The curved part of this figures is a semicircle.

What is the best approximation for the area of this figure?

Responses

28+16.25π units²
18 plus 16.25 pi, units²

14+16.25π units²
14 plus 16.25 pi, units²

14+8.125π units²
14 plus 8.125 pi, units²

28+8.125π units²
28 plus 8.125 pi, units²
Coordinate plane with axes labeled x and y. A closed figure is formed by two segments and a semicircle. A segment extends from negative 4 comma negative 2 to negative 4 comma 2. Another segment extends from negative 4 comma 2 to 3 comma 2. A semicircle extends from 3 comma 2 to negative 4 comma negative 2.

The equation formed when x is the subject of the function f(x) = x² - 9, has two values of output for each input value to the function, therefore;

f(x) = x² - 9 does not have an inverse.

An inverse of a function is an anti function that reverses the values in the output into the input values thereby undoing the operations performed by the function.

A function f has an inverse if and only if it is bijective, such that there is a one to one correspondence between the set of the input elements and the set of the output elements

A function that has an inverse is said to be a bijective or invertible function or a function with one-to-one correspondence

The function in the question f(x) = x² - 9

Making x the subject of the function to verify if it has an inverse gives;

x² = f(x) + 9

[tex]x = \pm\sqrt{f(x) +9}[/tex]

Putting x = f⁻¹(x) gives;

[tex]f^{-1}(x) = \pm\sqrt{x +9}[/tex]

Therefore, each value of x gives two values of f⁻¹(x), such that the set of the output of inverse function, f⁻¹(x) does not have a one-to-one correspondence with the set of values of x.

The function f(x) = x² - 9 is not invertible and therefore does not have an inverse function.

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The function f(x) is decreasing on the interval x∈(1/2,∞) and all the real values.

A function from a set X to a set Y in mathematics assigns to each element of X exactly one element of Y. The domain of the function is the set X, and the codomain of the function is the set Y.

The first known approximation to the concept of function is attributed to the Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were originally idealistic representations of how one variable quantity depended on another. The location of a planet, for example, changes throughout time. Historically, the concept was formed with infinitesimal calculus near the end of the 17th century, and the functions that were analyzed were differentiable until the 19th century.

Given function,

f(x)=[tex]e^{2 x^{2} +5}[/tex]/-6x

f'(x)=-1/6x([tex]e^{2 x^{2} +5}[/tex])(4x)+[tex]e^{2 x^{2} +5}[/tex](1/6x²)

=[tex]e^{2 x^{2} +5}[/tex]/6x((1/x)-4x)

f'(x)=0

((1/x)-4x)=0

1-4x²=0

4x²=1

x=±1/4

Given that, f(x) is decreasing function then,

f'(x)<0

((1/x)-4x)<0

(1-4x²)/x<0

1-4x²<0

1<4x²

1/4<4x²

x²>1/4

x>1/2

x∈(1/2,∞)

Hence, f(x) is decreasing on the interval x∈(1/2,∞)

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The number of points scored by Tyger will be 132 points.

From the information, Captain scores 120 points on Space Invaders. Tyger scores 10% more points than Captain.

Therefore, the number of points scored by Tyger will be:

= Points scored by Captain + (Percentage × Captain point)

= 120 + (10% × 120)

= 120 + 12

= 132

Tyger scored 132 points.

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The number of points scored by Tyger will be 132 points.

From the information, Captain scores 120 points on Space Invaders. Tyger scores 10% more points than Captain.

Therefore, the number of points scored by Tyger will be:

= Points scored by Captain + (Percentage × Captain point)

= 120 + (10% × 120)

= 120 + 12

= 132

Tyger scored 132 points.

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Answer:

positive 3

Step-by-step explanation:

Steps:

1. first you must get y by itself/isolate it to one side of the equation to get it in the format of y = mx + b

-3x + 2y = 6

+3x           +3x            add 3x to both sides to get 2y by itself
____________

2y = 3x + 6                -3x+3x cancels out and becomes 0

-------------------------
         2                        divides both sides by 2 to get y by itself

y = (3/2)x + 3

2. Looking at the equation, we know that 3 is the y-intercept because the "b" in the slope-intercept equation is always the y-intercept.

Step-by-step explanation:

r - 535 = 175

r = 175 + 535 = 710

Answer:

take - 535 to the other side (over equal to side)

which makes it +535

r = 175 + 535

r = 710

The graph of the linear equation can be seen in the image at the end.

