Need help!

Classify the following numbers as rational
2/3
3.1415926535...
0
Squared 1
7.4(bar over 4)
15
Squared 3

Which numbers are rational? Select all that apply!

Also can you identify which are irrational too?
That would be a great help.
Select all that apply!

<3 ASAP if u can!

To find missing value with distance.we write given points and distance value then we write distance formula for two points.

What is distance formula?

The distance between two points is the length of the line joining the two points. If the two points lie on the same horizontal or same vertical line, the distance can be found by subtracting the coordinates that are not the same.

In analytic geometry, distance formula used to find the distance measure between two lines, the sum of the lengths of all the sides of a polygon, perimeter of polygons on a coordinate plane, the areen a of polygons and many more.

Let's suppose 2 points (0,2) and (x,6) distance between these points \(\sqrt{52}\)

How to find x?

we will use distance formula

d = \(\sqrt{(x2-x1)^2+(y2-y1)^2}\).

d= \(\sqrt{(x-0)^2+(6-2)^2}\)

d = \(\sqrt{x^2+16}\)

\(\sqrt{52}\) = \(\sqrt{x^2+16}\)

x^2 = 52-16

x^2 = 36

x = 6,-6

By this way we can find missing value with distance.

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Answer:

42:60

Step-by-step explanation:

Answer:

7:10

Step-by-step explanation:

Simplify the ratio until you can't divide it anymore

Answer:

3x+3

Step-by-step explanation:

rise over run and y-intercept

Answer:

Step-by-step explanation:

The measure of angle ∠WOV is 60 degrees and The measure of angle ∠YOZ is also 60 degrees.

What is an angle?

Angle is the space between the line or the surface that meets.  And the angle is measured in degree. For complete 1 rotation, the angle is 360 degrees.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

∠WOX = 30

It can be seen that the ∠XOY and ∠VOX are equal and 90 degrees.

The measure of angle ∠WOV will be

∠WOV + ∠WOX = 90

     ∠WOV + 30 = 90

             ∠WOV = 60

The measure of angle ∠YOZ will be

∠WOX + ∠XOY + ∠YOZ = 180   (Supplementary angle)

          30 + 90 + ∠YOZ = 180

                           ∠YOZ = 60

The total profit when a well 50 feet deep is drilled is approximately $1164.10, rounded to two decimal places.

The total profit for drilling a well that is 50 feet deep need to integrate the marginal profit function P'(x) with respect to x from 0 to 50.

This gives us the total profit function P(x):

P(x) = ∫ P'(x) dx from 0 to 50

Substituting P'(x) = \(4 \times x^{(1/3)\) into the integral we get:

P(x) = \(\int 4 \times x^{(1/3)\) dx from 0 to 50

Integrating with respect to x get:

P(x) = 4/4 * 3/4 * x^(4/3) + C

C is the constant of integration.

The value of C we need to use the given information that the marginal profit is zero when the well is 0 feet deep.

This means that the total profit is also zero when the well is 0 feet deep.

P(0) = 0

= \(4/4 \times 3/4 \times 0^{(4/3)} + C\)

C = 0

So the total profit function is:

P(x) = \(3x^{(4/3)\)

The profit when a well 50 feet deep is drilled is:

P(50) = \(3 \times 50^{(4/3)\) dollars

Using a calculator to evaluate this expression, we get:

P(50) = \(3 \times 50^{(4/3)\)

≈ $1164.10

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To find the function y(x) satisfying the given conditions, we need to integrate the differential equation d³y/dx³ = 18 three times and apply the initial conditions y''(0) = 12, y'(0) = 5, and y(0) = 8.

Given the differential equation d³y/dx³ = 18, we integrate it three times to obtain y(x). Integrating once gives us y'(x) = 18x + C₁, where C₁ is the constant of integration. Integrating again yields y''(x) = 9x² + C₁x + C₂, where C₂ is another constant of integration. Finally, integrating a third time leads to y(x) = 3x³/3 + C₁x²/2 + C₂x + C₃, where C₃ is the constant of integration.

Now, we can apply the initial conditions to determine the values of the integration constants. From y''(0) = 12, we have 0 + C₂ = 12, which gives us C₂ = 12. Applying y'(0) = 5, we get 0 + 0 + C₁ = 5, resulting in C₁ = 5. Finally, using y(0) = 8, we have 0 + 0 + 0 + C₃ = 8, giving us C₃ = 8.

Substituting the values of the integration constants back into the equation, we obtain the function y(x) = x³ + 5x²/2 + 12x + 8. This function satisfies the given differential equation and the initial conditions y''(0) = 12, y'(0) = 5, and y(0) = 8.

