What is the distance between
(2,3) (8,9)

Answer:

The sum has a degree of 6, but the difference has a degree of 7.

Step-by-step explanation:

Which is true about the degree of the sum and difference of the polynomials 3x5y - 2x3y4 - 7xy3 and -8x5y + 2x3y4 + xy3? ... The sum has a degree of 6, but the difference has a degree of 7.

The properties used were the distributive property of multiplication over addition, the subtraction property of equality, and the multiplication property of equality.

Properties are statements that are true for a wide range of numbers or equations. They are rules that describe the behavior of mathematical objects and relationships between them.

1) Given 4x-1=27, we can use the addition property of equality to add 1 to both sides:

4x-1+1 = 27+1

Simplifying, we get:

4x = 28

Then, we can use the multiplication property of equality to divide both sides by 4:

4x/4 = 28/4

Simplifying, we get:

x = 7

Therefore, we have proved that if 4x-1=27, then x=7.

The properties used were the addition property of equality and the multiplication property of equality.

2) Given (a/(-6))+2=5, we can use the subtraction property of equality to subtract 2 from both sides:

(a/(-6))+2-2 = 5-2

Simplifying, we get:

a/(-6) = 3

Then, we can use the multiplication property of equality to multiply both sides by -6:

(a/(-6))(-6) = 3(-6)

Simplifying, we get:

a = -18

Therefore, we have proved that if (a/(-6))+2=5, then a=-18.

3) The properties used were the subtraction property of equality and the multiplication property of equality.

Given -9(2x-3)=63, we can use the distributive property of multiplication over addition to simplify the left-hand side:

-9(2x-3) = -18x + 27

Then, we can use the subtraction property of equality to subtract 27 from both sides:

-18x + 27 - 27 = 63 - 27

Simplifying, we get:

-18x = 36

Finally, we can use the multiplication property of equality to divide both sides by -18:

(-18x)/(-18) = 36/(-18)

Simplifying, we get:

x = -2

Therefore, we have proved that if -9(2x-3)=63, then x=-2.

The properties used were the distributive property of multiplication over addition, the subtraction property of equality, and the multiplication property of equality.

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To complete the double reflection transformation over the lines x = 1 and x = 3, we need to reflect each point twice.

For point a(-5,2), the first reflection over x = 1 will give us a'(-9,2).

The second reflection over x = 3 will give us a"(-7,2).
For point b(-1,5), the first reflection over x = 1 will give us b'(-3,5).

The second reflection over x = 3 will give us b"(-5,5).
For point c(0,3), the first reflection over x = 1 will give us c'(2,3).

The second reflection over x = 3 will give us c"(4,3).
So, the coordinates after the double reflection transformation are:
a"(-7,2), b"(-5,5), and c"(4,3).

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-2a(a - d) + 2a(2a - 3d)

(-2a * a) + (-d * -2a) + (2a * 2a) + (2a * -3d)

-2a^2 + 2ad + 4a^2 - 6ad

(4a^2 - 2a^2) + (2ad - 6ad)

2a^2 - 4ad

---The above expression is simplified, though not fully. The below expression is fully simplified.

2a(a - 2d)

Hope this helps!

Answer: A

Step-by-step explanation:

- and - = +

-8 (4 - x) = 16

-32 + 8x = 16

8x = 16 + 32

8x = 48

x = 6

Based on the given clues, we can determine the person, drink, and price paid for each individual:

Calvin: Root Beer, $4.99

Dean: Lemonade, $7.99

Kelli: Water, $6.99

Lee: Iced Tea, $5.99

From clue 1, we know that either Calvin or the person who got the Root Beer paid $4.99. Since Calvin paid more than Lee according to clue 4, Calvin cannot be the one who got the Root Beer. Therefore, Calvin paid $4.99.

From clue 2, Kelli paid $6.99.

From clue 3, the person who got the water paid $1 less than Dean. Since Dean paid the highest price, the person who got the water paid $1 less, which means Lee paid $5.99.

From clue 5, the person who got the Root Beer paid $1 less than the person who got the Iced Tea. Since Calvin got the Root Beer, Lee must have gotten the Iced Tea.

Therefore, the final assignments are:

Calvin: Root Beer, $4.99

Dean: Lemonade, $7.99

Kelli: Water, $6.99

Lee: Iced Tea, $5.99

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The payments each month do not cover all interest and no principal. The correct answer would be an option (B).

A credit card trap occurs when the minimum payments required each month do not cover all the interest charges and do not reduce the principal balance. This means that even if the cardholder makes the minimum payments on time, they will still be paying only the interest charges and not reducing the amount of debt. This can result in a cycle of high-interest debt that is difficult to escape from.

