Use your own paper to plot the points M(–3, 2) A(5, 2) T(3, –4), and H(–5, –4) to create a parallelogram on a coordinate grid.

The equivalent equation to (2/3)x - 5/6 = (-5/12)x + 1/4 is x = 13/9.

To find an equation equivalent to the given equation, we can start by simplifying both sides and rearranging the terms. Let's go step by step:

Given equation: (2/3)x - 5/6 = (-5/12)x + 1/4

First, let's eliminate the fractions by multiplying the entire equation by the least common denominator (LCD) of the fractions involved. In this case, the LCD is 12.

12 * [(2/3)x - 5/6] = 12 * [(-5/12)x + 1/4]

Simplifying:

4x - 10 = -5x + 3

Now, let's gather like terms on each side of the equation:

4x + 5x = 3 + 10

Combining like terms:

9x = 13

Finally, to isolate x, divide both sides of the equation by 9:

(9x)/9 = 13/9

x = 13/9

So, the equivalent equation to (2/3)x - 5/6 = (-5/12)x + 1/4 is x = 13/9.

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Answer:

option C. 180 cars

Step-by-step explanation:

24 = 2

x = 15

cross multiply

2x = 24 × 15

2x = 360

x = 360/2

x = 180

Answer:

180

Step-by-step explanation:

Answer:

  2/15

Step-by-step explanation:

You want to know the fraction that is 2/3 of 1/5.

In this context, "of" means "times."

  2/3 of 1/5 = (2/3)×(1/5) = (2·1)/(3·5) = 2/15

2/15 of the pets are alley cats.

well, since the y-intercept is at -5, or namely when the line hits the y-axis is at -5, that's when x = 0, so the point is really (0 , -5), and we also know another point on the line, that is (-1 ,6), to get the equation of any straight line, we simply need two points off of it, so let's use those two

\(\stackrel{y-intercept}{(\stackrel{x_1}{0}~,~\stackrel{y_1}{-5})}\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{(-5)}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{0}}} \implies \cfrac{6 +5}{-1} \implies \cfrac{ 11 }{ -1 } \implies - 11\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{- 11}(x-\stackrel{x_1}{0}) \implies y +5 = - 11 ( x -0) \\\\\\ y+5=-11x\implies {\Large \begin{array}{llll} y=-11x-5 \end{array}}\)

The value of c>0 such that the average value of f(x) on the interval [-5,c] is equal to 0 is the x-coordinate of the point where the curve of f(x) crosses the x-axis for the first time in the interval [-5,∞).

To find the value of c>0 such that the average value of f(x) on the interval [-5,c] is equal to 0, we need to use the formula for the average value of a function:

avg(f) = (1/(b-a)) × ∫[a,b] f(x) dx

where a=-5, b=c, and avg(f) = 0.

Substituting these values, we get:

0 = (1/(c-(-5))) × ∫[-5,c] f(x) dx

Multiplying both sides by (c+5), we get:

0 = ∫[-5,c] f(x) dx

This means that the area under the curve of f(x) on the interval [-5,c] is 0. Geometrically, this implies that the curve must cross the x-axis at least once on the interval [-5,c].

Therefore, we need to find the value of c such that the equation f(x) = 0 has a solution on the interval [-5,c]. Since we do not know the specific function f(x), we cannot find the exact value of c. However, we can say that c must be greater than or equal to the x-coordinate of the point where the curve of f(x) crosses the x-axis for the first time in the interval [-5,∞).

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The probability that the sample mean differs from the population mean by 1.8mm and is rounded off to 4 decimal places is 0.8220

According to the given problem the mean diameter μ= 140 mm (population mean) and the standard deviation is σ=8mm

random sample size, n= 49 steel bolts is selected

Let the random variable that represents the diameter of steel bolts be denoted by x and from the problem we have x = 1.8mm

Let z = (x-μ) / (σ/√n )         (1)

using formula (1) and when the sample mean differs from the population mean by more than 1.8mm

z = 1.8/(8/√49 )

⇒z = 63/40 = 1.575

The probability that the sample mean will differ from the population mean by more than 1.8 mm

P( z > 1.575) = 1 - P(z< 1.575) = 1 - 0.178 = 0.822

The probability that the sample mean will differ from the population mean by more than 1.8 mm = 0.8220

