Find the surface area of the part of the plane z=4+6x+5y that lies inside the cylinder x2+y2=16

The net of the cube is attached to this answer, and;

a. The surface area of the cube = 6X^2 squared centimeters

b. The volume of the cube = x^3 cubic centimeters

The net of a shape or figure is the shape gotten when it is opened through its edges and spread out on a flat surface. If this shape is folded with respect to its edges, the original shape would be reproduced.

The net of the given cube is attached to this answer.

a. To determine surface area of the cube, we have;

surface area of a cube = 6*length*length

                                      = 6l^2

Given that the length of the sides of the cube is x centimeters,

area of the cube = l^2

                            = x^2

surface area of the cube = 6x^2

b. The volume of a cube = length^3

                                         = l^3 ;l

The volume of the cube = x^3

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Define the problem , Gather information, Generate possible solutions, Evaluate ideas and then choose one, Evaluate are the 5 types of problem-solving.

What are fundamental techniques for fixing issues?

Identifying the issue, considering potential solutions, and selecting the best course of action are the three primary components of problem-solving.

               Different problem-solving techniques include elucidating, ideating, developing, and implementing.

What advantages does problem-solving have?

Making decisions is necessary to solve issues. People who are "happier, more confident, and more autonomous" are typically those who have good problem-solving abilities.

                     Children develop resilience when they take on challenges individually or in groups. They pick up the ability to approach problems from a different angle.

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Slope = 1/4. Now let's put it into point slope form to find out the y-intercept. Then convert it into y=mx+ b form, the standard slope intercept form

How to calculate the linear equation?

Step1:

(-4,-2) and (4,0)

y=1/4x-1

Let's find the slope first, with the two given ordered pairs.

Slope = 1/4.

Now let's put it into point slope form to find out the y-intercept.

Then convert it into y=mx+ b form, the standard slope intercept form.

y + 2 = 1/4(x+4)

Then we convert it into y=mx+ b form (our final answer);

y=1/4x-1

Step 2:

(0,1)and(5,3)

y=2/5x+1

the equation of a line in slope-intercept form is.

y=mmx+ b

where m is the slope and b the y-intercept

to calculate the slope use the gradient formula

m=y2-y1/x2-x1

(x1,y1)=(0,1) and (x2,y2)=(5,3)

m=3-1/5-0=2/5

using m=2/5 and b=1

y=2/5x+1

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The range of the relation on the graph is:

R: {1, 2, 6}

For a relation y = f(x), the range is defined as the set of the possible outputs of the function (the possible values of y).

Here we can see a graph of 3 points, such that the coordinates of these points (on the form (x, y)) is:

(3, 6), (5, 2) and (6, 1)

The range is the set of the second values of each of these pairs, so the range in this case is:

R: {1, 2, 6}

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Answer:

3.50 × 12 = 42

Therefore, she spent 42 dollars.

The height of the redwood has been calculated as 372 meters.

In  order to get the height of this tree, I would have to make use of the similar triangles method. The proportion is set as

tree height / tree shadow = Eric's height / Eric's shadow

Eric's height is 6 feet, his shadow is 8 feet

The proportion is 6 / 8

= 3 / 4

To get the height of the tree we have to multiply the proportion by the distance with which Eric is away from the tree

= 3 / 4 * 496

= 372 feet

The redwood is 372 feet

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Answer:

The simplest form would be 5 1/8

Step-by-step explanation:

You don't have a common factor with 41 and 8, so the real reduced answer would just be mixed, as 5 1/8.

Best saker out of 5 participants is Contestant D because his speed of skating is the highest. He has a speed 30 m/min.

Skating is a kind of sports as well as exercise. It is such a sport in where a participant needs to move on skates.

Best skater is determined by the performance of each participant.

The performance can be detected by observing the speed of skater.

speed = distance travelled by skater / time

we notice from the above question that contestant A covered a distance 1100m within 40 minutes.

so, speed of A = 1100 m/ 40 min = 27.5 m/min

Contestant B covered a distance 1800m within 1 hour and 10 minutes.

speed of B contestant = 1800m/ 70 min= 25.71 m/min

Contestant C covered a distance 1000m within 60 minutes.

speed of contestant C = 1000m/ 60 min = 16.67 m/min

Contestant D covered a distance 900m within half an hour.

speed of D = 900m /30 min = 30 m/min

Contestant E covered a distance 1500m within 55 minutes.

speed of contestant E = 1500m/ 55 min = 27.27 m/min

from the above discussion, we find that contestant D has the highest speed among all other skaters.

speed of contestant D = 30 m/min

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There can be an infinite number of integer values of x possible.

