subtract the sum of 12ab-10b²-18a² and 9ab+12b²+14a² from ab+2b² and 3b²-a²​

The equilibrium real output, Y, is approximately 1,460 (rounded to the nearest integer) in the given IS-LM model, using the provided IS and LM equations.

To find the equilibrium real output, we need to set the IS equation equal to the LM equation and solve for Y.

Given:

IS equation: Y = 1,586.27 - 3,145.45i

LM equation: i = 0.04

Substituting the LM equation into the IS equation:

1,586.27 - 3,145.45(0.04) = Y

Simplifying:

1,586.27 - 125.82 = Y

1,460.45 = Y

Therefore, the equilibrium real output, Y, is approximately 1,460 (rounded to the nearest integer).

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Answer: I am fairly sure the answer is 56

Step-by-step explanation:

If the credentials to this question match with mine, your answer should be 56. I am sorry if this is wrong.

Answer:

Angle 1 = 115 degrees

Angle 2 = 65 degrees

Step-by-step explanation:

Angle 1: Same-side interior angle of Line 1

Angle 2: Same-side interior angle of Line 2

We know that the difference between the angles is 50 degrees. Since the angles are supplementary, we can write the equation:

Angle 1 + Angle 2 = 180

Now, we need to express the difference between the angles in terms of Angle 1 or Angle 2. We can choose either angle, so let's express it in terms of Angle 1:

Angle 1 - Angle 2 = 50

We can rewrite this equation as:

Angle 1 = 50 + Angle 2

Now substitute this expression for Angle 1 into the first equation:

(50 + Angle 2) + Angle 2 = 180

Combine like terms:

2Angle 2 + 50 = 180

Subtract 50 from both sides:

2Angle 2 = 130

Divide by 2:

Angle 2 = 65

Now substitute this value back into the equation for Angle 1:

Angle 1 = 50 + Angle 2

Angle 1 = 50 + 65

Angle 1 = 115

Therefore, the angles are as follows:

Angle 1 = 115 degrees

Angle 2 = 65 degrees

The inequality can be written as y < 1/4x + 3.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.

The inequality can be written by finding the equation of the line. The two points on the line are ( 0,3) and ( 4,4).

The slope of the line is,

Slope = ( 3 - 4 ) / 9 0 - 4 )

Slope = 1 / 4

The y-intercept of the line will be calculated as:-

y = mx + c

3 = 0 +c

c = 3

The equation of the inequality can be written as:-

y < (1/4)x + 3

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The measure of angle A is 21.75°. Therefore, option 3 is the correct answer.

Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.

The formula for sine rule is sinA/a=sinB/b=sinC/c

From the given triangle ABC, BC=19 units, AC=43 units and ∠B=123°.

Using sine rule,

sinA/19 =sin123°/43

sinA/19 = 0.8386/43

sinA/19 = 0.8386/43

sinA/19 = 0.0195

sinA=0.0195×19

sinA=0.3705

A=21.75°

Therefore, option 3 is the correct answer.

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Answer:

Refraction

Step-by-step explanation:

Since the line bends (and this can apply to light too), the line refracts, or changes the angle of direction.

Answer:

absorption

diffraction

refraction

reflection

Step-by-step explanation:

Answer:

200-178=22

22/200*100=2200/200

2200/200=11

11%

Answer:

Let the first term be "a" and common difference be "d". Then, the fifth term is 3a.

Quarter of the fifth term is 9, so (1/4) * 3a = 9. Solving for a, we get:

a = 36.The sum of the first 8 terms of an arithmetic progression can be found using the formula:

S_n = n/2 * (2a + (n - 1)d)

where n is the number of terms.In this case, n = 8, so:

S_8 = 8/2 * (2 * 36 + (8 - 1) * d)

= 4 * (72 + 7d)

= 288 + 28dSince the common difference is "d", the sum of the first eight terms is 288 + 28d.

Correct me if I’m wrong

The sum of the first eight terms of the arithmetic progression is 264.

An arithmetic sequence is a set of numbers where each phrase is created by multiplying the previous term by a constant amount (referred to as the common difference). In other terms, an arithmetic sequence is a set of numbers that changes in value from one term to the next by a fixed amount.

Let the first term of the arithmetic progression be represented by 'a', and let the common difference between terms be represented by 'd'.

