Find the area of the shaded figure

The Justification for the 5th statement is option B Distance formula.

The distance formula is one that is seen as a mathematical formula used to calculate the distance that exist between two points in a coordinate plane.  it is seen as:

The distance between two points (x₁, y₁) and (x₂, y₂) is given by:

d = \(\sqrt{(x_{2} - x_{1} )^2 + (y_{2} -y_{1} )^2}\)

In this formula,  (0,0) to  (0, 2) will be inputted as:

d = \(\sqrt{(0 - 0 )^2 + (2 -0 )^2} = \sqrt{2^2} = 2\)

Therefore  this statement of the justification is also the distance Formula,  so we assume the distance from (0,0) to  (1, √2) that brings about 2 and is also seen as the radius of the circle.

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4 - 7x ≥ 11,  The graph will be a straight line parallel to y axis passing through x = -1 and the right hand side of the graph will be the solution.

-9x - 3 ≤ -57, The graph will be a straight line parallel to y axis passing through x = 6 and the left hand side of the graph will be the solution.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), larger than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

A assertion that an inequality exists between two values is known as an equation. It is often expressed as a pair of expressions specifying the relevant values and a relational sign showing the particular inequality connection between them.

Treat the,≥, >, or sign as a = sign when putting an inequality on a graph. Graph the equation as a dotted line if the inequality is either or. Graph the equation as a solid line if the inequality is either or.

The Equation are :

4 - 7x ≥ 11

⇒ x ≥ -1

The graph will be a straight line parallel to y axis passing through x = -1 and the right hand side of the graph will be the solution.

Again

-9x - 3 ≤ -57

-9x ≤ -54

x ≤ 6

The graph will be a straight line parallel to y axis passing through x = 6 and the left hand side of the graph will be the solution.

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Answer:

5h=25

/5    /5

1h= 5

h=5

(hope this helped)

Daniel will read approximately 193 pages in one hour if he continues reading at the same rate.

Since Daniel read 77 pages in $\frac{2}{5}$ of an hour, we can set up the proportion:

$\frac{77}{\frac{2}{5}} = x$

where $x$ is the number of pages he would read in 1 hour.

To solve for $x$, we can simplify the left side of the equation by multiplying both the numerator and denominator by 5, which gives:

$\frac{77 \times 5}{2} = x$

Simplifying this expression gives:

$192.5 = x$

Therefore, if Daniel continues reading at the same rate, he will read 192.5 pages in one hour. However, since the number of pages must be a whole number, we can round this answer to the nearest whole number to get:

$x \approx 193$

So, Daniel will read approximately 193 pages in one hour if he continues reading at the same rate.

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Answer: Average time a customer will spend in the queue is zero minutes.

Given

Customers arrive once every 4 minutes (standard deviation = 7) and services take 3 minutes (standard deviation = 6.6).

We have to find the average time a customer will spend in the queue (in minutes).

Formula used:

To find the average time a customer will spend in the queue,

we need to use

Little's Law: L = λ

Where,

L is the average number of customers in the queue,

λ is the arrival rate and

W is the average time a customer spends in the queue.

Calculation:

λ = 1/4 = 0.25 per minute

Using Little's Law:

L = λW ⇒ W = L/λ

Now we have to calculate

L.L = λ² / (μ - λσ)

where,

μ is the average service rate, and σ is the standard deviation of service times.

μ = 1/3 = 0.333 per minute

σ = 6.6L = (0.25)² / (0.333 - 0.25 x 6.6)≈ 0.004/(0.333 - 1.65)≈ -0.004/1.317L ≈ -0.003W = L/λ = -0.003/0.25 ≈ -0.012 minutes

Since the average time a customer cannot be negative, the answer must be zero.

Therefore, the average time a customer will spend in the queue is zero minutes.

Answer: Average time a customer will spend in the queue is zero minutes.

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Example of  linear inequalities; y ≤ x – 1 and y < –2x + 1

A combination of linear inequality equations with the same variables is referred to as a system of linear inequalities.

There are five inequality symbols used to represent equations of inequality.

These are less than (<), greater than (>), less than or equal (≤), greater than or equal (≥), and the not equal symbol (≠). Inequalities are used to compare numbers and determine the range or ranges of values that satisfy the conditions of a given variable.

Example of  linear inequalities;

Graph the following system of linear inequalities:

y ≤ x – 1 and y < –2x + 1

Graph the first inequality y ≤ x − 1.

We will draw a solid border and shade below the line due to the "less than or equal to" mark.

On the same x-y axis, graph the second inequality, y -2x + 1.

In this instance, the less-than symbol will cause our boundaries to be dashed or dotted. Under the border, cast a shade.

As a result, the darker-colored zone extending indefinitely downward is the solution to this inequality problem, as seen below.

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Answer: 45

Step-by-step explanation:

Hello there!