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The algorithm design technique best describes Dijkstra's SSSP algorithm is (c) Greedy.

Dijkstra's Single Source Shortest Path (SSSP) algorithm is considered a greedy algorithm because it makes locally optimal choices at each step in order to find the globally optimal solution. The algorithm starts from the source vertex and maintains a priority queue of vertices, where the priority of a vertex is determined by the length of the shortest path from the source to that vertex.

At each step, the algorithm chooses the vertex with the smallest priority, updates the distances of its neighbors, and adds them to the priority queue. This process continues until all vertices have been processed or a target vertex has been found. The algorithm always makes the choice that appears to be the best at the moment, with the goal of finding the shortest path from the source to all vertices.

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Answer:

x=-13/47

Step-by-step explanation:

Answer:

\(2\sqrt{13}\)

Step-by-step explanation:

Lets call the axes x and y.

Distance in x axis is (9 - 5) = 4

Distance in y axis (3 - (-3)) = 6

The total distance is \(\sqrt{4^2 + 6^2} = \sqrt{16 + 36} = \sqrt{52} = \sqrt{4 \cdot 13} = 2\sqrt{13}\)

Answer:

2 sqrt(13)

Step-by-step explanation:

We can use the distance formula

d =sqrt( ( x2-x1)^2 + (y2-y1)^2)

   =sqrt( (-3-3)^2 + ( 5-9)^2)

  = sqrt( (-6)^2 + (-4) ^2)

  = sqrt( 36+ 16)

  = sqrt( 52)

  = sqrt (4 * 13)

  = 2 sqrt(13)

Answer:

Therefore, the measure of ∠x is 33 degrees.

Step-by-step explanation:

As angle ∠S is a right angle and angles ∠R and ∠x are complementary, we have:

∠R + ∠x = 90 degrees

Substituting the given values, we get:

57 + ∠x = 90

∠x = 90 - 57

∠x = 33 degrees

Answer: x = 32°

Step-by-step explanation: triangle of ABC = 58°, 90° & x°

                                              x = 180°-148° = 32°

(x° is equal to the unknown° where C is, as well as 58° where A is)

Using reference angles, it is found that the correct option is:

Angle \(\frac{5\pi}{6}\) is on the second quadrant, \(\frac{\pi}{2} < \frac{5\pi}{6} < \pi\).

\(\pi - \frac{5\pi}{6} = \frac{6\pi}{6} - \frac{5\pi}{6} = \frac{\pi}{6}\)

Angle \(\frac{5\pi}{3}\) is on the fourth quadrant, \(\frac{3\pi}{2} < \frac{5\pi}{3} < 2\pi\).

\(2\pi - \frac{5\pi}{3} = \frac{6\pi}{3} - \frac{5\pi}{3} = \frac{\pi}{3}\)

They have different reference angles, hence:

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Answer:

A

Step-by-step explanation:

A

Answer:

8mph

Step-by-step explanation:

I can't see the reasons but Lewis should multiply his answer by two since he went that far in only half an hour.

The sin(x) = -3/5, cos(x) = -4/5, and tan(x) = 3/4.

Given that cos(x) = -4/5 and 180° < x < 270°, we can determine the values of sin(x) and tan(x) using trigonometric identities.

Using the identity \(sin^2(x) + cos^2(x) = 1\), we can find sin(x) as follows:

\(sin^2(x) = 1 - cos^2(x)\\sin^2(x) = 1 - (-4/5)^2\\sin^2(x) = 1 - 16/25\\sin^2(x) = 9/25\)

sin(x) = ±√(9/25) = ±3/5

Since 180° < x < 270°, the sine value should be negative:

sin(x) = -3/5

Next, we can find tan(x) using the identity tan(x) = sin(x)/cos(x):

tan(x) = (-3/5) / (-4/5)

tan(x) = 3/4

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The correct answer for the given question is option A.\(4e^_(t/2 ln3)\).

Given table of values is:y 3 12 48 192 t 0 2 4 6As we can see the table of values given, if t increases by 2 times, y becomes 4 times of the original value.

Hence, it is an exponential function.Let y = f(t) be a solution to the differential equation dy/dt = ky, where k is a constant.The above equation is a separable differential equation and can be solved by separating variables:

dy/dt = ky

⟹ dy/y = k dt

⟹ ∫(1/y) dy = ∫k dt

⟹ ln |y| = kt + C

⟹ |y| =\(e^_(kt+C)\)

⟹ |y| = \(e^_(kt) _. e^C\)

⟹ y =\(A . e^_(kt),\)

where A = \(\pm e^C\) is a constant.