Then, according to the problem statement, we know that the fifth term is three times the first term, so:

a + 4d = 3a

Simplifying this equation, we get:

2a = 4d

a = 2d

Now we can use the fact that a quarter of the fifth term is 9 to solve for d:

(1/4)(3a) = 9

3a = 36

a = 12

d = a/2 = 6

So the arithmetic progression is: 12, 18, 24, 30, 36, 42, 48, 54

The sum of the first eight terms can be found using the formula:

S₈ = (n/2)(2a + (n-1)d)

where n = 8 is the number of terms.

Plugging in the values we have found, we get:

S₈ = (8/2)(2(12) + (8-1)(6))

S₈ = 4(24 + 42)

S₈ = 4(66)

S₈ = 264

Therefore, the sum of the first eight terms of the arithmetic progression is 264.

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32.1

The measures of triangle exists 45 45 90 then the length of the hypotenuse is 6√2 units.

Due to the fact that the triangle's legs are always the same length, d = 8. Always on the other side of the right angle is the hypotenuse. The hypotenuse of this triangle, represented by the letter e, is at its base. You must multiply the leg of a 45-45-90 triangle by the square root of two to determine the hypotenuse.

The hypotenuse of a 45°, 45°, and 90° triangle measures about two times the length of a leg.

In the right triangle ABC, AB is equal to AC

AB = AC = 6 units

BC is the hypotenuse

Applying the Pythagorean Theorem

BC² = AB² + AC²

substitute the values in the above equation, we get

BC² = 6² + 6²

Simplifying the above equation, we get

BC² = 72

BC = √72

BC = 6 √2 units

Therefore, the length of the hypotenuse is 6√2 units.

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Answer:

Step-by-step explanation:

L = 3x

w = 2x

Area = 294 ft^2

Formula

Area = L * w

Solution

Area = L * w                   Substitute into formula

294 - 3x  *   2x              Combine the right and switch

6x^2 = 294                    Divide by 6

x^2 = 294/6

x^2 = 49                         Take the square root of both sides

√x^2 = √49

x = 7

w = 2*7 = 2x = 14

L  = 3*7 = 3x  =21

Answer:

2500m³

Step-by-step explanation:

A = length x width x height

50m x 25m x 2 m

=2500m³

Answer:

Hello!

Let's simply divide our two numbers to find how many carriages we need.

22/4=5.5

The thing is, we cannot have 5.5 carriages. We can just have an extra carriage with only 2 people. This gives us 6 carriages.

Therefore, our answer is 6.

I hope this helps!

Six carriages are needed to move a group of 22 people.

In mathematics, divides left-hand operands into right-hand operands in the division operation.

To find the number of carriages needed for a group of 22 people to ride, we need to divide the total number of people by the number of people each carriage can hold.

Each carriage can hold 4 people,

⇒ 22 / 4 = 5.5 carriages.

Since we cannot have half a carriage, we will need to round up to the nearest whole number, which means we will need 6 carriages.

Therefore, the number of carriages needed for a group of 22 people to ride is 6.

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Answer:

It is C. 3

Step-by-step explanation:

Hope this helped have an amazing day!

The sides 7cm , 24cm and 25cm ; forms a right angled triangle because the condition of Pythagoras Theorem is satisfied .

What is Pythagoras Theorem ?

The Pythagoras Theorem states that the square of hypotnuse (longest sides) is equal to the sum of the square of the other two sides .

The sides are given as ⇒ 7cm , 24cm and 25cm ;

here the longest side (hypotnuse) is = 25 cm ;

According to Pythagoras theorem ,

⇒ \(25^{2} =24^{2} +7^{2}\) ;

⇒ \(625=576+49\) ;

⇒ \(625 = 625\) ;

The condition of Pythagoras theorem is satisfied .

Therefore , the given sides can form a Right Angled Triangle .

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The valid conclusion we can have is W(Ahmed).Ans: The valid conclusion that can be derived is W(Ahmed).

We can use the rule of inference, Modus ponens and Modus Tollens to find the valid conclusion of the given argument. The given premises are,C(Ahmed) ∀x(C(x)→P(x)) Vx(P(x)→W(x)).The term C(x) means "x is in this class".The term P(x) means "x owns a PC".The term W(x) means "x can use a word processing program".Modus ponens: Modus ponens states that if a conditional statement is true and its hypothesis is true, then the conclusion is also true. This rule of inference can be applied to the given premises which lead to the conclusion that Ahmed can use a word processing program. Here is how we can use the Modus Ponens rule of inference here.∀x(C(x)→P(x)) → Premise 1.C(Ahmed) → Premise 2.C(Ahmed) → P(Ahmed) from Premise 1 and 2, using Modus ponens.P(Ahmed) → W(Ahmed) from Vx(P(x)→W(x)) using Universal instantiation.W(Ahmed) from P(Ahmed) → W(Ahmed) and P(Ahmed) using Modus ponens.

