hello help me show my work on number 6 please

The equation of the circle that is internally tangent to the given circle; (x - 2) ² + (y + 10)² = 6²

(h₁, k₁) -Dimensionless coordinates of the first circle's center.

(h₂, k₂) - Dimensionless coordinates for the center of a second circle.

Furthermore, circles are represented in standard form by the following equation:

(x - h) ² + (y - k)² = r² .......(Eq. 2)

r is the radius of the circle.

The following information about the two circles is known from the statement:

The first circle; (x - 2) ² + (y + 6)² = 100

The second circle; points  (2,-10).

(x - 2) ² + (y + 10)² = r₂²

If we know C1 (2, -6)and C2 =  (2,-10), the distance between the centers is:

d = √(2 - 2)² + (- 10 + 6)²

d = 4

The radius of a second circle is then:

d = 4, r₁ = 10

r₂ = 10 - 4

r₂ = 6

As a result, the equation of the circle that is internally tangent to the given circle; (x - 2) ² + (y + 10)² = 6².

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The correct statement is;

False,  because x = \(cos^-^1({\frac{-1}{2} )\) is in the interval \(( -\frac{\pi }{2} , \frac{\pi }{2} )\) that is, \(cos^-^1({\frac{-1}{2} )\) = \(\frac{2\pi }{3}\). So all solutions of cos x = -1/2 will be  x = 2π/3 + 2nx and x = 4π/3 + 2nx.

Option D

From the information given, we have that;

All solutions are cos x = -1/2 are given by x = 4x/2 + 2πx

There are multiple solutions to the equation cos x = -1/2, and they are denoted by the values x = 2π/3 + 2nx and x = 4π/3 + 2nx

Such that n is an integer.

This is so because the cosine function repeats itself every 2π, or its period. We therefore multiply the general answer by multiples of 2 to obtain all solutions.

The formula x = 4x/2 + 2πx implies that each solution can be reached by x being multiplied by 4/2 and 2πx being added.

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There were 14 players on the soccer team.

In the given problem, the members of a soccer team raised $1210.50 to go to a tournament. They rented a bus for $769.50 and budgeted $31.50 per player for meals. We need to find how many players were on the team.To solve this problem, we can start by subtracting the cost of the bus rental from the total amount raised by the team:$1210.50 - $769.50 = $441Now, we can divide this remaining amount by the amount budgeted per player for meals:$441 ÷ $31.50 = 14Therefore, there were 14 players on the soccer team. We can check our answer by multiplying the number of players by the amount budgeted per player for meals:14 x $31.50 = $441This is equal to the remaining amount after the bus rental was paid, which confirms that our answer is correct.

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The area of the rectangle is 108cm²

The area can be defined as the amount of space covered by a flat surface of a particular shape. It is measured in terms of the "number of" square units.

So, the area of a rectangle is the number of unit squares within the boundary of the rectangle or the space occupied within the perimeter of this shape is called the area of the rectangle.

The area of a rectangle is Length ×width

perimeter of a rectangle = 2(l+w)

l= 3w

therefore P= 2(3w+w)

P= 2(4w)

p= 8w

p=48cm

48= 8w

divide both sides by 8

w= 6cm

from l= 3w

l= 3×6= 18cm

therefore the area of the rectangle is 18×6= 108cm²

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The equivalent expression is 5 - 3x/2. Option D

Algebraic expressions are described as expressions that are made up of variables, their coefficients, factors and constants.

these algebraic expressions are also composed of mathematical operations. These operations includes;

From the information given, we have that;

1/ 4(8 - 6x + 12)

expand the bracket, we have;

Add the like terms

1/4(20 - 6x)

now, multiply the values, we have;

20 - 6x/4

Divide by the denominator

5 - 3x/2

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The complete question:

Simply the expression:

1/ 4(8 - 6x + 12)

The value of x is 10.0

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

sin(tetha) = opp/hyp

cos(tetha) = adj/hyp

tan(tetha) = opp/adj

here, 15 is the hypotenuse and x is the adjascent.

therefore cos 48° = x/15

x = cos 48 × 15

x = 0.669 × 15

x= 10.0

therefore the value of x is 10.0

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Answer:

\( c = 25\)

Step-by-step explanation:

Given :-

And we need to find out the value of c for which the given trinomial is a perfect square. On looking at the given expression all the terms are having positive signs before them .So we can rewrite it on the basis of ,

Identity :-

\(\implies (a+b)^2=a^2+b^2+2ab\)

Let's try to set the equation on this Identity .

