Quadratic work problems Task 1

Answer:

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Michelle biked approximately 37.68 miles in the shape of a circle.

A circle's diameter and radius are connected because the diameter is twice as long as the radius. Mathematically, this connection may be written as d = 2r, where d stands for the diameter and r for the radius. On the other hand, we can alternatively state that the radius is equal to half the diameter's length: r = d/2

The circumference of a circle can be found using the formula:

C = πd

Given that,

Michelle biked around the trail 4 times.

The circumference is:

C = π x 3 = 9.42 miles

Also,

4 x 9.42 = 37.68 miles

Hence, Michelle biked approximately 37.68 miles in the shape of a circle.

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Answer:

Julia should buy at least 5 sets of glasses.

Step-by-step explanation:

The inequality will be

286 +6s ≥ 316

Solve for s to get s ≥ 5

No, it is not possible for Mario to have drawn this figure.

The circumference, which is the distance around the object, the diameter, which is the length of a circle measured from one end to the other and passing through its center, and the radius, which is equal to half of the diameter, are the three key characteristics.

If two tangents to a circle meet at a point outside the circle, they must be parallel to each other.

If the two points where the two tangents meet the circle separate the circle into two semicircles, then the center of the circle must lie on the line containing the two points.

However, since the tangents are parallel, they do not intersect the line containing the two points, and therefore, the center of the circle cannot lie on this line.

This contradicts the definition of a circle, which states that the center of a circle is equidistant from all points on the circle.

Therefore, Mario's reasoning is flawed, and it is not possible for him to have drawn this figure.

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The piecewise function that models model the water level L (x) (in inches) as a function of the number of days x since the beginning of the drought is given as follows:

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which;

A piecewise function is a function with different definitions, based on the input of the function.

For the first 14 days, the parameters are given as follows:

Hence:

L(x) = 60 - 2x, 0 ≤ x ≤ 14.

For the last 5 days, the parameters are obtained as follows:

Hence:

L(x) = 30 + 5x, 15 ≤ x ≤ 19.

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One example of a quantity in the life sciences that is modeled by a function of time is the population size of a species.

This can be modeled using a differential equation, where the rate of change of the population size is proportional to the current population size.

If we knew the values of the derivative of this function (i.e., the first derivative), we would be able to make inferences about the growth or decline of the population.

A positive derivative value would indicate that the population is growing, while a negative derivative value would indicate that the population is declining. The magnitude of the derivative would also give us information about the rate of growth or decline of the population. If the derivative is large, the population is changing quickly, while a small derivative indicates slower change.

If we had information about the second derivative of the function (i.e., the rate of change of the derivative), we would be able to make further inferences about the behavior of the population.

A positive second derivative value would indicate that the population is accelerating in its growth, while a negative second derivative value would indicate that the population is decelerating in its growth. This information could be useful in predicting future trends in population size and in making decisions about conservation efforts or resource management.

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The graph of the linear inequality y ≥ 2·x - 1 is the region on or above the graph of the line y = 2·x - 1

Option A is correct;

(A) On or above

An inequality is a comparison that expresses an unequal relationship between two expressions.

An example of an inequality is; V < W, R > Q, X ≥ W, etc

The region of the graph of a linear inequality is indicated by shading above the line when the inequality is >, and below the line when the inequality symbol is <

The specified linear inequality can be presented as follows;

y ≥ 2·x - 1

Therefore, w get;

The values of y are larger than 2·x - 1

The shaded region is the region on or above the graph of the line y = 2·x - 1

The correct option is therefore; (A) On or above the line y = 2·x - 1

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9 people prefer strawberry.

A pie chart is a circular chart used to represent data as a proportion of a whole. The whole is represented by the complete circle, while the individual parts are represented by slices of the circle, each corresponding to a particular category or value.

Pie charts are often used to display data that is divided into a few distinct categories, where the size of each category can be easily compared. The size of each slice is proportional to the quantity it represents, and the slices are typically labeled with their corresponding categories or values.

