Please help with problems 19 and 20 I'm stuck on how to solve these.
And show work please
Will give brainliest!!

Please Help With Problems 19 And 20 I'm Stuck On How To Solve These. And Show Work Please Will Give Brainliest!!

Answers

Answer 1

19) Length of AB is a fourth of the circumference of the circle.

C=2πr

Length of AB = [tex]\frac{1}{4} 2\pi r=\frac{1}{2} \pi r[/tex]

=0.5π(12)

Length of AB =1 8.8495559215 in

Area = 1/4*π*r²

Area = 1/4*π*12²

Area = 113.097335529 in²

20) Arc length = θr

[tex]\frac{3 }{4} \pi *10[/tex]

Length = 23.5619449019 in

Area = [tex]\frac{angle}{2\pi } *\pi r^{2}[/tex]

= [tex]\frac{3\pi }{8} *10^2[/tex]

Area = 117.80972451 in²


Related Questions

Find a1 for each geometric series described. Sn=1550, n=3, r=5

Answers

Answer:

An=31n-49

Step-by-step explanation:

1550=A1(1-5^3) / 1-5 =31

1550=A1 × 31 / 31

A1= 50

Pre Alg Need help on this writing Question on both parts

Answers

Answer:

a = 2b - x

Step-by-step explanation:

2(x + a) = 4b  Divide both sides of the equation by 2

x + a = 2b   Subtract x from both sides

a = 2b - x

Helping in the name of Jesus.

I NEED HELP ON THIS ASAP!!!

Answers

part a.

Carter needs 116 yards of fencing to enclose the flat area of his backyard.

part b.

Carter needs 720 square yards of sod to cover the flat area of his backyard.

How do we calculate?

estimating the coordinates of the vertices of the figure and using  the distance formula to calculate the length of each side:

AB: √((16-(-16))^2 + (4-4)^2) = 32 yards n

BC: √((16-4)^2 + (4-12)^2) = 14 yards

CD: √((4-8)^2 + (12-16)^2) = 5 yards

DE: √((8-(-12))^2 + (16-(-8))^2) = 37 yards

EA: √((16-(-16))^2 + (4-(-8))^2) = 28 yards

The total perimeter is: 32 + 14 + 5 + 37 + 28 = 116 yards

b.

Rectangle ABED: 32 yards × 16 yards = 512 square yards

Triangle BCD: (1/2) × 4 yards × 8 yards = 16 square yards

Triangle DEA: (1/2) × 24 yards × 12 yards = 144 square yards

Triangle EFA: (1/2) × 8 yards × 12 yards = 48 square yards

The total area is: 512 + 16 + 144 + 48 = 720 square yards

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roger drives at a constant speed he travels 440 miles in 8 hors how many miles does roger travel in one hour​

Answers

To find how many miles Roger travels in one hour, we need to divide the total distance he traveled by the time he took:

miles per hour = total miles ÷ total time

In this case, Roger traveled 440 miles in 8 hours, so:

miles per hour = 440 miles ÷ 8 hours

miles per hour = 55 miles per hour

Therefore, Roger travels 55 miles in one hour.

Answer:

To find how many miles Roger travels in one hour, we can divide the total distance he traveled by the total time he took to travel that distance.

We are given that Roger traveled 440 miles in 8 hours, so:

miles per hour = total distance / total time

miles per hour = 440 miles / 8 hours

miles per hour = 55 miles per hour

Therefore, Roger travels 55 miles in one hour.

Hope This Helps!

The ages of all ten Mathematics teachers at a school are recorded below. 31, 43, 25, 37, 28, 22, 25, 32, 31, 36 Two new Mathematics teachers then join the school. When their ages are added to this list: the range increases by 5 the mean increases by 1 the median remains unchanged the mode remains the same. How old are the two new Mathematics teachers? You must show your working.​

Answers

Hence, one teacher must be 21 years old, while the other must be 3 years old.

WHAT IS RANGE?

The difference between a dataset's highest and lowest values is known as the range. For instance, suppose we have the dataset shown below:

1, 3, 5, 7, 9

This dataset's range is 9 - 1 = 8.

