6n²-39n-21
How To Solve This Factoring Perfect Squares Trinomials problem?

The sample space of the spinner after spinning it twice is given by { (A, A) , (A, B ) , (A, C ), (A, D ) , ( B, A ), ( B, B ) , ( B, C ) ,  ( B, D ) ,  ( C, A ),

(C, B ) , ( C, C ) , (C, D ) , ( D, A ) , ( D, B ) , ( D, C ) , ( D, D ) }

Game played by Savannah using a spinner.

She spin the spinner twice.

To create a sample space for two spins of a spinner,

List all the possible outcomes of the first spin in one column.

And then list all the possible outcomes of the second spin in another column.

Then combine each outcome from the first column with each outcome from the second column to create all possible pairs of outcomes.

For example, suppose the spinner has 4 equally sized sections labeled A, B, C, and D.

The sample space for two spins would be,

{ (A, A) , (A, B ) , (A, C ), (A, D ) , ( B, A ), ( B, B ) , ( B, C ) ,  ( B, D ) , ( C, A ),

(C, B ) , ( C, C ) , (C, D ) , ( D, A ) , ( D, B ) , ( D, C ) , ( D, D ) }

Here, there are 16 possible outcomes for two spins of the spinner.

Therefore, the sample space of all possible outcomes of two spins is equal to  { (A, A) , (A, B ) , (A, C ), (A, D ) , ( B, A ), ( B, B ) , ( B, C ) ,  ( B, D ) ,  ( C, A ), (C, B ) , ( C, C ) , (C, D ) , ( D, A ) , ( D, B ) , ( D, C ) , ( D, D ) } .

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Answer:

Step-by-step explanation:

Therefore, the sample space of all possible outcomes of two spins is equal to  { (A, A) , (A, B ) , (A, C ), (A, D ) , ( B, A ), ( B, B ) , ( B, C ) ,  ( B, D ) ,  ( C, A ), (C, B ) , ( C, C ) , (C, D ) , ( D, A ) , ( D, B ) , ( D, C ) , ( D, D ) } .

Answer:

Step-by-step explanation:

see it simple it's not asking quite much if I do my calculation right it would be 8[tex]\pi[/tex]

An equivalent expression for the expression 6x + 15 is 3(2x + 5)

Part A:

The equation 6x + 15 = 6(x + 15) is false for all values of x because it does not follows the distributive property of multiplication over addition.

The equation 6x + 15 = x + x + x + x + x + x + 15 is true for all values of x because it is true when x has a specific value

Part B:

Another equivalent expression for 6x + 15 can be obtained by factoring out the greatest common factor (GCF) of the terms 6x and 15, which is 3:

6x + 15 = 3(2x + 5)

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Answer:

Part A: The equation 6x + 15 = 6(x + 15) is true for all values of x because it follows the distributive property of multiplication over addition. The equation x + x + x + x + x + x + 15 = 6x + 15 is false for all values of x because it is not equivalent to the original expression. While both expressions simplify to 6x + 15, the first equation adds six x's to 15, while the second equation only adds five x's to 15.

Part B: Another equivalent expression for 6x + 15 is 3(2x + 5). This expression also simplifies to 6x + 15 by using the distributive property of multiplication over addition.

Step-by-step explanation:

We have shown that the diagonals of rectangle MNOP bisect each other and are congruent.

In geometry, a diagonal is a line segment connecting two non-adjacent vertices of a polygon, such as a triangle, quadrilateral, or higher-order polygon. For example, in a rectangle, the diagonals are the line segments connecting opposite corners.

A diagonal can also refer to a line segment connecting two opposite corners of a three-dimensional solid, such as a cube or rectangular prism.

In many cases, diagonals have important properties and can be used to solve geometric problems. For example, in a rectangle, the diagonals are congruent and bisect each other. In a regular polygon with n sides, the number of diagonals can be calculated using the formula (n(n-3))/2. The length of a diagonal in a right triangle can be found using the Pythagorean theorem.

To show that the diagonals of rectangle MNOP bisect each other, we need to prove that the midpoint of diagonal MP is the same as the midpoint of diagonal NO.