Pie charts are a useful tool for quickly and easily visualizing data, and they are commonly used in business, marketing, and other fields. However, it is important to use them appropriately, as they can be misleading if the slices are not sized correctly or if there are too many categories to be displayed effectively.

18% of 50 people prefer strawberry.

To find out how many people prefer strawberry, we can start by finding out what 1% of 50 is:

1% of 50 = 0.01 x 50 = 0.5

Then, we can multiply this value by the percentage of people who prefer strawberry:

0.18 x 50 = 9

Therefore, 9 people prefer strawberry.

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The complete question is:

Answer:

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

Step-by-step explanation:

use desmos graphing calculator! it's very helpful and free :)

Answer:

From the graph,

The zeros of the function are at x= -2 and x= 5

But since at root -2,it doesn't cross the x axis, the root has even multiplicity

Ans:(x+2)^2 (x-5).....option B

Yes, the set of coordinate points (5, 31), (6, 28), (7, 25), (8, 22), and (9, 19) forms a function.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

To determine whether the set of coordinate points (5, 31), (6, 28), (7, 25), (8, 22), and (9, 19) forms a function, we need to check whether each x-value is paired with a unique y-value.

We can see that for each x-value in the set, there is only one corresponding y-value.

Therefore, the set of coordinate points does form a function.

We can also verify this by using the vertical line test.

If we draw a vertical line anywhere on the graph of this set of points, the line will intersect the graph at most once, indicating that each x-value is paired with a unique y-value.

Therefore, the coordinate points does form a function.

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By using distributive property, an estimate for sin((π/6 + ε)(1 - ε)) is approximately 0.5108.

What is sinx ?

sinx is a trigonometric function that represents the ratio of the length of the side opposite to an angle x in a right-angled triangle to the length of the hypotenuse of the triangle. In other words, it is the sine of the angle x.

The sine function is typically denoted as sin(x), where x is the measure of an angle in radians. It is defined as follows:

sin(x) = opposite side / hypotenuse

According to the question:
We can use the small angle approximation sin(x) ≈ x for small angles x to estimate[tex]sin((\pi /6 + \epsilon)(1 - \epsilon))[/tex], where ε = 0.01.

First, we can expand the expression using the distributive property:

[tex]sin((\pi /6 + \epsilon)(1 - \epsilon)) = sin(\pi /6 - \epsilon^2 +\epsilon /6)[/tex]

Since ε is small, we can use the small angle approximation to estimate the value of sin(ε/6):

[tex]sin(\epsilon /6) =\epsilon/6[/tex]

Next, we can use the fact that [tex]sin(\pi /6) = 1/2[/tex] to estimate [tex]sin(\pi /6 - \epsilon ^2)[/tex] :

[tex]sin(\pi /6 - \epsilon ^2) ≈ sin(\pi /6) = 1/2[/tex]

Substituting these approximations into the original expression, we get:

[tex]sin((\pi /6 + \epsilon)(1 - \epsilon)) =sin(\pi /6 - \epsilon^{2} + \epsilon/6) =sin(\pi /6) + sin(\epsilon/6) - sin(\epsilon^{2} )sin((\pi /6 + \epsilon)(1 - \epsilon)) = 1/2 + \epsilon/6 - sin(\epsilon^{2} )[/tex]

Finally, we can use the fact that sin(x) is approximately equal to x for small values of x to approximate [tex]sin(\epsilon^{2} ) as \epsilon^{2}[/tex]:

[tex]sin(\epsilon^2) = \epsilon^2[/tex]

Substituting this approximation into the previous expression, we get:

[tex]sin((\pi /6 + \epsilon)(1 - \epsilon)) ≈ 1/2 + \epsilon/6 - \epsilon^2[/tex]

Now, we can substitute the value of ε = 0.01 into this expression to get an estimate:

[tex]sin((\pi /6 + \epsilon)(1 - \epsilon)) ≈ 1/2 + 0.01/6 - 0.01^2[/tex]

[tex]sin((\pi /6 + \epsilon)(1 - \epsilon)) =0.5108[/tex]

Therefore, an estimate for sin((π/6 + ε)(1 - ε)) is approximately 0.5108.

