Sketch a graph of a function that satisfies the given limit statement:
[tex]\lim_{x \to \ 2^+} h(x)=5[/tex]

Answer:

To graph y = 1/2x and y = x + 2, follow these steps:

Make a table of values for each equation. Choose several values of x, plug them into the equation, and solve for y. For y = 1/2x, you might choose x = -2, -1, 0, 1, and 2. For y = x + 2, you might choose the same values of x.

For y = 1/2x:

x | y

-2 | -1

-1 | -1/2

0 | 0

1 | 1/2

2 | 1

For y = x + 2:

x | y

-2 | 0

-1 | 1

0 | 2

1 | 3

2 | 4

Plot the points from each table on a graph. For y = 1/2x, plot the points (-2, -1), (-1, -1/2), (0, 0), (1, 1/2), and (2, 1). For y = x + 2, plot the points (-2, 0), (-1, 1), (0, 2), (1, 3), and (2, 4).

Draw a line through each set of points. The line for y = 1/2x should have a slope of 1/2 and pass through the point (0, 0). The line for y = x + 2 should have a slope of 1 and pass through the point (0, 2).

Label the axes and the lines. You can label the x-axis "x" and the y-axis "y". Label the line for y = 1/2x "y = 1/2x" and the line for y = x + 2 "y = x + 2".

Check your graph. Make sure each point is plotted correctly and the lines are drawn accurately. You can also check your graph by plugging in other values of x and making sure the corresponding points are on the lines.

Use simultaneously equation to eliminate one value and find the other then you find the value of the other one by substituting the value that u find from the other one eg: eliminate X find the value of y and then substitute y in one of your equation to find the value of X.

The answer is sin(2x) = 0.8824.

If cot(x) = 5/3, we can use the identity cot(x) = 1/tan(x) to find the value of tan(x). Therefore, tan(x) = 1/(5/3) = 3/5.

Now, we can use the identity sin(2x) = 2sin(x)cos(x) to find the value of sin(2x). First, we need to find the values of sin(x) and cos(x).

Since tan(x) = 3/5, we can use the Pythagorean identity 1 = sin^2(x) + cos^2(x) to find the values of sin(x) and cos(x).

Let's assume sin(x) = 3/a and cos(x) = 5/a. Then, we can plug these values into the Pythagorean identity and solve for a:

1 = (3/a)^2 + (5/a)^2

1 = 9/a^2 + 25/a^2

1 = 34/a^2

a^2 = 34

a = √34

Therefore, sin(x) = 3/√34 and cos(x) = 5/√34.

Now, we can plug these values into the identity sin(2x) = 2sin(x)cos(x) to find the value of sin(2x):

sin(2x) = 2(3/√34)(5/√34)

sin(2x) = 30/34

sin(2x) = 0.8823529411764706

To 4 decimal places, sin(2x) = 0.8824.

the answer is sin(2x) = 0.8824.

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The domain of the expression is \( [-1,1] \).

To rewrite the quantity as an algebraic expression of \( x \), we need to use the definition of the cotangent function and the relationship between the sine and cosine functions. The cotangent function is defined as \[ \cot (\theta)=\frac{1}{\tan (\theta)}=\frac{\cos (\theta)}{\sin (\theta)} \]Using the relationship between the sine and cosine functions, \[ \cos^{2} (\theta)=1-\sin^{2} (\theta) \]we can rewrite the cotangent function in terms of the sine function as \[ \cot (\theta)=\frac{\sqrt{1-\sin^{2} (\theta)}}{\sin (\theta)} \]Substituting \( \arcsin (x) \) for \( \theta \) gives us \[ \cot (\arcsin (x))=\frac{\sqrt{1-\sin^{2} (\arcsin (x))}}{\sin (\arcsin (x))} \]Since \( \sin (\arcsin (x))=x \), we can simplify the expression to get \[ \cot (\arcsin (x))=\frac{\sqrt{1-x^{2}}}{x} \]This is the algebraic expression of the quantity in terms of \( x \).

The domain of the expression is the set of values of \( x \) for which the expression is defined. Since the expression involves a square root, we need to ensure that the radicand is non-negative. This gives us the inequality \[ 1-x^{2}\geq 0 \]Solving for \( x \) gives us the inequality \[ -1\leq x\leq 1 \]Therefore, the domain of the expression is \( [-1,1] \).

In conclusion, the quantity can be rewritten as an algebraic expression of \( x \) as \[ \cot (\arcsin (x))=\frac{\sqrt{1-x^{2}}}{x} \]and the domain on which the equivalence is valid is \( [-1,1] \).

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The probability of Steve picking a lime at random from the fruit bowl is 1/3.

