i-Ready
■ Dilate ARST by a scale factor
3
of with the center of dilation
4
at the origin.

To find a sequence of elementary matrices whose product is the given nonsingular matrix, first you need to multiply it by a sequence of elementary matrices. This can be done by performing row operations such as swapping rows, multiplying or dividing a row by a non-zero number, and adding a multiple of one row to another.

For example, to get the following matrix:

1 2 3
2 5 6
1 3 4

We can perform the following sequence of operations:

1. Multiply row 1 by 2:

2 1*2  4*2  6*2
2 5    6    12
1 3    4    8

2. Subtract 3 times row 1 from row 3:

2  4   6
2  5   12
-1 -1  -2

3. Multiply row 2 by 1/2:

2  4   6
1  2.5 6
-1 -1  -2

4. Add -2 times row 2 to row 3:

2  4   6
1  2.5 6
0  0   0

The sequence of elementary matrices that correspond to these operations are:

Matrix 1:

2 0 0
0 1 0
0 0 1

Matrix 2:

1 0 0
0 1 0
-3 0 1

Matrix 3:

1 0 0
0 0.5 0
0 0 1

Matrix 4:

1 0 0
0 1 0
2 0 1

The product of these matrices is the given matrix.

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The area of the triangle is approximately 36.83 square units.

To find the area of a triangle using calculus, we can use the formula:

A = (1/2) ∫(x2 - x1)dy

Where x1 and x2 are the x-coordinates of the vertices, and dy is the change in the y-coordinate.

First, we need to find the equations of the lines that make up the sides of the triangle. The line between (0,0) and (6,1) has the equation y = (1/6)x. The line between (6,1) and (3,7) has the equation y = -2x + 13. The line between (3,7) and (0,0) has the equation y = (7/3)x.

Now we can use the formula to find the area of the triangle. We'll integrate from y = 0 to y = 1 for the first side, from y = 1 to y = 7 for the second side, and from y = 7 to y = 0 for the third side:

A = (1/2) ∫(x2 - x1)dy

= (1/2) ∫[(6x - 0) - (0 - 0)]dy from y = 0 to y = 1

+ (1/2) ∫[(13 - 2x) - (6x - 0)]dy from y = 1 to y = 7

+ (1/2) ∫[(0 - 0) - (7x/3 - 0)]dy from y = 7 to y = 0

= (1/2) ∫6xdy from y = 0 to y = 1

+ (1/2) ∫(13 - 8x)dy from y = 1 to y = 7

+ (1/2) ∫(-7x/3)dy from y = 7 to y = 0

= (1/2) [(3 - 0) + (49 - 8) + (-49/3 - 0)]

= (1/2) [(3) + (41) + (-49/3)]

= (1/2) [(147/3) + (123/3) + (-49/3)]

= (1/2) [(221/3)]

= 36.83

So the area of the triangle is approximately 36.83 square units.

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Jessica has completed 95% of her total deliveries.

What is percentage ?

A percentage is a number or ratio expressed as a fraction of 100. The symbol for percentage is "%". Percentages are commonly used to express parts of a whole or to compare one value to another.

Percentages are often used in many areas of everyday life, including finance, economics, statistics, and science. They are used to express changes in values, calculate discounts or taxes, and compare data across different groups or time periods.

According to the question:
To find the percentage of deliveries completed by Jessica, we can use the formula:

percentage = (completed deliveries / total deliveries) x 100%

Plugging in the given values, we get:

percentage = (38 / 40) x 100%

percentage = 0.95 x 100%

percentage = 95%

Therefore, Jessica has completed 95% of her total deliveries.


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Answer:

the outer edge of the circular path is approximately 25.32 feet farther than the inner edge.

