation:

Write out problem using Pythagorean Theorem: [tex]7^2+x^2=(x+1)^2[/tex]

Simplify and expand right side: [tex]49+x^2=x^2 + 2x + 1[/tex]

Subtract [tex]x^2[/tex] from both sides: [tex]49 = 2x + 1[/tex]

Subtract 1 from both sides: [tex]48=2x[/tex]

Divide by 2 on both sides: [tex]24 = x[/tex]

[tex]x = 24[/tex]

The main answer is that it takes Cindy 4 hours to weed the garden alone, which was found using the equation 1/x + 1/(3x) = 1/6 where x is the time it takes Cindy to weed the garden alone.

Let x be the time it takes Cindy to weed the garden alone. Then, it takes Tom 3x time to weed the garden alone. Using the formula for the work done by each person, we can create an equation in terms of x:

1/x + 1/(3x) = 1/6

Solving for x, we get:

x = 4 hours

Therefore, it takes Cindy 4 hours to weed the garden alone.

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To find the equation of the line passing through the point (6, -3) with a slope of -2, we can use the point-slope form of the equation of a line:y - y1 = m(x - x1)where (x1, y1) is the given point and m is the slope.Substituting the given values, we get:y - (-3) = -2(x - 6)Simplifying, we get:y + 3 = -2x + 12Subtracting 3 from both sides, we get:y = -2x + 9So, the equation of the line is y = -2x + 9

The number of  pounds that he will have left over from 11 3/7 pounds is  4 2/7

To find out how many bags of granola Alex can fill, we need to divide the total amount of granola he made by the amount of granola in each bag.

We can convert 11 3/7 pounds to an improper fraction:

11 3/7 pounds  = 80/7 pounds

Also, we have

2 2/3 pounds  = 8/3 pounds

Now we can divide the total amount of granola by the amount in each bag:

(80/7) ÷ (8/3)

To divide fractions, we invert the second fraction (change it to its reciprocal) and multiply:

(80/7) × (3/8)

Simplifying, we get:

(80 x 3) / (7 x 8) = 30/7

Divide

(80 x 3) / (7 x 8) = 4 2/7

Hence, the bags is 4 2/7

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Answer: 22

Step-by-step explanation:

Substitude 1 for i and 19 for H.

19+1(3) = 19+3 = 22

Answer:

Step-by-step explanation:

Answer:$10

Step-by-step explanation: We are given the ratio 9:1. Meaning for every 9 dollars he spends on healthy food, he can spend a dollar on snacks. If he intends on paying 100 dollars total, how much will he spend on snacks?

He would have spent 90 dollars on healthy food, and 10 dollars on snack food. Totaling 100 dollars.

The sum of the first 10 terms of the geometric progression that is given in the question is 1023.

What is geometric progression ?

Geometric progression, also known as geometric sequence, is a sequence of numbers in which each term after the first is obtained by multiplying the preceding term by a fixed constant. This fixed constant is called the common ratio.

The given series is a geometric progression, where each term is obtained by multiplying the preceding term by 2. The first term is 1, and the common ratio is 2.

The sum of the first n terms of a geometric progression is given by the formula:

[tex]S_n = a(1 - r^n) / (1 - r)[/tex]

where a is the first term, r is the common ratio, and n is the number of terms.

Using this formula, we can find the sum of the first 10 terms of the given series as:

[tex]S_{10} = 1(1 - 2^{10}) / (1 - 2)[/tex]

[tex]= 1(1 - 1024) / (-1)[/tex]

[tex]= 1023[/tex]

Therefore, the sum of the first 10 terms of the series 1 + 2 + 4 + 8... is 1023.

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Answer: 3

Step-by-step explanation:

Thus, the values of x for the given secant lines on the circle is found to be: x = 3 cm.

A straight line connecting two points on such a function is known as a secant line.  The average change rate or just the slope across two locations can also be used to describe it.

The slope between two points and the average rate of shift in a function among two points are interchangeable terms.

Given data:

AE = 6 cm, AB = 3 cm, ED = x cm, BC = 15 cm

Now,

AD = AE + ED

AD = 6 + x ...eq 1

AC = AB + BC

AC  = 3 + 15

AC = 18 ....2

As the given two chords are intersecting internally,

AC x AB = AD x AE

18 x 3 = (6 + x) x 6

6 + x = 18 x 3 / 6

6 + x = 9

x = 3

Thus, the values of x for the given secant lines on the circle is found to be: x = 3 cm.

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Complete question:

Solve for x, using the secant lines.

AE = 6 cm, AB = 3 cm,ED = x = [?] cm, BC = 15 cm

Remember a.b = c.d

The diagram is attached.

Using equations, we can find that the number of sale-priced songs is 5 and the number of regularly priced songs is 7.