Now, let us substitute the given values of t and y into this equation to obtain an expression for A:

When t = 0, y = 3

⟹ A = 3.

When t = 2,

y = 12

⟹ 12 =\(3e^_(2k)\)

⟹\(e^_(2k)\) = 4

⟹ 2k = ln4

⟹ k = (1/2) ln

4.When t = 4,

y = 48

⟹ 48 = \(3e^_(4k)\)

⟹ e^(4k) = 16

⟹ 4k = ln16

⟹ k = (1/4) ln16.

Substituting the value of k = (1/2) ln4 in the above equation, we get:

A = 3/√3 = √3.

Similarly, substituting the value of k = (1/4) ln16 in the above equation, we get:A = 3/2.As A has two different values, it is necessary to find an expression that includes both of them.The required expression is

\(f(t) = 3/√3 . e^_(t/2 ln3)\)\(+ 3/2 . e^_(t/4 ln16) ...\)[As A

= 3/√3,

when k = (1/2) ln4,

and A = 3/2,

when k = (1/4) ln16]

This can be simplified further:

f(t) = \(3^_(1/2)\)\(+ (3/2) e^_(t/2 ln2)\)\(f(t)\)

= \(3^_(1/2)\)\(e^_(t/2 ln3)\) \(+ (3/2) e^_(t/2 ln2)\)\(f(t)\)

=\(3^(1/2)\)\(e^_(t/2 ln3)\) +\(3 e^_(t/2 ln2)\)\(f(t)\)

= \(3^(1/2)\) \((e^_(t/2 ln3)\) \(+ e^_(t/2 ln2 ln2))f\)\((t)\)

=\(3^_(1/2)\) \(e^_(t/2 ln(3*2^2))\)\(f(t)\)

= \(3^_(1/2)\) \(e^_(t/2 ln12)\)\(f(t)\)

= \(3^_(1/2)\)\(4^_(t/2)\)

[as ln12

= \(\lnt(3*2^2)\)

=\(ln3 + ln(2^2)\)

= \(ln3 + 2 ln2]f(t)\)

= \(3^_(1/2) .\)\(2^_(t/2) . 2\)

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Answer:

\( \frac{51}{17} \)is a rational number.

Step-by-step explanation:

As, \( \frac{51}{17} \)

can be written in the form p/q where p is a integer and q is not equally to 0.

Answer:

yes it is a rational because ia in the form of p\q

Answer:

\(4x + 5 \: if \: x = 9 \\ 4(9) + 5 \\ = 41 \\ \\ 3x = 3(9) \\ = 27\)

\(41 + 27 \\ = 68\)

Answer:

x = -11 5/17

Step-by-step explanation:

3x + 2y = 12

2x - 3y = -57

5x + y =  -45

y = -5x - 45

2x - 3 (-5x - 45) = -57

2x + 15x + 135 = -57

17x + 135 = -57

17x = -192

x = -11 5/17

Considering the absolute value function, the correct statement is given by:

|-53| = |53|.

The absolute function is defined by:

It measures the distance of a point x to the origin. For this problem, we have that:

Thus, the correct statement is given by:

|-53| = |53|.

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Probability that the arrow will stop on the same letter twice = 1/3 (c).

What is probability?

The area of arithmetic called likelihood deals with numerical representations of the chance that a happening can occur or that an announcement is true.

Main body:

Given : Maria will spin the arrow on the spinner 2 times.

To find : What is the probability that the arrow will stop on the same letter twice.

Solution : We have given a spinner that spin twice and stop on the same letter.

Formula for probability = no. of favourable outcome/ total outcomes

Here, total part of spinner = 3 and it spin two times

So, total possible outcome = 6.  Arrow stay on same letter twice( favorable outcome) =2.

Plugging the values in formula :

Probability =  2/6

Probability =  1/3

Therefore,  probability that the arrow will stop on the same letter twice =  (c).

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Answer:10

Step-by-step explanation:

Answer: The answer is 10.

Step-by-step explanation:

These steps will help you!

STEP 1: You need to multiply them and use the process of elimination.

8 is obiviously too little.

9 is still too little.

10 when you multiply it with $1.78, it's simple enough that it equals just right!

11 is too over.

STEP 2: Try multiplying 1.78 x 10.

         1.78

      x    10          

               0

+  1  7  8  0         _______always add the 0.

 $ 1 7 . 8  0

Mark also has $1.20 left to spare.