Identifying examples of attributive, discrete, or continuous variablesVariables can be classified into three categories: Attributive, Discrete, and Continuous. The type of variable determines the type of statistical analysis that should be employed.

a. Polling registered voters as to which candidate they support is an example of an attributive variable.

b. The length of time required for a wound to heal when using a new medicine is an example of a continuous variable.

c. The number of telephone calls arriving at a switchboard per 10-minute period is an example of a discrete variable.

d. The distance first-year college women can kick a football is an example of a continuous variable.

e. The number of pages per job coming off a computer printer is an example of a discrete variable.

f. The kind of tree used as a Christmas tree is an example of an attributive variable.

g. The breaking strength of a given type of string is an example of a continuous variable.

h. The hair color of children auditioning for the musical Annie is an example of an attributive variable.

i. The number of stop signs in towns of less than 500 people is an example of a discrete variable.

j. Whether or not a faucet is defective is an example of an attributive variable.

k. The number of questions answered correctly on a standardized test is an example of a discrete variable.

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The right answers are for Cartesian equation is   [tex]a =\frac{1}{16},[/tex] [tex]b = \frac{5}{4}[/tex] , [tex]c = \frac{25}{4}[/tex] . A parameter is a constant number that controls the output or behavior of a mathematical entity. Parameters and variables are closely connected, and also the distinction is occasionally merely a question of perspective.

We are given:

[tex]x=t^{2} \\ y=10+4t[/tex]

Rearrange the parametric equation [tex]y = 10+4t[/tex]

[tex]y -10=10+4t-10[/tex]

[tex]y - 10 = 4t[/tex]

[tex]\frac{y - 10 }{4} = \frac{4t}{4}[/tex]

[tex]\frac{y - 10}{4} =t[/tex]

[tex]t = \frac{y - 10}{4}[/tex]

Simplify the descriptive formula by substituting the determined value for [tex]x= t^{2}[/tex]

Comparing the obtained cartesian equation with [tex]x=ay+by+c[/tex], the required coefficients are

[tex]a =\frac{1}{16}[/tex]

[tex]b = \frac{5}{4}[/tex]

[tex]c = \frac{25}{4}[/tex]

In mathematics, a parameter is a variable whose range of potential values indicates a group of unique situations in a problem. A parametric solution is any calculation that is represented in terms of variables.

What exactly are parameters and variables?

Variables are quantities that differ from one person to the next. Parameters, on the contrary hand, don't really refer to direct measurements or traits, instead referring to values that define a computational foundation.

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The expression that is equivalent to the given fraction is three raised to the sixth power divided by six raised to the fifteenth power.

What do you mean by fraction?

In mathematics, a fraction is a way to represent a part of a whole or a ratio between two quantities. A fraction consists of a numerator, which is the number above the line, and a denominator, which is the number below the line. The numerator represents the number of parts being considered, and the denominator represents the total number of parts in the whole or the ratio. Fractions are often expressed as a/b, where a is the numerator and b is the denominator. For example, 1/2 represents one-half, which means one of two equal parts, and 3/4 represents three-fourths, which means three of four equal parts. Fractions can be used in a wide range of mathematical operations, including addition, subtraction, multiplication, and division.

Simplifying the given expression-

we can use the rules of exponents.

First, we can rewrite the numerator as 1 divided by six raised to the third power, since a negative exponent means we take the reciprocal of the base raised to the positive exponent.

Next, we can expand the denominator by using the product rule of exponents, which gives us (three raised to the negative second power) times (six raised to the second power).

Simplifying each part separately, we get 1/(six cubed) divided by (three squared times six squared).

Now, we can use the quotient rule of exponents to divide the numerator by the denominator, which gives us 1/(six cubed times three squared times six squared).

Finally, we can simplify this expression by combining the like terms in the denominator, which gives us 1/(three squared times six raised to the fifth power). Since the entire fraction is cubed, we can cube both the numerator and the denominator to get three raised to the sixth power divided by six raised to the fifteenth power.

Therefore, the expression that is equivalent to the given fraction is three raised to the sixth power divided by six raised to the fifteenth power.

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The correct option is b. the cross elasticity of demand between these two products is positive.

