What is the meaning of "Lagrange’s theorem"?

The relationships represent proportional relationships and the constant of proportionalities are 5/7 and 12

Does it represent a proportional relationship?

Yes, the graph represents a proportional relationship

This is so because the graph is a linear equation and it passes through the origin

How to find the constant of proportionality (K=Y/X)

On the graph, we have the following point

(X, Y) = (28, 20)

So, we have

K = 20/28

Evaluate

K = 5/7

Here, we have

Y = K * X

This gives

Y = 5/7X

Does it represent a proportional relationship?

Yes, the table represents a proportional relationship

This is so because the table is a linear equation and it has a value (0, 0)

How to find the constant of proportionality (K=Y/X)

On the graph, we have the following point

(X, Y) = (5, 60)

So, we have

K = 60/5

Evaluate

K = 12

Here, we have

Y = K * X

This gives

Y = 12X

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Let's use the variable L to represent the length and W to represent the width.

If the perimeter is 600 ft, we have:

The width is half the length, so we have:

Now, if each fence segment is 5 ft, we number of segments needed is:

Answer:

Step-by-step explanation: [-2.19] = -3

[3.67] = 3

[-0.83] = -1

The domain of this function is a group of real numbers that are divided into intervals such as [-5, 3), [-4, 2), [-3, 1), [-2, 0) and so on. This explains the domain and range relations of a step function.

This can be generalized as given below:

[x] = -2, -2 ≤ x < -1

[x] = -1, -1 ≤ x < 0

[x] = 0, 0 ≤ x < 1

[x] = 1, 1 ≤ x < 2

Answer:

y = - \(\frac{3}{2}\) x

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 2, 3) and (x₂, y₂ ) = (0, 0) ← 2 points on the line

m = \(\frac{0-3}{0-(-2)}\) = \(\frac{-3}{0+2}\) = - \(\frac{3}{2}\) , then

y = - \(\frac{3}{2}\) x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (0, 0 )

0 = - \(\frac{3}{2}\) (0) + c = 0 + c , so

c = 0

y = - \(\frac{3}{2}\) x + 0 , that is

y = - \(\frac{3}{2}\) x

Answer:

x= -10

Step-by-step explanation:

PEMDAS

First you multiply- -2x?

You don't know what x is so you subtract 4 for 16

16-4=12

2-12= -10

Given,

\(h(x) = {6x}^{2} + {4x}^{4} + 7x\)

\(g( x) = {6x}^{2} - 4x + {3x}^{4} \)

Therefore,

\(h(x) + g(x)\)

\(( {6x}^{2} + {4x}^{4} + 7x) + ({6x}^{2} - 4x + {3x}^{4})\)

\( {6x}^{2} + {4x}^{4} + 7x + {6x}^{2} - 4x + {3x}^{4}\)

\((4 {x}^{4} + 3 {x}^{4} ) + ( {6x}^{2} + {6x}^{2} ) + (7x - 4x)\)

\( {7x}^{4} + {12x}^{2} + 3x\)

The number of tiles demanded is 27 tiles. Then the number of packages of tiles that Tamara requires will be 5.

Let W be the rectangle's width and L its length. Then the rectangle's space will be noted as,

Area of the rectangle = L × W square units

The area of the boundary is given as,

A = 9 x (1/3)

A = 3 square feet

The area of each tile is given as,

a = (1/3) x (1/3)

a = 1 / 9

The number of tiles demanded is given as,

⇒ A/a

⇒ 9 / (1/3)

⇒ 9 x 3

⇒ 27

The number of boxes of tiles that Tamara requires is given as,

⇒ 27 / 6

⇒ 4.5 ≈ 5

The number of tiles demanded is 27 tiles. Then the number of packages of tiles that Tamara requires will be 5.

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Trigonometric Equations

Solve:

We'll do the calculations with a precision of 4 decimal places throughout the procedure, but we'll round to 2 decimal places when giving the results.

To solve this equation, we need a scientific calculator or any other calculating device or app (like Excel) and it must be set to radians.

To solve for x, we first need to use the inverse sine function:

Now we subtract 1.5:

Divide by 2:

The expression above is the exact solution, but it's required to give the answer in radians, so we must evaluate it.

When we enter arcsin(-0.3) in our calculator, it returns -0.3047 (in radians).