The firsr term is 9x² . We can write it as ,

\(\implies 9x^2=(3x)^2\)

Hence the middle term here should contain 3 and 2 as their factors. Let's Break the middle term .

\(\implies 30x = 2.3x.5 \)

Therefore in order to make the whole expression as perfect square 5² must be replaced by c . The expression would become ,

\(\implies 9x^2+30x + 5^2 \\\\\implies (3x)^2+2.3x.5 +5^2\\\\\implies (3x+5)^2\)

Hence the value of c should be 25 .

Answer:

1. Its about 14.90697674418605. I’m not sure if u want it rounded up if u want it rounded up to the nearest whole it would be 15 if I wanted it rounded up to the nearest tenth then it would be 14.9

2. It’s about 173.4814814814815. I wasn’t sure if I wanted this one rounded up too. Rounded up to the nearest whole it would be 173 and rounded up to the nearest tenth it would be 173.5

3. It’s about 100.859375. I wasn’t sure on this one too. Rounded up to the nearest whole would be 101 and rounded up to the nearest tenth it would be 100.9

Step-by-step explanation:

Answer:

x=12 , y= 49

Step-by-step explanation:

X= 180 - (90+78)= 12

180-(90+41)= 49

y=49 (isosceles triangle)

1. The scale factor here in the dilation is 4/3.

2. Yes, dilation occurred on the coordinate plane below. The scale factor for the dilation is -4/3.

During the process of dilatation, an object must be reduced in size or changed. It is a transformation that uses the given scale factor to shrink or expand the objects. The image is the new figure that forms as a result of dilatation, whereas the pre-image is the original figure. There are two kinds of dilation:

A rise in an object's size is referred to as expansion.

Contraction is the term used for a reduction in size.

Here in the question,

The coordinates of the point B change from (-3,6) to (-4,8).

The scale factor here is -4/-3=4 or 8/6=4/3.

Now, when the dilation happens below the plane, the coordinates will be (x,-y)

So, the dilation factor will be -4/3.

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Answer:

16

Step-by-step explanation:

the amount of peppers are double the amount of servings, 8x2 = 16

Answer:

16

Step-by-step explanation:

8-4/ 4-2= 2

8 x 2= 16

The expected number of times for the probability of getting at least one heads after flipping a two coins at the same time is equal to 1/4.

Total number of coins flipped at the same time = 2

Sample Space of coin 1  and coin 2 = { H, T}

Let 'y' represents number of times getting heads

Probability of each outcome head and tail is = 1/2

y      :     0              1                

p(y)  :      1 / 2        1/2            

Expected value of getting heads by flipping each coin

E(Y) = ∑y p(y)

Y₁ and Y₂ are two expected number for each coin to get head

Both coins are independent of each other.

E(Y₁) = 1/2

E(Y₂ ) = 1/2

E(Y₁ × Y₂)

= E(Y₁)  × E(Y₂ )

= ( 1/2) ( 1/2)

= 1/4

Therefore, the expected number of times for the probability of getting at least one head is equal to 1/4.

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9514 1404 393

Answer:

  65°, 35°, 90°, 115°, 80°

Step-by-step explanation:

There are 9 of the longer tick marks in 90°, so each of them represents 10°. The shorter tick marks are halfway between, so are on multiples of 5°. This lets us make a list of the angle value associated with each of the letters.