The given scenario implies a positive cross elasticity of demand between the two products. When the price of product A decreases by 1 percent, there is a 3 percent increase in the sales of product B. This indicates that the products are related, but not necessarily substitutes or complements. If the two products were substitutes, a decrease in the price of product A would lead to a decrease in demand for product B. Conversely, if the two products were complements, a decrease in the price of product A would lead to an increase in the demand for product A and a decrease in the demand for product B. Therefore, the correct option is (b).

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The mean number of chocolate bars eaten is given as follows:

3.9 chocolate bars.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.

Considering the absolute frequencies, the total number of observations in this problem is given as follows:

19 + 6 + 15 = 40 observations.

The sum of the 40 observations is given as follows:

3 x 19 + 4 x 6 + 5 x 15 = 156.

Then the mean number of chocolate bars eaten is obtained as follows:

156/40 = 3.9 chocolate bars.

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The chi-squared statistic measures the difference between observed and expected frequencies in a categorical data analysis. It is used to test the hypothesis that there is no significant difference between the observed frequencies and the expected frequencies.

Specifically, the chi-squared statistic is the sum of the squared differences between the observed and expected frequencies, divided by the expected frequencies, and is distributed according to the chi-squared distribution.

The higher the value of the chi-squared statistic, the greater the difference between the observed and expected frequencies, indicating a larger deviation from the null hypothesis.

When the sample sizes are large, a chi-squared test is a statistical hypothesis test used in the study of contingency tables. To put it another way, the main purpose of this test is to determine whether two category factors have independent effects on the test statistic.

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Answer:

21 or 10

Step-by-step explanation:

I

Need to get myself together, I'm a mess

In Bikini Bottom, I'm with Sandy

Moesha keep on drinkin' all the brandy

Keisha eat the molly like it's candy

Answer: 44cm

Step-by-step explanation:

A= 44

r= 7 cm

Circumference of circle =2mr

= 2 x 722 x 7

= 44 cm

The probability that a simple random sample of 35 students will spend an average amount between 600 and 700 dollars is approximately 0.6579, or 65.79%.

To find the probability that a sample of 35 students will spend an average of between 600 and 700 dollars, we need to standardize the sample mean using the formula:

z = (x - μ) / (σ / √(n))

where z is the z-score, x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Plugging in the values given in the problem, we get:

z₁ = (600 - 650) / (120 / √(35)) = -1.51

z₂ = (700 - 650) / (120 / √(35)) = 1.51

We now need to find the area under the standard normal curve between these two z-scores. We can use a standard normal distribution table or a calculator to find that the area between -1.51 and 1.51 is approximately 0.6579 or 65.79%

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a =  -3 is the answer

Option B is correct

The given equation is 24x2+25x−47 ax−2 =−8x−3− 53 ax−2

multiplying both sides  equation by ax−2.

24x2+25x−47   =  (−8x−3)(ax−2)−53

We  then multiply (−8x−3) and (ax−2) using FOIL(First, Outer, Inner, Last)

24x2+25x−47=−8ax2−3ax+16x+6−53

We then  reduce on the right side of the equation

24x2+25x−47=−8ax2−3ax+16x−47

The coefficients of the x2-term have to be equal on both sides of the equation, we then can write

−8a=24,

a=−3.

In conclusion,  the value of a is -3

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Complete question:

The equation 24x2+25x−47 ax−2 =−8x−3− 53 ax−2 is true for all values of x≠ 2 a , where a is a constant. What is the value of a?

The required number of percent 30 is 40%.

In essence, percentages are fractions with a 100 as the remainder. We place the percent sign (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on an examination (75/100).

To write a proportion to answer the question "What percent of 30 is 12?", we can use the formula:

[tex]$\frac{part}{whole} = \frac{percent}{100}$[/tex]

In this case, we want to find the percent, which is the unknown value we will represent with "x". So we have:

[tex]$\frac{12}{30} = \frac{x}{100}$[/tex]

To solve for "x", we can cross-multiply and simplify:

[tex]$12 \cdot 100 = 30x$[/tex]

1200 = 30x

x = 40

Therefore, 12 is 40% of 30.

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The reflection of the graph of g(x) = log x about the x-axis is the graph of f(x) = log x.

