what is the sum of (2x−6)+4(x−3)

Answer:

no no yes yes

Step-by-step explanation:

Triangles may or may not be congruent.

The truth values of the claims are:

(a and b) Corresponding sides and angle must be equal

This is true, because the corresponding sides and angles of the triangles must be equal for both triangles to be congruent

Hence, the truth value of (a) and (b) is Yes

(c) Sequence translation of the triangles

Translation simply means moving a shape across the coordinate grid.

Translating one triangle onto the other may not be enough to prove that both triangles are congruent.

Hence, the truth value of (c) is No

(d) Sequence rigid motion of the triangles

Rigid motion simply means transformations that do not alter the size of the triangles.

This must be true, because the triangles may be reflected, rotated or translated onto one another

Hence, the truth value of (d) is Yes

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Answer:

Step-by-step explanation:

2.06

Answer:

35/17 = 2.06 (to the nearest hundredth)

Answer:

yes and b

Step-by-step explanation:

The approximate area under the curve y = x² + 8 on the interval [0, 1] using rectangles and the right endpoints of each subinterval is approximately 0.

to approximate the area under the curve y = x² + 8 on the interval [0, 1] using angle and the right endpoints of each subinterval as the evaluation points, we can use the right riemann sum.

the width of each subinterval, δx, is given by:

δx = (b - a) / n,

where b and a are the endpoints of the interval and n is the number of subintervals.

in this case, b = 1, a = 0, and n = 18, so:

δx = (1 - 0) / 18 = 1/18.

next, we calculate the x-values of the right endpoints of each subinterval. since we have 18 subintervals, the x-values will be:

x1 = 1/18,x2 = 2/18,

x3 = 3/18,...

x18 = 18/18 = 1.

now, we evaluate the function at each x-value and multiply it by δx to get the area of each rectangle:

a1 = (1/18)² + 8 * (1/18) * (1/18) = 1/324 + 8/324 = 9/324,a2 = (2/18)² + 8 * (2/18) * (1/18) = 4/324 + 16/324 = 20/324,

...a18 = (18/18)² + 8 * (18/18) * (1/18) = 1 + 8/18 = 10/9.

finally, we sum up the areas of all the rectangles to approximate the total area under the curve:

approximate area = a1 + a2 + ... + a18 = (9 + 20 + ... + 10/9) / 324.

to calculate this sum, we can use the formula for the sum of an arithmetic series:

sum = (n/2)(first term + last term),

where n is the number of terms.

in this case, n = 18, the first term is 9/324, and the last term is 10/9.

sum = (18/2)((9/324) + (10/9)) = 9/2 * (9/324 + 40/324) = 9/2 * (49/324) = 49/72. 6806 (rounded to four decimal places).

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The number which best completes the sequence is 13, but since it's not in the given options, there might be an error in the question or the answer choices.

The pattern in this sequence is not immediately obvious, but we can try to identify some relationships between the numbers.

Starting with the first two numbers, we can see that the second number is obtained by multiplying the first number by 3 and adding 3:

2 x 3 + 3 = 9

Next, we can see that the third number is obtained by subtracting 4 from the second number:

9 - 4 = 5

The fourth number is obtained by adding 8 to the third number:

5 + 8 = 13

The fifth number is obtained by subtracting 3 from the fourth number:

13 - 3 = 10

The sixth number is obtained by adding 9 to the fifth number:

10 + 9 = 19

At this point, we can see that the pattern seems to be alternating between adding and subtracting some value. We can try to extend this pattern to find the missing number:

Starting with the sixth number, we subtract 2:

19 - 2 = 17

Next, we can add some value to get the next number. Based on the pattern we've seen so far, it seems likely that this value is 11:

17 + 11 = 28

However, 28 is not one of the options given. We can try to use the pattern to find another option. If we subtract 1 from the sixth number instead of 2, we get:

19 - 1 = 18

And if we add 8 instead of 11, we get:

18 + 8 = 26

26 is not one of the options given either, but it seems like a reasonable choice based on the pattern we've identified. Therefore, the number which best completes the sequence below is:

c) 25

To find the number that best completes the sequence, let's first identify the pattern. The sequence is as follows:

2 9 5 13 10 19 17 ?

Looking closely, we can see that there are two alternating patterns:

Pattern 1: Add 7 (2 to 9, 5 to 13, 10 to 17)
Pattern 2: Subtract 4 (9 to 5, 13 to 10, 19 to ?)

