What are the center and radius of the circle
with equation (x-4)^2 + (y- 9)^2 = 1?

The equivalent expressions to \(24^{-7}\) are given as follows:

C. \(\left(\frac{1}{24^{-7}}\right)^{-1}\)

F. \((24^3 \times 24^4)^{-1}\)

Equivalent expressions are expressions that have the same value for all possible values of the variables. In other words, equivalent expressions are different ways of writing the same mathematical idea.

The exponent in the denominator can be moved to the numerator with the changed signal, hence:

\(\left(\frac{1}{24^{-7}}\right)^{-1} = (24^7)^{-1}\)

Applying the power of power rule, we multiply the powers, hence:

\((24^7)^{-1} = 24^{-7}\)

When two terms with the same base and different exponents are multiplied, we add the bases and keep the exponents, hence:

\((24^3 \times 24^4)^{-1} = (24^7)^{-1} = 24^{-7}\)

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Answer:

Step-by-step explanation:

500,000+0+900+60+9

Answer:

\(k=35\)°

Step-by-step explanation:

The degree measure of a straight line is (180) degrees. Therefore, when a line intersects another line, the sum of angle measures on any one side of the line is (180). One can apply this here to find the supplement (the angle on the same side of the line) of the angle with a measure of (130) degrees, and (85) degrees.

\(130 + (unknown_1)=180\\unknown_1=50\\\\85+(unknown_2)=180\\unknown_2=95\)

The sum of angle measures in a triangle is (180) degrees, one can apply this here by stating the following;

\((unknown_1)+(unknown_2)+(k)=180\)

Substitute,

\(50+95+k=180\)

Simplify,

\(50+95+k=180\\\\145+k=180\\\\k=35\)

\(\sf \bf {\boxed {\mathbb {TO\:FIND :}}}\)

The measure of angle \(k\).

\(\sf \bf {\boxed {\mathbb {SOLUTION:}}}\)

\(\implies {\blue {\boxed {\boxed {\purple {\sf {k\:=\:35°}}}}}}\)

\(\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:\:EXPLANATION:}}}\)

We know that,

\(\sf\pink{Sum\:of\:angles\:on\:a\:straight\:line\:=\:180°}\)

➪ \(x\) + 85° = 180°

➪ \(x\) = 180° - 85°

➪ \(x\) = 95°

Also,

Exterior angle of a triangle is equal to sum of two opposite interior angles.

And so we have,

➪ 130° = \(k\) + \(x\)

➪ \(k\) + 95° = 130°

➪ \(k\) = 130°- 95°

➪ \(k\) = 35°

Therefore, the value of \(k\) is 35°.

\(\sf \bf {\boxed {\mathbb {TO\:VERIFY :}}}\)

\(\sf\blue{Sum\:of\:angles\:of\:a\:triangle\:=\:180°}\)

➪ 50° + 35° + 95° = 180°

( where 50° = 180° - 130°)

➪ 180° = 180°

➪ L. H. S. = R. H. S.

Hence verified.

(Note: Kindly refer to the attached file.)

\(\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{ヅ}}}}}\)

To establish trust with Martina, the nurse should show respect, use non-verbal communication, incorporate play, involve the parent, and individualize the approach.

To establish a trusting relationship with Martina, the nurse can employ several approaches:

Respect and empathy: The nurse should approach Martina with genuine respect and empathy, recognizing her unique needs and individuality. This can be conveyed through a calm and patient demeanor.

Non-verbal communication: Since Martina may not be responsive to verbal cues, the nurse can utilize non-verbal communication to establish connection and trust. This can include maintaining eye contact, using gentle touch, and respecting Martina's personal space.

Play and familiar objects: Given Martina's engagement with the blue stuffed dog, the nurse can incorporate play into their interactions. Bringing familiar objects or toys that Martina finds comforting can help create a sense of familiarity and security.

Parental involvement: Involving Martina's mother in the care process can be beneficial. The nurse can communicate with the mother, seek her input, and involve her in the administration of medications. This helps build trust not only with Martina but also with her caregiver.