Let's first review the graph of g(x) = log x to see how this works. The collection of all points (x, y) in the coordinate plane where y = log x is known as the graph of g(x).

The point (1, 0) is where the graph of g(x) passes. It is an ascending curve with a positive infinity as it approaches positive infinity as x approaches infinity.

Let's now examine the f(x) = log x graph. The collection of all (x, y) coordinate plane points where y = log x exists is the graph of f(x).

The logarithm property that states: log a (1/b) = log a to determine the relationship between the graphs of f(x) and g(x) (b) To rewrite f(x) as follows using this property: f(x) = log x = log (1/x)

This demonstrates that the negative logarithm of x, or the logarithm of 1/x, is what f(x) is. As a result, the graph of f(x) and g(x) are identical, with the f(x) graph being reflected about the x-axis.

The graph of f(x) = log x is a mirror of the graph of g(x) = log x about the x-axis, which is the answer to the question.

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The first six terms of the sequence defined by each of these recurrence relations and initial conditions are

a) -1, 2, -4, 8, -16, 32.

b) 2, -1, -3, -2, 1, 3.

c) 1, 3, 9, 27, 81, 243.

a) The first recurrence relation is given by an = -2an-1 with an initial condition of a0 = -1. To find the first six terms of this sequence, we need to use the recurrence relation to generate each term, starting with the initial condition. Using the formula, we can find:

a1 = -2a0 = -2(-1) = 2

a2 = -2a1 = -2(2) = -4

a3 = -2a2 = -2(-4) = 8

a4 = -2a3 = -2(8) = -16

a5 = -2a4 = -2(-16) = 32

a6 = -2a5 = -2(32) = -64

Therefore, the first six terms of the sequence defined by an = -2an-1 with a0 = -1 are: -1, 2, -4, 8, -16, 32.

b) The second recurrence relation is given by an = an-1 - an-2 with initial conditions a0 = 2 and a1 = -1. To find the first six terms of this sequence, we need to use the recurrence relation to generate each term, starting with the initial conditions. Using the formula, we can find:

a2 = a1 - a0 = -1 - 2 = -3

a3 = a2 - a1 = -3 - (-1) = -2

a4 = a3 - a2 = -2 - (-3) = 1

a5 = a4 - a3 = 1 - (-2) = 3

a6 = a5 - a4 = 3 - 1 = 2

Therefore, the first six terms of the sequence defined by an = an-1 - an-2 with a0 = 2 and a1 = -1 are: 2, -1, -3, -2, 1, 3.

c) The third recurrence relation is given by an = 3a2n-1 with an initial condition of a0 = 1. To find the first six terms of this sequence, we need to use the recurrence relation to generate each term, starting with the initial condition. Using the formula, we can find:

a1 = 3a0 = 3(1) = 3

a2 = 3a3 = 3(3) = 9

a3 = 3a2 = 3(9) = 27

a4 = 3a7 = 3(27) = 81

a5 = 3a14 = 3(81) = 243

a6 = 3a29 = 3(243) = 729

Therefore, the first six terms of the sequence defined by an = 3a2n-1 with a0 = 1 are: 1, 3, 9, 27, 81, 243.

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The sample space of the game is: S = {1, 2, 3, 4, 5, 6}.

The idea of probability describes the possibility of an event happening.

We frequently have to make forecasts about the future in real life.

We may or may not be aware of the outcome of an event.

When this happens, we declare that there is a chance the event will take place.

In summary, probability has a wide range of fantastic applications in entertainment, business, and this recently expanding branch of artificial intelligence.

The probability formula can be used to determine the likelihood of an event by only dividing the favorable number of possibilities by the entire number of possible outcomes.

S = {1, 2, 3, 4, 5, 6}

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500

because 6.25x 80=500, so that gives u the answer. I hope this helps u

To find the length of the altitude drawn from ∠F to the opposite side, we can use the formula for the area of a triangle:

A = (1/2)bh

where A is the area of the triangle, b is the length of the base, and h is the length of the altitude.

