is the equation true or false

The system of linear equations from the first table

Equation 1: 2 = a × 0 + b

Equation 2: 0 = a × (-4) + b

Equation 3: 5 = a × 6 + b

Equation 4: -1 = a ×  (-6) + b

The system of linear equations from the first table of values can be identified as:

Equation 1: 2 = a × 0 + b

Equation 2: 0 = a × (-4) + b

Equation 3: 5 = a × 6 + b

Equation 4: -1 = a ×  (-6) + b

Table 2:

The system of linear equations from the second table of values can be identified as:

Equation 1: 1 = a × 0 + b

Equation 2: 0 = a ×  (-2) + b

Equation 3: -1 = a ×  (-4) + b

Equation 4: 2 = a × 2 + b

In the equations, 'a' and 'b' represent the coefficients to be determined.

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Assuming QF is the full employment equilibrium then in the Figure, if the level of spending is equal to AD1, the AD shortfall would be greater than XZ. The answer is B.

The respective figure as referred in the question is as attached.

Full employment equilibrium refers to the equilibrium where all resources in the economy are fully utilized (employed). Full employment is a situation in which all available labor resources are being used in the most economically efficient way, so there is no cyclical or deficient-demand unemployment.

When the natural rate of unemployment is equal to the unemployment rate, this means the cyclical rate of unemployment is zero. So, when this relationship happens, the economy is considered to be at full employment.

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Answer:

  100 square inches

Step-by-step explanation:

The width of the shelf is BC = 20 - 10 = 10 inches.

The height of the shelf is AB = 30 - 10 = 20 inches.

The area of a triangle with these dimensions is ...

  A = (1/2)bh

  A = (1/2)(10 in)(20 in) = 100 in^2

The area of the shelf is 100 square inches.

Step-by-step explanation:

Check the attached photo out

Answer:

6 hours

Step-by-step explanation:

292-70=222

222/37=6

Answer:

900°

Step-by-step explanation:

The interior angles sum = 180° ( n - 2 )

~~~~~~~~

n = 7

180° ( 7 - 2 ) = 900°

Answer:

900 degrees

Step-by-step explanation:

just apply the formulas discussed in class !

The sum of interior angles in a triangle is 180°. To find the sum of interior angles of a polygon, multiply the number of triangles in the polygon by 180°.

The number of triangles in each polygon is two less than the number of sides.

The formula for calculating the sum of interior angles is:

(n−2)×180∘ (where n is the number of sides)

in our case we have 7 sides.

so, we could split this polygon into 5 triangles.

each of these triangles would have an angle sum of 180°.

so, the angle sum of the polygon is

5×180 = 900°

Raising the temperature from 20°C to 30°C would increase the rate of the reaction as it increases the energy available for the reaction to proceed. This is because the activation energy (Ea) of the reaction decreases with an increase in temperature, allowing the reaction to proceed faster.

Raising the temperature from 20°C to 30°C would increase the rate of the reaction due to the effect of temperature on the activation energy (Ea). The activation energy is a measure of the energy required for a reaction to take place, and as the temperature increases, the energy available for the reaction also increases. This decrease in activation energy allows the reaction to proceed at a faster rate as more energy is available for the reactants to overcome the energy barrier. As such, raising the temperature from 20°C to 30°C would have the effect of increasing the rate of the reaction, other things equal.

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The intersection of two events A and B contains only those outcomes that are in both A and B.

The intersection of two events A and B, denoted by A ∩ B, is the set of all outcomes that are common to both A and B. In other words, it contains only those outcomes that are in both A and B.

For example, if event A is "rolling an even number on a fair six-sided die" and event B is "rolling a number greater than 3 on a fair six-sided die", then the intersection of A and B is the event "rolling an even number greater than 3 on a fair six-sided die", which contains the outcome 4 and has probability \(\frac{1}{6}\).

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Here's how to prove the statement "Z PQS = Z ROS" given that Z PQS and Z RQS are right angles.Given: Z PQS and Z RQS are right angles. To Prove: Z PQS = Z ROSStep 1:

Draw the figureDraw a diagram to help you see what is happening. You will also get a better understanding of the problem by doing this.Step 2: Identify your givensLooking at the diagram, you see that Z PQS and Z RQS are right angles. So, you have the following givens:Z PQS is a right angleZ RQS is a right angleStep 3: Identify what you need to proveYou need to prove that Z PQS is equal to Z ROS. Step 4: Begin your proof statementUse the given information to help you write your proof statement.Z PQS and Z RQS are right angles by givenTherefore, Z PQS + Z RQS = 180° (by the sum of angles in a triangle is 180°)

Since Z RQS = 90° (by given),

then Z PQS + 90° = 180°

Subtracting 90° from both sides will give you Z PQS = 90°

.Since Z ROS is also a right angle, Z ROS = 90°.

Z PQS = 90°

and Z ROS = 90°

Therefore, Z PQS = Z ROS

The statement is now proved.

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Answer: 80°

Step-by-step explanation:

The sum of the angles in a triangle is 180°. Since the two angles of a triangle measure 15° and 85°.

The measure for the third angle will be:

= 180° - (15° + 85°)

= 180° - 100°

= 80°

The third angle is 80°

Answer:

29

Step-by-step explanation:

just substitute x with 4 in the equation :)

Solution :-

First of all we have to find out the least common multiple of the given three numbers.

27 , 30 and 45

27 = 3 x 3 x 3

30 = 2 x 3 x 5

45 = 3 x 3 x 5

Form these factors we have to find the numbers which are common in all the three .

LCM = 2 x 3 x 3 x 3 x 5 = 270 .

Now 270 is completely divisible but the number which we want leaves 3 as remainder.

So adding 3 in 270 .

→ 273 is the required answer.

Answer:

Step-by-step explanation:

the answer is 785.51

The pair of acute angles that correspond to the solution of the equation sin(-x + 13°) = cos(3x + 75°) is (12°, 192°). Note that the angles are expressed in degrees.

To find the acute angles that correspond to the solution of the equation sin(-x + 13°) = cos(3x + 75°), we need to use the inverse trigonometric functions. The inverse sine function is denoted as sin^-1 and the inverse cosine function is denoted as \(cos^-1.\)

We start by isolating the cosine term on one side of the equation and taking the inverse cosine of both sides:

\(cos^-1(sin(-x + 13°)) = cos^-1(cos(3x + 75°))\)