STEP 3: Declare the answer!

Mark can buy 10 stamp packets and have $1.20 left for himself.

Hope this helps!

If a and b are rational numbers, b = 0, and r is an irrational number, then a + br is irrational can be proved by contradiction.

A proof by contradiction is an argument in which the desired conclusion is proved to be true by showing that its opposite assumption (i.e., the statement's negation) is false. It is an indirect method of proof, which is employed by mathematicians when a direct proof seems impossible.

This is done by supposing that the proposition is false and then showing that this supposition leads to a contradiction. As a result, it is concluded that the proposition must be true.

The following statement is true by contradiction: If a and b are rational numbers, b = 0, and r is an irrational number, then a + br is irrational. To prove the given statement by contradiction, suppose that there exist rational numbers a and b such that b = 0, r is an irrational number, and a + br is rational. This is the appropriate statement to start the proof.

We can assume that a and b are both rational numbers with b = 0 and r is an irrational number such that a + br is a rational number.Suppose that a and b are both rational numbers with b = 0 and r is an irrational number such that a + br is a rational number. Since b = 0, then we have: b x r = 0, and a + br = a + 0 = a which is a rational number.

Since a + br is rational, it follows that a + br = p/q where p and q are integers and q ≠ 0. This implies that: r = (p/q - a) / b Since a, b, and r are rational and irrational numbers, respectively, the numerator of the right-hand side of the equation above must be irrational. However, the denominator of the right-hand side is zero which is a rational number.

Therefore, the quotient is an undefined number which cannot be a rational number. This contradicts our assumption that a + br is rational.The conclusion is that the assumption is false and hence the given statement is true. Thus, the statement is proved by contradiction.

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Answer:

He can expect to pay $7.92 for 4 pounds of strawberry

Unitary Method: A problem can be solved using the unitary method by first determining the value of a single unit, and then multiplying that value to determine the required value.

Given that

Cost price for 2 pound strawberry=$3.96

So, cost price for 1 pound strawberry=$\(\frac{3.96}{2}\)=$1.98

Therefore,

Cost price for 4 pound strawberry=$\(1.98*4\)=$7.92

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At a local fruit land, Luia pend $3. 96 for 2 pound of strawberries. He can expect to pay $7.92 for 4 pounds of strawberry.

Unitary Method: A problem can be solved using the unitary method by first determining the value of a single unit, and then multiplying that value to determine the required value.

Given that

Cost price for 2 pound strawberry=$3.96

So, cost price for 1 pound strawberry=$=$1.98

Therefore,

Cost price for 4 pound strawberry=$=$7.92

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The particular solution to the differential equation by undetermined coefficients is Y_p = 6 * e^(x/2).

Explanation:

To solve the given differential equation by undetermined coefficients, we first need to find the complementary solution by solving the characteristic equation:

r^2 - (1/4)r = 0
r(r - 1/4) = 0
r1 = 0, r2 = 1/4

Thus, the complementary solution is:

y_c(x) = c1 + c2*e^(x/4)

Next, we need to find the particular solution by assuming a form for y_p(x) that is similar to the nonhomogeneous term. In this case, we assume:

y_p(x) = A*e^(x/2)

where A is the undetermined coefficient to be found.

Substituting y_p(x) into the differential equation, we get:

y''(x) - y'(x)/4 - y(x)/4 = 6e^(x/2)

y_p''(x) = (1/4)*A*e^(x/2)
y_p'(x) = (1/2)*A*e^(x/2)
y_p(x) = A*e^(x/2)

Substituting these expressions into the differential equation, we get:

(1/4)*A*e^(x/2) - (1/2)*A*e^(x/2)/4 - (1/4)*A*e^(x/2) = 6e^(x/2)

Simplifying, we get:

(3/16)*A*e^(x/2) = 6e^(x/2)

Thus, A = 64/3.

Therefore, the particular solution is:

y_p(x) = (64/3)*e^(x/2)

The general solution is the sum of the complementary and particular solutions:

y(x) = y_c(x) + y_p(x)
y(x) = c1 + c2*e^(x/4) + (64/3)*e^(x/2)

where c1 and c2 are constants determined by the initial or boundary conditions.
To solve the given differential equation using the method of undetermined coefficients, first rewrite the equation:

y'' - y' + (1/4)y = 6e^(x/2)

Now, make a guess for the particular solution (Y_p) of the form:

Y_p = A * e^(x/2)

where A is an undetermined coefficient.