Let's find the coordinates of the midpoints of MP and NO:

Midpoint of MP:

((x1 + x2)/2, (y1 + y2)/2)

= ((-7 + 5)/2, (1 - 7)/2)

= (-1, -3)

Midpoint of NO:

((x1 + x2)/2, (y1 + y2)/2)

= ((5 - 7)/2, (1 - 7)/2)

= (-1, -3)

As we can see, the midpoint of MP and NO are both (-1, -3), which means the diagonals bisect each other.

To show that the diagonals of rectangle MNOP are congruent, we need to find the length of both diagonals and prove that they are equal.

Let's find the length of diagonal MP:

MP = √((5 - (-7))² + ((-7) - 1)²)

= √(12² + (-8²)

= √(144 + 64)

= √(208)

Let's find the length of diagonal NO:

NO = √((5 - (-7))² + (1 - (-7)²)

= √(12² + 8²)

= √(144 + 64)

= √(208)

As we can see, the length of both diagonals is sqrt(208), which means the diagonals are congruent.

Therefore, we have shown that the diagonals of rectangle MNOP bisect each other and are congruent.

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Answer:

780

Step-by-step explanation:

To find out what number 117 is 15% of, you can use the following formula

(15/100) x n = 117

where n is the number you're trying to find.

To solve for n, you need to isolate it on one side of the equation. You can do this by dividing both sides by (15/100):

n = 117 / (15/100)

n = (117 x 100) / 15

n = 11700 / 15

n = 780

Therefore, 117 is 15% of 780.

4,396 flowers are needed to surrond the circular garden.

We know that the circumference of a circle of radius R is:

C = 2*3.14*R

Here the radius is 175ft, then the circumference is:

C = 2*3.14*175ft = 1,099ft

And we know that:

1ft = 12in

Then the circumference in inches is:

1,009*12 in = 13,188 in

If each flower is separated by 3 inches, the number needed is:

13,188 in/3in = 4,396 flowers.

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Answer:

 92.5°

Step-by-step explanation:

You want the angle where chords cross, given that they intercept arcs of 55° and 130°.

The angle x° is the average of the measures of the intercepted arcs:

  x° = (55° +130°)/2

  x° = 92.5°

The man is 23 km west of his home after driving 169 km to the east and 192 km to the west.

To determine how far the man is from his home after driving 169 km to the east and 192 km to the west, we can think of his movements as a displacement vector.

The vector representing the man's movement to the east has a magnitude of 169 km and is directed towards the east. Similarly, the vector representing his movement to the west has a magnitude of 192 km and is directed towards the west.

Since these two vectors are in opposite directions, we can subtract them to find the net displacement vector.

Net displacement = 169 km east - 192 km west

= -23 km west

The negative sign indicates that the net displacement vector is directed towards the west, which means that the man is 23 km west of his home.

To determine the distance between the man and his home, we can use the Pythagorean theorem. Since the man moved only in the east-west direction, the distance between him and his home is the absolute value of the net displacement, which is 23 km.

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Given right triangle ABC with altitude BD drawn to hypotenuse AC. If BD = 3 and DC = 9, the length of AC is:  4 units.

In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments. Let's call the length of the hypotenuse AC as x, and the length of the segment containing point B as y. Then, the length of the other segment containing point C is x - y.

Using similar triangles, we can set up the following proportion:

BD/DC = y/(x - y)

Substituting the given values, we get:

3/9 = y/(x - y)

Simplifying this equation, we get:

x - y = 3y/9

x = 4y/3

We also know from the Pythagorean theorem that:

AC^2 = AB^2 + BC^2

Since triangle ABC is a right triangle, we have:

AB^2 + BC^2 = x^2

Substituting x = 4y/3, we get:

AB^2 + BC^2 = (4y/3)^2

But we also know that:

AB/BC = 3/4

So we can set up another proportion:

AB/BC = y/(x - y)

Substituting x = 4y/3, we get:

AB/BC = y/(4y/3 - y)

Simplifying this equation, we get:

AB/BC = y/((4/3)y - y)

AB/BC = y/((1/3)y)

AB/BC = 3

So we have:

AB = 3BC

Substituting this into AB^2 + BC^2 = (4y/3)^2, we get:

(3BC)^2 + BC^2 = (4y/3)^2

10BC^2 = 16y^2/9

But we also know that:

BC^2 + y^2 = x^2

Substituting x = 4y/3, we get:

BC^2 + y^2 = (4y/3)^2

5BC^2 = 7y^2/9

Combining this with 10BC^2 = 16y^2/9, we get:

15BC^2 = 21y^2/9

BC^2 = (7/3)y^2/3

Substituting this into BC^2 + y^2 = (4y/3)^2, we get:

(7/3)y^2/3 + y^2 = 16y^2/9

7y^2/9 + 9y^2/9 = 16y^2/9

16y^2/9 = 16y^2/9

So this equation is true for any value of y. Therefore, the length of AC is:

AC = x = 4y/3

Substituting y = BD = 3, we get:

AC = 4(3)/3 = 4

Therefore, the length of AC is 4 units.

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The measure of angle Y is m - 8 = 72.25 - 8 = 64.25 degrees.

What is the supplementary angle?

Two angles are said to be supplementary if their sum is equal to 180 degrees. In other words, if angle A and angle B are supplementary, then:

A + B = 180.

Since angles X and Y are supplementary, their measures add up to 180 degrees. So we have:

X + Y = 180

Substituting the given values, we get:

115.75 + (m - 8) = 180

Simplifying, we get:

m - 8 = 180 - 115.75

m - 8 = 64.25

Adding 8 to both sides, we get:

m = 72.25

Therefore, the measure of angle Y is m - 8 = 72.25 - 8 = 64.25 degrees.

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If a pizza with an 18-inch diameter is divided into 10 equal pieces, then each slice will have a surface area of roughly 25.45 square inches.

Diameter is defined as a straight line across the middle of a body or figure, particularly a circle or sphere. Pizza diameter is the length of a straight line that touches two locations on the edge of a pizza pie and passes through its center.

Each sector of the pizza, which is divided into 12 equal sections, has an arc measurement of 360/10= 36 degrees.

As = (360÷Ф) ×X r² where x is the measure of the intercepted wave, yields the area of a sector.

We know that x=36 and

d=18→r=9 in. Thus, r is the radius and A is the area of each intersecting arc of a sector.

A=1/10×81π

then each slice will have a surface area of roughly 25.45 square inches.

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The equation of the circle centered at (4, -5) with radius 7 is (x - 4)²+ (y + 5)² = 49.

A circle is a two-dimensional form that may be described as a collection of points (locus) that are equally spaced apart from a central fixed point. The radius of a circle is the separation between its centre and any other point on the circle. Another way to think of a circle is as the collection of all points at a certain radius from the centre.

The equation of a circle with center (h, k) and radius r is given by:

(x - h)² + (y - k)²= r²

In this case, the center of the circle is (4, -5), and the radius is 7. So the equation of the circle is:

(x - 4)² + (y - (-5))² = 7²

(x - 4)² + (y + 5)² = 49

Therefore, the equation of the circle centered at (4, -5) with radius 7 is (x - 4)² + (y + 5)² = 49.

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The value of k given the absolute value functions is (a) k = -5

Given that

graph = f(x)

table = g(x)

Since the vertex of the function f(x) is at (0,1), we have f(0) = 1.

Also, from the given table, we have g(0) = -4.

Therefore, if g(x) = f(x) + k, we must have g(0) = f(0) + k = 1 + k.

But we also know that g(0) = -4. Thus, we have:

1 + k = -4

Solving for k, we get:

k = -5

Therefore, the value of k is -5.

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The area of the equilateral triangle is approximately 58.78 square inches.

An equilateral triangle has all sides equal, so we can divide the perimeter by 3 :

45 inches ÷ 3 = 15 inches

Therefore, each side of the equilateral triangle measures 15 inches.

Area = (√3 / 4) x (side length)²

After putting the values,

Area = (√3 / 4) x 15 x 15 square inches

Area = (√3 / 4) x 225 square inches

Area = 58.78 square inches

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Hence, after 40 years, Davey will have $1,476,289.64 in his retirement account as n = the number of cycles.