Individualized approach: Recognizing Martina's autistic disorder, the nurse should tailor their approach to her specific needs. Understanding her sensory sensitivities and preferences can help create a safe and comfortable environment.

By implementing these strategies, the nurse can foster trust and a positive therapeutic relationship with Martina, promoting her overall well-being and care.

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Complete Question:

What approach would help the nurse establish a trusting relationship with Martina, a 3-year-old with bronchitis and autistic disorder, who is intensely occupied with a blue stuffed dog and does not seem responsive to the nurse's presence in the room, while the mother is also present?

The list of elements in the sets are as follows:

A.  A ∩ B = {2, 9}

B. B ∩ C = {2, 3}

C. A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}

D. B ∪ C = {2, 3, 5, 7, 9, 10}

Set are defined as the collection of objects whose elements are fixed and can not be changed.

Therefore,

universal set = U = {1,2,3, 4, 5, 6, 7, 8, 9, 10​}

A = {1, 2, 7, 8, 9}

B = {2, 3, 5, 9}

C = {2, 3, 7, 10}

Therefore,

A.

A ∩ B = {2, 9}

B.

B ∩ C = {2, 3}

C.

A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}

D.

B ∪ C = {2, 3, 5, 7, 9, 10}

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The system of equations has one solution.

To check this, we can graph the two equations of the system:

y = (-1/3)x + 7

y = -2x³ + 5x² + x - 2

On the same coordinate axis, and check how many times do the graphs intercept.

The graph can be seen in the image at the end, there you can see that there is only one intecept point. Thus, the system of equations has only one solution.

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Answer:

\(f^{-1}(6) = 50\)

Step-by-step explanation:

Given

\(f(x) = \sqrt{2x} - 4\)

Required

Find \(f^{-1}(6)\)

First, we calculate the inverse function

\(f(x) = \sqrt{2x} - 4\)

Express f(x) as y

\(y = \sqrt{2x} - 4\)

Swap the positions of x and y

\(x = \sqrt{2y} - 4\)

Solve for y: Add 4 to both sides

\(4 + x = \sqrt{2y} - 4+4\)

\(4 + x = \sqrt{2y}\)

Square both sides

\((4 + x)^2 = 2y\)

Divide both sides by 2

\(y = \frac{(4 + x)^2}{2}\)

Express y as an inverse function

\(f^{-1}(x) = \frac{(4 + x)^2}{2}\)

Next, solve for: \(f^{-1}(6)\)

Substitute 6 for x

\(f^{-1}(6) = \frac{(4 + 6)^2}{2}\)

\(f^{-1}(6) = \frac{(10)^2}{2}\)

\(f^{-1}(6) = \frac{100}{2}\)

\(f^{-1}(6) = 50\)

The bakery should use the range to determine whether or not the equipment changes have worked. The correct answer is C.

To determine whether the equipment changes made by the bakery have resulted in more uniform-sized muffins, they should use the measure of variability. The most suitable measure, in this case, would be the range.

The range is calculated by finding the difference between the maximum and minimum values in a data set. In this scenario, the bakery made 25 muffins and measured each one. By finding the range of the measurements, they can assess the spread of sizes among the muffins.

Here's how they can use the range to evaluate the effectiveness of the equipment changes:

Collect the measurements of all 25 muffins.

Determine the maximum and minimum measurements.

Calculate the range by subtracting the minimum measurement from the maximum measurement.

If the range of the muffin sizes is smaller compared to the range before the equipment changes, it suggests that the modifications have resulted in more uniform-sized muffins. Conversely, if the range remains similar or larger, it indicates that the changes might not have effectively improved the uniformity of muffin sizes.

Therefore, the bakery should use the range to determine whether or not the equipment changes have worked. The correct answer is C.

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Answer:

The answer is 168!

Step-by-step explanation:

6*4=24 (There are two triangles so you don't have to divide by 2, 24 is simply the answer to both), 6*9=54, 5*9*2=90, 90+54+24=168! I hope this helps! Have a great rest of your day!