Now let's apply the pattern to find the next number in the sequence:

17 (the last number) - 4 (following Pattern 2) = 13

So, the number which best completes the sequence is 13, but since it's not in the given options, there might be an error in the question or the answer choices.

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the solution to the system of equations is x = 1/2 and y = -31/2. The solution set is {(1/2, -31/2)}.

ToTo solve the system of equations using the substitution method, we can solve one equation for a variable and substitute it into the other equation. Let's solve the first equation for x:

x - Sy = 16

x = 16 + Sy

Now substitute this expression for x in the second equation:

2(16 + Sy) - 1 = 0

32 + 2Sy - 1 = 0

2Sy + 31 = 0

2Sy = -31

Sy = -31/2

Now substitute this value of Sy back into the first equation:

x - (-31/2) = 16

x + 31/2 = 16

x = 16 - 31/2

x = 1/2

Therefore, the solution to the system of equations is x = 1/2 and y = -31/2. The solution set is {(1/2, -31/2)}.

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It shows that the values of the mileages are close to 24 mpg. Hence statistics refes 24 as the mean.

Mean is one of the measure of dispersion and is the avearage of a set of data.

According to the question, the magazine reports that the most common gas mileage was 24 mpg. This shows that reports have published several gas mileages for cars and truck and the average of this mileage is 24mpg

It shows that the values of the mileages are close to 24 mpg. Hence statistics refes 24 as the mean.

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We can use the properties of the normal distribution to calculate the probability that the total volume shipped is more than 100,000 ft3.

Assuming that the xis are independent with each one having a normal distribution, the total volume shipped can be modeled as the sum of these individual normal distributions. Since the sum of independent normal distributions is also a normal distribution, we can use the properties of the normal distribution to calculate the probability that the total volume shipped is more than 100,000 ft3.

To do this, we need to find the mean and variance of the sum of the xis. The mean of the sum is simply the sum of the means of the individual distributions, while the variance of the sum is the sum of the variances of the individual distributions.

Once we have the mean and variance of the sum, we can standardize the distribution and use a normal probability table or calculator to find the probability that the total volume shipped is more than 100,000 ft3.

In general, the probability of the sum of independent normal distributions exceeding a certain value depends on the number of distributions being summed, their means and variances, and the level of significance chosen for the test. Therefore, we need to specify these parameters to calculate the desired probability.

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The general solution to the given difference equation is:

Xr = A(-2 + i)^r + B(-2 - i)^r

To solve this equation using the E-operator method, we first assume that the solution is of the form Xr = λ^r for some constant λ.

Substituting this into the given equation, we get:

λ^(r+2) + 4λ^(r+1) + 9λ^r = 0

Dividing both sides by λ^r, we get:

λ^2 + 4λ + 9 = 0

This is a quadratic equation in λ and can be solved using the quadratic formula:

λ = (-4 ± √(4^2 - 419))/2*1

λ = (-4 ± 2i)/2

λ = -2 ± i

Therefore, the general solution to the given difference equation is:

Xr = A(-2 + i)^r + B(-2 - i)^r

where A and B are constants determined by the initial conditions.

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The decrease in diameter of the bar due to the applied load is -0.005434905d and the final diameter of the bar is 1.005434905d.

A compressive load of 80,000 lb is applied to a bar with a circular section of 0.75 in diameter and a length of 10 in.

if the modulus of elasticity of the bar material is 10,000 ksi and the Poisson's ratio is 0.3.

We have to determine the decrease in diameter of the bar due to the applied load.

Let d be the initial diameter of the bar and ∆d be the decrease in diameter of the bar due to the applied load, then the final diameter of the bar is d - ∆d.

Length of the bar, L = 10 in

Cross-sectional area of the bar, A = πd²/4 = π(0.75)²/4 = 0.4418 in²

Stress produced by the applied load,σ = P/A

= 80,000/0.4418

= 181163.5 psi

Young's modulus of elasticity, E = 10,000 ksi

Poisson's ratio, ν = 0.3

The longitudinal strain produced in the bar, ɛ = σ/E

= 181163.5/10,000,000

= 0.01811635

The lateral strain produced in the bar, υ = νɛ

= 0.3 × 0.01811635

= 0.005434905'

The decrease in diameter of the bar due to the applied load, ∆d/d = -υ

= -0.005434905∆d

= -0.005434905d

The final diameter of the bar,

d - ∆d = d + 0.005434905d

= 1.005434905d

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The most appropriate choice for trigonometry will be given by -

Angle between beam and road is 0.33°

What is Trigonometry?

