In the diagram below, ST is parallel to PQ ​ . If ST is 5 more than PS, SR=10, and PQ=15, find the length of PS . Figures are not necessarily drawn to scale. State your answer in simplest radical form, if necessary.

Answer:

Y=5

Step-by-step explanation:

The right response is that the two linear equation never intersect , because the graph of these two linear equation will be two parallel lines.

How many types of solution are there for two linear equations ?

There are 2 types of solution :
Consistent :

A consistent system is said to be an independent system if it has a single solution.

A consistent system is said to be a dependent system if the equations have the same slope and the same y-intercepts. In other words, the lines coincide, so the equations represent the same line. Each point on the line represents a pair of coordinates that fits the system. So there are an infinite number of solutions.

Non-consistent :

Another type of system of linear equations is the inconsistent system, in which the equations represent two parallel lines. The lines have the same slope and different y-intercepts. There are no common points for both lines; therefore, there is no solution to the system and if we draw the graph of these equations then the graphs of both equation becomes parallel to each other.

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The two linear equations never intersect.

When a system of two linear equations in two variables has no solution, it means that there is no set of values for the variables that satisfies both equations simultaneously. Geometrically, this corresponds to the two lines represented by the equations being parallel. Since parallel lines never intersect, the statement "The two linear equations never intersect" accurately describes the situation.

If the two linear equations were graphed on a coordinate plane, they would appear as two distinct lines that run parallel to each other without ever crossing or intersecting. This indicates that there is no common point of intersection between the lines, and therefore no solution exists for the system of equations.

It is important to note that this scenario is different from the case where the two linear equations represent the same line. In that case, the equations would be equivalent, and every point on the line would satisfy both equations. However, when there is no solution, it means that the lines do not share any common points and never intersect.

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The slopes of GH, HI, IJ, and JG include the following:

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the formula for the slope of a line, we have the following;

Slope GH = (-3 + 9)/(-4 + 7)

Slope GH = 6/3

Slope GH = 2.

Slope HI = (5 + 3)/(-6 + 4)

Slope HI = -8/2

Slope HI = -4.

Slope IJ = (-1 - 5)/(-9 + 6)

Slope IJ = -6/-3

Slope IJ = 2.

Slope JG = (-9 + 1)/(-7 + 9)

Slope JG = -8/2

Slope JG = -4.

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Answer:

B.

4 2

Step-by-step explanation:

Simplify the expression.

9-fraction

The result can be shown in multiple forms.

Exact Form:

8

+

2

√

2

Decimal Form:

10.82842712-square root

…

Simplify the expression.

8- subtracting

Simplify the expression.

12-addition

Evaluate.

30

=

30

The equation is always true.

True

Answer: c

Step-by-step explanation:

c

The solutions of the quadratic equation x^2 + 3x - 10 = 0 are x = 4 and x = -1.

The solution of the quadratic equation x^2 + 3x - 10 = 0 can be found by using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

Where (a, b, and c) are 1, 3, and -10

So, the solutions of the equation x^2 + 3x - 10 = 0 are:

x = (-3 ± √(3^2 - 4(1)(-10)) ) / 2(1)

x = (-3 ± √(9 + 40)) / 2

x = (-3 ± √49) / 2

x = (-3 ± 7) / 2

x = (4, -1)

Complete question:

Which of the following is the solution of the quadratic equation x^2 - 3x − 10 = 0?

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Answer:

The slope is 20x

The y-intercept is 175

The absolute maximum of f(x) is e^(2pi), which occurs at x = 2pi, and the absolute minimum of f(x) is approximately -1.30, which occurs at x = 5*pi/4

a. To find the absolute maximum and minimum values of f(x), we can use the first derivative test and the endpoints of the given interval.

First, we find the first derivative of f(x):

f'(x) = e^xcos(x) - e^xsin(x)

Then, we find the critical points of f(x) by setting f'(x) = 0:

e^xcos(x) - e^xsin(x) = 0

e^x(cos(x) - sin(x)) = 0

cos(x) = sin(x)

x = pi/4 or x = 5*pi/4

Note that these critical points are in the domain [0, 2*pi].