Answer:

A≈114.12

Step-by-step explanation:

A=2AB+(a+b+c)h   AB=s(s﹣a)(s﹣b)(s﹣c)

              s=a+b+c/2

                              A=ah+bh+ch+1

2﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4=9·5+6·5+4·5+1

2·﹣94+2·(9·6)2+2·(9·4)2﹣64+2·(6·4)2﹣44≈114.12459

here is the full explanation , I took a blackboard pavcs math quiz

Vertical multiplication of trinomials:

Step 1: Multiply the top trinomial by the last term in the bottom trinomial.

Step 2: Multiply the top trinomial by the next term:

Step 3: Multiply the top trinomial by the first term:

Step 4: Algebraically add the three polynomials:

8x² - 10x + 6

12x³ - 15x² + 9x

20x⁴ - 25x³ + 15x²

------------------------------------------------

ANSWER

20x⁴ - 13x³ + 8x² - x + 6

Answer:

tis is not confirmed aswer

Step-by-step explanation:

daily commission: 27%

Answer:

-3

Step-by-step explanation:

we take two points to find slope m

lets take ( 1, 4) and ( 2, 1)

then m=(1-4)/(2-1)

m=(-3)/(1)

m= -3

Answer:

-5/6

Step-by-step explanation:

(9, 5) and (21, -5)

slope = m = (difference in y)/(difference in x)

m = (-5 - 5)/(21 - 9)

m = -10/12

m = -5/6

Answer: -5/6

The slope of the line that passes through points (9,5) and (21,-5) is -5/6.

We can use the two-point formula to find the slope for the given line. The formula is as follows:

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

Where (x1, y1, x2, and y2) represent the points on the line, and m is the slope of the line.

In the given case:

x1=9, x2=21

y1=5, y2=-5

Using these values in the two-point formula, we get:

(-5-5)=m*(21-9)

-10=m*12

m=-10/12

m=-5/6

Hence the slope of the line is -5/6.

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Answer:

8.75

Step-by-step explanation:

Answer:

53\(x_{123}\) == 134 cf

Step-by-step explanation:

A - on the po boyds at a emase the foot, 1, of building. He. Observes an obje- et on the top, P of the building at an angle of ele- building of 66 Aviation of 66 Hemows directly backwards to new point C and observes the same object at an angle of elevation of 53° · 1P) |MT|= 50m point m Iame horizontal level I, a a​

The height of the building is approximately 78.63 meters.

The following is a step-by-step explanation of how to solve the problem. We'll need to use some trigonometric concepts and formulas to find the solution.

Therefore, the height of the building is approximately 78.63 meters.

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Answer: D (t−3)(t−5)(t+4)

Step-by-step explanation:

Hope this helps! :)

Answer:

523.3 cm³

Step-by-step explanation:

Formula for the volume of a sphere :

Volume (sphere) = 4/3πr³

=============================================================

Given :

⇒ Diameter = 10 cm

→ Radius = 5 cm

===========================================================

Solving :

⇒ Volume = 4/3 × 3.14 × 5³

⇒ Volume = 4/3 × 3.14 × 125

⇒ Volume = 392.5 × 4/3

⇒ Volume = 1570/3

⇒ Volume = 523.3 cm³

The equation y = 4x-1 matches the graph, which has a slope of 4 and a y-intercept of -1. This is because the coefficient of x is 4 (slope) and the constant term is -1 (y-intercept).

A line's slope is a measure of how steeply it rises or falls as it goes from left to right on a coordinate plane. It is defined as the shift in vertical coordinate (y) to horizontal coordinate (x) between any two locations on a line. The slope (m) may be written symbolically as:

m = (change in y) / (change in x)

Positive, negative, zero, or undefined slopes are all possible. A horizontal line has a slope of zero, while a vertical line has an indeterminate slope.

Based on the given options, the equation that matches the graph is:

b. y = 4x-1

This is because the graph has a slope of 4 (meaning it increases by 4 units in the y-direction for every 1 unit in the x-direction), and a y-intercept of -1 (meaning the line crosses the y-axis at -1). This matches the equation y = 4x-1, where the coefficient of x is 4 (slope) and the constant term is -1 (y-intercept).