Trigonometry shows the relationship between sides and angles of a right angled triangle.

There are six trigonometrical functions. They are \(sin\theta, cos\theta, tan\theta, cos\theta, sec\theta, cosec\theta\)

\(sin\theta = \frac{perpendicular}{hypotenuse}\\\\cos\theta = \frac{base}{hypotenuse}\\\\tan\theta = \frac{perpendicular}{base}\\\\cot\theta = \frac{base}{perpendicular}\\\\sec\theta = \frac{hypotenuse}{base}\\\\cosec\theta = \frac{hypotenuse}{perpendicular}\\\)

Trigonometry is a very important tool in mathematics.

Here,

The headlights of an automobile are set such that the beam drops 2.00 in. for each 28.0 ft in front of the car.

According to the figure attached here, 2.0 inch forms the height of the triangle and 28.0 ft forms the base of the triangle

Let the angle be \(\theta\). Now trigonometry is applied here

\(tan\theta = \frac{\frac{2}{12}}{28}\\tan\theta = \frac{1}{6 \times 28}\\tan\theta = \frac{1}{168}\\\theta = tan^{-1}\frac{1}{168}\\\theta = 0.33^{\circ}\)

Angle between beam and road is 0.33°

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Answer:

Step-by-step explanación

0.02

When the mean number of points scored per game next season is 60, the model predicts that the mean home attendance will be 11902

The function that predicts the attendance is given as:

\(y = -7628+325.5x\)

When the mean number of points scored per game next season is 60, it means that the value of x is 60

i.e. x = 60

Substitute 60 for x in the function

So, we have:

\(y = -7628+325.5 \times 60\)

Evaluate the product

\(y = -7628+19530\)

Add -7628 and 19530

\(y = 11902\)

Hence, the model predicts that the mean home attendance will be 11902

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Answer:

By using the Vertically Opposite Angles property

79 = 6x + 7 where value we get is x = 12

By using Linear pair property

79 + z = 180 where we get the value of z = 101

To find the volume of the solid, whose base is the region between the curve y=20 sin x.

We know that the base of the solid is the region between the curve y=20 sin x. We also know that the solid is bounded by the x-axis and the plane z=0.

Therefore, the height of the solid is the distance between the curve and the plane z=0. This distance is simply given by the function y=20 sin x.

To find the volume of the solid, we need to integrate the area of each cross-sectional slice of the solid as we move along the x-axis. The area of each slice is simply the area of the base times the height.

The area of the base is given by the integral of y=20 sin x over the region of interest. This integral is:

∫ y=20 sin x dx from x=0 to x=π

= -cos(x) * 20 from x=0 to x=π

= 40

Therefore, the area of the base is 40 square units.

The height of the solid is given by y=20 sin x. Therefore, the volume of each slice is:

dV = (area of base) * (height)

= 40 * (20 sin x) dx

Integrating this expression from x=0 to x=π, we get:

V = ∫ dV from x=0 to x=π

= ∫ 40 * (20 sin x) dx from x=0 to x=π

= 800 [cos(x)] from x=0 to x=π

= 1600

Therefore, the volume of the solid is 1600 cubic units.

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To find the volume of the solid, whose base is the region between the curve y=20 sin x.

We know that the base of the solid is the region between the curve y=20 sin x. We also know that the solid is bounded by the x-axis and the plane z=0.

Therefore, the height of the solid is the distance between the curve and the plane z=0. This distance is simply given by the function y=20 sin x.

To find the volume of the solid, we need to integrate the area of each cross-sectional slice of the solid as we move along the x-axis. The area of each slice is simply the area of the base times the height.

The area of the base is given by the integral of y=20 sin x over the region of interest. This integral is:

∫ y=20 sin x dx from x=0 to x=π

= -cos(x) * 20 from x=0 to x=π

= 40

Therefore, the area of the base is 40 square units.

The height of the solid is given by y=20 sin x. Therefore, the volume of each slice is:

dV = (area of base) * (height)

= 40 * (20 sin x) dx

Integrating this expression from x=0 to x=π, we get:

V = ∫ dV from x=0 to x=π

= ∫ 40 * (20 sin x) dx from x=0 to x=π

= 800 [cos(x)] from x=0 to x=π

= 1600

Therefore, the volume of the solid is 1600 cubic units.

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Therefore , the solution of the given problem of triangle comes out to be  the equilateral triangle are is 62.28 cm².