Equations are mathematical statements with the equals (=) symbol and two algebraic expressions on either side. This illustrates the equality of the relationship between the expressions printed on the left and right sides. The formula LHS = RHS (left hand side equals right hand side) is utilised in all mathematical equations. To determine the value of an unknown variable that represents an unknown quantity, you can solve equations. A statement is not regarded as an equation if it has no "equal to" symbol.

As per the question, equation given are:

x + y = 12

x = 12 - y

Now, substituting the value in:

0.99x+1.25y = 13.7

= 0.99(12-y) +1.25y = 13.7

= 11.88 - 0.99y + 1.25y = 13.7

= 0.26y = 13.7 - 11.88

0.26y = 1.82

y = 1.82/0.26

y = 7

Now, substitute this value,

x = 12 - 7

x = 5

As a result, there are 5 songs on sale and 7 songs that are regularly priced.

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The probability that no more than four of the college graduates plan to pursue a graduate degree is approximately 0.1437. b. X= 7 = 0.2004.

With a set number of independent trials, each of which has just two potential outcomes—success or failure—a binomial distribution defines the number of successes. The chance of success, represented by p, and the number of trials, denoted by n, are the two factors that define the distribution.

Given that, 58% of recent college graduates plan on pursuing a graduate degree.

Using the binomial probability formula we have:

[tex]P(X \leq 4) = \sum (i = 0 \to 4) (n C i) * p^i * (1 - p)^{(n-i)}\\\\[/tex]

Here, n = 13, p = 0.58.

[tex]P(X \leq 4) = Σ(i = 0 \to 4) (13 C i) * 0.58^i * (1 - 0.58)^{(13-i)}= 0.1437[/tex]

Hence, the probability that no more than four of the college graduates plan to pursue a graduate degree is approximately 0.1437.

b. For X = 7:

[tex]P(X = 7) = (13 C 7) * 0.58^7 * (1 - 0.58)^{(13-7)}= 0.2004[/tex]

Hence, the probability that exactly seven of the college graduates plan to pursue a graduate degree is approximately 0.2004.

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Answer:

Step-by-step explanation:

First you need to find the balance amount that she paid in instalments which is 42000 * 15% which is equalled to 6300.

Then you need to minus 42000 - 6300 as 630l is the price she paid as cash deposit which is equalled 35700.

Now, to find the interest the formula is I = p * r/100 which equalled 7890 for a year. To calculate her monthly instalments, you have to divide 7890 divided by 12 months which equals 665.

Answer:

6 carnivore's and 18 herbivore's

Step-by-step explanation:

Three consecutive odd integers are -3, -1, and 1.

A detailed explanation of the answer.

To find 3 consecutive odd integers such that 3 times the sum of the first and second equals 13 less than the third, we can follow these steps:

Therefore, the three consecutive odd integers are -3, -1, and 1.

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The side opposite to angle Y is the longest, and angle Y is the largest angle in triangle XYZ. So, the angles can be ordered from greatest to least as follows:

angle Y > angle Z > angle X.

What is triangle ?

A triangle is a three-sided polygon, or a closed two-dimensional shape with three straight sides and three angles. The sum of the angles in a triangle always adds up to 180 degrees. The sides of a triangle can be of different lengths, and the angles can be acute (less than 90 degrees), right (equal to 90 degrees), or obtuse (greater than 90 degrees).  

To order the angles from greatest to least in triangle XYZ, we need to determine which side is the longest. By the Law of Cosines, we know that:

[tex]c^2 = a^2 + b^2 - 2ab*cos(C)[/tex]

where c is the side opposite to angle C, and a and b are the other two sides.

So, let's calculate [tex]c^2[/tex] for each angle:

For angle X: [tex]c^2 = 25^2 + 27^2 - 2(25)(27)*cos(X)[/tex] ≈ 173.65

For angle Y: [tex]c^2 = 24^2 + 27^2 - 2(24)(27)*cos(Y)[/tex] ≈ 267.43

For angle Z: [tex]c^2 = 24^2 + 25^2 - 2(24)(25)*cos(Z)[/tex] ≈ 121.97

Therefore, the side opposite to angle Y is the longest, and angle Y is the largest angle in triangle XYZ. So, the angles can be ordered from greatest to least as follows:

angle Y > angle Z > angle X

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The Rule of 72 is a simple mathematical formula that allows investors to quickly estimate the number of years required for an investment to double in value.

To use this formula, we divide the number 72 by the annual interest rate earned on the investment.

However, it is important to note that this formula provides only an estimate, and the actual time required for an investment to double in value will depend on a variety of factors, such as market conditions, investment fees, and taxes.

Nevertheless, the Rule of 72 can be a helpful starting point for investors who want to set realistic expectations for their investments.

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b + 2p = 10 ,we have an equation that relates the number of bracelets to the number of purses and the total cost of the purchase. if Evelyn buys two purses, she also buys six bracelets.

Let's start by defining our variables. We'll let "b" represent the number of bracelets that Evelyn buys and "p" represent the number of purses she buys.