So this problem looks a lot more complex than it really is. First, we need to know that a straight line is 180 degrees. Since both of these angles must add up to 180, we just subtract 135 from 180. We then get 45.

Hope this helped! :D

Sorry if any information was incorrect or if i didn’t understand what you were asking. Just comment and I will reply back ready to help!

Answer:

The answer is 64

Step-by-step explanation:

When you are dealing with exponents you have to multiply the main number as many times as the exponent number. \(4^{3}\)

In this case, you multiply 4 three times

\(4*4 = 16\\16*4=64\)

Hey there! I'm happy to help!

We want to get m all by itself on one side of the equation. To do this, we use inverse operations on both sides of the equation to cancel out variables on one side to isolate m.

am/c=n

We multiply both sides by c.

am=nc

We divide both sides by a.

m=(nc)/a

I hope that this helps! Have a wonderful day! :D

Answer:

1.14, (11) Id.k

Step-by-step explanation:

I think you would do 64 divided by 7/8 which would be

1.14, which could be rounded to 11 students? Id.k

Answer:

56 students gave their speeches

Step-by-step explanation:

7/8 of 64 = 56

total divided by the denominator (bottom number)

64 / 8 = 8

answer to that multiplied by the numerator (top number)

8 x 7 = 56

The vertex of the function is (10, 0) which represents the minimum length of the paddle boards.

The vertex of a function is the point where the function reaches its maximum or minimum value.

For a quadratic function in standard form, f(x) = a(x - h)² + k, the vertex is located at the point (h, k).

If the leading coefficient (a) is positive, the parabola opens upwards and the vertex represents the minimum value of the function.

If the leading coefficient is negative, the parabola opens downwards and the vertex represents the maximum value of the function.

Here we have

The length of paddle boards function, v(x) = |x - 10|

Convert the given function into the standard form i.e  

=> f(x) = a(x - h)² + k

where (h, k) is the vertex of the function.

As we know |y| is the same as √(y²),  

=> v(x) = √[(x - 10)²]

On simplifying the expression we get:

v(x) = √[ x²- 20x + 100 ]

Now we can see that this is a quadratic function in standard form, with a = 1, h = 10, and k = 0. Therefore, the vertex of the function is:

=> (h, k) = (10, 0)

Therefore,

The vertex of the function is (10, 0) which represents the minimum length of the paddle boards.

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"meso-" and "medi-" both relate to the middle or intermediate position, but they may be used in different contexts and have distinct origins (Greek and Latin, respectively).

The prefixes "meso-" and "medi-" have different meanings:

Meso-: The prefix "meso-" generally means "middle" or "intermediate." It is derived from the Greek word "mesos," which carries the same meaning. In scientific and medical terminology, "meso-" is often used to indicate something that is located in the middle or intermediate position.

For example:

Mesoderm: The middle germ layer in the early development of an embryo.

Mesozoic: The era between the Paleozoic and Cenozoic eras, often referred to as the "Age of Reptiles."

Medi-: The prefix "medi-" typically means "middle" or "between." It is derived from the Latin word "medius," which conveys a similar sense. In various contexts, "medi-" is used to indicate something that is in the middle or intermediary position.

For example:

Median: Referring to the middle value in a set of numbers or the middle line or point dividing something into equal halves.

Mediastinum: The central area within the thoracic cavity, located between the lungs, which contains the heart, great vessels, and other structures.

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Answer:

0,7

Step-by-step explanation:

3,1 -> 2,3 -> 1,5 -> 0,7

The trigonometric inequality csc(x) > -sec(x) holds true in the interval (0, π/2) excluding π/4. The trigonometric inequality csc(x) > ~sec(x) holds true in the interval (0, π/2) excluding π/4.

The trigonometric inequality csc(x) > -sec(x) holds true in the following intervals:

1) In the interval (0, π/2) excluding π/4, the inequality csc(x) > -sec(x) is always true.

The trigonometric inequality csc(x) > ~sec(x) (approximately greater than) holds true in the following intervals:

1) In the interval (0, π/2) excluding π/4, the inequality csc(x) > ~sec(x) is always true.

Please note that the symbol "~" indicates approximate equality.

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Answer:

Try your legs a lot do some do triceps cause like if you dont do streteches your body will hurt  a lot

Step-by-step explanation:

The value of x in the given figure is 10.

In the given triangle,

∠ADC = ∠BDC =  90°

Hence the triangles ΔACD and ΔBCD are right-angle triangles. Thus we can apply Pythagoras' theorem in both triangles.