In geometry, triangular polygons are ones that have three vertices and a right side. This object in two dimensions has three straight sides. Triangles are examples of three-sided polygons. The sum of a triangle's three angles is 180 degrees. The triangle lies on one plane.

Here,

Given : side = 12cm

Area of an equilateral triangle

=> √3/4 * side²

Side of triangle =12 cm

Area of an equilateral triangle

= >  √3/4 * 12²

=>√3/4 * 12*12

=> 62.28 cm²

Therefore , the solution of the given problem of triangle comes out to be  the equilateral triangle are is 62.28 cm².

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Answer:

8x³ - 2x² - 51x - 45

Step-by-step explanation:

Given

(x - 3)(2x + 3)(4x + 5) ← expand second/third factors using FOIL

= (x - 3)(8x² + 22x + 15) ← distribute

= x(8x² + 22x + 15) - 3(8x² + 22x + 15) ← distribute parenthesis

= 8x³ + 22x² + 15x - 24x² - 66x - 45 ← collect like terms

= 8x³ - 2x² - 51x - 45

Answer:

8x^3-2x^2-51x-45

Step-by-step explanation:

(x − 3)(2x + 3)(4x + 5)

(2x^2+3x-6x-9)*(4x+5)

(2x^2-3x-9)*(4x+5)

= 8x^3-2x^2-51x-45

Answer:

B) sin55/8 = sin30/b

Step-by-step explanation:

Just did it on AP3X :)

A discrete probability distribution is a statistical distribution that relates to a set of outcomes that can take on a countable number of values, whereas a continuous probability distribution is one that can take on any value within a given range.Therefore, the main difference between the two types of distributions is the type of outcomes that they apply to.

An example of a discrete probability distribution is the probability of getting a particular number when a dice is rolled. The possible outcomes are only the numbers one through six, and each outcome has an equal probability of 1/6. Another example is the probability of getting a certain number of heads when a coin is flipped several times.

On the other hand, an example of a continuous probability distribution is the distribution of heights of students in a school. Here, the range of heights is continuous, and it can take on any value within a given range.

The expected value of a probability distribution measures the central tendency or average of the distribution. In other words, it is the long-term average of the outcome that would be observed if the experiment was repeated many times.

For a discrete probability distribution, the expected value is computed by multiplying each outcome by its probability and then adding the results. In mathematical terms, this can be written as E(x) = Σ(xP(x)), where E(x) is the expected value, x is the possible outcome, and P(x) is the probability of that outcome.

For example, consider the probability distribution of the number of heads when a coin is flipped three times. The possible outcomes are 0, 1, 2, and 3 heads, with probabilities of 1/8, 3/8, 3/8, and 1/8, respectively. The expected value can be computed as E(x) = (0*1/8) + (1*3/8) + (2*3/8) + (3*1/8) = 1.5.

Therefore, the expected value of the distribution is 1.5, which means that if the experiment of flipping a coin three times is repeated many times, the long-term average number of heads observed will be 1.5.

The probability that an electron will tunnel through a 0.50 nm air gap from a metal to a STM probe if the work function is 4.0 eV is 3.4 × 10^-5

The air gap from a metal to a STM = 0.50 nm

The work function = 4.0 eV

The probability is the ratio of the number of favorable outcomes to the total number of outcomes

The probability = Number of favorable outcomes / Total number of outcomes

The value of η = h / \(\sqrt{2m(U_0-E)}\)

Substitute the values in the equation

= \(\frac{1.05(10^{-34})}{\sqrt{2(9.11(10^{-31})(4(1.6)(10^{-19})} }\)

Do the arithmetic operation

= 0.0972 nm

The probability = exp (-1 / 0.972)

= 3.4 × 10^-5

Therefore, the probability is 3.4 × 10^-5

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Answer:80

Step-by-step explanation:

take 20 from 100 and give them to 60.

take 10 from 90 and give to 70.

adds ut to avg 80

Answer:

4

Step-by-step explanation:

because i know

Answer:

Acceleration and velocity

Newton's second law says that when a constant force acts on a massive body, it causes it to accelerate, i.e., to change its velocity, at a constant rate. In the simplest case, a force applied to an object at rest causes it to accelerate in the direction of the force.

Gabriella skied for 6 hours, Let x be the number of hours that Gabriella skied. We know that she paid $35 for ski rental and $15 per hour for skiing,

for a total of $95. We can set up the following equation to represent this information:

35 + 15x = 95

Solving for x, we get:

15x = 60

x = 4

Therefore, Gabriella skied for 6 hours.