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No, -(p « › q) and p «> -q are not logically equivalent.

When two logical assertions have the same truth value for all conceivable truth value assignments to their constituent propositions, the two statements are said to be logically equivalent. In other words, two assertions are comparable logically if and only if all feasible permutations of the truth values of their component propositions are equal.

First, let's rewrite the statements using the standard logical operators of negation, conjunction, and implication:

-(p « › q) is equivalent to ¬(p ∧ ¬q)

p «> -q is equivalent to ¬p → ¬¬q, which simplifies to p → q

Now, we can construct a truth table with columns for p, q, ¬(p ∧ ¬q), and p → q:

p |      q |   ¬(p ∧ ¬q)    |    p → q

--|----------|------------------|-----

T        T          F               T

T        F          T               F

F       T           T               T

F       F           T               T

We can see that the truth values of the two statements are not always the same.

For example, when p is true and q is false, ¬(p ∧ ¬q) is true and p → q is false.

Therefore, -(p « › q) and p «> -q are not logically equivalent.

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Answer: Cylinders and Cones don't have a vertex or vertices.

Step-by-step explanation: I had the same question and got it right.

Have a good day! <3

Answer x is 7

Step-by-step explanation:

The three angles are 104degrees, (9x-25) and unknown

The pictures shows that the two sides are equal therefore the two opposite angles are equal

104 + (9x-25) +(9x-25) =180

RE write

104 +2(9x-25) =180

Subract 104 from both sides

2(9x-25) = 180-104

2(9x-25) = 76

Divide both sides by 2

9x - 25 = 38

Add 25 to both sides

9x = 63

Divide both sides by 9

X =7

The angle is 9x-25 = 38

Answer:

Any series of temperatures between -4° and 4° could occur during the day, as long as they stay within that range. For example, the temperature could start at -3°, then rise to 1°, fall to -2°, and rise again to 3°, and so on. Another example could be the temperature staying constant at 0° throughout the day. Therefore, there are many possible series of temperatures that could occur during the day, as long as they stay within the given temperature range.

The probability that a person is 64 or over and has a loan is 0.20 × 0.28 = 0.056.

Probability is the study of the likelihood of certain outcomes or events occurring. It is the measure of how likely it is for something to happen. Probability can be expressed as a percentage, a fraction, or a number between zero and one. Probability is used to help make decisions in a variety of situations, from games of chance to business decisions and scientific research.
(b) The probability that a person has a loan is 0.20 × 0.28 + 0.80 × 0.53 = 0.464.

(c) The events that a person is 64 or over and that the person has a loan are not independent. This is because the probability of having a loan depends on whether the person is 64 or over. Therefore, the two events are not independent.

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Answer:

To use the Pythagorean Theorem to determine if the triangle is right, acute, or obtuse, we need to find the length of the longest side (also known as the hypotenuse) by squaring each side, adding the results, and taking the square root of the sum.

So,

63^2 = 3969

58^2 = 3364

30^2 = 900

Now, we add 3969 and 3364 to get 7333, and take the square root to get approximately 85.62.

Since 63, 58, and 30 are the lengths of the sides of the triangle, we can compare the length of the longest side (85.62) to the sum of the other two sides (63 + 58 = 121) to determine if the triangle is right, acute, or obtuse.

85.62^2 = 7326.23

121^2 = 14641

Since 7326.23 is less than 14641, the triangle is acute.

The area of the part that is painted blue is 679 ft.

What are the basic arithmetic operations?

The four basic arithmetic operations are addition, subtraction, multiplication, and division.