We start by defining the variables we will use:

x = number of weeks.

y = money that Anika has.

We assume that Anika starts with $0, and then she wins $5 each week, so after x weeks she has:

y = $5*x

To graph this linear equation we need to find two points on the line, if x = 0 we get:

y = $5*0 = $0

So we have the point (0, 0)

if x = 1

y = $5*1 = $5

So we have the point (1, 5)

Now we can graph these two points and connect them with a line, the graph can be seen below.

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Option A. The statement that can be said to be true for h is h(2) = 16

If we look at the domain and range, we can rule out some straight away.

For h - 3 = -1

this is outside of the range of the such that -1 ∉ 1 ≤ hx ≤ 25

When h is 13 = 18

This is also outside of the domain such that 13 ∉ -3 ≤ x ≤ 11

When h is 8 = 21

there is going to be a contradiction with what the question has stated earlier. This is because we are told that h(8) = 19

Therefore on h(2) = 16

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Answer:

5 is added each time. the next numbers are, 29, 34 and 39

Step-by-step explanation:

9+5 = 14 14+5=19 19+5=24

If you multiply by 12 you will get rid of all your fractions.

In mathematics, a linear equation is one that may be written in the form where the variables are alphabets, and the coefficients are frequently real integers. An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

It is rather simple to locate both intercepts when an equation is stated in this way (x and y).

The given linear equation is

6 - (3/4)x + (1/3) = (1/2)x + 5

In this equation the fractions are
(3/4), (1/3) and (1/2)

Take the LCM of 4, 3, and 2

LCM(4, 3, 2) = 12

So, if we multiply the equation with the number 12  we can eliminate the fractions.

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Answer:

[tex]\frac{4}{7}[/tex]

Step-by-step explanation:

Slope = m

m = [tex]\frac{y_{2}- y_{1}}{x_{2}-x_{1}}[/tex]

m = [tex]\frac{7-3}{9-2}[/tex] = [tex]\frac{4}{7}[/tex]

According to the histogram, the percentage of participants aged 40 to 59, who attended the restaurant's food festival, is 35%.

A histogram approximately represents a distribution of grouped data with numerical values.

A histogram uses rectangular bars to show the frequency of data items in successive numerical intervals of equal sizes.

Age Group (year)  Number of People

0 to 19                            20

20 to 39                         40

40 to 59                         60

60 to 79                         50

Total                             170

Percentage of ages 40 to 59  =  60/170 x 100 = 35.29%

Thus, using the histogram, we can assure the restaurant manager that 35% of the festival participants are between 40 and 59 years old.

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Answer:

The letter a in an ellipse equation is:

Step-by-step explanation:

General equation of an ellipse

[tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex]

where:

If a > b the ellipse is horizontal, a is the major radius, and b is the minor radius.

If b > a the ellipse is vertical, b is the major radius, and a is the minor radius.

The major axis is the longest diameter of an ellipse, so the major radius is one half of the major axis.

The minor axis is the shortest diameter of an ellipse, so the minor radius is one half of the minor axis.

Therefore the letter a in an ellipse equation is:

Step-by-step explanation:

the area of a triangle is

base × height / 2

in our case

base × height / 2 = 196 mm²

base × height = 392

base = height / 2

so, using that in our main equation :

(height / 2) × height = 392

height² = 784

height = sqrt(784) = 28 mm

base = height / 2 = 28/2 = 14 mm

The perpendicular distance from R to PQ is ​346 feet.

What are the trigonometric functions?

The right-angled triangle's angle and the ratio of its two side lengths are related by the trigonometric functions, which are actual functions. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.

We have,

consider the sides of leaning tower are,

opposite side of the angle 56° (x) = 180.5 feet.

Adjacent side of the angle 56° (y) = 125 feet.

We know,

[tex]tan\theta =\frac{ opposite \ side}{ adjacent \ side} = \frac{x}{y}[/tex]

[tex]\theta = \ tan^{-1} \left(\frac{ opposite \ side}{ adjacent \ side} \right)[/tex]

The angle of elevation is  [tex]\theta = \ tan^{-1} \left(\frac{180.5 }{125} \right)[/tex]

θ = 56°

The perpendicular distance from R to PQ is RQ ​

[tex]sin\theta = \frac{opposite side}{hypotanous} = \frac{180.5}{y}[/tex]

sin(56) = 180.5/PQ

RQ = 180.5/sin(56)

RQ = - 346.08

RQ = 346 (distance never be negative),

Hence, the perpendicular distance from R to PQ is ​346 feet.