Next, we find the second derivative of f(x):

f''(x) = -2e^xsin(x)

We can see that f''(x) is negative for x in [0, pi/2) and (3pi/2, 2pi], and f''(x) is positive for x in (pi/2, 3*pi/2).

Therefore, x = pi/4 is a relative maximum of f(x), and x = 5*pi/4 is a relative minimum of f(x). To find the absolute maximum and minimum of f(x), we compare the values of f(x) at the critical points and the endpoints of the domain:

f(0) = e^0cos(0) = 1

f(2pi) = e^(2pi)cos(2pi) = e^(2pi)

f(pi/4) = e^(pi/4)cos(pi/4) ≈ 1.30

f(5pi/4) = e^(5*pi/4)cos(5pi/4) ≈ -1.30

Therefore, the absolute maximum of f(x) is e^(2pi), which occurs at x = 2pi, and the absolute minimum of f(x) is approximately -1.30, which occurs at x = 5*pi/4.

b. To find the intervals on which f(x) is increasing, we look at the sign of f'(x) on the domain [0, 2pi]. We know that f'(x) = 0 at x = pi/4 and x = 5pi/4, so we can use a sign chart for f'(x) to determine the intervals of increase:

x 0 pi/4 5*pi/4 2*pi

f'(x) -e^0 0 0 e^(2*pi)

f(x) increasing relative max relative min decreasing

Therefore, f(x) is increasing on the interval [0, pi/4) and decreasing on the interval (pi/4, 2*pi].

c. To find the x-coordinate of each point of inflection of the graph of f, we need to find where the concavity of f changes. We know that the second derivative of f(x) is f''(x) = -2e^xsin(x), which changes sign at x = pi/2 and x = 3*pi/2.

Therefore, the point (pi/2, f(pi/2)) and the point (3pi/2, f(3pi/2)) are the points of inflection of the graph of f.

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The length of the third side of the triangle with a perimeter of 7x + 8 is 2x + 3

An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.

A triangle is a polygon that has three sides. The perimeter of a triangle is the sum of all the three sides.

Hence:

Perimeter of triangle = side 1 + side 2 + side 3

A triangle has a perimeter of 7x + 8. the first side of the triangle has a length of 3x, and the second side has a length of 2x − 5.

Hence:

Perimeter of triangle = side 1 + side 2 + side 3

7x + 8 = 3x + (2x - 5) + side 3

7x + 8 = (5x - 5) + side 3

side 3 = 7x + 8 - (5x - 5)

side 3 = 2x + 13

The length of the third side is 2x + 3

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A second linearly independent solution of y₂ is \(-\frac{1}{6x^3}\)

The general Equation is y" + P(x)y' + q(x)y = 0 ...............(i)

where P(x), Q(x) are continues in the internal I ≤ R.

If y₁(x) is a solution of equation 1 in I then y₁(x) ≠ 0.

Then y₂(x) = y₁(x)\(\int{\frac{e^{-\intP(x)dx}}{(y_{1}x)^2}}dx\) is another solution.

The differential equation is x²y" + xy' – 9y = 0 where x > 0.

As y₁(x) = x³ is one solution of differential equation.

Divide throughout by (x²) to given differential equation.

1/x² (x²y" + xy' – 9y = 0)

y" + (y'/x) – (9/x²)y = 0 ................(ii)

By comparing equation (i) & (ii) we get:

p(x)=1/x , q(x)= –are continuous for x>0

So, another solution,

y₂(x) = y₁(x)\(\int{\frac{e^{-\intP(x)dx}}{(y_{1}x)^2}}dx\)

Now putting the values of P(x) And Q(x)

y₂(x) = \(x^3\int\limits {\frac{e^{\int(1/x)dx} }{(x^3)^2}} \, dx\)

y₂(x) = \(x^3\int\limits {\frac{\frac{1}{x} }{x^6} }} \, dx\)

y₂(x) = \(x^3\int\limits {\frac{1}{x^7} }} \, dx\)

y₂(x) = \(x^3\int\limits {x^-7} } \, dx\)

y₂(x) = \(x^3\left[\frac{x^{-7+1}}{-7+1}\right]\)

y₂(x) = \(-\frac{1}{6}(x^3\times x^{-6})\)

y₂(x) = \(-\frac{1}{6x^3}\)

So, the answer of this question is \(-\frac{1}{6x^3}\).