Arithmetic operations are the building blocks for all mathematical processes and methods. (Yeah, they’re kind of a big deal!) These types of operations are part of the “arithmetic” branch of math.

Arithmetic operations strip math down to the basics that we use every day, whether we realize it or not. Those basics are addition, subtraction, multiplication, and division.

The area

= 20×30+(1/2)×20×(40-30) -3x5 - 2×3

= boot 10x10- 15-6

= 700-21

= 679

Hence, The area of the part that is painted blue is 679 ft.

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Answer:

number is 8

Step-by-step explanation:

let the number be n then trebling it ( multiplying it by 3 ) is 3n, then subtracting 6 from this is 3n - 6 , so

3n - 6 = 18 ( add 6 to both sides )

3n = 24 ( divide both sides by 3 )

n = 8

that is the number thought of is 8

The required number of tubs are 17.55 tubs.

To solve the problem, we need to find the total amount of ice cream used in ounces and then convert it to pounds to find the number of tubs used.

Number of scoops for regular cones = 2 scoops/cone

Number of scoops for large cones = 3 scoops/cone

Total number of scoops of ice cream used for regular cones = 2 scoops/cone x 234 cones = 468 scoops

Total number of scoops of ice cream used for large cones = 3 scoops/cone x 156 cones = 468 scoops

Total number of scoops of ice cream used = 468 scoops + 468 scoops = 936 scoops

Total amount of ice cream used in ounces = 936 scoops x 3 ounces/scoop = 2808 ounces

Total amount of ice cream used in pounds = 2808 ounces / 16 ounces/pound = 175.5 pounds

Number of tubs of ice cream used = 175.5 pounds / 10 pounds/tub = 17.55 tubs

Rounding up to the nearest whole number, we get:

Answer: (C) 17.55 tubs.

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Step-by-step explanation:

We can solve for x using the properties of logarithms as follows:

log2 (5x - 2) = -2

2^(-2) = 5x - 2 (using the definition of logarithms)

1/4 = 5x - 2 (simplifying 2^(-2))

5x = 2 + 1/4 = 9/4

x = 9/20

Therefore, the solution to the equation log2 (5x - 2) = -2 is x = 9/20.

Set 2:

T. Slope = (9-5)/(10-7) = 4/3 __16.  Slope = (2-(-2))/(9-(-5)) = 4/14

B. Slope = (-4-2)/(-5-(-8)) = -6/3 __ 8.  Slope = (-8-(-6))/(2-(-10)) = -2/12

H.  Slope = (-1-(-2))/(-4-2) = -3/-6 __ 3.  Slope = (-7-1)/(-8-(-2)) = -8/6

S.  Slope = (7-9)/(-11-(-4)) = -2/-7 __ 5. Slope = (3-(-2))/(-3-(-4)) = 5/1

O. Slope = (-6-(-1))/(4-5) = -5/-1 __ 14.  Slope = (6-(-4))/(-7-(-2)) = 10/-5

Set 3:

K. Slope = (-3-(-3))/(2-1) = 0/1 __ 9.  Slope = (-4-(-1))/(6-8) = -3/-2

R. Slope = (5-0)/(-3-3) = 5/-6 __ 1.  Slope = (-5-(-6))/(-8-(-11)) = 1/3

E. Slope = (-2-4)/(8-12) = -6/-4 __ 15. Slope = (3-4)/(-5-(-5)) = -1/0

U.  Slope = (-9-(-3))/(7-7) = -6/0 __ 12. Slope = (9-(-3))/(-5-(-2)) = 12/3

O.  Slope = (5-1)/(2-3) = 4/-1 ____ 6.  Slope = (8-8)/(7-(-3)) = 0/10

H.  Slope = (-8-(-6))/(-7-(-1)) = -2/-6 _ 10. (-5, 3) and (7, -7) Slope = (-7-3)/(7-(-5)) = -10/12

A set is a collection of distinct objects, usually numbers, that are grouped together in a manner that follows specific rules. Sets can be used to determine if an element belongs to the set or not, and can also be used to perform operations such as unions and intersections. Sets are an important tool in mathematics, and they can help simplify complex problems.