A problem-solving strategy known as the unitary technique is determining the worth of one unit of such a quantity and utilising that value to determine the value of an other number of units related to that quantity. For issues where the price of one unit is given and the value of some other quantity is needed, it is a proportionality strategy. The unitary method's fundamental principle is to establish a ratio between two numbers, where one of the numbers is represented in the form of one unit while the other quantity is defined in terms of a greater number of units.

given

If Davey doesn't add any more money to his retirement account for the next 20 years, it will increase to:

[tex]FV = P * (1 + r)^n[/tex]

where FV is the lump sum's future value

P is the lump sum's present value, which in this example is $214,111.26.

R is the annual interest rate, which in this case is 9.35%.

n = the number of cycles (in this case, 20 years)

The following equation can be used to determine Davey's retirement account's potential value after 40 years:

[tex]FV = 214,111.26 * (1 + 0.0935)^20 = $1,476,289.64[/tex]

Hence, after 40 years, Davey will have $1,476,289.64 in his retirement account as n = the number of cycles.

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The rounded number to 1 significant figure is 10000m.

Significant figures are a way of indicating the precision of a measurement or calculation. They represent the digits in a number that are known with certainty, plus one additional digit that is estimated. The rules for determining significant figures include:

Significant figures are important because they allow us to communicate the accuracy and precision of a measurement or calculation. By using the appropriate number of significant figures, we can avoid misleading others with inaccurate or imprecise information.

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Answer:

4 or ≈ 12.6

Step-by-step explanation:

L = r * θ

r = 12

θ = 60 = (/3) when converted to radians by multiplying (/180)

then multiply

(/3)*12 = 4 or ≈ 12.6

The volume of the candle is,⇒ V = 31.4 in³.What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.Given that;A candle in the shape of a cylinder has the dimensions shown, in inches.And, Diameter of candle = 5 in.Height of candle = 8 in.We know that;Volume of cylinder = πr²hHence, We get;The volume of the candle is,⇒ V = 3.14 × (5/2)² × 8⇒ V = 3.14 × 10⇒ V = 31.4 in³.Thus, The volume of the candle is,⇒ V = 31.4 in³.

Each box needs to have a minimum space of 576 cubic inches to hold the toy.

What is a cuboid?

A cuboid is a three-dimensional solid shape that has six rectangular faces, where each face meets at right angles with adjacent faces.

To calculate the space required for each box to hold a toy that is 8 inches tall by 12 inches wide and 6 inches deep, we need to calculate the volume of the toy.

The volume of the toy can be calculated as:

Volume = height x width x depth

Volume = 8 inches x 12 inches x 6 inches

Volume = 576 cubic inches

Therefore, each box needs to have a minimum space of 576 cubic inches to hold the toy.

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As per the unitary method, the chef has 9.14 pounds of celery left after cutting up 3 pounds to serve with chicken wings and dicing 8 ounces to put on garden salads.

To start, let's convert all of the weights to the same units. The chef bought 4 bunches of celery, each weighing 2 pounds, so in total she bought:

4 bunches * 2 pounds per bunch = 8 pounds

Next, we know that she used 3 pounds of celery for the chicken wings and 8 ounces (which is half a pound) for the garden salads. So in total she used:

3 pounds + 0.5 pounds = 3.5 pounds

To find the value of one pound of celery, we can subtract the amount of celery the chef used from the total amount of celery she bought, and then divide by the number of pounds she bought:

(8 pounds - 3.5 pounds) / 8 = 0.4375 pounds per pound

So one pound of celery is worth 0.4375 pounds. Now we can use this value to find out how many pounds of celery the chef has left. We know she started with 8 pounds of celery, and she used 3.5 pounds, so she must have:

(8 pounds - 3.5 pounds) / 0.4375 pounds per pound = 9.14 pounds left

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Answer:

Step-by-step explanation:

To determine which function has the greatest y-intercept, we need to look at the constant term, which represents the y-intercept, of each function. The function with the largest constant term will have the greatest y-intercept.

For example, consider the following three functions:

1. f(x) = 2x + 5

2. g(x) = 3x - 7

3. h(x) = -4x + 10

The constant term for each function is 5, -7, and 10 respectively. Therefore, h(x) has the greatest y-intercept of 10, since its constant term is larger than those of f(x) and g(x).