A: 0 or 180

B: 65 or 115

C: 90

D: 145 or 35

E: 180 or 0

__

Using this list, we can find the measure of each angle by finding the positive difference of the corresponding angle values associated with each of its rays.

arc AOB = 65 -0 = 65°

arc DOE = 35 -0 = 35°

arc AOC = 90 -0 = 90°

arc EOB = 115 -0 = 115°

arc DOB = 145 -65 = 80°

The solution of the linear equation  is determined as x = -4.

The solution of the linear equation is calculated by applying the following method as follows;

The given linear equation;

2/x+3 - 1/x = -4/x² +3x

We can start by simplifying the equation and getting rid of the fractions.

Multiplying every term by x will help us achieve that:

2 + 3x - 1 = -4/x + 3x²

Simplifying further:

2 + 3x - 1 = (-4 + 3x²) / x

Combining like terms:

3x + 1 = (-4 + 3x²) / x

(x)(3x + 1) = -4 + 3x²

3x² + x = -4 + 3x²

We can subtract 3x² from both sides:

x = -4

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AC is not equal to CE based on the angle bisector theorem. The answer is: C. NO, you cannot use the angle bisector theorem to determine that AC = CE.

According to the angle bisector theorem, when a line segment divides an angle of a triangle, the line segment also divides the opposite side but does so in such a way that the two segments are proportional to the other two sides of the triangle. However, the two segments are not congruent to each other.

In the diagram given below that shows the suspect, the police officer, and the 26th Street toward Cherry Street, the angle bisector divides the side opposite to the angle divided into AC and CE. Thus, their length cannot be ascertain to be congruent to each other, however, based on the angle bisector theorem, we can only prove that their length is proportional to the other two sides of the triangle.

Therefore, we can conclude as saying:

C. NO, you cannot use the angle bisector theorem to determine that AC = CE.

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Answer:

16

Step-by-step explanation:

The outlier in the given dataset is "16".

Given is a data set 69, 16, 79, 80, 82, we need to determine the outliners of the set,

To identify outliers in a dataset, we generally use a statistical method such as the z-score or the IQR (interquartile range).

Since, the provided dataset is small with only five values, we can manually identify the outliers by observing the data.

An outlier is a value that significantly deviates from the rest of the dataset.

Let's examine the given dataset:

69, 16, 79, 80, 82

To identify outliers, we can consider any data points that are notably different from the others.

In this case, it seems that the value "16" is considerably lower than the other values.

Let's label it as a potential outlier.

Therefore, the outlier in the given dataset is "16".

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The expansion of (3x-4y)¹¹ using Pascal's Triangle is:

177147x¹¹ - 2598156x¹⁰y - 17321040x⁹y² - 69284160x⁸y³ - 184757760x⁷y⁴ -  344881152x⁶y⁵ - 458941536x⁵y⁶ - 437944320 x⁴y⁷ - 291962880x³y⁸ - 129761280x²y⁹ + 34603008xy¹⁰ - 4194304y¹¹.

So, the expression is:

Now, use Pascal's Triangle to expand as follows:

Therefore, the expansion of (3x-4y)¹¹ using Pascal's Triangle is:

177147x¹¹ - 2598156x¹⁰y - 17321040x⁹y² - 69284160x⁸y³ - 184757760x⁷y⁴ -  344881152x⁶y⁵ - 458941536x⁵y⁶ - 437944320 x⁴y⁷ - 291962880x³y⁸ - 129761280x²y⁹ + 34603008xy¹⁰ - 4194304y¹¹.

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The length of the hypotenuse is 12.52 yards.

Given that a right triangle, we need to find the value of the hypotenuse x,

Trigonometric ratios can be calculated by taking the ratio of any two sides of the right-angled triangle.

We can evaluate the third side using the Pythagoras theorem, given the measure of the other two sides. We can use the abbreviated form of trigonometric ratios to compare the length of any two sides with the angle in the base.

Let us consider a right-angled triangle with one of its acute angles to be x. Then the cosine formula is, cos x = (adjacent side) / (hypotenuse), where "adjacent side" is the side adjacent to the angle x, and "hypotenuse" is the longest side (the side opposite to the right angle) of the triangle.