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side for it to be a valid triangle. So, for a triangle with side lengths 15, 47 and  [tex]$\dfrac{x}{2}$[/tex] the condition for the triangle to be valid is:

15 + 47 >[tex]$\dfrac{x}{2}$[/tex]

30 > [tex]$\dfrac{x}{2}$[/tex]

2\times30 > x

x > 60

Since xmust be an integer, the possible values of x are any integer greater than 60. Thus, there can be an infinite number of integer values of x possible.

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D) 2, 3, 4 is not a pythagorean triplet.

Pythagoras theorem is in the form of;

a²+b²=c²

Applying this formula to the given options we get'

a) 3, 4, 5 is a Pythagorean triplet because 3^2 + 4^2 = 9 + 16 = 25 = 5^2

b) 6, 8, 10 is not a Pythagorean triplet because 6^2 + 8^2 = 36 + 64 = 100 = 10^2

c) 5, 12, 13 is a Pythagorean triplet because 5^2 + 12^2 = 25 + 144 = 169 = 13^2

d) 2, 3, 4 is not a Pythagorean triplet because 2^2 + 3^2 = 4 + 9 = 13 ≠ 4^2

In other words the pythagorean theorem states that in a right angled triangle, the square of the hypotenuse is the sum of the squares of the other 2 sides.

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For a triangle with vertices L (1 , 8),, M (0 , 0) , and N (-8 , 1)  the plot is plotted and the slope and lengths are

slope of LM =  8

slope of MN = 8

slope of NL =  7/9

length of LM = √65

length of MN = √65

length of NL = √130

The slope, m of the lines is calculated the formula

m = (y₀ - y₁) / (x₀ - x₁)

where

m = slope

x₂ and x₁ = points in x coordinates

y₂ and y₁ = points in y coordinates

Slope of LM  L (1 , 8), M (0 , 0)

m = (8 - 0) / (1 - 0)

m = (8) / (1)

m = 8

Slope of LM  L (1 , 8), M (0 , 0)

m = (8 - 0) / (1 - 0)

m = (8) / (1)

m = 8

Slope of NL,  N (-8 , 1), L (1 , 8)

m = (1 - 8) / (-8 - 1)

m = (-7) / (-9)

m = 7/9

The length of line in an ordered pair is calculated using the formula

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

where

d = distance between the points

x₂ and x₁ = points in x coordinates

y₂ and y₁ = points in y coordinates

For LM  L (1 , 8), M (0 , 0)

d = √{(1 - 0)² + (8 - 0)²}

d =√{1 + 64}

d = √65

For MN  M (0, 0) N (-8 , 1)

d = √{(0 + 8)² + (0 - 1)²}

d =√{64 + 1}

d = √65

For NL N (-8 , 1), L (1 , 8)

d = √{(-8 - 1)² + (1 - 8)²}

d =√{81 + 49}

d = √130

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3 seconds.

The problem states that the ball was kicked from a height of 12 ft, this would be the initial height of the ball. Hence:

h₀= 12 ft

Also, initial velocity is 44ft/s. Hence:

v₀= 44ft/s

[tex]h(x)=-16x^{2} +v_{0} x+h_{0} \\ \\h(x)=-16x^{2} +(44ft/s) x+(12ft)[/tex]

[tex]h(x)=-16x^{2} +44 x+12[/tex]

Since the height when the ball hits the ground is 0, we need to substitute the height value (h(x)) by 0, and then solve the equation for "x".

Using the quadratic formula (check the attached image) we can get the value of time.

Taking the coefficients:

A= -16

B= 44

C= 12

[tex]x_{1} =\frac{-(44)+\sqrt{(44)^{2}-4(-16)(12) } }{2(-16)}= -0.25s\\ \\x_{2} =\frac{-(44)-\sqrt{(44)^{2}-4(-16)(12) } }{2(-16)} =3s[/tex]

Since "x" is being used to represent time, and time is a variable that can only be positive, we're only taking the positive value.

Hence, we can conclude that after 3 seconds after being kicked, the ball wil hit the ground.

Answer:

x= 92 degrees

Y=44 degrees

Answer:

B

Step-by-step explanation:

3x + 8 = 2(x + 4) ← distribute parenthesis

3x + 8 = 2x + 8 ( subtract 2x from both sides )

x + 8 = 8 ( subtract 8 from both sides )

x = 0

B is the correct answer

Step-by-step explanation:

B is the correct answer

The first time that she will have tutoring and cooking class at the same time is given as follows:

6 weeks.