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The monthly payment required to amortize a loan of $40,000 over 15 years, with an interest rate of 6% per year, and monthly compounding, is approximately $331.13.

To calculate the monthly payment, we can use the formula for the amortization of a loan, which is:

Monthly Payment = P * (r * (1 + r)^n) / ((1 + r)^n - 1),

where P is the principal amount (loan amount), r is the monthly interest rate, and n is the total number of payments.

Given:

Principal amount (P) = $40,000,

Annual interest rate = 6%,

Number of years (n) = 15.

First, we need to convert the annual interest rate to a monthly interest rate. Since interest is compounded monthly, the monthly interest rate (r) is calculated by dividing the annual interest rate by 12 and converting it to a decimal:

Monthly interest rate (r) = 6% / 12 / 100 = 0.005.

Next, we calculate the total number of payments (n) by multiplying the number of years by 12 (since there are 12 months in a year):

Total number of payments (n) = 15 years * 12 months/year = 180.

Now we can plug these values into the formula to calculate the monthly payment:

Monthly Payment = $40,000 * (0.005 * (1 + 0.005)^180) / ((1 + 0.005)^180 - 1).

Using a calculator or spreadsheet, we find that the monthly payment is approximately $331.13.

Therefore, the monthly payment required to amortize the loan of $40,000 over 15 years, with a 6% annual interest rate and monthly compounding, is approximately $331.13.

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What monthly payment is required to amortize a loan of $40,000 over 15 years if interest at the rate of 6%/year is charged on the unpaid balance and interest calculations are made at the end of each month?

A differential equation with some initial conditions is used to solve an initial value problem.

The required particular solution is given by the relation:

\($4y^{(3/2)} = 9e^{(-2x/3)} + 23\)

An initial value problem in multivariable calculus is an ordinary differential equation with an initial condition that specifies the value of the unknown function at a given point in the domain. In physics or other sciences, modeling a system frequently entails solving an initial value problem.

Let the given equation be \($y^{1/2} dy\ dx y^{3/2} = 1\), y(0) = 9

\($(\sqrt{y } ) y^{\prime}+\sqrt{(y^3\right\left) }=1\) …..(1)

Divide the given equation (1)  by \($\sqrt{ y} $\)  giving

\($y^{\prime}+y=y^{(-1 / 2)} \ldots(2)$\), which is in Bernoulli's form.

Put \($u=y^{(1+1 / 2)}=y^{(3 / 2)}$\)

Then \($(3 / 2) y^{(1 / 2)} \cdot y^{\prime}=u^{\prime}$\).

Multiply (2) by \($\sqrt{ } y$\) and we get

\(y^{(1 / 2)} y^{\prime}+y^{(3 / 2)}=1\)

(2/3) \(u^{\prime}+u=1$\) or \($u^{\prime}+(3 / 2) y=3 / 2$\),

which is a first order linear equation with an integrating factor

exp[Int{(2/3)dx}] = exp(2x/3) and a general solution is

\(u. $e^{(2 x / 3)}=(3 / 2) \ln \[\left[e^{(2 x / 3)} d x\right]+c\right.$\)  or

\(\mathrm{y}^{(3 / 2)} \cdot \mathrm{e}^{(2x / 3)}=(9 / 4) \mathrm{e}^{(2x / 3)}+{c}\)

To obtain the particular solution satisfying y(0) = 4,

put x = 0, y = 4, then

8 = (9/4) + c

c = (23/4)

Hence, the required particular solution is given by the relation:

\($4y^{(3/2)} = 9e^{(-2x/3)} + 23\)

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The probability to determine the time needed to complete the project, we simply added the time required for activities 1 and 2.

1 (1): the chance that a given event will occur

 (2): the ratio of the number of outcomes in an exhaustive set of equally     likely outcomes that produce a given event to the total number of possible outcomes a branch of mathematics concerned with the study of probabilities

2 : something (such as an event or circumstance) that is probable

3: the quality or state of being probable

4: a logical relation between statements such that evidence confirming one confirms the other to some degree

The best-case scenario's calculation of the project's completion time is displayed below;

= Week spent on Activities A1 +  Week spent on Activities A2.