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Answer:

C. None of these

Step-by-step explanation:

EXPLANATION

Given the line on the graph, we need to find the slope and the y-intercept.

Considering two ordered pairs, as for instance (x₁,y₁)=(50,-90) and (x₂,y₂)=(80,90)

The slope-equation is:

Replacing terms:

The point-slope form of the line is:

y-y₁= m(x-x₁)

Finally, we need to represent as a point-slope form considering either one ordered pair, as for instance, (x₁,y₁)=(50,-90)

y-(-90) = 6(x-50) [Simplifying terms]

y + 90 = 6(x-50) [ANSWER]

Answer:

x = 12

Step-by-step explanation:

From the question given above, the following data were obtained:

m < EDG = 112°

m < EDH = 6x – 9

m < HDG = 4x + 1

x =.?

Thus, we can obtain the value of x as shown below:

m < EDG = m < EDH + m < HDG

112 = 6x – 9 + 4x + 1

112 = 6x + 4x – 9 + 1

112 = 10x – 8

Collect like terms

112 + 8 = 10x

120 = 10x

Divide both side by 10

x = 120/10

x = 12

Therefore, the value of x is 12.

The break-even point is the level of output at which total revenue (TR) equals total cost (TC). In this case, with TR(x) = 20x and TC(x) = 120 + 10x, we need to find the value of x where TR(x) = TC(x).

To find the break-even point, we set TR(x) equal to TC(x) and solve for x.
TR(x) = TC(x) can be expressed as:
20x = 120 + 10x
Simplifying the equation, we combine like terms:
20x - 10x = 120
10x = 120
To isolate x, we divide both sides of the equation by 10:
x = 12
Therefore, the break-even point occurs when x is equal to 12. At this level of output, the total revenue is equal to the total cost.

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The composition of functions that achieve the desired result is given as follows:

d. f(x) = 1/x and g(x) = x² - 6.

The composite function of f(x) and g(x) is given by the rule presented as follows:

(f ∘ g)(x) = f(g(x)).

It means that the output of the inside function serves as the input for the outside function.

For item d, the functions are given as follows:

Applying the composite function, we have that h(x) (f(g(x)) = f(x² - 6), hence the lone instance of x in f(x) is replaced by x² - 6, as follows:

h(x) = 1/(x² - 6).

Meaning that it is the correct option.

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Answer: 33 degrees

Step-by-step explanation: Angle x=angle m

Answer:

the triangle on the left is named XYZ

the triangle on the right is named MNL

therefore ∠X ≅ ∠M, ∠Y ≅∠N, and ∠Z ≅ ∠L

since ∠X = 33º, then ∠M = 33º

hope this helps :)

Step-by-step explanation:

Thus, the drawing's scale factor is 8:1, or simply 8. This implies that each function measurement on the design is eight times bigger than its actual-world equivalent.

Mathematicians research numbers, their variants, equations, forms, and related structures, as well as possible locations for these things. The relationship between a group of inputs, each of which has a corresponding output, is referred to as a function. Every input contributes to a single, distinct output in a connection between inputs and outputs known as a function. A domain, codomain, or scope is assigned to each function. Often, functions are denoted with the letter f. (x). The key is an x. There are four main categories of accessible functions: on functions, one-to-one capabilities, so many capabilities, in capabilities, and on functions.

One inch on the illustration equals one eighth of an inch in reality if the scale is 1 inch = 1/8 inch.

We must divide the length of the drawing by the comparable length in reality to determine the scale factor. The scale factor is: because one inch on the design corresponds to 1/8 inch in reality.

1 / (1/8) = 8

Thus, the drawing's scale factor is 8:1, or simply 8. This implies that each measurement on the design is eight times bigger than its actual-world equivalent.

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Answer:

4.25=17/4

4 1/4= 17/4

Step-by-step explanation:

The limit of f(x) as it approaches -1 is given as 3/2

In mathematics and computation, the limit can be described to be the value that a sequence is going to approach in such a way that the input would approach or tend towards a given value

The unit is used to assign values to numbers at certain points where there are no defined values.

we have 3/x-1

We have to take the value of x here to be three as the equation tends to 1.

Then we apply it in the formula

3/3-1

= 3/2

Hence the limit of f(x) is given as 3/2

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