Option A is incorrect as it's describing a common way payments work on credit cards.

Option C is not a trap, as it's describing a credit card issuer with a low-interest rate.

Option D is also incorrect, as it's describing a common way payments work on credit cards.

Hence, the correct answer would be an option (B).

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Mean = Sum of all observations/Number of observations

The value of the middlemost observation, obtained after arranging the data in ascending or descending order, is called the median of the data.

Given,

The set of scores =  0, 40, 60, 70, 75, 80, 85, 95, 95, 100

                           = 700/9

                           = 77.777

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The total area of the glass used in making the rectangular prism-shaped aquarium is 60 square feet.

The rectangular crystal formed aquarium has a base area of 6 feet by 2.5 feet, which is equivalent to 15 square feet. The level of the aquarium is 4 feet. To compute the complete region of the glass utilized in making the aquarium, you really want to duplicate the base region by the level, which is 15 x 4 = 60 square feet. This implies that 60 square feet of glass were utilized in making the aquarium. The glass some portion of the aquarium incorporates the four sides and the top, while the base is normally made of an alternate material, like acrylic.

The foundation of the rectangular crystal formed aquarium is 6 feet by 2.5 feet, which gives an all out area of 15 square feet (6 x 2.5). The level of the aquarium is 4 feet. Hence, the absolute region of the glass utilized in creating the aquarium can be determined by duplicating the base region by the level: 15 x 4 = 60 square feet.

The glass a piece of the aquarium would be the four sides and the top. The base would ordinarily be made of another material, like acrylic.

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a. It's true that ∑x = 244, ∑x² = 16058, ∑y = 201 and ∑y² = 9153.

b. The sample mean, variance and standard deviation of x are 48.80, 830.16 and 28.81

c. The sample mean, variance and standard deviation of y are 40.20, 214.56 and 14.65

d. The coefficient of the variation for successful mallard duck nests and Canada goose nests is 0.59 and 0.36.

Given that,

The percentages of successful nests is

x: Percentage success for mallard duck nests

86, 44, 11, 25, 77

y: Percentage success for Canada goose nests

18, 60, 30, 45, 48

a. We have to verify ∑x = 244, ∑x² = 16058, ∑y = 201 and ∑y² = 9153.

∑x = 86 + 44 + 11 + 26 + 77 = 244

∑y =18 + 60 + 30 + 45 + 48 = 201

∑y² =182 + 602 + 302 + 452 + 482 = 9153

∑x² =  862 + 442 + 112 + 262 + 772 = 16058

Therefore, It's true that ∑x = 244, ∑x² = 16058, ∑y = 201 and ∑y² = 9153.

b. We have to find the sample mean, variance and standard deviation of x.

Mean is the ratio of sum of percentage to number of percentages

\(\bar X\)= \(\frac{244}{5}\)

\(\bar X\)= 48.80

Variance = \(\frac{\sum (X-\bar X)^2}{n}\)

S²= \(\frac{[(86-48.80)^2 +(44-48.80)^2 + (11-48.80)^2 + (26-48.80)^2 + (77-48.80)^2 ]} { 5 }\)

S² = 830.16

Standard Deviation S = \(\sqrt{830.16}\) = 28.81

Therefore, The sample mean, variance and standard deviation of x are 48.80, 830.16 and 28.81

c. We have to find the sample mean, variance and standard deviation of y.

Mean \(\bar X\)= \(\frac{201}{5}\)

\(\bar X\)= 40.20

Variance S²= \(\frac{[(18-40.20)^2 +(60-40.20)^2 + (30-40.20)^2 + (45-40.20)^2 + (48-40.20)^2 ]} { 5 }\)

S² = 214.56

Standard Deviation S = \(\sqrt{214.56}\) = 14.65

Therefore, The sample mean, variance and standard deviation of y are 40.20, 214.56 and 14.65

d. We have to find the coefficient of the variation for successful mallard duck nests and Canada goose nests.

CV formula is the ratio of standard deviation by mean

CV for X = \(\frac{28.81}{48.80}\) = 0.59

CV for Y = \(\frac{14.65}{40.20}\) = 0.36

Therefore, The coefficient of the variation for successful mallard duck nests and Canada goose nests is 0.59 and 0.36.

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Answer and Step-by-step explanation:

First off, we need to know the volume formula for a cylinder.

The volume formula for a cylinder is:

V = \(\pi r^{2} h\)

Where:

V = Volume

r = Radius

h = Height.

We are given the diameter and the height of the cylinder.

The radius is half of the diameter.

d (Diameter) = 3

r = 1.5

h = 15

Now, we plug it into the equation.