= 5 weeks plus 7 weeks.

= 12

To determine the time needed to complete the project, we simply added the time required for activities 1 and 2.

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Using the product rule of exponents, the expression can be simplified to 3²⁰/25.

What is expression?
Expression in math is a combination of numbers, symbols, and other mathematical terms used to represent a quantity or an operation. It can be defined as a statement that uses mathematical symbols to form a mathematical equation or to express a mathematical relationship. Expressions are used to calculate the value of a mathematical equation and to determine the solution to a problem. They can also be used to represent relationships between different variables.


The given expression can be simplified using the product rule of exponents which states that when two terms with the same base are multiplied together, the exponents can be added together.

Therefore, 3¹¹/5 ÷ 3⁻⁹/⁵ can be rewritten as 3¹¹/5 x 3⁻⁹/⁵

Using the product rule of exponents, the expression can be simplified to 3²⁰/25.

Therefore, the simplified expression is 3²⁰/25.

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Complete questions as follows-
Simplify the following expression. 3^11/5 divided by 3^-9/5

Answer:

Im so depresd Dont do not him me up

Step-by-step explanation:

Answer:

what? uhm okay?

The mass of the decoration is 200 kg and for each passenger car is 550 kg

From the question, we have the following parameters that can be used in our computation:

These can be represented as

(6, 3500) and (4, 2400)

The slope of the above points represent the mass of each passenger car

This is calculated as

Slope = Difference in mass/Difference in number of cars

So, we have

Slope = (3500 - 2400)/(6 - 4)

Evaluate

Slope = 550

When there are no passenger cars in the train, we have

(0, Mass of decoration)

Using the slope formula, we have

Slope = (Mass of decoration - 3500)/(0 - 6)

So, we have

Slope = (Mass of decoration - 3500)/(-6)

This gives

(Mass of decoration - 3500)/(-6) = 550

Cross multiply

Mass of decoration - 3500 = -3300

Add 3500 to both sides

Mass of decoration = 200

Hence, the mass of decoration is 200 kg

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Answer:

What are we supposed to do on this

Step-by-step explanation:

Answer:   the dilated point will be 2 units at the right of P, and 3 units above P.

Step-by-step explanation:

Arithmetic average return of the company is 2.57%.Geometric average return of the company is 13%.Variance of the company is 56.Standard deviation of the company is 7.48%.

Given, Returns of the company for the last few years are 5%, 10%, -15%, 20%, -12%, 22%, 8%
Arithmetic Average return:
Arithmetic Average return = (sum of all returns) / (total number of returns)
Arithmetic Average return = (5 + 10 - 15 + 20 - 12 + 22 + 8) / 7= 18 / 7= 2.57
Therefore, the arithmetic average return of the company is 2.57%.
Geometric average return:
Geometric average return = [(1+R1) * (1+R2) * (1+R3) * …….. * (1+Rn)]1/n - 1
Geometric average return = [(1.05) * (1.1) * (0.85) * (1.2) * (0.88) * (1.22) * (1.08)]1/7 - 1= 0.13
Therefore, the geometric average return of the company is 13%.
Variance:
Variance = (sum of (return - mean return)2) / (total number of returns)
Mean return = (5 + 10 - 15 + 20 - 12 + 22 + 8) / 7= 18 / 7= 2.57
Variance = [(5-2.57)2 + (10-2.57)2 + (-15-2.57)2 + (20-2.57)2 + (-12-2.57)2 + (22-2.57)2 + (8-2.57)2] / 7= 392.12 / 7= 56
Therefore, the variance of the company is 56.
Standard Deviation:
Standard Deviation = Square root of Variance
Standard Deviation = √56= 7.48
Therefore, the standard deviation of the company is 7.48%.

Thus, Arithmetic average return of the company is 2.57%.Geometric average return of the company is 13%.Variance of the company is 56.Standard deviation of the company is 7.48%.

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The first blank is leaning to the left, the second blank is in the middle, and the third blank has 9 alternatives that are legitimate.

We've done that.

Data from Gretchen can be characterized as having a __ shape. As a result, the __ will serve as this data set's best measure of center.

For the best measure of center, the real value is .