Since the range of the inverse cosine function is [0, π], we have to consider the acute angle solutions, which are the solutions in the interval [0, 90°].

Using the identity sin(-x + 13°) = sin(180° - (-x + 13°)) = sin(x - 13° + 180°), we can express the left side in terms of a sine function:

\(cos^-1(sin(-x + 13°)) = cos^-1(sin(x - 13° + 180°)) = 180° - (x - 13°)\)

Using the identity cos(3x + 75°) = cos(75° - 3x), we can express the right side in terms of a cosine function:

\(cos^-1(cos(3x + 75°)) = cos^-1(cos(75° - 3x)) = 75° - 3x\)

Equating the expressions for both sides of the equation, we have:

180° - (x - 13°) = 75° - 3x

Solving for x, we find:

4x = 105° - 57° = 48°

x = 12°

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Answer:

they bought 23 adult tickets and 2 child tickets

Step-by-step explanation:

the explanation is in the screenshot below

please mark brainliest

Answer:

shape 1

Step-by-step explanation:

The question requires us to find the

Laplace transform of the function f(t), where a and b are real constants.

Let's assume that the necessary elementary

integration formulas extend to this case.

Finding the Laplace transform of f(t):

Let F(s) be the Laplace transform of f(t). Then, we have:F(s) = L{f(t)} = ∫_0^∞ e^(-st) f(t) dt

We know that the Laplace transform of a

constant function is given by:

L{1} = ∫_0^∞ e^(-st)

dt = [-1/s * e^(-st)]_0^∞ = 1/sIf

we replace the constant function 1 in the above formula with e^(at), we get:

L{e^(at)} = ∫_0^∞ e^(-st) e^(at) dt

Now, let's express f(t) as a sum of two

exponential functions

:

f(t) = e^(at) + e^(bt)

Taking the Laplace transform of both the terms separately, we get:

L{e^(at)} = 1/(s-a) and

L{e^(bt)} = 1/(s-b)

Therefore, the Laplace transform of f(t) is given by:

F(s) = L{f(t)} = L{e^(at)} + L{e^(bt)}= 1/(s-a) + 1/(s-b) = (b + a - s)/[(s - a)(s - b)]

This is the Laplace transform of the function f(t).

Hence, the required answer is:(a) f(t) = e^(at) + e^(bt) => F(s) = L{f(t)} = (b + a - s)/[(s - a)(s - b)]

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To find the Laplace transform of the function f(t) with constants a and b, substitute f(t) into the integral F(s) = ∫[0 to ∞] f(t)e^(-st) dt and evaluate it using the integration formulas mentioned.

The question asks for the Laplace transform of a function, denoted as f(t), where a and b are real constants. To find the Laplace transform of f(t), we need to apply the necessary elementary integration formulas.

The Laplace transform of a function f(t) is denoted as F(s), where s is a complex variable. It is defined by the integral:

F(s) = ∫[0 to ∞] f(t)e^(-st) dt

To find the Laplace transform of f(t), we substitute f(t) into the integral and evaluate it using the integration formulas.

The necessary elementary integration formulas include:

1. ∫ e^(at) dt = 1/a * e^(at) + C, where a is a constant and C is the constant of integration.
2. ∫ t^n dt = (1/(n+1)) * t^(n+1) + C, where n is a positive integer and C is the constant of integration.

By applying these formulas, we can find the Laplace transform of f(t) with the given values of a and b. It is important to note that the specific form of f(t) must be known in order to apply the correct integration formulas.

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The density of the tank is  D. 0.37 goldfish per cubic foot.

To find the density of the tank, we need to divide the number of goldfish by the volume of the tank. In this case, we have 19 goldfish and a tank volume of 52 cubic feet. So, the density of the tank can be calculated as follows:

Density = Number of goldfish / Volume of tank

Density = 19 / 52

Density = 0.365

Therefore, the density of the tank is 0.37 goldfish per cubic foot, which is option d.

The density is a measure of the amount of matter (in this case, goldfish) that is present in a given volume (in this case, the tank). A higher density means that there are more goldfish per unit volume, while a lower density means that there are fewer goldfish per unit volume.

In this case, we can see that the density is relatively high, meaning that there are a significant number of goldfish in the tank. This could potentially be a problem, as overcrowding can lead to poor water quality and health problems for the fish. It's important to monitor the density of fish in a tank and ensure that it stays at a healthy level. Therefore the correct option is D.

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Answer: 11,500 grams

Step-by-step explanation: 920/8=115 115*100= 11,500

An equation for the function g(x) when g(x) = f(-x) is g(x) = -x/3 - 6, which is shown in the graph attached below.

In Mathematics, a reflection can be defined as a type of transformation which moves every point of the geometric figure by producing a flipped, but mirror image of the geometric figure.