So in ΔACD,

CB² = BD² + DC²

And in ΔBCD,

CA² = AD²+ DC²

But, CA = 15 and CB = x + 5

So, (x + 5)² = BD² + DC²

15² = AD² + DC²

⇒225 = AD² + DC²

Here, BD = AD as given in the figure

Replacing BD with AD in the first equation we get,

(x + 5)² = AD² + DC²

Now, equate the values of AD² + DC² to obtain the value of x,

(x + 5)² = 225

⇒ x² + 25 + 10x = 225

⇒ x² + 10x - 200 = 0

⇒ x² + 20x - 10x - 200 = 0

⇒x(x + 20) - 10(x + 20) = 0

⇒(x + 20)(x - 10) = 0

Thus x = -20, 10

Hence the value of x is 10.

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Answer:

B

Step-by-step explanation:

In order for something to be a function, they must not have repeating x-values. Looking at the answer choices provided, B is the only answer that does not have repeating x-values.

Answer:

B or D but i think its B

Step-by-step explanation:

Answer:

5.4 is the answer

Step-by-step explanation:

Answer: Option 4

Step-by-step explanation:

I put the wrong answer oof

Answer:

sometimes used to distinguish between the measure of the angle

Step-by-step explanation:

Answer:

$40

Step-by-step explanation:

If the perimeter of the larger farm is 80 yards in a 8:5 ratio, the perimeter of the smaller farm will be 50 yards.

Multiply this value by the cost of 0.50 per yard to get $40.

Answer:

Step-by-step explanation:

The dimension of the basis is {[1 0 0 2], [-1 1 0 0]}.

To find a basis for the subspace S = span {[1 -1 0 2], [3 -5 4 8], [0 1 -2 -1]}, we can use the same method as in the example. First, we put the vectors in a matrix and row-reduce it:

[1 -1 0 2]
[3 -5 4 8]
[0 1 -2 -1]

R2 - 3R1 -> R2
R3 -> R3 + 2R1

[1 -1 0 2]
[0 -2 4 2]
[0 1 -2 -1]

-1/2R2 -> R2

[1 -1 0 2]
[0 1 -2 -1]
[0 1 -2 -1]

R3 - R2 -> R3

[1 -1 0 2]
[0 1 -2 -1]
[0 0 0 0]

We can see that the last row is all zeros, so we have only two pivots and one free variable. This means that the dimension of the subspace S is 2. To find a basis, we can write the pivots as linear combinations of the original vectors:

[1 -1 0 2] = [1 0 0 2] + [-1 1 0 0]
[0 1 -2 -1] = [0 1 -2 -1]

Therefore, a basis for S is {[1 0 0 2], [-1 1 0 0]}.

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Question 13.

The estimated monthly cost of an energy-efficient refrigerator is $57, meaning the yearly cost is

Question 14.

The least energy-efficient refrigerator costs $72 per month, meaning the annual cost is

Therefore, the amount you will save on an energy-efficient refrigerator be

Hence, the amount saved on an energy-efficient refrigerator will be $180.

Step-by-step explanation:

-4x + 3 < 23

-4x < 20

x > -5

hmm,I don't think we need to put equal sign instead of (<) , for when we started calculating.

we can just keep the question as it is and calculate.

The error Clare made in solving the inequality -4x + 3 < 23 is in the last step. The correct solution should be x > -5, not x < -5.

When dividing or multiplying both sides of an inequality by a negative number, the direction of the inequality symbol should be flipped. In this case, since we are dividing by -4, which is negative, the inequality should be reversed.

The correct steps to solve the inequality are as follows:

-4x + 3 < 23

Subtract 3 from both sides:

-4x < 20

Divide both sides by -4 (remembering to flip the inequality symbol):

x > -5

Therefore, the correct solution is x > -5, indicating that x is greater than -5, not less than -5 as Clare mistakenly wrote.

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Clare made an error when solving -4x + 3 < 23

-4x + 3 < 23

-4x < 20

x < - 5

Describe the error she made

A set of transformations that have been performed on the graph of f(x) = ∛x to obtain the graph of g(x) = 1/4(∛(x + 3) + 6 include the following:

A. Translate the graph up

B. Stretch the graph away from x-axis

E. Translate the graph to the left

In Mathematics, the translation a geometric figure or graph upward simply means adding a digit to the value on the y-coordinate of the pre-image or function.

In Mathematics, a horizontal translation to the left is modeled by this mathematical expression g(x) = f(x + N) while a vertical translation to the positive y-direction (upward) is modeled by this mathematical expression g(x) = f(x) + N.

Where:

In conclusion, we can logically deduce that the graph of the parent function was stretched away from x-axis.

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Answer:

w(t-4)=t^2-9t+20

Step-by-step explanation:

w(t)=t^2-t

w(t-4)=(t-4)^2-(t-4)

w(t-4)= t^2-8t+16-t+4

w(t-4)=t^2-9t+20

Answer:

64 cubic inches

Step-by-step explanation:

The formula to find the volume of a rectangular prism is

Length x Width x Height

Therefore, 2 x 8 x 4 = 64.