The word in the blank must be identified using the provided diagram.

What is left that is skewed?

A left-skewing distribution has a long left tail. Left-skewed distributions are another name for negatively skewed distributions. This is caused by the number line's huge negative tail. Furthermore, the peak is offset from the mean. A right-skewed distribution has a long right tail.

Consequently, the appropriate choices are,

the third blank is 9, the second blank is middle, and the first blank is tilted to the left.

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The distance is always positive.

We want the distance between -1 and 1.

Lets look at a number line:

From -1 to 1, we can see that there are 2 units.

Hence, the distance between -1 and 1 is TWO

From the diagram, we can see that the angle of interest is opposite to a side of length 15 and adjacent to a side of length 8. Therefore, tangent of 62° is equal to opposite (15) divided by adjacent (8), which is approximately 1.875.

Answer:

2661,62 ml

Step-by-step explanation:

Answer:

2661,62 milliliters are in 90 ounces

Step-by-step explanation:

If you're using US customary fluid ounces, your 90 fl oz is equal to 2661,62 ml when rounded off.

Answer:

number 5 is a function but number 6 is not

Step-by-step explanation:

Hence, the area of the outer ripple increases with time as t increases in seconds and it is represented by 0.04t².

Given: The radius r (in feet) of the outer ripple is given by r(t) = 0.2t, where t is time in seconds after the pebble strikes the water.

Area function : A(r) = r²To find and interpret (A ∘ r)(t).We know that (A ∘ r)(t) = A(r(t))Substitute r(t) in A(r) to find (A ∘ r)(t).(A ∘ r)(t) = A(r(t))=(r(t))²= [0.2t]²= 0.04t²

Therefore, (A ∘ r)(t) = 0.04t².Interpretation: The expression (A ∘ r)(t) represents the area of the outer ripple as a function of time t, which can be found by substituting r(t) into the area function.

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Alternate interior angles and interior angles are both types of angles that are formed by two parallel lines and a transversal intersecting them.

Interior angles are the angles that are formed on the inside of the parallel lines by the transversal. Alternate interior angles, on the other hand, are a pair of non-adjacent interior angles that are located on opposite sides of the transversal and on the inside of the parallel lines. In other words, alternate interior angles are interior angles that are not adjacent to the angle in question. The key difference between alternate interior angles and interior angles is their location. Interior angles are any angles that are formed on the inside of the parallel lines by the transversal, while alternate interior angles specifically refer to a pair of non-adjacent interior angles that are on opposite sides of the transversal. Understanding the difference between these two types of angles can be helpful in solving geometric problems involving parallel lines and transversals.

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Answer:

80

Step-by-step explanation:

\(f(7)=2(7)^{2} -3(7)+3\)

\(= 2(49)-21+3\\=98-21+3\\=80\\\)

Answer:It is what it is

Step-by-step explanation:

Answer:

Parallel lines do not intersect.

Parallel lines are like an equal sign

========================

They go Straight across

While perpendicular lines intersect.

A lot of squares are parallelograms, they only have parallel lines.

Hope this helps

~ヾ(・ω・)

The mean/standard error of the sampling distribution of the proportion is 0.0111.

Its root-mean The square root of the mean of the squares of all the values in a series calculated from the arithmetic mean is the square deviation, also referred to as the standard deviation and denoted by the symbol.

The standard deviation reveals the degree of data dispersion. It expresses how far away from the mean each observed value is.

Almost 95% of the values in any distribution will be within two standard deviations of the mean. The degree of data dispersion from the mean is described by the term "standard deviation" (or " σ").

The data tend to cluster around the mean when the standard deviation is low; when it is high, the data are more dispersed.

The formula to calculate the standard error of sampling distribution of sample proportion is:

\($ SE(p) =\sqrt{\frac{p(1-p)}{n} }\)

It is given that the bank believes that 8% of people who receive loans will not make payments on time. That is,

Population proportion, p =0.08

Sample size, n= 800

Using the formula defined :

\($ SE(p) =\sqrt{\frac{0.08(1-0.08)}{600} }\)

\($ SE(p) =\sqrt{0.000123}\)

SE(p) = 0.0111

Thus, the mean/standard error of sampling distribution of the proportion is 0.0111.

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