Which of the following r one dimensional figures?
check all that apply.
a. ray
b. angle
c. square
d. point
e. segment
f. line

We have to show that the set of numbers of the form a + b√2, where a and b are rational numbers, forms a field with respect to addition and multiplication.

To start, we need to show that the set of numbers is closed under addition and multiplication. This means that if we add or multiply two numbers in the set, the result must also be in the set.

For addition, let's take two numbers in the set, say (a1 + b1√2) and (a2 + b2√2). When we add them, we get (a1 + a2) + (b1 + b2)√2. Since a1, a2, b1, and b2 are all rational numbers, their sum is also a rational number. So, the result of adding two numbers in the set is always another number in the set, which means that the set is closed under addition.

For multiplication, let's take two numbers in the set, say (a1 + b1√2) and (a2 + b2√2). When we multiply them, we get (a1a2 + 2b1b2) + (a1b2 + a2b1)√2. Again, since all the numbers involved are rational, the result is also a rational number. This means that the set is closed under multiplication as well.

Next, we need to show that the set satisfies the commutative, associative, and distributive laws for both addition and multiplication. This means that the order in which we add or multiply numbers in the set does not matter, and that addition and multiplication can be combined in a predictable way.

The commutative, associative, and distributive laws for addition and multiplication are well-known for rational numbers, and it can be easily verified that they hold for this set as well.

Finally, we need to show that the set has additive and multiplicative inverses. This means that for each number in the set, there exists another number in the set such that when added (or multiplied) to the original number, the result is 0 (or 1).

It can be shown that for any number of the form a + b√2, its additive inverse is -a - b√2, and its multiplicative inverse is (a / (a^2 + 2b^2)) - (b / (a^2 + 2b^2))√2, assuming that a^2 + 2b^2 is not equal to 0. Both of these are also rational numbers, since they are obtained by dividing rational numbers.

So, we have shown that the set of numbers of the form a + b√2, where a and b are rational numbers, is closed under addition and multiplication, satisfies the commutative, associative, and distributive laws, and has additive and multiplicative inverses. This means that the set of numbers forms a field with respect to addition and multiplication.

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The result of the division of dividend 3 1/6 by divisor 1 3/8 is computed as 76/33.

For the stated question;

The dividend is  3 1/6, which is given in mixed fraction.

In proper fraction; 3 1/6 = 19/6.

The divisor is  1 3/8 = 11/8.

Thus,

= 19/6 / 11/8

= 19*8 / 6*11

= 76/33

Thus, the result of the division of dividend 3 1/6 by divisor 1 3/8 is computed as 76/33.

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Answer:

Should have paid attention in class

Step-by-step explanation:

But the answer is

Ué é só colocar 6x vezes 2

15:4.

Step-by-step explanation:

1 hour = 60 min

3 hours = 60 x 3 = 180 min

Ratio:

180/48

Simplest form 15/4

Therefore, the simplest form of the ratio will be 15:4

Answer:

48 mins : 3 hours

48 mins : 180 mins

DIVIDING 48 & 180 BY 3 AS BOTH ARE FACTORS OF THREE.

48/3 : 180/3

16 : 60

DIVIDING 16 & 60 BY 2 AS BOTH ARE FACTORS OF TWO.

16/2 : 60/2

8 : 30

DIVIDING 8 & 30 BY 2 AS BOTH ARE FACTORS OF 2

8/2 : 30/2

4 : 15

NOW WE HAVE 4 : 15 WHICH WILL BE THE SIMPLEST FORM.

The equation in slope-intercept form for the line that passes through (-0,7), parallel to y = 4x-19 is y = 4x + 7.

The slope intercept form of a line is:-

y = mx + b

Where:-

m represents the slope of a line

b represents the y-intercept of a line

x and y represent the ordered pairs (x,y) throughout a line

We are given the line y = 4x-19 is parallel to the line whose equation we have to find.

Hence,

slope of the line = 4 = slope of the given line

Also, (0,7) passes through the line,

Hence,

7 = 4*(0) + b

7 = 0 + b

b = 7

Hence, the equation of the line in slope intercept form is y = 4x + 7.

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Using tangents theorem, we can find the value of the missing length,

n = 18.7units.

"To touch" is how the word "tangent" is defined. The same idea is conveyed by the Latin word "tangere". A tangent, in general, is a line that, while never entering the circle, precisely touches it at one point on its circumference. A circle has a number of tangents. They make a straight angle with the radius.

Here in the diagram,

We can see that as per the central angle and tangent theorem,

AB/BC = ED/DC

⇒ 17/10 = n/11

Cross multiplying:

⇒ 17 × 11 = n × 10

⇒ 10n = 187

⇒ n = 187/10

⇒ n = 18.7

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Answer:

both of the solution is B and C

Answer:

Here you go!