Considering periodic events, they will repeat on the same day for the least common factor of the periods of each event.

The periods for each event in this problem are given as follows:

The least common factor of 3 and 2 is given as follows:

3 x 2 = 6.

(prime numbers, hence we just multiply them to obtain the least common factor).

The least common factor of six means that the period is of six weeks.

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Therefore , the solution of the given problem of slope intercept comes out to be  y = 0.66x +12.65.

The gradient intercept method can be used once you are satisfied that Y = mx + b holds true. The direction form can be used to illustrate a hypothesis for a line by focusing on a single point directly and its slope. The slope is determined by the increase across the run and is first represented by the point form (x,y). The slope can be determined using slope intercept method, which is y = mx + b. (0, b). The direct form is a method for formulating a prediction equation for a line by making just one precise declaration about a vector slope.

Here,

Given : slope = 2/3

and coordinates = (0 , 12.65)

Thus ,

the equation of the given line by using formula of slope intercept:

=> y- y1  = m(x-x1 ) + c

=> y - 12.65 = 2/3*x

=> y = 0.66x +12.65

Therefore , the solution of the given problem of slope intercept comes out to be  y = 0.66x +12.65.

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A linear equation can either be y = 5x + 2 or y = 3/x + b.

But the equation y= x² + b would not be a linear equation.

An equation is said to be a linear equation if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.

The general equation of a linear equation is given below:

y = mx + b

Hence, the equation y = x (square root sign on it) + b would not be a linear equation because the power of the variable x is greater than 1.

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The factorization of the given expression is 16x² + 8x + 1- 9y² = (4x +3y +1)(4x -3y +1).

What is the meaning of  Factorize?

Factorization or factoring is defined in mathematics as the breaking or breakdown of one entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, which when multiplied together provide the original number or matrix, etc.

Given expression is 16x² + 8x + 1- 9y²

Now make two groups of the expression:

(16x² + 8x + 1)- (9y²)

= (16x² + 8x + 1)- (3y)²

Now applying Algerical identity (a + b)² = a² + 2ab + b².

= ((4x)² + 2×4x×1 + 1²)- (3y)²

= (4x + 1)² - (3y)²

Now applying Algerical identity (a² - b²) = (a+ b)(a - b)

= (4x + 1 + 3y)(4x + 1 - 3y)

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The number and percentages of the parameters in the question are;

A percentage is a representation of a part of a whole as a fraction with a hundred (100) as the denominator.

T

From the attached table in the question, we get;

The number of people that make more than $60,000 = 388 + 198 + 66 = 652

The number of police officers in the survey  = 224 + 703 + 198 = 1125

The number of police officers that make less than $40,000 = 224

The percentage of police officers that make less than $40,000 is therefore;

Other information obtainable from the table are as follows;

The number of police officers that make more than $40,000 = 703 + 198 = 901

The percentage of all police officers that make more than $40,000 is therefore;

(901 ÷ 1125) × 100 ≈ 80.09%

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A. Using the given information, y expressed in terms of x is y = x + 50

B. The table that shows the relationship between y and x is

x               y

10             60

20            70

30             80

40             90

50             100

From the question, we are to express y in terms of x

From the given information,

There are x sparrows in a tree and 50 sparrows on the ground beneath the tree

If y represent the total number of sparrows in the tree and on the ground,

Then,

We can write that

y = x + 50

B.

We are to make a table to show the relationship between y and x

Using the equation above

y = x + 50

When x = 10

y = 10 + 50

y = 60

When x = 20

y = 20 + 50

y = 70

When x = 30

y = 30 + 50

y = 80

When x = 40

y = 40 + 50

y = 90

When x = 50

y = 50 + 50

y = 100

Thus,

The table is:

x               y

10             60

20            70

30             80

40             90

50             100

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Isosceles, equilateral, scalene, obtuse, acute, and right triangles are the six different forms of triangles. Shapes with three sides are called triangles. The various triangle varieties go under various names.

Having three sides, three angles, and three vertices, a triangle is triangular. Every triangle's internal angles add up to 180 degrees. We refer to this as the triangle's angle sum attribute. Any two triangle sides can be added up to make any two sides longer than the third side.