We know that, the cosine of the angle is the ratio of the base to the hypotenuse,

So,

Cos 37° = 10 / x

x = 10 / Cos 37°

x = 12.52

Hence the length of the hypotenuse is 12.52 yards.

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Ans

2 / 8^(1/6) * 2 ^(1/2) = 2 / sqrt(2) * sqrt(2) = 2

Left side of equation = 2

Right Side of equation = - - 4 = 4

equation = 2 +4 = 6

Step-by-step explanation:

Answer:

(0,8)

Step-by-step explanation:

here you go!

it's the same thing

\(slope = \frac{Δy}{Δx} or \frac{change \: in \: y}{change \: in \: x} = \frac{y2 - y1}{x2 - x1} = \frac{rise}{run} \)

Answer:

The cost of one share of the stock on Friday is $41.45

Step-by-step explanation:

The initial cost of one share of the stock on Monday is $41.45.

On Tuesday, the cost goes up by $0.58, so the cost becomes:

$41.45 + $0.58 = $42.03

On Wednesday, the cost goes down by $0.26, so the cost becomes:

$42.03 - $0.26 = $41.77

On Thursday, the cost also goes down by $0.26, so the cost becomes:

$41.77 - $0.26 = $41.51

Finally, on Friday, the cost goes down by $0.06.

So the expression to represent the cost of one share of the stock on Friday is:

$41.51 - $0.06

To evaluate this expression, we simply subtract $0.06 from $41.51:

$41.51 - $0.06 = $41.45

Therefore, the cost of one share of the stock on Friday is $41.45

Answer:

x = 612

Step-by-step explanation:

x = 2(y + z)        Divide by 2 to isolate y + z

x/2 = y + z         Set up the sum of three numbers        

x + y + z = 918   Substitute x / 2 for y + z

x + x/2 = 918     Combine like terms

3/2 x = 918        Multiply both sides by 2/3

2/3 * 3x/2 = 2/3 * 918

x = 612    

The intersection of sets M and F contains the elements "c" and "d".

To find the intersection of sets M and F, we need to identify the elements that are common to both sets.

M = {a, b, c, d}

F = {c, d, e, f}

The intersection of M

and F is denoted by M ∩ F, which represents the set containing elements that are present in both M and F.

Looking at the elements in M and F, we can see that the common elements between the two sets are "c" and "d".

Therefore, the intersection of M and F can be expressed as:

M ∩ F = {c, d}

So, the intersection of sets M and F contains the elements "c" and "d".

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Answer:

12 divided by 12 is 1

Step-by-step explanation:

A calculator helped me

Answer:

1

Step-by-step explanation:

cos

Answer:

p+7>24

Step-by-step explanation:

An exponential equation in the form \(y=a(b)^x\) that can model the amount of caffeine, y, in Kendall's body x hours after drinking the coffee is

The amount of caffeine that will be in Kendall's body after 12 hours is 18 milligrams.

In Mathematics, an exponential function can be modeled by using the following mathematical equation:

f(x) = a(b)^x

Where:

Since Kendall drank a cup of coffee that had 95 milligrams of caffeine which is decreasing at a rate of 5% per day, this ultimately implies that the relationship is geometric and the rate of change (decay rate) is given by:

Rate of change (decay rate) = 100 - 13 = 87% = 0.87.

By substituting the parameters into the exponential equation, we have the following;

\(f(x) = 95(0.87)^x\)

When x = 12, we have;

\(f(12) = 95(0.87)^{12}\)

f(12) = 17.86 ≈ 18 milligrams.

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Answer:

B. Similar - AA

Step-by-step explanation:

Two angles in ∆ABC are congruent to two corresponding angles in ∆DEF. Thus, it follows that the third pair of angles of both triangles would also be congruent.

Therefore, the three sides of ∆ABC and corresponding sides of ∆DEF will be proportional to each other.

This satisfies the AA Similarity Criterion. Therefore, ∆ABC ~ ∆DEF by AA.