Let's first estimate the age ranges of the school's ten mathematics instructors. The range of a dataset is the difference between its highest and lowest values. It is therefore 21 since 22 - 43 = 21.

Let's now include the ages of two additional Maths teachers in this list. Let's use x and y as their ages.

When their ages are included in this list, the range is increased by five. We thus have:

43 - 22 = 21 (the original range) (the original range)

max(x,y) = 5 - min(x,y) (the new range)

We can find the solutions to x and y from these two equations:

maximum(x,y) = 21 + 5 = 26 minutes

(x,y) = maximum (x,y) - 5 = 21

Let's now determine the average age of the school's twelve maths teachers. Addition is used to calculate the mean.

Adding together all the values in a dataset and dividing by the total number of values yields the mean. Here are the facts:

(31 + 43 + 25 + 37 + 28 + 22 + 25 + 32 + 31 + 36 + x + y) / 12

If we are aware that x and y together raise the mean by 1, we may write:

(31 + 43 + 25 + 37 + 28 + 22 + 25 + 32 + 31 + 36 + x + y) / 12 = (31 + 43 + 25 + 37 + 28 + 22 + 25 + 32 + 31 + 36) /10 +1

When we simplify this equation, we get:

x+y=24

Let's now determine the median age of the school's twelve mathematics instructors. When a dataset is ordered from lowest to highest, the median is the midway value (or highest to lowest). Here are the facts:

22,25,25,28,31,31,32,36,37,43,x,y

The median is equal to (31.5 (31 + 32) / 2)

Let's finally figure out the average age of the school's twelve math teachers. The value that appears most frequently in a dataset is the mode. In this instance, "25" and "31" both appear twice, giving us two modes.

We are aware that this dataset's mode is unaffected by the addition of x and y.

We thus have:

x+y=24

max(x,y)=26

min(x,y)=21

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5) A sample of men is found to be normally distributed with an average height of 70.5 inches and a standard deviation of 2.5 inches. Where do 95% of the men fall?

A) Between 63 inches and 70.5 inches

B) Between 65.5 inches and 75.5 inches

C) Between 68 inches and 73 inches

D) Between 63 inches and 78 inches

Answers

For the given information of standard deviation, the correct answer is option B) Between 65.5 inches and 75.5 inches.

What is standard deviation?

Standard deviation is a statistical measure that measures the amount of variation or dispersion of a set of data values from the mean. It tells how much the data deviates from the average of the data set.

We can use the z-score formula to solve this problem. If we assume a normal distribution, we can find the z-score associated with the 95th percentile (or 0.95 probability) using a standard normal distribution table or calculator. The z-score is approximately 1.96.

Then we can use the formula:

z = (x - μ) / σ

where z is the z-score, x is the height we want to find, μ is the mean height, and σ is the standard deviation.

Solving for x:

1.96 = (x - 70.5) / 2.5

Multiplying both sides by 2.5:

4.9 = x - 70.5

Adding 70.5 to both sides:

x = 75.4

So 95% of the men fall between 65.5 inches and 75.5 inches (option B).

Therefore, the correct answer is option B) Between 65.5 inches and 75.5 inches.

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Daniel is playing a video game. He has 7,985 points at the end of round one, then the following events happen, in order: • He doubles his points. • He loses 3,500 points. • He earns 4,972 additional points. • The game ends.

Answers

Starting points = 7,985

Doubling the points: 7,985 x 2 = 15,970

Subtracting 3,500 points: 15,970 - 3,500 = 12,470

Adding 4,972 points: 12,470 + 4,972 = 17,442

Therefore, Daniel has 17,442 points at the end of the game.

Nicholas listened to 2 songs from each act of a musical. Each act has an equal number of songs.


Is this sample of the songs in the musical likely to be representative?

Answers

The sample of the songs in the musical is likely to be representative.

As per the given details, Nicholas listened to 2 songs from each act of a musical.

Each act has an equal number of songs.

In order to determine whether the sample of the songs in the musical likely to be representative, we need to determine the number of acts of the musical.

Let the number of songs in each act be x.