Take the first and second derivatives of Y_p:

Y_p' = (1/2)A * e^(x/2)

Y_p'' = (1/4)A * e^(x/2)

Plug these derivatives into the original differential equation:

(1/4)A * e^(x/2) - (1/2)A * e^(x/2) + (1/4)A * e^(x/2) = 6e^(x/2)

Simplify the equation:

A * e^(x/2) = 6e^(x/2)

Divide both sides by e^(x/2):

A = 6

Now we have found the undetermined coefficient. The particular solution is:

Y_p = 6 * e^(x/2)

This is the solution to the given differential equation using the method of undetermined coefficients.

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The vendor sold 172 sodas and 58 hotdogs at the hockey game.

An equation of degree one is known as a linear equation.

A linear equation of two variables can be represented by ax + by = c.

let, the number of soda cans be 'x' and the number of hot dogs be 'y'.

So, From the given information x = 3y and the vendor sold a total of 232.

Therefore, x + y = 232.

3y + y = 232.

4y = 232.

y = 232/4.

y = 58.

So, He sold 58 hot dogs and 3×58 = 172 soda cans.

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The inequality that correctly represents this scenario is given as follows:

\(2x + 5y \leq 25\)

The graph is given at the end of the question.

A system of inequalities is when two or more variables are related, and inequalities are built to find the values of each variable.

In this problem, the variables are given as follows:

Chocolate chips are $2 per pound and pecans are $5 per pound. She wants to spend at most $25, hence:

\(2x + 5y \leq 25\)

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Answer:

A would make sense

Step-by-step explanation:

Answer:

Maya collected data about the number of ice cubes and milliliters of juice in several glasses of juice and organized the data into this table.

Ice Cubes 4 2 3 5 5 3 1

Juice (milliliters) 177 234 202 140 155 210 265

She used a graphing tool to display the data in a scatter plot, with x representing the number of ice cubes and y representing the milliliters of juice. Then she used the graphing tool to find the equation of the line of best fit:

y = -29.202x + 293.5.

Based on the line of best fit, approximately how many milliliters of juice will be in a glass with 7 ice

Step-by-step explanation:

Based on the line of best fit, approximately how many milliliters of juice will be in a glass with 7 ice.

Maya collected data about the number of ice cubes and milliliters of juice in several glasses of juice and organized the data into this table.

Ice Cubes             4        2      3        5       5      3        1

Juice (milliliters)  177    234   202   140   155   210   265

She used a graphing tool to display the data in a scatter plot, with x representing the number of ice cubes and y representing the milliliters of juice. Then she used the graphing tool to find the equation of the line of best fit:

y = -29.202x + 293.5.

A line of best fit refers to a line through a scatter plot of data points that best expresses the relationship between those points. Statisticians typically use the least-squares method to arrive at the geometric equation for the line, either through manual calculations or regression analysis software.

Based on the line of best fit, approximately how many milliliters of juice will be in a glass with 7 ice.

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Answer:

$305.9022863 or $305.90 (rounded to 2 decimal places)

Step-by-step explanation:

It is a compound interest, meaning an interest accumulates on an initial amount every period. The formula  

A= P(1+R)^n

A= the total amount P=Initial amount       R= rate  n=time period

P=$100 R=15% or 0.15(decimal)  n=8 (years)  

A= 100 (1.15)^8

A= 100(3.059022863)

A=305.9022863

The amount you will have after 8 years is $220

The formula for calculating simple interest is expressed as:

SI =PRT

P is the principal = $100

T is the time = 8 years

R is the rate. = 15%

SI = 100 * 8 * 0.15
SI = $120

Amount after 8years = $100 + $120
Amount after 8years = $220

Hence the amount you will have after 8 years is $220

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Answer; present value of $12,200 to be received 4 years from today, with a discount rate of 5 percent, is $10,027.51.

The present value of $12,200 to be received 4 years from today can be calculated using the formula for present value. The formula is:

Present Value = Future Value / (1 + Discount Rate)^n

Where:
- Future Value is the amount to be received in the future ($12,200 in this case)
- Discount Rate is the interest rate used to discount future cash flows (5 percent in this case)
- n is the number of periods (4 years in this case)

Plugging in the given values into the formula:

Present Value = $12,200 / (1 + 0.05)^4

Calculating the exponent first:

(1 + 0.05)^4 = 1.05^4 = 1.21550625

Dividing the future value by the calculated exponent:

Present Value = $12,200 / 1.21550625

Calculating the present value:

Present Value = $10,027.51

Therefore, the present value of $12,200 to be received 4 years from today, with a discount rate of 5 percent, is $10,027.51.

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