This value is not between the required limits, so we must add 2π to convert it to a positive angle in the same position, thus:

arcsin(-0.3) = -0.3047 + 2π = 5.9785 rad

But this is not the only angle whose sine is -0.3. There is another angle in Quadrant III with the same value of the sine. We find it by subtracting the original angle from π radians:

arcsin(-0.3) = π - (-0.3047) = 3.4463 radians

We now have the two angles whose sine is -0.3, but we must add 2π to find them in the next rotation because the variable x comes with a coefficient of 2 and we could miss some solutions if we didn't.

Thus, the other two solutions for arcsin(-0.3) are:

arcsin(-0.3) = 5.9785 + 2π = 12.2617 radians

arcsin(-0.3) = 3.4463 + 2π = 9.7295 radians

Now substitute all four results in the general solution:

In ascending order:

x = 0.97 rad

x = 2.24 rad

x = 4.11 rad

x = 5.38 rad

Note: All of the solutions are in the required range.

2 1/4 miles => 1 week

1 mile => 1 ÷ 9/4

( 9/4 is an improper fraction of 2 1/4 )

12 1/2 miles => ( 1 ÷ 9/4 ) × 25/2

= 50/9

= 5 5/9 weeks

( 25/2 is an improper fraction of 12 1/2 )

Therefore, it will take 5 5/9 weeks for the company to replace the stretch of road.

( you can round it off to 6 weeks if the qn specify to give to the nearest whole number )

The monthly cell phone bill when shared data equals zero is given as follows:

$26.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

The intercept of the line in this problem is given as follows:

b = 26.

Hence $26 is the monthly cell phone bill when shared data equals zero.

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Answer:

81

Step-by-step explanation:

Average | x = 81

Count | n = 5

Sum | Sum = 405

Solution:

The average (mean) is equal to the sum of all the data values divided by the count of values in the data set.

Average = Sum / Count

= 405 / 5

= 81

The method you would use to prove the two triangles are congruent include the following: B. ASA.

In Mathematics and Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Additionally, the lengths of corresponding sides are proportional to the  lengths of corresponding altitudes when two (2) triangles are similar.

In Mathematics and Geometry, ASA is an abbreviation for Angle-Side- Angle and it states that when two (2) angles and their included side in two (2) triangles are congruent, then the triangles are said to be congruent.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

you did not provide enough information to answer the question

The density in trees per acre upon completion will be 500 trees per acre.

In this scenario, let's say the landscaping provider donates 2750 seedlings.

Density of trees per acre = Total number of trees / Total area of land

Hence, applying the formula leads us to:

Density of trees per acre = 2750 trees / 5.5 acres

The answer comes out to be roughly around 500 trees/acre. So when completed, approximately 500 trees are estimated to be present in each acre of the landscape.

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The given graph shows that the function is periodic and fluctuates between y = -2 and y = 2. So, the range of the function is [-2,2].

The graph covers one period, which is from x = -3 to x = 3, and then repeats itself indefinitely in both directions. So, the domain of the function is (-∞, ∞).

In general, the domain of a function consists of all the possible input values that the function can take. In this case, since the function repeats itself indefinitely, it can take any input value from negative infinity to positive infinity.

So, the domain is (-∞, ∞). The range of a function, on the other hand, consists of all the possible output values that the function can produce.

In this case, the function oscillates between y = -2 and y = 2, so the range is [-2,2]. The interval notation for the domain is (-∞, ∞) and for the range is [-2,2].

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Answer:

her score in sixth game is 270

Step-by-step explanation:

The computation of the Jasmine score in her sixth game is shown below:

Let us assume her sixth game score is x

And, the first five games are 252, 227, 210, 239, 242

And, the average score is 240

So, the following formula should be used

(252 + 227 + 210 + 239 + 242 + x) ÷ 6 = 240

252 + 227 + 210 + 239 + 242 + x = 240 × 6  

252 + 227 + 210 + 239 + 242 + x = 1,440

x = 270

Hence, her score in sixth game is 270

To divide 3/4 by 1/2 using unit rate proportionality, we can set up a proportion with 3/4 as the numerator and 1/2 as the denominator, and then cross-multiply and solve for the unknown value.

3/4 / 1/2 = X

To solve for X, we can cross-multiply to get:

(3/4) * (2/1) = X * (1/2)

Which simplifies to:

3/2 = X

So 3/4 divided by 1/2 is equal to 3/2.

