what is the coefficient of x^4y^4 in the expansion of (x+y)8?

The secant-secant product theorem states that if 2 secant segments are drawn to a circle from an external point, then the product of the length of one of the secants and its external portion is equal to the product of the length of the other secant and its external portion.

The length of the first secant in the image is x + 18, and the second is 24 + 16.

x + 18 times 18 = 40 times 16

18x + 324 = 640

18x = 316

x= approximately 17.6

The given problems are solved:

An equation is a statement that asserts the equality of two expressions, the expressions are written one on each side of an '=' equal to sign.

Question 4:

To calculate angle A,

Consider tan function.

[tex]tan A=\frac{opposite side }{adjacent side}[/tex]

[tex]tan A=\frac{9.6}{7.2}[/tex]⇒ 1.34

A= 53.26°

Question 7:

In triangle PQR, ∠Q=80°, PQ=8 and QR= 6,

PR=?

Area of triangle = 1/2 *a*b*sinC

                          = 1/2*8*6*sin°80

                          =24*0.984

Area of triangle = 23.616 square units.

Question 8:

Consider the triangle JKL, here two sides and one angle is given,

we can use cosine law,

The equation set us is given by,

           [tex]a^{2} = b^{2}+ c^{2} -2bcCos\alpha\\b ^{2} = a^{2}+c^{2} -2acCos\beta\\ c^{2} = b^{2} +a^{2} -2baCos\gamma[/tex]

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Answer:

To solve this problem, we need to calculate the cost of each travel and instruction option and then determine which options Treena can afford with her $1000 scholarship.

Option 1: Air travel and individual instruction

Travel cost: $335

Instruction cost: 7 x $60 = $420

Total cost: $335 + $420 = $755

Option 2: Air travel and group instruction

Travel cost: $335

Instruction cost: 7 x $40 = $280

Total cost: $335 + $280 = $615

Option 3: Train travel and individual instruction

Travel cost: $125

Instruction cost: 7 x $60 = $420

Total cost: $125 + $420 = $545

Option 4: Train travel and group instruction

Travel cost: $125

Instruction cost: 7 x $40 = $280

Total cost: $125 + $280 = $405

Now we need to determine which options Treena can afford with her $1000 scholarship. We'll start with the most expensive option and work our way down.

Option 1: $755

This option is too expensive for Treena's $1000 scholarship.

Option 2: $615

This option is also too expensive for Treena's $1000 scholarship.

Option 3: $545

This option is within Treena's budget, but she won't have any money left for food.

Option 4: $405

This option is also within Treena's budget, and she'll have $595 left for food.

Therefore, Treena's choices of travel and instruction plans that she could afford to make are:

- Train travel and group instruction with $595 left for food

- Train travel and individual instruction with no money left for food

Answer:

x = 8

Step-by-step explanation:

Vertically opposite angles are congruent.

          5x + 9 = 57 - x

 Add x to both sides,

      5x +x + 9 = 57

           6x + 9 = 57

Subtract 9 from both sides,

                  6x = 57 - 9

                  6x = 48

Divide both sides by 6,

                 x = 48 ÷ 6

                x = 8

To find the missing dimension of a cone when the height is 4.2 and the volume is 3.6 cubed is to equate the general formula with the given information.

A cone is a three-dimensional geometric shape with a smooth and curving surface and a flat base, with an increase in the height radius of a cone decreasing to a certain point.

The volume of a cone is (1/3)πr²h.

The total surface area of a cone is πr(r + l).

The curved surface area is πrl.

To obtain the missing dimension of a cone we must equate the general formula for the volume of a cone to the given information.

Therefore, (1/3)πr²×4.2 = 3.6

(1/3)πr² = 0.86.

r² = 0.86/1.05.

r² = 0.82.

r = 0.9

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The following expressions solved with the properties of exponents;

b³

ax

a³ × b⁵

b

b³ / b⁰

= b^(3-0)

= b³

a•x⁵ / a•x⁴

= ax⁵ / ax⁴

= ax^(5-4)

= ax¹

= ax

a • b²• a²•b³

= a^(1+2) × b^(2+3)

= a³ × b⁵

b^-2•b²•a⁰

= b^(-2+2) × a⁰

= b¹ × 1

= b

Therefore, the properties of exponents states that when numbers of the same base are divided, the exponent will be subtracted and

when numbers of the same base are multiplied, the exponent will be added.

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Khadija would have to pay $27.8 (7.5 x 4 - 1.7) to buy 4 pounds of apples.

Cost the monitorial associated with the purchase of production of food or service if can include the prices of materials of which is over it and other expenses that are related to the production of the good of service cost is a major fraction when deciding whether to purchase a product something as it is and indicator of the value of the product of sound service.

The expression for the cost to buy  x  pounds of apples is: 7.5x - 1.7, where x represents the number of pounds of apples purchased. For example, if Khadija wanted to buy 3 pounds of apples, the cost would be calculated by 7.5x - 1.7, which is equal to 22.6 dollars.

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Answer:

0.000154

Step-by-step explanation:

Answer:

x=7

Step-by-step explanation:

You graph it and find the middle point that would create a line through it and see where it his the x-axis.