We know that each bracelet costs $6 and each purse costs $12. We also know that her total purchase is $60.

Using this information, we can create an equation:

6b + 12p = 60

Now we want to solve for "b", which represents the number of bracelets. To do this, we need to isolate "b" on one side of the equation. We can start by simplifying the equation by dividing both sides by 6:

b + 2p = 10

Now we have an equation that relates the number of bracelets to the number of purses and the total cost of the purchase. We can use this equation to find the value of "b" given any value of "p". For example, if Evelyn buys two purses, we can substitute "p = 2" into the equation and solve for "b":

b + 2(2) = 10

b + 4 = 10

b = 6    

So if Evelyn buys two purses, she also buys six bracelets.

In general, we can see that the equation tells us that for every two purses that Evelyn buys, she buys one less bracelet. This makes sense because purses are more expensive than bracelets, so as she buys more purses, she can afford fewer bracelets.

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The answer is: 1 triangle is possible  given the following side maesurment: 3 feet , 5 feet, 4 feet.

To determine how many triangles are possible with these side measurements, we can use the triangle inequality theorem, which states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.

What is inequality theorem?

In this case, we have three side measurements: 3 feet, 5 feet, and 4 feet. Let's call these sides a, b, and c, respectively. Using the triangle inequality theorem, we can see that:

a + b > c

a + c > b

b + c > a

Substituting in the values of a, b, and c, we get:

3 + 5 > 4

3 + 4 > 5

4 + 5 > 3

All three of these inequalities are true, so it is possible to form a triangle with these side measurements.

To determine how many distinct triangles are possible, we can use the fact that any two triangles are distinct if and only if they have at least one side with a different length. In this case, all three sides have different lengths, so there is only one distinct triangle that can be formed with these side measurements.

Therefore, the answer is: 1 triangle.

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Complete question is: 1 triangle is possible given the following side maesurment: 3 feet , 5 feet, 4 feet.

The correct option is (b) i.e. The area of the remaining figure is 136 in².

What is Right angled triangle?

A right angled triangle, also known as a right triangle, is a triangle in which one of the interior angles measures 90 degrees (a right angle). The side opposite the right angle is called the hypotenuse, and the other two sides are called the legs or the adjacent and opposite sides. The length of the hypotenuse can be found using the Pythagorean theorem, which states that the sum of the squares of the two legs is equal to the square of the hypotenuse.

Given : length = 20 and breadth = 8

The area of given rectangle = l × b

                                               = 20 × 8

                                               = 160 in²

Similarly, area of right angled triangle = 1/2 × b × h

                                                               = 1/2 × (20-8) × 4

                                                               = 1/2 × 12 × 4

                                                               = 24 in²

Hence, The area of remaining figure :

 = The area of given rectangle -  area of right angled triangle

= 160 - 24

= 136 in²

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End of unit 4 assessment on right triangle trigonometry is an evaluation of a student's understanding of the basic concepts and applications of trigonometry involving right triangles.

This assessment may cover topics such as the trigonometric functions, Pythagorean theorem, special right triangles, and solving right triangles.

Trigonometry is the study of the relationships between the angles and sides of triangles, particularly right triangles. It is a branch of mathematics that has numerous applications in fields such as physics, engineering, and astronomy.

The trigonometric functions are sine, cosine, and tangent, which are ratios of the sides of a right triangle. These functions can be used to solve problems involving angles and sides of right triangles, such as finding the missing side or angle.

The Pythagorean theorem is another fundamental concept in right triangle trigonometry. It states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

Special right triangles, such as the 30-60-90 triangle and the 45-45-90 triangle, have specific ratios of their side lengths that can be used to solve problems more easily.

Solving right triangles involves finding the measures of all the angles and sides of a right triangle given certain information, such as the length of one side and the measure of one angle.

In conclusion, the end of unit 4 assessment on right triangle trigonometry evaluates a student's understanding of the basic concepts and applications of trigonometry involving right triangles. This assessment is important for students to demonstrate their mastery of the subject and to prepare them for further studies in mathematics and related fields.

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End of unit 4 assessment right triangle trigonometry describe the importance of Side ratios in right triangles as a function of the angles ?

According to the information, the surface area of the prism is 3200 square meters.

To find the surface area of the prism, we need to add up the areas of all its faces.

The prism has 2 triangle sides with a height of 15m and a base of 40m. The area of each triangle can be calculated using the formula A = 1/2 × b × h, where b is the base and h is the height of the triangle. So, the total area of these two triangles is:

The prism also has 2 triangle sides with a height of 25m and a base of 40m. The total area of these two triangles is:

Finally, the prism has 2 rectangular sides with a height of 40m and a base of 40m. The area of each rectangle is simply the product of its height and base, so the total area of these two rectangles is:

To find the total surface area of the prism, we add up the areas of all its faces:

Therefore, the surface area of the prism is 3200 square meters.

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