Answer:

0 and 1

Step-by-step explanation:

hope this helps ;)

To price the derivative using the two-period binomial model, we need to calculate the expected payoff of the derivative using the risk-neutral probabilities.

The possible outcomes for the two-period binomial model are H and T,  there are four possible states of the world: HH, HT, TH, and TT.

To calculate the expected payoff we need to calculate the probability of each state occurring. The probability of HH occurring is pp=0.60.6=0.36, the probability of HT and TH occurring is pq+qp=0.60.4+0.40.6=0.48, and the probability of TT occurring is qq=0.40.4=0.16.

Next, we can calculate the expected payoff in HH and TT states, the derivative pays off 1, and in the HT and TH states, the derivative pays off 0. The expected payoff of the derivative in the HH and TT states is 10.36=0.36, and the expected payoff in the HT and TH states is 00.48=0.

We need to discount the expected payoffs back to time 0 using the risk-neutral probabilities.

The probability of that state occurring multiplied by the discount factor, which is 1/(1+r), where r is the risk-free interest rate.

Since this is a risk-neutral model, the risk-free interest rate is equal to 1. Therefore, the risk-neutral probability of each state occurring is

HH: 0.36/(1+1) = 0.18

HT/TH: 0.48/(1+1) = 0.24

TT: 0.16/(1+1) = 0.08

Finally, we can calculate the price of the derivative

Price = 0.181 + 0.240 + 0.240 + 0.081 = 0.26

Therefore, the price of the derivative is 0.26.

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There is a volume of  14,000 gallons of water in the tank after 4 minutes.

To answer your question, let's consider the given terms: the rate at which water is poured into the tank (2000t + 1000 gallons per minute) and the initial volume of water in the tank (5000 gallons).

Since the rate is given in terms of time t, we can find the volume of water poured in after 4 minutes by plugging t = 4 into the rate equation:

Volume poured in 4 minutes = 2000(4) + 1000
Volume poured = 8000 + 1000
Volume poured = 9000 gallons

Now, add this to the initial volume of water in the tank:

Total water in tank after 4 minutes = Initial volume + Volume poured
Total water = 5000 + 9000
Total water = 14,000 gallons

So, after 4 minutes, there are 14,000 gallons of water in the tank.

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To find line segment AB, you'd have to use the principle of proportions. Thus, Line AB is 10.5.

To derive line segment AB,

6/4 = AB/7

To solve for AB, we can cross-multiply and simplify:

6/4 = AB/7

Multiply both sides by 7:

(6/4) * 7 = AB

Simplify:

10.5 = AB

Therefore, AB is equal to 10.5.

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Sara used 3/5 cup of milk in the recipe. The answer corresponds to option (B) in the given answer choices.

The total amount of liquid used by Sara in the recipe is 1 cup. Out of this 1 cup, Sara used 2/5 cup of vinegar. Therefore, the amount of milk she used would be the difference between the total amount of liquid used and the amount of vinegar used.

Mathematically, we can represent this as:

Amount of milk = Total amount of liquid - Amount of vinegar

Amount of milk = 1 cup - 2/5 cup

Simplifying the expression on the right side, we get:

Amount of milk = 5/5 cup - 2/5 cup

Amount of milk = 3/5 cup

Therefore, Correct option is B.

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Complete question is:

Sara used a total of 1 cup of liquid for a recipe. She used 2/5 cup of vinegar, and the rest of the liquid she used was milk.

How much milk, in cups, did sara use for the recipe?

A) 2/5

B)3/5

C)5/5

D) 1 2/5​

The surface area for each package is given as follows:

Hence:

Package A has the greater surface area.

The surface area of a rectangular prism of height h, width w and length l is given by:

S = 2(hw + lw + lh).

This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas.

For Package A, the dimensions are given as follows:

l = 14 in, h = 12 in, w = 3 in.

Hence the surface area is given as follows:

S = 2 x (12 x 3 + 14 x 3 + 12 x 14)

S = 492 in².

For Package B, the dimensions are given as follows:

l = 11 in, h = 6 in, w = 8 in.

Hence the surface area is given as follows:

S = 2 x (11 x 6 + 11 x 8 + 6 x 8)

S = 404 in².

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