Step-by-step explanation:

Answer:

If circles A and B are congruent, then AC, CD, DB, and BA are all congruent since they are all radii. We then have:

ACDB is a rhombus.

ADB is an equilateral triangle.

CD is perpendicular to AB.

CD bisects AB.

Answer:

x < -7

Step-by-step explanation:

The circle is open meaning -7 is not included in the answer

She needs 50 successful serves in the first 100 to attain her target. A 2% chance exists that this will occur.

She therefore has a 98% chance of requiring more than 100 serves to achieve her objective.

The study of probability, which is the potential of any event happening, is a field of mathematics that deals with the occurrence of random events. The probability value is given on a scale from 0 to 1.

The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood that something will occur by the likelihood that it won't.

Jo must not complete 50 successful serves in her first 100 attempts in order to need more than 100 serves.

With n=100 and p=0.4, our probability sample of potential outcomes has a binomial distribution.

We will use a normal distribution to approximate n because it is a big enough number. The normal distribution's characteristics are as follows:

To ensure that she receives more than 100 serves, we must determine the likelihood that there will be fewer than 50 successful services. Such is:

We determine X's z value as follows:

Next, we have

That indicates that there is a 98% chance she will require more than 100 serves to accomplish her objective.

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Answer:

Number of students who uses pencils = 64 students

Step-by-step explanation:

Pens : pencils = 3 : 2

Pen = 3

Pencil = 2

Total = 3 + 2 = 5

If there is a total of 160 middles school students how many of them used pencils?

Number of students who uses pencils = ratio of pencil / Total × number of students

= 2 / 5 × 160

= (2 * 160) / 5

= 320/5

= 64

Number of students who uses pencils = 64 students

Number of students who uses pen = ratio of pen / Total × number of students

= 3/5 × 160

= (3*160)/5

= 480/5

= 96 students

Answer:

l = 194999.45

Step-by-step explanation:

I'm going to assume that you meant 3.14 by 3,14.

336,765 = 3.14 × 0.55 × (l + 0.55)

336,765 ÷ (3.14 × 0.55) = l + 0.55

(336,765 ÷ (3.14 × 0.55)) - 0.55 = l

l = 194999.45

The largest subset of the complex plane on which the function f(z) = tan(z) \(e^z\) is harmonic is the set of all complex numbers excluding the points where the tangent function has singularities.

For a complex function to be holomorphic, it must be differentiable at every point in its domain. The function f(z) = tan(z) \(e^z\) is holomorphic except at the points where the tangent function has singularities, which occur when z is equal to π/2 + kπ, where k is an integer. Therefore, the largest subset of the complex plane on which f(z) is holomorphic is the set of all complex numbers excluding these singular points.

On the other hand, for a complex function to be harmonic, it must satisfy the Laplace's equation, which states that the sum of the second-order partial derivatives of the function with respect to the real and imaginary parts of z is equal to zero. The function f(z) = tan(z) \(e^z\) does not satisfy the Laplace's equation, as the tangent function introduces singularities that violate the equation. Therefore, there is no subset of the complex plane on which f(z) is harmonic.

In conclusion, the largest subset of the complex plane on which f(z) = tan(z) \(e^z\) is holomorphic is the set of all complex numbers excluding the singular points of the tangent function. However, there is no subset on which f(z) is harmonic due to the violation of the Laplace's equation.

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The value of y when the plane intersect the y-axis of the cartesian plane is: y = 5

We are given that the cartesian equation of the plane is give by the expression:

3x + 1y + 2z = 5

Now, if the plane intersects the y-axis, it simply means that the values of x and y are zero at that point of intersection.

Thus, we will input x = 0 and z = 0 into the equation to get:

3(0) + y + 2(0) = 5

y = 5

Thus, that is the value of y when the plane intersect the y-axis of the cartesian plane.

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Answer:

Es cierto se usan 16 paquetes de salchichas y 12 paquetes de panes para pancho.

Step-by-step explanation:

Lo que debemos hacer en este caso es dividir la cantidad total de panchos primero por la cantidad de unidades de salchichas que vienen en su paquete y segundo por la cantidad de unidades de panes para panchos que vienen en su paquete, si el resultado nos da un numero entero podemos decir que usa una cantidad completa de paquetes de salchichas y de panes:

96/6 = 16

96/8 = 12

Es decir que para 96 panchos se usan 16 paquetes de salchichas y 12 paquetes de panes para pancho, por lo tanto es cierto.

Using multiple line and angle theorems, the values of each of the 14 angles are given.

Using the geometry theorems :

1.)

∠2 is a right angle = 90°

2.)