Since Nicholas listened to 2 songs from each act, the total number of songs Nicholas listened to will be equal to 2x. Thus, we can represent the number of acts in the musical as a function of the total number of songs listened to as follows:

Number of acts = total number of songs listened to / x = 2x / x = 2.

Since there are 2 acts in the musical, Nicholas listened to all the songs in the musical.

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Someone please help me answer this question correctly

Answers

The equation of the linear function that fits the given data is y = 10x - 2.

Equations

To find the equation of a linear function in slope-intercept form, we need to determine the slope (m) and y-intercept (b).

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

(x1, y1) = (0, -2)

(x2, y2) = (4, 38)

m = (38 - (-2)) / (4 - 0)

= 40 / 4

= 10

y = mx + b

To find the y-intercept, we can use any point on the line. Let's use (0, -2):

-2 = 10(0) + b

b = -2

So,

y = 10x - 2

We can check that this equation satisfies all the given data points:

When x = 0, y = 10(0) - 2 = -2

When x = 1, y = 10(1) - 2 = 8

When x = 2, y = 10(2) - 2 = 18

When x = 3, y = 10(3) - 2 = 28

When x = 4, y = 10(4) - 2 = 38

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three relationships are described below: i. the amount of fuel used on a trip increases as the size of the car increases and as the distance traveled increases. ii. as the number of people helping mow a lawn increases, the time it takes to mow the lawn decreases. iii. the cost of having a house painted increases as the size of the house increases. what type of variation describes each relationship? i is joint, ii is direct, and iii is inverse. i is direct, ii is inverse, and iii is joint. i is direct, ii is joint, and iii is inverse. i is joint, ii is inverse, and iii is direct.

Answers

The described point iii is joint variation.

In the given question,

Three relationships are described.

They are:

i. The amount of fuel used on a trip increases as the size of the car increases and as the distance traveled increases.

ii. As the number of people helping mow a lawn increases, the time it takes to mow the lawn decreases.

iii. The cost of having a house painted increases as the size of the house increases.

Type of variation that describes each relationship:

Direct variation describes the relationship i between the amount of fuel used on a trip and the size of the car and distance traveled.

This is because the amount of fuel used is directly proportional to the size of the car and distance traveled. As the size of the car and distance traveled increases, the amount of fuel used also increases.

Hence,

i is direct variation.

Inverse variation describes the relationship

ii between the number of people helping mow a lawn and the time it takes to mow the lawn.

This is because the number of people helping is inversely proportional to the time it takes to mow the lawn.

As the number of people helping increases, the time it takes to mow the lawn decreases.

Hence, ii is inverse variation.Joint variation describes the relationship iii between the cost of having a house painted and the size of the house.

This is because the cost of having a house painted is jointly proportional to the size of the house. As the size of the house increases, the cost of having it painted also increases.

Hence, iii is joint variation.

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Find the equation of the line joining Q(-1/2, 3.5) and midpoint AP [A(4, 1) P(3, 7).

Answers

Answer:

The equation of the line joining Q(-1/2, 3.5) and midpoint AP [A(4, 1) P(3, 7)] is y = (-5/19)x + (117/38)

Final answer:

The equation of the line joining Q(-1/2, 3.5) and the midpoint of AP (4, 1) and P(3, 7) is y = 0.125x + 3.5625. This is found using the two-point form of the equation of a line and the midpoint formula.

Explanation:

First, find the midpoint, M, of AP using the formula M = [(x1+x2)/2, (y1+y2)/2]. Plugging in the coordinates given for A(4,1) and P(3,7), M = [(4+3)/2, (1+7)/2] = [7/2, 8/2] = [3.5, 4]. Now, use the two-point form of the equation of a line to find the equation of the line QM: (y - y1) = m(x - x1), where m is the slope of the line. The slope is found by the formula (y2-y1)/(x2-x1). Substituting Q(-1/2, 3.5) and M(3.5, 4), you get m = (4 - 3.5)/(3.5 - (-1/2)) = 0.5/4 = 0.125. Now substitute Q(-1/2, 3.5) and m = 0.125 into the formula to get the equation of the line: (y - 3.5) = 0.125(x +1/2). This can be simplified as: y = 0.125x + 3.5625. So the

equation of the line

joining Q(-1/2, 3.5) and the midpoint of AP is y = 0.125x + 3.5625.