Using the ratio given to find the proportion of oranges and kiwis in the fruit bowl. Let the number of oranges be 3x and the number of kiwis be 5x. Then the total number of fruits in the bowl is 3x + 5x + L, where L is the number of limes.

Given probability of picking an orange is 1/4, probability of picking a particular fruit from the bowl is calculated as:

number of that fruit / total number of fruits

1/4 = 3x / (3x + 5x + L)

Simplifying this equation, we get:

3x + 5x + L = 12x

L = 4x.

Substituting L = 4x and simplifying, we get:

probability of picking a lime = 4x / (3x + 5x + 4x) = 4/12 = 1/3

Therefore, the probability of picking a lime from the fruit bowl is 1/3.

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Answer:

- 75.00

Step-by-step explanation:

400 - 475 = - 75

Helping in the name of Jesus.

Answer:

She's in debt $75

Step-by-step explanation:

475-400=-75

Answer:

Mate show the full picture please..half of the question is not shown.

Step-by-step explanation:

Answer: p = (3.6 x 10^4)(0.03)^2

Step-by-step explanation:

The length of the segment indicated is c = c = 9.92.

Pythagoras discovered that the square of the hypotenuse in a right-angled triangle with a 90° angle is equal to the sum of the squares of the other two sides.

The triangle has three sides: the hypotenuse, which is always the longest, the opposite, which doesn't touch the hypotenuse, and the adjacent (which is between the opposite and the hypotenuse).

a² = b² + c²

a = 19

b = 16.2

c or x =?

19² = 16.2² + c²

361 = 262.4 + c²

c² = 98.6

c = √98.6

c = 9.92

Therefore, the length of the segment indicated is c = 9.92.

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Answer:

No

Step-by-step explanation:

6x-2

Factor out -1

( - -6x + -2)

- ( -6x +2)

- ( 2 -6x)

This is not equal to (2+6x) because of the negative sign out front.

Answer:

$445.10

Step-by-step explanation:

The amount withheld for federal income tax depends on several factors, including Steve's filing status, income, and deductions. However, we can make an estimate based on some assumptions.

Assuming Steve is paid weekly and is paid for 52 weeks a year, his gross income would be:

$255.75 x 52 = $13,293

We also assume that Steve is claiming two allowances. Each allowance reduces the amount of taxable income subject to federal income tax withholding. For 2021, each allowance is equal to $4,300.

Therefore, Steve's taxable income for federal income tax purposes would be:

$13,293 - (2 x $4,300) = $4,693

To estimate the federal income tax withholding, we can use the IRS tax tables. For a single person claiming two allowances and earning $4,693 per week, the estimated federal income tax withholding would be:

$445.10

However, this is just an estimate, and the actual federal income tax withholding may be different based on Steve's specific circumstances. It's always best to consult with a tax professional for accurate tax advice.

Answer and Step-by-step explanation:

1 cm: 12 m

This scale reduces the size of an actual object. For example, if a car is 4 meters long in real life, it would be represented as 0.33 cm on a map that uses this scale (4 meters divided by 12).

6 ft: 10 in

This scale enlarges the size of an actual object. For example, if a room is 10 feet wide in real life, it would be represented as 60 inches on a blueprint that uses this scale (10 feet multiplied by 6).

1 km: 1000 m

This scale preserves the size of an actual object. For example, if a park is 2 kilometers wide in real life, it would be represented as 2000 meters on a map that uses this scale.

Therefore , the solution of the given problem of angles comes out to be  Lines I and m can be inferred to be parallel by the Corresponding Angles Converse .

An angle is a shape in Euclidean geometry consisting of two rays, or sides of a circular, that split at the angle's apex and the angle's apex, which is in the middle. Where they are located, two rays can join to form an angle. Angle is another outcome of two entities interacting. They are known as dihedral angles.

Here,

The Corresponding Angles Converse states that if two parallels are intersected by a transversal such that a set of corresponding angles are congruent, then perhaps the two lines are parallel.

This can be used to demonstrate that lines I and m are parallel.

We can infer that 1 and 2 are corresponding angles because 1 2.

We can infer that they have the same measure because they are congruent.

Let's now think about the transversal line t. Lines I and m can be inferred to be parallel by the Corresponding Angles Converse because 1 and 2 are corresponding angles and t crosses both I and m.

We have thus demonstrated that I / m.

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Answer:

30%

Step-by-step explanation:

First, I added up the number of minutes in 2 1/2 hours. 2 hours is 120 minutes, and 1/2 hour is 30 minutes. 120 + 30 = 150.