Three edges and three vertices define a triangle as a polygon. One of geometry's fundamental shapes is this one. The designation "triangle A B C" refers to a triangle with the vertices A, B, and C. When three points are non-collinear in Euclidean geometry, they each determine a distinct triangle and plane. 12 times the base plus the height, Triangle's side lengths added together to form the perimeter. 3, vertices total. 3 edges total Inside angle: 60 degrees (for equilateral) 180  degrees is the sum of interior angles. Consists of convex, cyclic, equilateral, isogonal, and isotoxal properties.

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The set of real numbers is a subset of the set of complex numbers because any real number, a, can be written as a + 0i

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The formulae that specify how much 8% solution in equation and how much 24% solution were utilized are x+ y=200 and x+3y=450.

A mathematical equation is a formula that uses the equals symbol (=) to link two expressions and represent their equivalence. A mathematical statement that demonstrates the equality of two mathematical expressions is an equation in algebra, in its most basic form. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."

Let x and y be the volume of the 8% and 24% solutions, respectively, that were utilized.

The entire solution volume, as stated in the question, will be 200ml. The resulting equation is: x +y=200

Now that it has been stated that 8%, 18%, and 24% saline mixes would be employed as the solution, the following equation will be:

[tex]0.08x+ 0.24y=0.18*200\\8x/100+24/100=18/100*200\\8x+24y=3600\\\\8(x+3y)=3600\\ x+3y=450\\[/tex]

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On solving the provided question, we can say that For the specified percentage, the 95% confidence interval is (0.864, 0.3580).

A confidence interval in statistics expresses the probability that a population parameter would fall between a set of values for a specific percentage of the time. Analysts commonly utilize 95% or 99% confidence intervals for their predictions.

If total samples = E = 36, then

8 results were obtained.

Chance = p = 8/36 = 0.2222

Z value at 95% confidence level = 1.96

p = [tex]0.2222 + 1.96 ( \sqrt{ 0.2222() 1 - 0.2222) / 36 } ) = 0.3580[/tex]

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The correct option is A) √0.036 as it is the only irrational number.

Irrational numbers are the set of real numbers that cannot be expressed in the form of a fraction, like p/q where p and q are integers.

Considering option A) √0.036, there is no number among integers and fractions that equals

√0.036

option B) is a terminating decimal and can be expressed as a fraction.

option C) will result to the whole number 1 just like the option D) 10 which is also a whole number.

In conclusion, only option A) √0.036 is an irrational number as it cannot be expressed as the quotient of two integers.

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On solving the provided question we can say that the equation will be -

37.79x + 39.71y = 0.69 = 75.4 +75.4 = 150.8

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

the equation will be -

37.79x + 39.71y = 0.69

x = 2

y = 2

75.4 +75.4 = 150.8

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Because the ten distances are not evenly distributed, Raul's overall performance should be determined by the median. Although nine distances are clustered together, the homerun is an outlier in the data set. The median is the best measure of centre for a data set with outliers.

The median is defined as the middle value in a given set of numbers or data. In mathematics, there are three different measures for determining the average value of a given set of numbers.

They are as follows: mean, median, and mode. These three measures are referred to as central tendency measures. Mean calculates the average value of the given data. A median defines the data's middle value.

The median is defined as the middle value of a sorted list of numbers in mathematics. By ordering the numbers, the middle number is discovered. The numbers are sorted ascending. After the numbers are ordered, the middle number is referred to as the data set's median.

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Full question:

Of the 10 swings, Raul hit 1ball over the outfield fence for a home run, but the other 9 hits were ground balls that stayed in the infield. Which measure of center will best summarize Raul’s overall performance? Why?

The solution is

a) The number of solutions to the equation is 1

b) Diego finishes the milkshake in 30 seconds and Lin finishes the milkshake in 36 seconds

c) Diego finishes the milkshake first

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the time to finish the milkshake by Lin and Diego be represented as A and B respectively

Now , the equation will be

The amount of milkshake with Lin = 12 ounce

The rate at which Lin finishes her milkshake = 1/3 milkshake per second

The time for Lin to finishes her milkshake A = amount of milkshake with Lin / rate at which Lin finishes her milkshake

Substituting the values in the equation , we get

The time for Lin to finishes her milkshake A = 12/ ( 1/3 )

The time for Lin to finishes her milkshake A = 36 seconds

Now ,

The amount of milkshake with Diego = 20 ounces

The rate at which Diego finishes his milkshake = 2/3

The time for Diego finishes his milkshake B = 20 / ( 2/3 )

The time for Diego finishes his milkshake B = 30 seconds

Hence , Diego finishes his milkshake faster

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