We know that the base of the triangle is EF, which has a length of 5. To find the altitude, we need to first find the length of the other side of the triangle. We can use the Law of Cosines to do this:

from the question:

where E is the angle opposite side EF. Substituting the given values, we get

[tex]16^2=DF^2+5^2-2DF5cos(55)[/tex]

[tex]DF^2[/tex]- 10DF×cos(55) + 231 = 0

Solving for DF using the quadratic formula, we get:

DF = (10cos(55) ± sqrt((10cos[tex](55))^2[/tex] - 4×231))/2

DF ≈ 12.3 (since we want a positive solution)

Now we can use the formula for the area of a triangle:

A = (1/2)bh

where b = 5 and h is the altitude drawn from ∠F to the opposite side.

To find h, we notice that ΔDEF can be split into two right triangles by drawing the altitude from ∠E to the opposite side. Let the foot of the altitude from ∠F to EF be point P, and let the foot of the altitude from ∠E to DF be point Q. Then we have:

sin(55) = PQ/16 (using the definition of sine)

cos(55) = PQ/5 (using the definition of cosine)

Solving for PQ in each equation and setting them equal to each other, we get:

PQ = 16×sin(55) = 13.0

Now we can use the formula for the area of a triangle:

A = (1/2)bh = (1/2)(5)(13.0) ≈ 32.5

Therefore, the area of ΔDEF is approximately 32.5 square units.

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The dimensions of the cylindrical can that will minimize the cost of the metal to manufacture it is 0.04 m and 0.027 m for height and radius respectively.

The given information of the question is that we have to create a cylindrical can that holds 1.4 litres of oil and we have to find the dimensions that will minimize the cost of the metal to manufacture the can.

We will solve the given problem through Lagrange Multipliers method.

Steps for solving the given problem are as follows:

Step 1: Let us assume that the cylindrical can has radius r and height h.

Therefore, we have to find the dimensions of r and h to minimize the cost of the metal.

Step 2: The total surface area (SA) of the cylindrical can is given as: SA = 2πr² + 2πrh

This equation represents the cost of the metal to manufacture the cylindrical can.

Step 3: The volume of the cylindrical can is given as: V = πr²h = 1.4 litres.

Now, let us convert 1.4 litres into cubic metres.

1 litre = 10⁻³ cubic metres 1.4 litres = 1.4 × 10⁻³ cubic metres

V = 1.4 × 10⁻³ = πr²h

Therefore, h = (1.4 × 10⁻³)/(πr²)

Step 4: Now, we have to use the Lagrange Multipliers method to find the dimensions that will minimize the cost of the metal.

Let us assume that C is the cost of the metal.

C = k(2πr² + 2πrh)

This is the objective function.

Now, let us assume that f is the constraint function.

f = πr²h - 1.4 × 10⁻³

This is the constraint function.

Step 5 : The next step is to find the partial derivatives of both the objective function and the constraint function with respect to r, h and λ (Lagrange Multiplier).

∂C/∂r = 4πrk + 2πh∂C/∂h

= 2πr(k + λ) + 2πr²∂C/∂λ

= f∂f/∂r

= 2πrh∂f/∂h

= πr²∂f/∂λ

= 0

Step 6: Now, we have to solve these equations and find the values of r and h that minimize the cost of the metal.

4πrk + 2πh = 2πr(k + λ) + 2πr²......(1)πr²h = 1.4 × 10⁻³......(2)

2πrh = λπr²......(3)

Substitute (3) in (1) and simplify it.

4πrk + 2πh = 2πr(k + λ) + 2πr²2πr(k + λ) + λπr² = 2πr² + 2πhλr² = 2h/k

Substitute λr² = 2h/k in (2) and simplify it.

π(2h/k) = 1.4 × 10⁻³h

= (1.4 × 10⁻³)(k/2π)π(2/k)(1.4 × 10⁻³)(k/2π)

= 1.4 × 10⁻³r²

= 1.4 × 10⁻³/(2πh/k)

= 0.00001003h

= 0.04 m and r

= 0.027 m.