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What is the place value of digit 4 in 405,799:

4: one hundred thousandth place

0: ten thousandth place

5: one thousandth place

7: hundredth place

9: tens place

9: ones place

Answer:

100,000 thousand

Step-by-step explanation:

The number 405799 has six digits, and each digit has a specific place value based on its position within the number. The rightmost digit, which is 9, is in the one's place. Moving to the left, the next digit is 9 again, but this time it is in the ten's place. Continuing left, the next digit is 7, which is in the hundred's place. The digit 5 is in the thousand's place, and the digit 0 is in the ten thousand's place. Finally, the digit 4 is in the hundred thousand's place, so the place value of the digit 4 in 405799 is 100,000.

Answer:

5 = 1

or

5 = 25

Step-by-step explanation:

I've seen two answers to this.

1. Since we are told 1 = 5, then 5 = 1.

One answer is 1 = 5

2. Since each number on the right is 5 times the number on the left, then 25 corresponds to 5, and 5 = 25.

Answer: 5=1 (The correct answer) 5=25 (The answer that makes sense but is not correct).

Step-by-step explanation:

Explanation for answer 1: It say's that 1 = 5.

Explanation for answer 2: If we follow the pattern of adding 5 each time we go up a number then 5 would equal 25.

Answer:

10x+6xy+4

Step-by-step explanation:

2(5x+2)-(3y) 2x-4x

By removing the bracket

10x+4-6xy+12xy

10x+4+6xy

10x+6xy+4

We can learn from the graph that ANNIE is required to walk 14 blocks.

How to solve a graph.-

acc to the question-

fruit vendor=(-3,7)

pet store-=(-1,6)

supermarket=(1,5)

annie's house=(1,4)

Hence,We can learn from the graph that ANNIE is required to walk 14 blocks.

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The calculation of the following income statement figures are as follows:

The income statement is the first financial statement that summarizes the revenues and expenses for a business period to arrive at different profit points.

One of the profit points is the gross profit, which is the difference between the sales revenue and the cost of goods sold.

The other profit points include the operating income, income before tax, and net income.

Gross sales                            $170,000

Sales returns and allowances   9,000

Net Sales                               $161,000

Cost of goods sold:

Beginning inventory $8,000

Net purchases           18,000

Ending inventory       (5,000) $21,000

Gross profit                          $140,000

Operating expenses             (56,000)

Net Income                          $84,000

Thus, the calculation of the income statement figures shows a net income of $84,000.

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Answer:

x+7=4/3x-1/3 One solution was found : x = 22 Rearrange: Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : ... 3x-9/4x-12: correct answer right here

Step-by-step explanation:

Answer:

72.624 kg

Step-by-step explanation:

1g = 0.001 kg

104g = 0.104kg

weight of 1 bag  = 12.104kg

weight of 6 bags = 12.104 x 6

weight of 6 bags = 72.624kg

By evaluating in x = 0, we can see that the function with the greater y-intercept is the first one:

y=-x+6

For any function y = f(x), we define the y-intercept as the value that y takes when we evaluate the function in x = 0.

For the first function:

y = -x + 6

The y-intercept is:

y = -0 + 6 = 6

While for the second function:

y = 2x - 3

Evaluating in 0 we get:

y = 2*0 - 3 = -3

So the y-intercept of the first function is 6, and the one of the second function is -3.

Then the first function has the greater y-intercept.

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Answer:

3:2

Step-by-step explanation:

You need to find two more equivalent ratio of cups of sparkling water to cups of juice concentrate that would make a mixture that tastes the same as this recipe.

Another mixture of sparkling water and grape juice that would taste different than this recipe is 3 : 2 of cups of sparkling water to cups of juice concentrate

Ratio of cups of sparkling water to cups of grape juice concentrate is 3 to 1

ratio of cups of sparkling water : cups of grape juice concentrate = 3 : 1

Equivalent ratio to 3 : 1 are

6 : 2,

9 : 3,

12 : 4

15 : 5

21 : 7

Non equivalent ratio of 3 : 1 are

3 : 2

4 : 2

5 : 5

6 : 4

Therefore, another mixture of sparkling water and grape juice that would taste different than this recipe is 3 : 2 of cups of sparkling water to cups of juice concentrate

Answer: Can't Say for sure but probably it is so I would Say Yes.