The side lengths form a proportional relationship, and the ratios are as follows:

17.955/11.97 = 14.565/9.71 = 5.415/3.61.

Similar triangles are triangles that share these two features presented as follows:

They must have Congruent angle measures.

They have Proportional side lengths.

Here, the triangles are similar, as they have the same angle measures.

17.955/11.97 = 14.565/9.71 = 5.415/3.61.

Thus, the side lengths form a proportional relationship, as the equivalent side have a ratio of 1.5.

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The statement t < –3 or t > 4 is the inequality that the graph represents.

Inequality in mathematics is when two values are not equal. It can be expressed using symbols such as >, <, ≥ and ≤. This can be used to compare two values, express a range of values, or indicate that one value is greater or less than another. Inequality is a powerful tool for solving mathematical problems, as it can be used to deduce relationships between different variables.

The graph represents the inequality t < –3 or t > 4. This can be seen by the number line, which has the integers -5 to 5 incrementally marked, with the bars extending beyond the -3 and 4 markers. This indicates that the value of t is less than -3 or greater than 4, but not equal to either of these values. Therefore, the statement t < –3 or t > 4 is the inequality that the graph represents.

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Answer: To multiply the expression, we first distribute the constant factors:

2p^3q^4r^2 * 2p^4q^2t^3 * 3r = 6p^3q^4r^3 * 2p^4q^2t^3

Next, we multiply the variables by combining like terms:

6p^3q^4r^3 * 2p^4q^2t^3 = 6p^7q^6r^3t^3

This is the final simplified expression, and we can circle or highlight it as the answer.

Step-by-step explanation:

Using the distributive property to write the expression, we have:

12+4 = 4(3 + 1)

The distributive property states that a(b + c) = ab + ac, where a, b, and c are any real numbers.

We can use this property to write an expression that is equivalent to 12 + 4 as follows:

12 + 4 = 4(3) + 4 (here, we have factored out 4 from 12 using the distributive property)

         = 4(3 + 1) (we have combined the terms inside the parentheses)

Therefore, 12 + 4 is equivalent to 4(3 + 1).

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Answer:

y=2/3x+-1

Step-by-step explanation:

the mean and the median of the given data set are 16.75 and 9.5 respectively.

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.

Given,  A data set 8, 9, 10, 40

From the general formula of mean:

mean =  (sum of observations) ÷ (total number of observations).

mean = (8 + 9 + 10+ 40)/4

mean = 67/4

mean = 16.75

Since the median is:

The median is the value that's exactly in the middle of a dataset when it is ordered. It's a measure of central tendency that separates the lowest 50% from the highest 50% of values.

Thus,

the median of the given data set = (9 +10)/2

the median of the given data set =  9.5

Therefore, the mean and the median of the given data set are 16.75 and 9.5 respectively.

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The volume of a rectangular prism is 320 m³.

A rectangular prism is a three-dimensional solid shape with six faces that including rectangular bases. A cuboid is also a rectangular prism. The cross-section of a cuboid and a rectangular prism is the same. Volume of a rectangular prism = Area of a base × Height.

1) Given that, base area is 40 m² and height is 8 m.

So, the volume = 40×8

= 320 m³

2) 2) In the basketball game, Scott attempted 14 free throws.

He made half of them = 14/2

= 7

So, he made 7 throws

3) Today's high is 47 degrees Fahrenheit.

The weatherman says it will hit freezing tonight.

So, the temperature is represented as -47 degrees.

4) The given numbers are 5489 and 6752

Now, the sum is 5489 +6752

= 12241

Estimated to the nearest thousand as 12000.

5) Jace had 38 paper airplanes at home.

Christopher gave him 14 more paper airplanes to play with at home. Then Ameera gave him 29 paper airplanes.

So, total airplanes= 38+14+29

= 81

So, Jace had total 81 paper airplanes.

Therefore, the volume of a rectangular prism is 320 m³.

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Visualizing Kruskal's algorithm involves representing the graph, its edges, and the minimum spanning tree in a visual format.

To visualize a Kruskal algorithm, you need to follow the steps below:

1. Sort all the edges in ascending order of weight.
2. Create a new graph G' with the same vertices as the original graph G, but no edges.
3. Start with the smallest edge and add it to G' if it doesn't create a cycle. Repeat this step until you have added all the edges or you have a minimum spanning tree.
4. If you have a minimum spanning tree, you can visualize it by drawing the graph with the edges included in G'.

Here is an example:

Original graph G:

A---2---B---3---C
|       |
4       1
|       |
D---5---E

Step 1: Sort the edges in ascending order of weight: 1, 2, 3, 4, 5

Step 2: Create a new graph G' with the same vertices as G, but no edges.

Step 3: Start with the smallest edge (1) and add it to G'. This doesn't create a cycle, so we can add it.

G':
A       B---1---C
|       |
4       1
|       |
D       E

Next, add the second smallest edge (2) to G'. This also doesn't create a cycle, so we can add it.

G':
A---2---B---1---C
|       |
4       1
|       |
D       E

Continue this process until you have added all the edges or you have a minimum spanning tree.