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the vertices of triangle ABC are A (-5,5) ​, B (-2,3) ​, and C (-4,3) . If ABC is reflected across the line y=1 to produce the image ​A'B'C', find the coordinates of the vertex C​'.

pls answer ASAP!!!!!!!!!!!!

Answers

Triangle ABC's vertices are A (-5,5), B (-2,3), and C (-4,3). The coordinates of the vertex C'are if ABC is reflected across the line y=1 to generate the image A'B'C' (-4, -1).

To reflect a point across the line y=1, we need to flip the y-coordinate over the line y=1.

The y-coordinate of point C is already 3, which is less than the line y=1. The distance between point C and the line y=1 is (1-3)= -2, which is negative, so we need to add twice this distance to the y-coordinate to get its reflection.

y-coordinate of C' = 3 + 2*(-2) = -1

Therefore, the coordinates of C' are (-4, -1).

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1. -10 = 5+y
2. 10x = 40
3. -2 = -4m = +10


if you can answer this I will brainliest

Answers

The solution to the equation -2 = -4m + 10 is m = 3.

Here are the solutions to the given equations:

1. -10 = 5+y

To solve for y, we need to isolate y on one side of the equation.

We can do this by adding 10 to both sides of the equation.

-10 + 10 = 5 + y + 10

Simplifying,

-0 = 5 + y

We can further simplify the equation by subtracting 5 from both sides of the equation.

-5 = y

Therefore, the solution to the equation -10 = 5+y is y = -5.2.

10x = 40

To solve for x, we need to isolate x on one side of the equation.

We can do this by dividing both sides of the equation by 10.10x/10 = 40/10

Simplifying,

x = 4

Therefore, the solution to the equation 10x = 40 is x = 4.3.

-2 = -4m + 10To solve for m, we need to isolate m on one side of the equation.

We can do this by subtracting 10 from both sides of the equation.-2 - 10 = -4m.

Simplifying,

-12 = -4mWe can further simplify the equation by dividing both sides of the equation by -4.-12/-4 = m3 = m.

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Math
Nia
A rectangular jewelry box is 9 1/3 Inches long, 7 1/2 Inches wide, and 4 2/5 Inches
tall. What is the volume of the jewelry box?
In³
V =

Answers

Therefore, the volume of the jewelry box is 462 cubic inches.

What is volume?

Volume is the amount of space occupied by a three-dimensional object or substance. It is a physical quantity that describes how much space an object takes up. The unit of measurement for volume depends on the system of measurement being used, but some common units include cubic meters (m³), liters (L), and fluid ounces (Fl oz).

In simple terms, volume is the measure of how much a container can hold. For example, if you pour water into a cup, the volume of water that the cup can hold is equal to the volume of the cup. Similarly, if you have a box, the volume of the box is the amount of space it occupies, and you can calculate it by multiplying its length, width, and height.

To find the volume of the rectangular jewelry box, we need to multiply its length, width, and height. However, we need to first convert the mixed numbers to improper fractions to perform the multiplication accurately.

[tex]V = length x width x height[/tex]

[tex]Width = 7 1/2 inches = (7 x 2 + 1)/2 inches = 15/2 inches[/tex]

[tex]Height = 4 2/5 inches = (4 x 5 + 2)/5 inches = 22/5 inches[/tex]

Now, we can calculate the volume using the formula:

[tex]V = length x width x height[/tex]

[tex]V = (28/3) x (15/2) x (22/5) cubic inches[/tex]

[tex]V = 13860/30 cubic inches[/tex]

V = 462 cubic inches (rounded to the nearest whole number)

Therefore, the volume of the jewelry box is 462 cubic inches.

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a jar contains 30 red marbles, 50 blue marbles, and 20 white marbles. you choose one marble from the jar at random. what is the theoretical probability of choosing a blue marble?

Answers

Answer: 1/2 chance of drawing a blue marble

Step-by-step explanation:

Add the total number of marbles.