Next, divide 45 (which is the number out of 150 we are determining the percentage for) by 150 (which is the total number of minutes). Multiply that number by 100 to get 30. The answer is 30%.

The given statement " If A is an m x n matrix and B is an n x n matrix, then A × B is an m x n matrix" is True.  Correct answer of (a) is T.

This statement is definately true because, it helps to consider the dimensions of a matrix. The dimensions of a matrix refer to the number of rows and columns it contains. In the case of an m x n matrix (A) and an n x n matrix (B), the dimensions of A are m rows and n columns, while the dimensions of B are n rows and n columns.

When A is multiplied by B, the result is an m x n matrix, meaning it contains m rows and n columns. This is due to the fact that the number of columns of the first matrix (A) must equal the number of rows of the second matrix (B) in order for the matrices to be compatible for multiplication.

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x<4 is the solution of the inequality 5 x < 20

A number system is defined as a system of writing to express numbers.

The given inequality is  5 x < 20

We have to solve for x

Divide both sides by 5

x<20/5

Divide numerator and denominator by 5

x<4

The graph of x<4 is given in the attachment.

Hence, x<4 is the solution of the inequality 5 x < 20

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The tοtal area οf the cοmpοsite figure is 358.38 mm² (rοunded tο twο decimal places).

Area is the measurement οf the size οf a surface οr a regiοn in a 2D plane, typically measured in square units. It is calculated by multiplying the length and width οf a surface οr regiοn fοr simple shapes like rectangles, οr by using fοrmulas specific tο each shape fοr mοre cοmplex shapes.

The area οf a semicircle with radius r is given by (π/2)r², and the area οf a trapezium with height h and parallel sides a and b is given by (h/2)(a+b).

Substituting the given values, we get

Area οf semicircle = (π/2)(9mm)² = 81π/2 mm²

Area οf trapezium = (13mm/2)(7mm+18mm) = 227.5 mm²

Therefοre, the tοtal area οf the semicircle and trapezium is:

81π/2 + 227.5 ≈ 358.38 mm²(rοunded tο twο decimal places).

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Answer:

16.1 is the closest asnwer

Step-by-step explanation:

if you didn't understand feel free to send me a message bro

According to the Pythagorean theorem, |AC| = 10 * sqrt(5/3)

The Pythagorean Theorem states that the square on the tangent line (the side across from the right angle) of a right triangle, or, in standard algebraic form, a2 + b2, are equal to a square just on legs.

The following are some significant applications of the Pythagoras theorem in daily life: used in architecture and building. used to determine the shortest distance in two-dimensional navigation.

Since the diagonals of a rectangle are identical, the Pythagorean theorem states that AB = CD and BC = AD.

Using the Trigonometry once more, but this times with the edges of the rectangle, we can get d.

Lastly, by applying the right triangle's sides to the Pythagorean theorem, we may determine AC. ACD:

[tex]AC=\frac{500}{3}=10*\frac{5}{3}[/tex]

Therefore, |AC| = 10*(5/3)

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We can write P(x) as P(x) = (x - 2)(x + 3)Q(x), where Q(x) is another polynomial.

This is the factored form of P(x), and it can be used to find other roots or to simplify the polynomial equation.

The factor theorem is a useful tool in finding the factors of a polynomial equation. The theorem states that if k is a root of the polynomial equation P(x) = 0, then x - k is a factor of P(x).

In our problem, we have P(2) = 0 and P(-3) = 0. This means that 2 and -3 are both roots of the polynomial equation P(x) = 0. According to the factor theorem, this means that x - 2 and x + 3 are both factors of P(x).

Therefore, we can write P(x) as P(x) = (x - 2)(x + 3)Q(x), where Q(x) is another polynomial. This is the factored form of P(x), and it can be used to find other roots or to simplify the polynomial equation.

In conclusion, the factor theorem is a useful tool in finding the factors of a polynomial equation. In our problem, we used the factor theorem to find the factors x - 2 and x + 3 of the polynomial equation P(x) = 0.

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To graph a quadratic function, follow the steps explained to obtain the smooth curve of the quadratic function.

Graphing quadratic functions involves plotting the points on a coordinate plane that satisfy the equation of the function. Quadratic functions are typically written in the form:

f(x) = ax^2 + bx + c

where;

To graph a quadratic function, you can follow these steps:

x = -b / 2a

y = f(x)

You can find the x-coordinate of the vertex by using the formula above, and then substitute it into the function to find the corresponding y-coordinate.

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The volume of a right rectangular prism is given by the formula below

[tex]V=whl[/tex]

Thus, in our case,

[tex]V=2.5\times13.5\times9=303.75[/tex]

The volume of the container is 1116.5ft^3.