∠1 + ∠2 + ∠3 = 180° (sum of angle on a straight line)

90 + ∠1 + 54° = 180°

∠1 = (180 - 144) = 36°

(∠2 and ∠5) ; (∠3 and ∠6) ; (∠1 and ∠4) are vertically opposite ;

Hence,

∠4 = 36°

∠5 = 90°

∠6 = 54°

∠3 = ∠8 = 54° (corresponding angles)

∠9 + ∠8 = 180° (sum of angle on a straight line)

∠9 = (180 - 54) =126°

∠7 = ∠9 = 126° (vertically opposite angles)

∠8 = ∠10 = 54° (vertically opposite angles)

∠4 = ∠13 = 36° (corresponding angles )

∠12 + ∠13 = 180° (sum of angle on a straight line)

∠12 = (180 - 36) =126°

∠11 = ∠13 = 36° (vertically opposite angles)

∠12 = ∠14 = 126° (vertically opposite angles)

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The surface area and volume of the real brick will be 983.2 cm²and 1738.11 cm³ respectively.

The term “volume” refers to the amount of three-dimensional space taken up by an item or a closed surface. It is denoted by V and its SI unit is in cubic cm.

The scale factor is ;

r = 630 cm /23

r = 27

L = 23 cm

b = 310 / 27 = 11.48 cm

h = 180/27 = 6.6 cm

The surface area of the brick;

A = 2(lb+bh+hl)

A = 2( 23 ×11.48+11.48×6.6+6.6×23)

A= 983.2 cm²

The volume of the brick is;

V= lbh

V=23 × 11.45 ×6.6

V=1738.11 cm³

Hence the surface area and volume of the real brick will be 983.2 cm² and 1738.11 cm³ respectively.

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The general solution to the differential equation dy/dx = 1/3(sin x − xy^2), y(0)=5 is: y = ±√[(sin x - e^(x/2)/25)/x], if sin x - xy^2 > 0 and y(0) = 5

To solve this differential equation, we can use separation of variables.

First, we can rearrange the equation to get dy/dx on one side and the rest on the other side:

dy/dx = 1/3(sin x − xy^2)

dy/(sin x - xy^2) = dx/3

Now we can integrate both sides:

∫dy/(sin x - xy^2) = ∫dx/3

To integrate the left side, we can use substitution. Let u = xy^2, then du/dx = y^2 + 2xy(dy/dx). Substituting these expressions into the left side gives:

∫dy/(sin x - xy^2) = ∫du/(sin x - u)

= -1/2∫d(cos x - u/sin x)

= -1/2 ln|sin x - xy^2| + C1

For the right side, we simply integrate with respect to x:

∫dx/3 = x/3 + C2

Putting these together, we get:

-1/2 ln|sin x - xy^2| = x/3 + C

To solve for y, we can exponentiate both sides:

|sin x - xy^2|^-1/2 = e^(2C/3 - x/3)

|sin x - xy^2| = 1/e^(2C/3 - x/3)

Since the absolute value of sin x - xy^2 can be either positive or negative, we need to consider both cases.

Case 1: sin x - xy^2 > 0

In this case, we have:

sin x - xy^2 = 1/e^(2C/3 - x/3)

Solving for y, we get:

y = ±√[(sin x - 1/e^(2C/3 - x/3))/x]

Note that the initial condition y(0) = 5 only applies to the positive square root. We can use this condition to solve for C:

y(0) = √(sin 0 - 1/e^(2C/3)) = √(0 - 1/e^(2C/3)) = 5

Squaring both sides and solving for C, we get:

C = 3/2 ln(1/25)

Putting this value of C back into the expression for y, we get:

y = √[(sin x - e^(x/2)/25)/x]

Case 2: sin x - xy^2 < 0

In this case, we have:

- sin x + xy^2 = 1/e^(2C/3 - x/3)

Solving for y, we get:

y = ±√[(e^(2C/3 - x/3) - sin x)/x]

Again, using the initial condition y(0) = 5 and solving for C, we get:

C = 3/2 ln(1/25) + 2/3 ln(5)

Putting this value of C back into the expression for y, we get:

y = -√[(e^(2/3 ln 5 - x/3) - sin x)/x]

So the general solution to the differential equation dy/dx = 1/3(sin x − xy^2), y(0)=5 is:

y = ±√[(sin x - e^(x/2)/25)/x], if sin x - xy^2 > 0 and y(0) = 5

y = -√[(e^(2/3 ln 5 - x/3) - sin x)/x], if sin x - xy^2 < 0 and y(0) = 5

Note that there is no solution for y when sin x - xy^2 = 0.

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Answer:

The total amount of candles is 768.

Step-by-step explanation:

Why? If there are 32 boxes of candles and 24 candles are in each box you would have to multiply 32x24 which is = to 768 candles in each box.