30+50+20=100

then put the number of marbles you are trying to find over the total number of marbles.

blue/total = 50/100 =.5

Answer:

P(blue) = 1/2

Step-by-step explanation:

P(blue) = number of blue marbles / total number of marbles

blue marbles = 50

Total marbles = 30+50+20 = 100

P(blue) = 50/100 = 1/2

Given f(x) = 3x2 − 6x − 13, what is the domain of f(x)? all real numbers x ≥ 1 x ≤ −6 x ≥ −13

Answers

In summary, the domain of the given function f(x) =[tex]3x^2 - 6x - 13[/tex] is all real numbers.

The domain of a function is the set of all possible input values (x-values) for which the function is defined. In this case, the function f(x) is a quadratic function, which is given by [tex]f(x) = 3x^2 - 6x - 13.[/tex]

Quadratic functions are defined for all real numbers.

There are no restrictions on the input values of x for this function.

Therefore, the domain of f(x) is all real numbers.
To answer the student question, the correct option is "all real numbers."

The other options, "x ≥ 1," "x ≤ -6," and "x ≥ -13," do not apply in this case as there are no constraints on the values of x for a quadratic function.

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What value of a satisfies the equation -3 (4x - 5) = 2 (1 - 5x)?

Answers

Answer:

x = 6.5

Step-by-step explanation:

-3 × ( 4x - 5 ) = 2 × ( 1 - 5x )     ------------->      (By multiplying each bracket times its coefficient)

= -12x + 15 = 2 - 10x      ------------->     (By subtracting "2" from each side)

= -12x + 13 = -10x       -------------> (By moving the "-10x" to the other side and the "13" to the right side different signs "-10x becomes +10x and 13 becomes -13")

= -12x + 10x = -13

= -2x = -13             ------------->   (Dividing by "-2")

then, x = 6.5

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Write f(x) = 5(x - 2)2 - 7 in standard form.​

Answers

To write f(x) = 5(x - 2)2 - 7 in standard form, we need to expand the squared term first:

f(x) = 5(x - 2)(x - 2) - 7

f(x) = 5(x2 - 4x + 4) - 7

f(x) = 5x2 - 20x + 13

Therefore, the standard form of f(x) = 5(x - 2)2 - 7 is f(x) = 5x2 - 20x + 13.

Answer: f(x)=5x2−20x+13

Step-by-step explanation:

which xxx best defines the function's integer vector parameter scores, if scores has a large amount of elements, and the function will not change scores?

Answers

The syntax function_name(const vector<int>& scores) best defines the function's integer vector parameter scores, if scores has a large amount of elements, and the function will not change scores.

To define a function's integer vector parameter scores if scores has a large amount of elements and the function will not change scores, we can use the following syntax in most programming languages:

function_name(const vector<int>& scores)

This defines a function called function_name that takes an integer vector parameter called scores, which is passed by reference using the '&' operator and is not modified by the function. The 'const' keyword indicates that the function will not modify the contents of the vector.

By using this syntax, we ensure that the function can accept any size of the integer vector scores and that it does not modify the contents of the vector. This is important because it allows us to write functions that can be used with different data sets without changing the original data.

It also ensures that the function is efficient and does not require unnecessary copying or allocation of memory.

Passing the vector by reference also means that the function can access the vector's elements without making a copy of the entire vector, which can be beneficial for performance when dealing with large data sets.

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3. Classify each of the given sets of measurements
as one unique triangle, multiple triangles, or no A.
Place the letter in the correct box.
a) 52, 63, 65°
b) 31°, 102°, 46°
c) 70.6°, 47.4°, 62°
e)
f)
7.9 cm, 2.4 cm, 2.9 cm
12% in, 6 % in, 5 % in
124 mm, 432 mm, 385 mm

Answers

The Classify each of the given sets of measurements is given below:

How to Classify each of the given sets of measurements

a) 52, 63, 65°: These measurements form a unique triangle. This is a right-angled triangle, also known as a Pythagorean triple.

b) 31°, 102°, 46°: These measurements do not form a triangle. The sum of the angles in a triangle is always 180°, but in this case, the sum is 179°, which is less than 180°.