Step 4: Visualize the minimum spanning tree by drawing the graph with the edges included in G'.

Minimum spanning tree:

A---2---B---1---C
|       |
4       1
|       |
D       E

I hope this helps! Let me know if you have any further questions.

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Answer:

y = - 1 , y = 17

Step-by-step explanation:

y² - 16y + 64 = 81 ← y² - 16y + 64 is a perfect square

)y - 8)² = 81 ( take the square root of both sides )

y - 8 = ± [tex]\sqrt{81}[/tex] = ± 9 ( add 8 to both sides )

y = 8 ± 9

then

y = 8 - 9 = - 1

x = 8 + 9 = 17

The length of edging material needed to enclose the garden is approximately 37.68 feet to the nearest hundredth.

The circumference of a circle is the distance around its outer boundary, also known as its perimeter. It is one of the fundamental properties of a circle, along with its radius and diameter.

Since the garden is circular, its widest point is its diameter, which is twice the radius. Therefore, the widest point of the garden is 12 feet across.

To find the length of the edging material needed to enclose the garden, we need to find the circumference of the circle. The formula for the circumference of a circle is C = 2πr, where r is the radius and π (pi) is approximately 3.14. Substituting,  r = 6 into the formula, we get:

C = 2π(6)

C = 12π

To approximate this value using 3.14, we can substitute π = 3.14 and get:

C ≈ 12(3.14)

C ≈ 37.68

Therefore, the length of edging material needed to enclose the garden is approximately 37.68 feet to the nearest hundredth.

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The value of n is 443 inches when using the triangle rule and law of sine.

The formula is given as

a / sin A = b / sin B = c / sin C

In this triangle NOP, we can find the value of angle P

∠N + ∠O + ∠P = 180

57 + 55 + ∠P = 180  : Sum of angles in a triangle is equal 180 degrees

∠P = 180 - 112

∠P = 68

Using law of sine

p/sin P = n/sin N

490/sin68 = n / sin57

n = [(490 × sin 57) / sin 68]

n = 443 inches

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Answer:

Step-by-step explanation:

The middle one

There are 15 total blocks that is your denominator.

There are 5 shaded that is your numerator.

5/15

Answer:

$0.30

Step-by-step explanation:

They tell you that a bag of 3 is $0.90. 3 can go into 90 a total of 30 times. 0.90/3 is 0.30

Answer:

first take a total price and then divided by the total bags to get price of each

Step-by-step explanation:

The next set of measurements for the triangle are as follows:

                        Triangle 1            Triangle 2           Triangle 3

Hypotenuse:    5.26                    7.89                     10.52

Opposite:          2.63                   3.945                   5.26

Adjacent:          4.556                  6.834                   6.834

This is done using the concept of similar triangles,

Similar triangles are two triangles that have the same shape but may be scaled to different sizes. In other words, similar triangles have the same angles, but their sides may be proportional.

In the problem, the proportion of the sides are equal and this will maintain the size of the angle

let the size of the angle be x

Sin x = opposite / hypotenuse

Sin x = 2.63 / 5.26 = 3.945 / 7.89 = 5.26 / 10.52 = 0.5

x = arc sin (0.5)

x = 30

To maintain same proportion the triangles where all a scaled version of the given triangle

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Answer:

Q1. The larger number is 54 and the smaller number is 37.

Q2. The number is 4.

Q3. The three numbers are 7, 8 and 9.

Step-by-step explanation:

Q1.

Let the larger number be x and the smaller number be y.

x+y= 91   (1)

x-y= 17   (2)

From (2) :

x= y+17   (3)

sub (3) into (1) :

y+17+y= 91

2y= 74

y= 37   (4)

sub (4) into (3) :

x= 37+17

 = 54

Q2.

Let the unknown number be x.

2x+16= 24

2x= 8

x= 4

Q3.

Let the smallest number be x.

2nd no. : x+1

3rd no. : x+2

x+(x+2)= (x+1)+8

2x+2= x+9

x= 7

x+1= 8

x+2= 9

The function notation that moves a pre-image 4 units right and 7 units down is f(x) ⇒ (x + 4, y - 7)

Translation is the movement of a point on the coordinate plane either left, right, up or down. Translation is a rigid transformation because it preserves the shape and size. Reflection and rotation are also rigid transformations.

If a point A(x, y) is translated a units right and b units down, then the new point is A'(x + a, y + b)

The function notation that moves a pre-image 4 units right and 7 units down is (x, y) ⇒ (x + 4, y - 7)

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Answer: (6y + 1) (y + 4)

Step-by-step explanation: (6y + 1) (y + 4)   (6y)(y) + (6y)(4) + (1)(y) + (1)(4) 6y^2 + 24y + 1y + 4 6y^2 + 25y + 4

Answer:

multiply 6×2 an you get 12

step:1 =4×12y⁴ ¹+25y¹ ¹

step:2=48y⁴ ¹ +25y¹ ¹

step:3=48y³+25y⁰

step:4=48y³+25×1

step:5=48y³+25

answer=48y³+25

Answer:

Step-by-step explanation:

where is the triangle