In Geometry, a reflection across the y-axis (y = x) is given by this transformation rule (x, y) → (-x, y). This ultimately implies that, a reflection over the y-axis would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.

By reflecting the given function across the across the y-axis (y = x), we have the following:

f(x) = x/3 - 6

g(x) = f(-x)

g(x) = -x/3 - 6.

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Answer:2

Step-by-step explanation:

Answer:

k

Step-by-step explanation:

Variables are usually letters. The only letter in this expression is k, so k is the variable.

The value of k for the parallel lines is 4.

Parallel lines have the same slope.

The equation of a line can be described as follows:

y = mx + b

where

Therefore,

The line go through (5, 4) and (k , 2) and is parallel to the line y = 2x.

Therefore, the slope of the line is 2.

let's find b using (5, 4)

y = 2x + b

4 = 2(5) + b

b = 4 - 10

b = - 6

Therefore, let's find k

y = 2x - 6

2 = 2(k) - 6

8 = 2k

k = 8 / 2

Therefore,

k = 4

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The area of the given triangle is 20 square kilometers.

Here, we are given a triangle as shown in the figure below.

There are many ways of calculating the area of a triangle but since here, we are given only one angle and 2 sides of the triangle we will use the following formula to calculate the area-

area of triangle = 1/2 × sinФ × side 1 × side 2

where, Ф = angle formed by side 1 and side 2

Here, Ф = 35

Sin 35 = 0.5736

Thus, the area of the triangle will be-

1/2 × 0.5736 × 7 × 10

= 35 × 0.5736

= 20.076

20.076 rounded off to nearest hundredth is 20

Thus, the area of the given triangle is 20 square kilometers.

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Your question was incomplete. Check for the missing figure below

The length of each piece of wood is 0.725 feet.

We are given that the Length= 3.5feet

Now,

This is a word problem that can be solved by using algebra and arithmetic.

Part A: Let x be the length of each of the four pieces of wood he cut. Then, according to the problem, we have:

4x + 0.6 = 3.5

This is the equation that could be used to determine the length of each piece of wood.

Part B: We know the equation from part A is correct because it represents the total length of the wood before and after cutting. The left side of the equation is the sum of the lengths of the four pieces of wood and the leftover piece of wood. The right side of the equation is the original length of the wood. Since cutting does not change the total length of the wood, these two sides must be equal.

Part C: To solve the equation from part A, we need to isolate x by using inverse operations. We get:

4x + 0.6 = 3.5 4x = 3.5 - 0.6 (subtract 0.6 from both sides) 4x = 2.9 x = 2.9/4 (divide both sides by 4) x = 0.725

Therefore, by the algebra the answer will be 0.725 feet.

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The mean is 6

The variance is 4/3

The standard deviation is approximately 1.15.

How we Calculate the mean?
The mean (μ) of a uniformly distributed random variable is the average of the endpoints of the interval. So, in this case:
μ = (4 + 8) / 2 = 12 / 2 = 6

How we Calculate the variance?
The variance (σ²) of a uniformly distributed random variable is given by the formula:
σ² = (b - a)² / 12
where a and b are the endpoints of the interval. In this case:
σ² = (8 - 4)² / 12 = 4² / 12 = 16 / 12 = 4 / 3

How we Calculate the standard deviation?
The standard deviation (σ) is the square root of the variance. So, in this case:
σ = √(4 / 3) ≈ 1.15

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The cost of one rose bush is $10 and the cost of one pot of ivy is $10.

Let's assume the cost of one rose bush is represented by "R" and the cost of one pot of ivy is represented by "I".

According to the given information:

Jaidee spent $140 on 2 rose bushes and 12 pots of ivy:

2R + 12I = 140 ...(1)

Beth spent $120 on 6 rose bushes and 6 pots of ivy:

6R + 6I = 120 ...(2)

We now have a system of two equations with two variables. To solve this system, we can use either substitution or elimination method. Let's use the elimination method.

Multiply equation (1) by 3 and equation (2) by 2 to make the coefficients of "R" in both equations equal:

6R + 36I = 420 ...(3)

12R + 12I = 240 ...(4)

Now, subtract equation (4) from equation (3):

(6R + 36I) - (12R + 12I) = 420 - 240

-6R + 24I = 180 ...(5)

Now we have a new equation (5) that relates "R" and "I".

Let's solve equations (5) and (2) together:

-6R + 24I = 180 ...(5)

6R + 6I = 120 ...(2)

Add equation (5) and equation (2):

(6R - 6R) + (24I + 6I) = 180 + 120

30I = 300

Divide both sides of the equation by 30:

I = 10

Now substitute the value of "I" into equation (2) to find the value of "R":

6R + 6(10) = 120

6R + 60 = 120

6R = 120 - 60

6R = 60

Divide both sides of the equation by 6:

R = 10

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