c) 70.6°, 47.4°, 62°: These measurements do not form a unique triangle. There are multiple possible triangles that can be formed with these measurements.

d) 3 cm, 4 cm, 5 cm: These measurements form a unique triangle. This is another example of a Pythagorean triple.

e) 7.9 cm, 2.4 cm, 2.9 cm: These measurements do not form a triangle. The sum of the two smaller sides is less than the length of the largest side, which violates the triangle inequality.

f) 12% in, 6% in, 5% in: These measurements do not form a triangle. The sum of the two smaller sides is less than the length of the largest side, which violates the triangle inequality.

g) 124 mm, 432 mm, 385 mm: These measurements form a unique triangle.

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Ryan Is in charge of planning a reception for 2600 people. He is trying to decide which snacks to buy. He has asked a random sample of people who are coming to the reception what their favorite snack is. Here are the results.

Answers

we get a predicted number of 1111 people whose favorite snack will be pretzels or cookies at the reception.

How to deal with random sample?

The sample provides information about the favorite snack of a random sample of people, but we need to use this information to make a prediction about the whole population of 2600 people.

First, we can calculate the proportion of the sample who chose pretzels or cookies as their favorite snack:

proportion = (number of people who chose pretzels + number of people who chose cookies) / total number of people in the sample

proportion = (16 + 54) / (30 + 16 + 54 + 64)

proportion = 70 / 164

proportion ≈ 0.4268

Next, we can use this proportion to estimate the number of people who will choose pretzels or cookies as their favorite snack out of the whole population:

predicted number of people = proportion × total number of people in the population

predicted number of people = 0.4268 × 2600

predicted number of people ≈ 1110.8

Rounding to the nearest whole number, we get a predicted number of 1111 people whose favorite snack will be pretzels or cookies at the reception.

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Find g(x), where g(x) is the translation 5 units left of f(x)=x2.
Write your answer in the form a(x–h)2+k, where a, h, and k are integers.

Answers

The function g(x) in the form a(x - h)² + k is g(x) = (x + 5)² + 0, where a = 1, h = -5, and k = 0.

What is the function?

Starting with the function f(x) = x², a translation 5 units left can be achieved by replacing x with (x + 5), since (x + 5) is 5 units to the left of x. Therefore, we have:

g(x) = f(x + 5)

g(x) = (x + 5)²

g(x) = x² + 10x + 25

This is the equation of the parabola obtained by translating the graph of y = x² five units to the left. We can write this equation in the desired form of a(x - h)² + k by completing the square:

g(x) = x² + 10x + 25

g(x) = 1(x² + 10x) + 25

g(x) = 1(x² + 10x + 25 - 25) + 25

g(x) = 1((x + 5)² - 25) + 25

g(x) = 1(x + 5)² - 1(25) + 25

g(x) = (x + 5)² + 0

Therefore, the function g(x) in the form a(x - h)² + k is g(x) = (x + 5)² + 0, where a = 1, h = -5, and k = 0.

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1) The fish population in a pond is increasing
at a rate of 5% per year. The starting
number of fish in the pond was 32 fish.
How many fish will be in the pond after 4
years.

Answers

The fish in the pond after 4 years will be 38 fish

I need help with these questions

Answers

1/9 times x to the power of 2

may someone solve this please and show work, thank u

Answers

Answer:

minutes took to finish the race = 54 minutes

Step-by-step explanation:

It's known that:

[tex]speed = \frac{distance}{time}[/tex]

then:

[tex]time = \frac{distance}{speed}[/tex]

IN THE 1ST 10 MILES:

time = [tex]\frac{10}{25} = \frac{2}{5} = 0.4 hours[/tex]

IN THE 2ST 10 MILES:

time = [tex]\frac{10}{20} = 0.5 hours[/tex]

Hence, Overall time took to finish the race = 0.4 + 0.5 = 0.9 hours

time in minutes = 0.9 × 60 = 54 minutes


Another Solution:

Overall speed = [tex]\frac{S_1 + S_2}{2}[/tex], Where: S1: 1st speed, S2: 2nd speed

then:

speed = [tex]\frac{25 + 20}{2}= 22.5 mph[/tex]

Hence, time took = [tex]\frac{20}{22.5} = 0.9 hours = 54 minutes[/tex]




hope you find this easy to understand....