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The amount to be paid is more on credit card 2 is more, it must be paid first.

Card 1:

Current balance = $8,312.69

Annual percentage rate APR = 24.16%

Credit limit = $10,000.

Used amount = $10,000 - $8,312.69

Used amount = 1687.31

A = P[tex](1 + r/n)^{nt}[/tex]

P = $1687.31

r = 24.16% = 0.2416

Take n = 1 and time = 1 year.

A =  1687.31*[tex](1 + 0.2416/n)^{1*1}[/tex]

A = 1687.31 * 1.2416

A = $2094.96

For Card 2:

Current balance = $1,180.34

APR = 21.15%

Credit limit = $75,00

Used amount = $75,00 - $1,180.34

Used amount = $6319.66

A = 6319.66*[tex](1 + 0.2115/n)^{1*1}[/tex]

A = 6319.66 * 1.2115

A = $7656.26

As the amount to be paid is more on credit card 2 is more, it must be paid first.

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Answer:

y(t) = 2t^3 - t^2 - t + 2.

Step-by-step explanation:

first need to integrate the equation twice with respect to t. Integrating the right-hand side of the equation gives:

y'(t) = 6t^2 - 2t + C1, where C1 is the constant of integration.

Integrating again gives:

y(t) = 2t^3 - t^2 + C1 t + C2, where C2 is the second constant of integration.

So the general solution is:

y(t) = 2t^3 - t^2 + C1 t + C2, where C1 and C2 are constants.

To find the particular solution that satisfies y(0) = 2 and y(1) = 4, we can use these conditions to solve for the constants C1 and C2.

First, we use the condition y(0) = 2:

y(0) = 2 = 2(0)^3 - (0)^2 + C1(0) + C2

Simplifying, we get:

C2 = 2

Next, we use the condition y(1) = 4:

y(1) = 4 = 2(1)^3 - (1)^2 + C1(1) + 2

Simplifying, we get:

C1 = 2 - 2(1)^3 + (1)^2 - 2 = -1

Therefore, the particular solution that satisfies y(0) = 2 and y(1) = 4 is:

y(t) = 2t^3 - t^2 - t + 2.

The general solution of the differential equation is y (t) = 2t^3 - t^2 + At + B, where A and B are the constants of integration.

The particular solution is y (t) = 2t^3 - t^2 + t + 2.

The general solution of the given differential equation y" (t) = 12t – 2 can be obtained by integrating both sides of the equation twice.

First, we integrate both sides with respect to t:

∫y" (t) dt = ∫(12t – 2) dt

y' (t) = 6t^2 - 2t + A

Next, we integrate both sides again with respect to t:

∫y' (t) dt = ∫(6t^2 - 2t + A) dt

y (t) = 2t^3 - t^2 + At + B

Therefore, the general solution of the differential equation is y (t) = 2t^3 - t^2 + At + B, where A and B are the constants of integration.

To find the particular solution for which y(0) = 2 and y(1) = 4, we can plug in the given values of t and y into the general solution and solve for the constants A and B.

When t = 0 and y = 2:

2 = 2(0)^3 - (0)^2 + A(0) + B

B = 2

When t = 1 and y = 4:

4 = 2(1)^3 - (1)^2 + A(1) + 2

A = 1

Therefore, the particular solution is y (t) = 2t^3 - t^2 + t + 2.

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Answer:

3 and (-3) are the values of x

Step-by-step explanation:

RAMP stands for Reading the Bible daily, Attending church, Memorizing Scripture, and Praying.

The simplified form of the expression is  [tex]-5-2\sqrt6[/tex].

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.