It's important to note that when dividing fractions, we can also simply invert the divisor and multiply the two fractions, 3/4 * 2/1 = 6/4 =3/2.

Answer: Lemniscate

Step-by-step explanation:

The name of the shape depicted in the graph is Lemniscate option (B) is correct.

It is defined as a two-dimensional shape that has a two-closed curve that meets at the center. The shape exactly looks like a mathematical symbol infinity ∞

The lemniscate is a Greek word that means a ribbon because the shape looks like a ribbon.

The algebraic equation for the lemniscate is given by:

\(\rm \left(x^{2}+y^{2}\right)^{2}=a \left(x^{2}-y^{2}\right)\)

Where a is the constant.

If we put x = 0 and a = 1 we get y = 0

If we put x = 1 and a = 1 we get y = 0

If we put x = -1 and a = 1 we get y = 0

And so on we will get a curved shape shown in the picture.

Thus, the name of the shape depicted in the graph is Lemniscate option (B) is correct.

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Answer:

a particular class of 31 students, 12 are men. What fraction of the students in the class are women.

Answer:

15/31

Step-by-step explanation:

31-16=15

Answer:

17, 27, 37, 47, 57, 67, 87, 97.
8

Step-by-step explanation:

all are 2 digit numbers with exactly one 7 in each.

Answer:

8

Step-by-step explanation:

Answer:

Convert 5 5/32 to an improper fraction.

Step-by-step explanation:

Exact Form:

165/32

Decimal Form:

5.15625

Mixed Number Form:

5 5/32

Answer:

\({ \tt{5 \frac{5}{32} = \frac{(32 \times 5) + 5}{32} }} \\ \\ = { \tt{ \frac{165}{32} }} \\ \\ = { \boxed{ \tt{5.15625}}}\)

Answer:

31/2

Step-by-step explanation:

hope this helps!

Answer:

8.8

Step-by-step explanation:

This is the correct answer because the 8 repeats.

The amount of money in both of Henry's account is $2160

Algebraic expressions are those mathematical expressions that are made up of coefficients, variables, constants, factors and terms.

They are also expressions that are identified with arithmetic operations, such as;

From the information given, we have that;

Henry has $432 in his checking account

Let the checking account be y

Let the account for savings be x

Then, in his savings account, he has;

x = 4(y)

substitute the values

x = 4(432)

x = $1728

Then, the total = $432 + $1728 = $2160

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Answer:

Just hoping this helps.

Answer:

The probability of obtaining a Merit Scholarship = 0.23

Step-by-step explanation:

From the given information:

The probability of obtaining a merit scholarship P(A) = 0.18

The probability of obtaining both P(A ∩ M) = 0.11

The probability of getting at least one P(A ∪ M)  = 0.3

The objective is to determine the probability of obtaining a Merit Scholarship.

So, as given:

if M represents Merit Scholarship and A represent Athletic Scholarship,

the probability of obtaining a Merit Scholarship is as follows;

P(M) = P(A ∪ M) + P(A ∩ M) - P(A)

P(M) = 0.3 + 0.11 - 0.18 = 0.23

P(M) = 0.23

The value of side TS is,

⇒ TS = 28

First, we are going to divide the figure and named new points X and Y as:

Now, we know that TS is the sum of TX and XS.

TS = TX + XS

Additionally, TX has the same length of HJ, so:

TX = HJ = 14

Now, we want to know the length of YK, and we can calculate it using the following equation:

LK = LY + YK

LY = HJ,

so, LY = 14

And, 42 = 14 + YK

42 - 14 = YK

28 = YK

Finally, since T and S are midpoints, the length of XS is the half of the length of YK. It means that XS is:

XS = YK/2

XS = 28/2

XS = 14

Therefore, TS is equal to:

TS = TX + XS

TS = 14 + 14

TS = 28

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If the Federal Reserve sells $60,000 in Treasury bonds to a bank at 8% interest, the immediate effect on the money supply is B. It is decreased by $60,000.

One of the monetary factors that decreases the money supply in the economic is when the Federal Reserve raises the banks' reserve requirements.

Another factor that can decrease the money supply is the sale of treasury bonds to banks.

Raising the interest rates also decreases the money supply.

Thus, by selling $60,000 in Treasury bonds to a bank at 8% interest, it decreases the money supply.

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Answer:

56/64 simplified is 0.875 or 7/8 as a fraction