The length of the railing is 105.81 inches.

Given,

The stair has 7 steps

The rise of each step = 8.5 inches

The tread of each step = 12.5 inches

Slope of each step = x

We have to find the length of the railing.

Length of railing = 7x

Then,

Slope of step, x can be determined using Pythagorean theorem.

Let rise be the height of the right angled triangle and tread be the base of the triangle

Then,

Hypotenuse= Slope, x  = [tex]\sqrt{Rise^{2} + Tread^{2} }[/tex]

x = [tex]\sqrt{8.5^{2}+ 12.5^{2} }[/tex]

x = [tex]\sqrt{72.25 + 156.25}[/tex]

x = √228.5

x = 15.12 inches

That is,

The slope, x of one step is 15.12 inches

Now,

Length of the railing = 7x = 7 × 15.12 = 105.81 inches

Therefore,

The length of the railing is 105.81 inches.

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The two z values that the middle 67% of the area is bounded by them are -3.999 and 3.999.

In all continuous probability distributions,  it is possible to calculate the percentiles, which are defined as the value of the random variable that leaves an area equal to the percentile to the left of the distribution. When it comes to a central percentile, the area is distributed and the percentile is determined using a table of values or technology.

The area between the two boundaries is 0.67and the remaining area is 0.33  (= 1-0.56) , which is to the left of it.

Look into the z table to find the area between z=-x and mean and z=x and mean. According to z score table z=0.44 has 0.67 of the area to the left of (below) it. That means z=-0.44 has 0.67 of the area to the right of (above) it.

Therefore, the two z values are 0.44  and -0.44.

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The two z values that the middle 67% of the area is bounded by them are -3.999 and 3.999.

In all continuous probability distributions,  it is possible to calculate the percentiles, which are defined as the value of the random variable that leaves an area equal to the percentile to the left of the distribution. When it comes to a central percentile, the area is distributed and the percentile is determined using a table of values or technology.

The area between the two boundaries is 0.67and the remaining area is 0.33  (= 1-0.56) , which is to the left of it.

Look into the z table to find the area between z=-x and mean and z=x and mean. According to z score table z=0.44 has 0.67 of the area to the left of (below) it. That means z=-0.44 has 0.67 of the area to the right of (above) it.

Therefore, the two z values are 0.44 and -0.44.

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[tex]log_{4}(2) + log_{4}(3)+ log_{4}(5+2x)[/tex] is the completely expanded logarithmic expression .

Logarithm, an exponent or power that must be raised to obtain a particular number. Mathematically, if bx = n then x = logb n then x is the logarithm of n to  base b. Example: 23 = 8; so 3 is the base 2 logarithm of 8, or 3 = log2 8.

The most common types of logarithms are  the base 10 common logarithm, the base 2 binary logarithm, and  the base  e ≈ 2.71828 natural logarithm.

the product rule for logarithms is

[tex]log_{b}(MN) = log_{b}(M) + log_{b}(N)[/tex]  for b > 0

now ,

[tex]log_{4}(6(5 + 2x)) \\\\log_{4}(6) + log_{4}(5 + 2x)\\ \\ log_{4}(2.3) + log_{4}(5 + 2x) \\\\ log_{4}(2) + log_{4}(3)+ log_{4}(5 +2x)[/tex]

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Answer:

its D

Step-by-step explanation:

calculator

4500 is the Cost price.

What do you mean by price at cost?

SP = 5625

Profit = 25%

CP = ?

 CP =    5625/125 * 100

       = 45 * 100

       = 4500

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The plane flies at a speed of 150mph

A plane can fly 300 miles in the same time as it takes a car to go 120 miles

Let the time taken be t

Let the speed of the plane be x

the car travels 90 mph slower than the plane,

Speed of the car is x - 90

Speed = distance / time

Time taken by plane = time taken by car

300/ x = 120/x - 90

300(x - 90) = 120x

300x - 27000 = 120x

300x - 120x = 27000

180x = 27000

x = 27000/180

x = 150

Therefore, the plane flies at a speed of 150mph

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