Finally, multiply the total volume by the density given in the problem, as follows

[tex]weight=303.75\times0.28=85.05[/tex]

             ⇒ [tex]weight[/tex] ≈ [tex]85[/tex]

Rounded to the nearest pound, the answer is 85 pounds.

3a and 4b are not like terms, hence they cannot be added, and the result of the expression is 3a + 4b and not 7ab.

Like terms are terms that share these two features:

If two terms are like terms, then they can be either added or subtracted.

3a and 4b on this problem are not like terms, as the letters, in this case a and b, are different.

Thus, the expression cannot be simplified, as only like terms, which are terms whose definition we gave in this explanation, can be simplified.

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The solution of the equation Bx =     1       2       3   is    x =        2      6      4.

To find the solution of the equation Bx =
1
2
3
, we can multiply both sides of the equation by the inverse of B, B^-1. This will give us:

B^-1 Bx = B^-1
1
2
3


Since the product of a matrix and its inverse is the identity matrix, I, we can simplify the left side of the equation to:

Ix = B^-1
1
2
3


And since the product of the identity matrix and any vector is just the vector itself, we can simplify further to:

x = B^-1
1
2
3


Now, we can plug in the given values for B^-1 and the right side of the equation to find the solution for x:

x =
-1 0 1
2 2 0
1 0 1
*
1
2
3


Multiplying the matrices gives us:

x =
(-1)(1) + (0)(2) + (1)(3)
(2)(1) + (2)(2) + (0)(3)
(1)(1) + (0)(2) + (1)(3)


Simplifying further gives us:

x =
2
6
4


So, the solution of the equation Bx =     1       2       3   is    x =        2      6      4

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Answer: 11 weekends

Step-by-step explanation: I did 470.80 divided by 37.50 and got 12 with a decimal, so then I multiplied 37.50 by 11 and got 412.5, then added the 58.30 .

Answer:

Step-by-step explanation:

So first you have to subtract the total that the computer costs by how much zach already has. Then you get 411.7. Then you have to divide 411.7 by 37.50 to get how many weeks it takes to get the computer. Which is 10.96 or 11. 11 weeks is the answer! You can check this by multiplying 37.50 by 11 and add 58 because he already has that money, you will get 470! which is close so there you go!

A dog eats soft food out of a 16oz packet. Every day the dog eats its meals split into three dishes breakfast, lunch, and dinner. If the dog needs to eat 11oz daily, each dish would have 3.67oz of food.

To find out  oz would be in each dish, we need to divide the total amount of food the dog needs to eat daily (11oz) by the number of dishes (3). This will give us the amount of food in each dish.

Here's the math:

11oz ÷ 3 dishes = 3.67oz per dish

So, each dish would have 3.67oz of food.

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Two comparations can be done:

I understand that we want to compare the numbers:

√144 and 12.9329...

Notice that the second number has infinite decimals after the decimal point (and there is no a clear pattern), so it is an irrational number.

For the first one, we know that:

12*12 = 144

So 144 is a perfect square, then when we apply the square root we will get:

√144 = 12

Then the two comparations are:

√144 is rational and 12.9329... is irrational.

And:

12.9329...> √144

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Answer:

x = 1

Step-by-step explanation:

17.25x+3.89=21.14
17.25x=17.25
x = 1

Answer:

The solution to the equation is x = 1

Step-by-step explanation:

Hi,

We need to isolate the term that contains the variable "x", so we will subtract 3.89.

17.25x + 3.89 - 3.89 = 21.14 - 3.89

We obtain:

17.25x = 17.25

Dividing both sides by 17.25:

x = 1

Therefore, the solution to the equation is x = 1.

Good luck!

The percentage of those standing is 60%

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

Seated : Standing = 1 : 2

Standing : VIP = 6 : 1

Multiply Seated : Standing = 1 : 2 by 3

Seated : Standing = 3 : 6

Standing : VIP = 6 : 1

Combine the ratios

Seated : Standing : VIP = 3 : 6 : 1

So, we have

Standing = 6/(3 + 6 + 1) * 100%

Evaluate

Standing = 60%

Hence, the percentage is 60%

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It took 24 days for the bank balance to increase from -$75 to $81 with daily deposits of $6.50.

Let's start by figuring out how much the bank balance increased by each day.

If the starting bank balance was -$75 and the ending bank balance was $81, then the total increase was:

$81 - (-$75) = $156

If she deposited $6.50 per day, then the bank balance increased by $6.50 each day.

So we can divide the total increase by the daily increase to find out how many days it took to reach $81:

$156 ÷ $6.50 per day = 24 days

Hence, the number of days is 24

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yes

im not sure though try it!