Here the given radical expression is ,

=> [tex]\frac{\sqrt2+\sqrt3}{\sqrt2-\sqrt3}[/tex]

To simplify this expression we need to multiply and divide by [tex]\sqrt2+\sqrt3[/tex] then,

=> [tex]\frac{\sqrt2+\sqrt3}{\sqrt2-\sqrt3}\times\frac{\sqrt2+\sqrt3}{\sqrt2+\sqrt3}[/tex]

=> [tex]\frac{(\sqrt2+\sqrt3)^2}{(\sqrt2)^2-(\sqrt3)^2}[/tex]

=> [tex]\frac{(\sqrt2)^2+(\sqrt3)^2+2\sqrt2\sqrt3}{2-3}[/tex]

=>[tex]\frac{2+3+2\sqrt6}{-1}[/tex]

=> [tex]-5-2\sqrt6[/tex]

Hence the simplified form of the expression is  [tex]-5-2\sqrt6[/tex].

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The solution of the differential equation ty − y = t2e−t, t > 0 is y = −t2e−t.

To solve the differential equation ty − y = t2e−t, t > 0, we can use the method of variation of parameters. Here are the steps to solve this equation:

1. First, we need to find the general solution of the homogeneous equation ty' − y = 0. This can be written as y' = y/t.

2. Separating the variables and integrating both sides gives us ln(y) = ln(t) + C, or y = Ct.

3. Next, we need to find a particular solution of the non-homogeneous equation. We can do this using the method of variation of parameters, by assuming that the particular solution is of the form y = u(t)t, where u(t) is a function of t.

4. Substituting this into the original equation and simplifying gives us tu' = t2e−t.

5. Separating the variables and integrating both sides gives us u = −te−t + C.

6. The general solution of the original equation is then y = Ct − t2e−t.

7. Since we are given that t > 0, we can set C = 0 and find the particular solution y = −t2e−t.

Therefore, the solution of the differential equation ty − y = t2e−t, t > 0 is y = −t2e−t.

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A triangular pyramid has 3 faces, 6 edges, and 4 vertices.

Faces: A triangular pyramid has 3 faces. These faces are triangular in shape.
Edges: A triangular pyramid has 6 edges. These edges connect the 3 triangular faces and the vertex of the pyramid.
Vertices: A triangular pyramid has 4 vertices. These are the 3 points that make up the triangular base and the point at the top of the pyramid.
To remember these numbers easily, use the phrase "3-6-4": 3 faces, 6 edges, and 4 vertices.
A triangular pyramid is a polyhedron, and it has a base that is a triangle. It is made up of four faces, six edges, and four vertices.  A pyramid is a three-dimensional figure that has a base, sides, and an apex.

The number of faces, edges, and vertices of a triangular pyramid is calculated as follows :Faces The triangular pyramid has four faces, which include one base triangle and three other triangles that converge at the top point of the pyramid .Edges A triangular pyramid has six edges. Three of these edges are part of the base triangle, while the other three are formed from the convergence of the three other sides of the pyramid at the apex .Vertices A triangular pyramid has four vertices.

Three of these vertices are at the base triangle's corners, while the fourth vertex is located at the apex of the pyramid, where all of the sides converge .

The following image shows a triangular pyramid, and you can see the base, edges, and vertices of the pyramid. Thus, a triangular pyramid has four faces, six edges, and four vertices.

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The highest possible score Devon could have achieved on her vault is 8.70 points.In Devon's case, the judges deducted 0.75 points from her score, resulting in a final score of 7.95 points and a highest possible score of 8.70 points.

This score is calculated by taking the highest possible score of 10.00 points, and subtracting the 0.75 points that the judges deducted from Devon's performance due to her mistakes. Mathematically, this can be represented as 10.00 - 0.75 = 8.70.The score of 10.00 points is the maximum score that a gymnast can receive for a vault and is based off of the judging panel's evaluation of the gymnast's form, technique, and execution. Any deductions from this score are based on mistakes made by the gymnast during the routine, such as a lack of control or a step on the landing. In Devon's case, the judges deducted 0.75 points from her score, resulting in a final score of 7.95 points and a highest possible score of 8.70 points.

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Answer:

Step-by-step explanation:

Thousandth is the third number after the decimal point, so we look at the number after it to determine if we move up

4 and below: keep it the same

5 and above: increase it

6.3579

the number after it is 9, so we increase it.

Therefore the answer is:

6.358