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give me brainliest if you found this answer useful

whats the answer plss hurryy upp plss

Answers

The correct answer would be 24 and 90 degrees due to the quadratic formula.

Can anyone please answer this question

Answers

The area of shaded part in the figures are

1. 7.07cm²

2. 19.54cm²

What's area of a shape?

The area is the amount of space within the perimeter of a 2D shape. It is measured in square units, such as cm², m², etc.

The area of a sector is expressed as:

A= tetha/360 × πr²

Area of the shaded part = area of big sector - area of small sector.

1. area of big sector = 90/360 × 3.14 × 5²

= 7065/360

= 19.63cm²

area of small sector = 90/360 × 3.14 × 4²

= 12.56cm²

area of shaded part = 19.63 - 12.56

= 7.07cm²

2. Area of big sector = 40/360 × 3.14 × 9²

= 28.26cm²

area of small sector = 40/360 × 3.14 × 5²

= 8.72

area of shaded part = 28.26-8.72

= 19.54cm²

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What is the minimum value of the function over the interval -5 < x < 5? h(x) = log[(x – 5)2 + 3]

Answers

The minimum value of the function h(x) = log[(x - 5)² + 3] over the interval -5 < x < 5 is approximately log[3.000001].

The minimum value of the function h(x) = log[(x - 5)² + 3] over the interval -5 < x < 5 can be found through the following.

Recognize that the logarithm function is increasing.

Minimize the argument of the logarithm, i.e., (x - 5)² + 3.

Observe that (x - 5)² is always non-negative since it is a square of a real number.

The minimum value of (x - 5)² occurs when x = 5 (in this case, (x - 5)² = 0).

However, x cannot be equal to 5 because the interval is -5 < x < 5.

Since the interval is open, find the minimum value for (x - 5)² in this interval, which occurs when x is as close to 5 as possible within the given interval. This would be x = 4.999.

Substitute this value of x into the function:

h(x) = log[(4.999 - 5)² + 3] = log[0.001² + 3] ≈ log[3.000001].

Hence, the minimum value of the function h(x) = log[(x - 5)² + 3] over the interval -5 < x < 5 is approximately log[3.000001].

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Mr James works a basic week of 40 hours at a rate of $16 an hour. His overtime rate
is $4 per hour MORE than his basic rate.

Calculate:
(a) his total wage for a basic week,

(b) his wage for a week in which he worked 47 hours,

(c) the number of hours he worked during one week if he was paid a wage of $860.

Answers

Answer:

Sure, I can help you with that. (a) His total wage for a basic week can be calculated as follows: Total wage for a basic week = Basic rate per hour x Number of hours worked in a basic week Total wage for a basic week = $16 x 40 Total wage for a basic week = $640 Therefore, his total wage for a basic week is $640. (b) His wage for a week in which he worked 47 hours can be calculated as follows: Wage for a week with overtime = (Basic rate per hour + Overtime rate per hour) x Number of overtime hours worked + Total wage for a basic week Overtime rate per hour = Basic rate per hour + $4 Overtime rate per hour = $16 + $4 Overtime rate per hour = $20 Wage for a week with overtime =$16

Which ordered pair is the best estimate for the solution of the
system of equations?
y=-1/5x+1
y=x+4
O (-2.25, 1.75)
O (-2.75, 1.25)
O(-2.75, 1.75)
O (-2.5,1.5)

Answers

The ordered pair is (-2.5, 1.5).


y=-1/5x + 1
y= x+4
First, substitute the lower equation in the system into the upper equation’s y variable. x+4 = (-1/5)x + 1
Now we want to isolate the variable, x.
x + (1/5)x = 1 - 4
Multiply both sides by 5.
5x + x = -15
Which simplifies to
6x = -15
Divide both sides by 6;
x = -2.5

To find y, substitute the x value we just found into the lower equation in the system (since it’s easier).
y = -2.5 + 4
which simplifies to
y = 1.5


So, the best estimate for the solution to the system of equations is the ordered pair (-2.5, 1.5)
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