Here is a more detailed explanation of how to solve the equation:

Subtract $35 from both sides of the equation.

15x = 60

15x - 35 = 60 - 35

15x = 25

Divide both sides of the equation by 15.

15x = 25

x = 25 / 15

x = 4

Therefore, x is equal to 4, which is the number of hours that Gabriella skied.

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Answer:

8.9

Step-by-step explanation:

1.move down 5.7 into the box below it

2. add the numbers

3.awnser is 8.9

Answer:

18m²

Step-by-step explanation:

area = areas of top left triangle + bottom left + top right + bottom right

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

= 3 + 3 + 6 + 6

= 18 m²

The correct option is; Yes, all the three expressions are equivalent to each other.

For the given question;

The three expressions are given as;

a: 20(1.1ˣ)   ...1

b: 20(1.1⁻¹)⁻¹ˣ

Simplifying as;

= 20(1.1⁻¹⁽⁻¹ˣ⁾)

= 20(1.1ˣ) ....2

c: 20(1.1¹/⁵)⁵ˣ

Simplifying.

= 20(1.1¹/⁵⁽⁵ˣ⁾)

= 20(1.1ˣ) ....3

So, a = b = c

Thus, all three expressions are equivalent to each other.

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Answer: chemical decomposition produced by passing an electric current through a liquid or solution containing ions. In chemistry and manufacturing, electrolysis is a technique that uses direct electric current to drive an otherwise non-spontaneous chemical reaction. Electrolysis is commercially important as a stage in the separation of elements from naturally occurring sources such as ores using an electrolytic cell. Electrolysis is used in industry for the production of many metals and non-metals (e.g., aluminium, magnesium, chlorine, and fluorine). Electrolysis is commonly employed for coating one metal with another. The method of coating one metal with another using an electric current is called electroplating.

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To solve the second-order linear homogeneous differential equation y'' - 2y' - 8y = 2e^(-3x) using the variation of parameters method,

we will first find the solutions to the homogeneous equation and then use the variation of parameters formula to find the particular solution.

Find the solutions to the homogeneous equation:

The characteristic equation is r^2 - 2r - 8 = 0.

Solving the quadratic equation, we get r = -2 and r = 4.

Therefore, the homogeneous solutions are y_h = c1e^(-2x) + c2e^(4x), where c1 and c2 are constants.

Find the particular solution using the variation of parameters:

Let's assume the particular solution has the form y_p = u1(x)e^(-2x) + u2(x)e^(4x).

We need to find u1(x) and u2(x).

Calculate the derivatives:

y_p' = u1'e^(-2x) + u2'e^(4x) - 2u1e^(-2x) + 4u2e^(4x)

y_p'' = u1''e^(-2x) + u2''e^(4x) - 4u1'e^(-2x) + 16u2'e^(4x) - 2u1'e^(-2x) + 4u2'e^(4x) - 4u1e^(-2x) + 16u2e^(4x)

Substitute y_p and its derivatives into the original equation:

u1''e^(-2x) + u2''e^(4x) - 4u1'e^(-2x) + 16u2'e^(4x) - 2u1'e^(-2x) + 4u2'e^(4x) - 4u1e^(-2x) + 16u2e^(4x) - 2(u1'e^(-2x) + u2'e^(4x)) - 8(u1e^(-2x) + u2e^(4x)) = 2e^(-3x)

Simplify and collect like terms:

(u1'' - 6u1'e^(-2x))e^(-2x) + (u2'' + 20u2'e^(4x))e^(4x) = 2e^(-3x)

Equate the coefficients of the exponential terms to zero:

u1'' - 6u1'e^(-2x) = 0 (1)

u2'' + 20u2'e^(4x) = 0 (2)

Solve equations (1) and (2) to find u1(x) and u2(x):

Integrating equation (1) twice, we get u1(x) = c3e^(2x) + c4.

Integrating equation (2) twice, we get u2(x) = c5e^(-4x) + c6.

Substitute u1(x) and u2(x) back into the particular solution:

y_p = (c3e^(2x) + c4)e^(-2x) + (c5e^(-4x) + c6)e^(4x)

= c3 + c4e^(-2x) + c5e^(4x) + c6e^(2x)

Finally, the particular solution to the differential equation is given by:

y_p(x) = u1(x) * y1(x) + u2(x) * y2(x).

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