V = \(\pi (1.5^{2} )(15)\)

Plug these values into a calculator and solve.

The volume we get is 106.03, which rounds to 106.0.

That means the answer choice that is correct is answer choice D. 106.0 \(in^3\).

#teamtrees #PAW (Plant And Water)

Answer:

there are 720 cm in 7.2 meters

Step-by-step explanation:

Answer:

I think it would be 72

Step-by-step explanation:

You would have to divided 2 by 12, which is 6. Then, you would have to multiply 6 by 12, which i s 72. I hope this is right, if not I'm sorry. I really hoped this helped :D

The phrase that best describes the relationship between the number of miles driven and the amount of gasoline used is "correlated, but not causal." So, the correct answer is B).

While there is a clear correlation between the number of miles driven and the amount of gasoline used (i.e., as the number of miles driven increases, the amount of gasoline used generally increases), this relationship is not necessarily causal.

There may be other factors at play, such as the efficiency of the vehicle, driving habits, and road conditions, that can affect the amount of gasoline used. Therefore, while the two variables are clearly related, it cannot be concluded that one variable causes the other. So, the correct option is B).

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--The given question is incomplete, the complete question is given

" Which phrase best describes the relationship between the number of miles driven and the amount of gasoline used?

A) causal, but not correlated

B) correlated, but not causal

C) both correlated and causal

D) neither correlated nor causal"--

Amanda would use 3 planks of lengths 3 feet, 5 feet, and 6 feet.

To determine which planks Amanda should use to build the triangular-shaped kennel:

Therefore, Amanda would use 3 planks of lengths 3 feet, 5 feet, and 6 feet.

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Answer: (4, -1) -- All real numbers -- [-1, ∞) -- (3,0) and (5,0). -- (0,15) -- x = 4 -- y = x^2-8x+15

Step-by-step explanation:

\(y = (x-4)^2 - 1\)

a) Vertex: (4, -1). In a quadratic in vertex form: \((x-h)^2 + k\), the vertex is the point (h,k)

b) Domain: Since it is a valid quadratic function, the graph extends for all x values. (in other words, you can plug in any value for x). The domain is thus all real numbers.

c) Range: You can plug in any value for x, but since x is being squared, you wont get every value out, you will only get positives out. But there is another condition; there is a -1 constant trailing the equation. this means the graph is shifted one unit down. thus, the y values, the range, is taken down by one as well. the range is thus all numbers from -1 to ∞, or in interval notation, [-1, ∞)

d) X-intercepts: from the graph we can see the intercepts are (3,0) and (5,0).

e) Also from the graph, the y-intercept can be seen as: (0,15)

f) Axis of Symmetry: It is always the line x = x-coordinate of vertex.

so in this case, the line will be x = 4

g) to find a congruent equation, simply expand this equation:

\(y = (x-4)^2 - 1\)

\(y = x^2-8x+16 - 1\)

\(y = x^2-8x+15\)

there ya go!

At point P (2, π/4, 2), vector A in Cartesian coordinates is A = <1, 2.5, 2>.

To express vector A in Cartesian coordinates, we can use the following conversions between cylindrical and Cartesian coordinates:

x = ρ * cos(θ)

y = ρ * sin(θ)

z = z

Given vector A = cos(θ) - ρ * sin(θ) + 2 * cos(θ) * sin(θ), we can substitute the corresponding expressions for ρ, θ, and z:

x = cos(θ) * cos(θ) - ρ * sin(θ) * sin(θ) + 2 * cos(θ) * sin(θ)

y = cos(θ) * sin(θ) + ρ * cos(θ) * sin(θ) + 2 * cos(θ) * sin(θ)

z = 2

Simplifying these expressions, we get:

x = cos^2(θ) + 2 * cos(θ) * sin(θ) - ρ * sin^2(θ)

y = cos(θ) * sin(θ) + ρ * cos(θ) * sin(θ) + 2 * cos(θ) * sin(θ)

z = 2

Now, we can evaluate vector A at point P (2, π/4, 2):

x = cos^2(π/4) + 2 * cos(π/4) * sin(π/4) - 2 * sin^2(π/4)

y = cos(π/4) * sin(π/4) + 2 * cos(π/4) * sin(π/4) + 2 * cos(π/4) * sin(π/4)

z = 2

Simplifying further, we have:

x = (1/2) + 1 - (1/2) = 1

y = (1/2) + 1 + 1 = 2.5

z = 2

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The patient will pay $452.20 in full today after applying the 15% discount.

If the patient receives a 15% discount for a visit to the healthcare provider and the total charge for the service is $532.00, the patient will pay 100% - 15% = 85% of the total charge.