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The length in feet of the longest part of the garden would be = 6ft

A garden is defined as an area that is prepared and set aside for the purpose of growing various flowers, shrubs and grasses.

The area of the given triangle = 54in²

The perimeter of the given triangle = 36 in.

Using the formula for area of a triangle ;

Area = ½ base(b) ×height(h)

where base = 9 in

54 = 1/2 × 9 × h

Make h the subject of formula;

h = 54×2/9

h = 108/9

h = 12

But the perimeter = sum of the whole sides of the triangle

perimeter = 36

side a = 9

side b = 12

side c = X

that is , 36 = 9+12+X

make X the subject of formula;

X = 36-21

X = 15in

Therefore, 15 in when converted to feet;

2 ft = 5 in

X ft = 15 in

xft = 2 × 15/5

X ft = 30/5

X ft = 6ft

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The correct answer is c) Other types of pseudo R-squares may be greater or less than 60% with the same logistic regression model.

Pseudo R-squares, such as the one used in logistic regression, are measures of how well the model fits the data, but they cannot be directly compared to R-squared values from other types of regression models. Therefore, we cannot conclude that the logistic regression model with a pseudo R-Square of 60% is better than another logistic regression with an R-square (CS) of 50% or a multiple linear regression model with an R-square of 55%. However, we can say that 60% of the variation in the data can be explained by the logistic regression model, based on its pseudo R-Square value.

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The perimeter of the given shape as represented in the task content is; 29 cm.

It follows from the task content that the perimeter of the given shape on the centimeter grid as required is to be determined.

Since each grid line has 1cm as it's length;

The perimeter of the shape is the sum of all side lengths of the shape;

Perimeter, P = 6+2+3+2+2+1+3+2+2+2+2+1

P = 29 cm

Hence, the perimeter of the shape is; 29 cm.

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Answer:

20 ounces of the 63% solution and 80 ounces of the 33% solution.

Step-by-step explanation:

Let x = number of ounces of 63% solution.

Let y = number of ounces of 33% solution.

The total solution to be made is 100 oz.

x + y = 100

x ounces of 63% solution is 0.63x ounces of acid.

y ounces of 33% solution is 0.33y ounces of acid.

100 ounces of 39% solution is 39 ounces of acid

0.63x + 0.33y = 39

The system of equations is

x + y = 100

0.63x + 0.33y = 39

Multiply the both sides of the first equation by -0.33. Then add it to the second equation.

         -0.33x - 0.33y = -33

    +    0.63x + 0.33y = 39

   ---------------------------------

             0.3x             = 6

x = 6/0.3

x = 20

x + y = 100

20 + y = 100

y = 80

Answer:

20 ounces of the 63% solution and 80 ounces of the 33% solution.

Answer:

6

Step-by-step explanation:

57=15+7x --> 57-15=7x --> 42=7x --> 42/7=x --> 6

Answer:

y - 8 = 2 (x - 6)

Step-by-step explanation:

The point-slope equation is ...

y - y1  = m ( x - x1 )

In the coordinate (6,8)

x = 6 and y = 8

m = 2

Plug in values to find the point-slope form

y - 8 = 2 (x - 6)

We are done!

Answer: it’s should be -300

Step-by-step explanation:

EXPLANATION

We can check the following facts with the triangles:

Triangle A: This is an Scalene triangle

Triangle B: This is an equilateral triangle

Triangle C: This is an equilateral triangle

Triangle D: This is an Isosceles triangle

Answer:

−12s2+11st−2t2

Step-by-step explanation:

Hope this helps!

Answer:

-12s - 2t

Step-by-step explanation:

First simplify the like terms.

-3s * 4s = -12s

(-12s + 2t)(-t)

Simplify the like terms again.

2t * (-t) = -2t

-12s - 2t.

Or

12s + 2t. (You can get this by multiplying the equation by -1)