The Mathematician had to calculate the slope between two points for each of the sets given. To calculate the slope, the Mathematician had to subtract the y-values of the two points and divide by the difference between the x-values of the two points. The Mathematician then had to match the answers to the corresponding letter or number and write the letter in the matching numbered box at the bottom of the page. By doing this, the Mathematician was able to solve the riddle and arrive at work on time.

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Answer:

Base = 5inches

Step-by-step explanation:

2(x+2) + x
2x+4+x
3x+4=19
3x=15
x=5

Answer:x5

Step-by-step explanation:

We can write the expression for {P} as -

P = a + b + 4ab - 2y

In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size

Given are the expressions as -

P = a + b + 2c

y = 2ab - C

We can write -

C = 2ab - y

Putting the values in the equation -

P = a + b + 2c

P = a + b + 2(2ab - y)

P = a + b + 4ab - 2y

Therefore, we can write the expression for {P} as -

P = a + b + 4ab - 2y

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According to the probability, the answer is option D: 1/98,000.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

The chance of Steve being selected is 1. This means that out of 1 individual, Steve is selected. The probability of Steve being selected is 1/1 or 1. Since the sample is a simple random sample, each individual in the population has an equal chance of being selected. If there are a total of 98,000 individuals in the population, then the probability of Silva being selected is 1 out of 98,000, or 1/98,000.

Therefore, the answer is option D: 1/98,000.

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The value of (AB)² + (BC)² = 130

The value of (AC)² = 130.

Therefore the triangle is a right angled triangle

Distance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by d=√((x2 – x1)² + (y2 – y1)²).

AB)² = 5-(-2)²+7-11)²

= 7² + 4²

= 49+16

AB)² = 65

BC)² = 1-5)² + 0-7)²

BC)² = 4² + 7²

= 16 +49

BC) ² = 65

BC)² + AB)² = 65+65 = 130

AC)² = 1-(-2)² +0-11)²

AC)² = 3²+ 11²

AC)² = 9+121

AC)² = 130

therefore the value of BC)² + AB)² = AC)²

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The area of the composite figure is 14.71 square units

The area of the composite figure is found by calculating the sum of the areas of the various parts.

The area of the figure = area of sector + area of triangle + area of trapezium

Area of sector = 135/360 * π * 2²

Area of sector = 4.71 square units

Area of triangle = ¹/₂ * 2 * 1

Area of triangle = 1 square unit

Area of trapezium = ¹/₂ (3 + 6) * 2

Area of trapezium = 9 square units

Therefore, area of composite figure =  (4.71 + 1 + 9) square units

The area of the composite figure = 14.71 square units

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You have $28.75 left to spend on diapers for Jake.

What is the percentage?

Percentage refers to a way of expressing a number as a fraction of 100. It is often denoted by the symbol "%". For example, if 30 out of 100 students in a class are girls, the percentage of girls in the class is 30%. Percentages are commonly used in many fields, such as finance, statistics, and science, to express proportions, rates, and changes over time.

The total percentage of money spent on the blanket, toys, and clothes is 15% + 25% + 40% = 80%.

Therefore, the amount of money spent on Jake's supplies is $115, which is 80% of the total budget. We can set up the equation:

0.8x = 115

Solving for x, we get:

x = 115 ÷ 0.8 = $143.75

So, the total budget for Jake's supplies is $143.75.

To find out how much money is left for diapers, we need to subtract the amount spent on blanket, toys, and clothes from the total budget:

$143.75 - 15% of $143.75 - 25% of $143.75 - 40% of $143.75

= $143.75 - $21.56 - $35.94 - $57.50

= $28.75

Therefore, you have $28.75 left to spend on diapers for Jake.

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