To calculate the amount the patient will pay in full today, we need to find 85% of $532.00.

85% of $532.00 can be calculated as:

(85/100) * $532.00 = $452.20

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Answer:

she earns $10 per hour, and can earn $1 in 6 minutes (60 min divided by $10)

Step-by-step explanation:

Answer:

\(m=4\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Point (3, 4)

Point (4, 8)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Answer:

m = 4

Step-by-step explanation:

\(m=\frac{rise}{run}=\frac{8-4}{4-3}=\frac{4}{1} =\boxed{4}\)

Hope this helps.

Answer:

H

Step-by-step explanation:

Answer:

114 pies

Step-by-step explanation:

If the pie get together only had 20 people with 15 pies, then each person had a portion of 3/4 (divide them). The pie party has 152 people with 3/4 portions each, which means there has to be 114 pies at the party (multiply them).

:)

Answer:

152÷20=7.6

7.6×15=114

114 pies

It took both Sandy and Tom 54 seconds to cover the same distance.

We can set up an equation based on their relative speed

Take the supposition that Tom needs "t" seconds to travel the distance. Sandy started jogging 12 seconds before Tom, so it will take her "t + 12" seconds longer to complete the same distance.

To determine the distance traveled by Sandy, multiply her speed (7 meters per second) by her time (t + 12) seconds. Tom's distance traveled may be determined by dividing his speed (9 meters per second) by his time (t) seconds.

Equating the distances covered by Sandy and Tom:

7(t + 12) = 9t

Expanding the equation:

7t + 84 = 9t

Subtracting 7t from both sides:

84 = 2t

Dividing both sides by 2:

t = 42

Tom traveled the distance in 42 seconds as a result. We add the 12-second lead Sandy had to determine the time it took for both Sandy and Tom to travel the same distance:

t + 12 = 42 + 12 = 54

So, it took both Sandy and Tom 54 seconds to cover the same distance.

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EXPLANATION :

The cost of a 12 nights camp accommodation is 6720.

We need to divide the cost by 12 to get the cost per day.

Now, we are asked to find the cost of 7 nights and 4 nights.

We just need to multiply the daily rate by the number of nights.

a. 7 nights :

7 x 560 = 3920

b. 4 nights :

4 x 560 = 2240

ANSWER :

a. 3920

b. 2240

The maximum burn rate ∣ΔM/Δt∣ that the engine could reach before the ship's acceleration exceeded 5 g and its human occupants began to lose consciousness is approximately 51.0 kg/s.

Acceleration is directly proportional to the force acting on an object. In simple terms, if the force on an object is greater, then it will undergo more acceleration. However, there are limitations to the acceleration that can be tolerated by the human body. At about 5 g (49.0 m/s2) for more than a few seconds, an average person starts to lose consciousness. Let's use this information to answer the given question.

Let the maximum burn rate |ΔM/Δt| that the engine could reach before the ship's acceleration exceeded 5 g be x.

Let the mass of the spaceship be m and the exhaust speed of the engine be v.

Using the formula for the thrust of a rocket,

T = (mv)e

After substituting the given values into the formula for thrust, we get:

T = (3.00 × 104)(2.50 × 103) = 7.50 × 107 N

Therefore, the acceleration produced by the engine, a is given by the formula below:

F = ma

Therefore,

a = F/m= 7.50 × 107/3.00 × 104= 2.50 × 103 m/s²

The maximum burn rate that the engine could reach before the ship's acceleration exceeded 5 g is equal to the acceleration that would be produced by a maximum burn rate. Therefore,

x = a/5g= 2.50 × 103/(5 × 9.8)≈ 51.0 kg/s

Therefore, the maximum burn rate ∣ΔM/Δt∣ that the engine could reach before the ship's acceleration exceeded 5 g and its human occupants began to lose consciousness is approximately 51.0 kg/s.

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Answer:

n=2.56

Step-by-step explanation:

No. of solution exist for the absolute value equation 2|x + 2| + 1 = 9  is 2

The two values are x =  -6,2

The given question has a small mistake, it needs to be written as

2|x + 2| + 1 = 9

Solving the absolute value equation,

2|x + 2| + 1 = 9

2|x + 2|  = 9 -1

2|x + 2| = 8

|x + 2| = 8/2

|x + 2|  = 4

Expanding the absolute value equation,

x + 2 = 4                                       x + 2 = -4

x = 4 -2                                         x = -4 -2

x = 2                                             x = -6

Therefore, the equation has two values ,x = -6,2

Total no. of solution that exist for the given absolute value equation is 2

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