Answer: It will take 2.5 hours for her to walk 7.2 miles

Step-by-step explanation:

Divide the total mile by the number of miles per hour

7.2/2.88=2.5

since it takes an hour walk of 2.88 miles per hour, multiply 2.5 by 1

2.5*1=2.5

It will take 2.5 hours for her to walk 7.2 miles

A woman 5-feet tall casts an 8-foot shadow. at the same time of day, the shadow of a tree nearby is 120 feet long. in feet, 75 feet  tall is the tree.

Let the tree height = x

From the question, we have

5/8 = x/120

x = (5*120)/8

x = 75 feet

Tree height = 75 feet

Multiplication:

Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

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Answer:

x=5

Step-by-step explanation:

     May I have brainiest I'm trying to level up!

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Answer:

x=5

Step-by-step explanation:

6x-3 = 3x +12

+3            +3

6x = 3x +15

-3x   -3x

3x = 15

divided both sides by 3 to get your answer

The given equation is a combined variation.

We have been given an equation is

\(\frac{xy}{z}\)

This is an equation in which we have three variables and one constant.

This can not be the case of direct or inverse variation because in direct or inverse variation we have only two variables. Whereas, here we have three variables.

So, Direct and inverse options are discarded.

So, either It can be joint or combined

In joint variation both the variables are directly proportional

Hence, given equation is not joint because if we rewrite the equation we will get \(y = \frac{cz}{x}\) both the variables are not directly proportional.

In combined, one variable is directly proportional and the other one is inversely proportional.

From \(y = \frac{cz}{x}\)  we can see that z is directly proportional and x is inversely proportional.

Hence the answer is, the given equation is combined variation.

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What is the question for this so I can answer it?

There are 0.00405 grams of salt in a 0.45 L 3% solution if the salt used is 30% pure.

To determine the amount of salt in a 0.45 L 3% solution if the salt used is 30% pure, we first need to understand what these percentages mean. 3% solution means 3 grams of salt is present in 100 ml (or 0.1 L) of the solution.

Therefore, the total amount of salt in 0.45 L of the solution can be calculated as follows: 0.45 L x (3 g/100 mL) = 0.0135 g of salt.

To determine the amount of salt in the 30% pure salt used, we need to understand that the 30% purity means 30 grams of salt are present in 100 grams of the salt. Therefore, the amount of salt in 1 gram of the salt can be calculated as follows:30 g/100 g = 0.3 g of salt/g of the salt.

So, the amount of salt present in the salt used is 0.3 g/g. To calculate the total amount of salt in 0.45 L of 3% solution if the salt used is 30% pure, we need to multiply the amount of salt in the solution by the amount of salt in the salt used.

Therefore:0.0135 g of salt x (0.3 g/g) = 0.00405 g of saltTherefore, there are 0.00405 grams of salt in a 0.45 L 3% solution if the salt used is 30% pure.

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Answer:

12

Step-by-step explanation:

All exterior angles = 30°

Sum of polygon = 360°

Number of sides= 360/30 = 12 sides

Hope this helps! :)

Answer:

12

Step-by-step explanation:

The sum of exterior angles of every polygon irrespective of the number of its sides is 360°.

As it is a regular polygon, all exterior angles are equal and are 30°. Hence the number of sides of the polygon is 360°/30°= 12

f(x) = x^2 -5

Find f(3)

This means find x when it is 3 so just substitute 3 for x

f(3) = 3^2 -5

= 9 - 5

f(3) = 4

Answer:

f(3)=4

Step-by-step explanation:

f(x)=x^2-5

f(3)=3^2-5

f(3)=3*3-5

f(3)=9-5

f(3)=4

Answer:

27/100?

Step-by-step explanation:

The percent change in height after the second bounce would be:

Percent change = [(h_2 - h_1) / h_1] * 100%

The expression \(25(0.93)^x\)represents the height of the ball after x bounces. To find the percent change in height after each bounce, we need to calculate the ratio of the change in height to the original height and express it as a percentage.

Let's denote the height after the first bounce as h_1, the height after the second bounce as h_2, and so on.

The percent change in height after the first bounce is given by:

Percent change = [(h_1 - original height) / original height] * 100%

Using the given expression, we can substitute x = 1 to find h_1:

h_1 = \(25(0.93)^1\) = 23.25

Therefore, the percent change in height after the first bounce is:

Percent change = [(23.25 - original height) / original height] * 100%

To find the percent change after subsequent bounces, we can continue this process. For example, after the second bounce:

h_2 = \(25(0.93)^2\)

And the percent change in height after the second bounce would be:

Percent change = [(h_2 - h_1) / h_1] * 100%

You can repeat this process for each subsequent bounce to find the percent change in height after each bounce using the given expression.

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