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\( \fbox{(2,5)}\)

Hello, substitute all the given coordinates & see if RHS match with LHS

given equation,

y = 4x-3

First coordinate,

(x,y) = (2,5)

5= 4×2-3

5=5

Hence, first solution satisfies the given equation,

let's solve for rest other cordinates,

second coordinate,

(x,y) = (5,5)

5= 4×5-3

5 ≠ 17

does not satisfy,

third coordinate,

(x,y) = (4,5)

5= 4×4-3

5 ≠ 13

does not satisfy,

fourth coordinate,

(x,y) = (4,5)

5 = 4×3-3

5 ≠ 9

does not satisfy.

Hence the correct answer is (2,5)

\( \sf \small Thanks \: for \: joining \: brainly \: community! \)

Answer:

ya its A just got it right on the test happy end of the year guys hope yall have a good one

Step-by-step explanation:

From the given option, the expression that represents a perfect trinomial is x^2 – 6x + 9

The perfect square trinomial are expressed according to the expression

(a+b)²

From the given option, the expression that represents a perfect trinomial is x^2 – 6x + 9

Simplify

x^2 – 6x + 9

x^2-3x-3x+9
x(x-3)-3(x-3)

(x-3)(x-3) = (x-3)²

From the given option, the expression that represents a perfect trinomial is x^2 – 6x + 9

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Answer:

(x+5)²+(y+5)²=18

Step-by-step explanation:

r=√(-8+5)²+(-2+5)²=√(-3)²+(3)²=√9+9

=√18

the equation is :

(x+5)²+(y+5)²=18

Answer:

A. 15%

Step-by-step explanation:

There's no other parts of this so I wouldn't really know the answer.

Hope this helps though! :))

Answer:

12.5

Step-by-step explanation:

Answer:

45 i think

Step-by-step explanation:

If λ = 5 is a factor of the characteristic polynomial of matrix A, then 5 is an eigenvalue of A.

Given that λ = 5 is a factor of the characteristic polynomial of matrix A, we need to determine whether 5 is an eigenvalue of A or not. Definition of Characteristic Polynomial:

A matrix A is a linear transformation whose characteristic polynomial is given by;

p(x) = \text{det}(xI - A)

Definition of Eigenvalue:

Let A be a square matrix of order n and let λ be a scalar.

Then, λ is called an eigenvalue of A if there exists a non-zero vector x, such that

A \bold{x} = \lambda \bold{x}

For some non-zero vectors x is known as the eigenvector.

Now, let's prove if 5 is an eigenvalue of A, or not.

According to the question, λ = 5 is a factor of the characteristic polynomial of A.Therefore, p(5) = 0.

\Rightarrow \text{det}(5I - A) = 0

Consider the eigenvector x corresponding to the eigenvalue λ = 5;

\Rightarrow (A-5I)x = 0$$$$\Rightarrow A\bold{x} - 5\bold{x} = 0

\Rightarrow A\bold{x} = 5\bold{x}

Since A satisfies the equation for eigenvalue and eigenvector, 5 is an eigenvalue of matrix A.

Therefore, if λ = 5 is a factor of the characteristic polynomial of matrix A, then 5 is an eigenvalue of A.

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Answer:

x=9-y^3

y=^3\(\sqrt{9-x\\}\)

Step-by-step explanation:

Answer:

46.80

Step-by-step explanation:

because 45/4%=1.80 and 45+1.80=46.80

Answer:

10

Step-by-step explanation:

Answer:

The answer is 10.

Step-by-step explanation:

25 - 5 = 20

20 - 10 = 10.

There are 273,028 people who live in the region.

To find the number of people who live in the region, we need to calculate the area of the region and then multiply it by the population density.

The area of a circle with radius r is given by the formula \(A = \pi r^2.\)Therefore, the area of the region with a 10-mile radius is:

\(A = \pi r^2 =\pi (10^2)\) = 100π square miles

The number of people who live in this region can be found by multiplying the area by the population density:

Number of people = Population density x Area

= 869 people/square mile x 100π square miles

= 86900π people

Using a calculator, we can approximate this to:

Number of people ≈ 273,028.4

Therefore, there are approximately 273,028 people who live in the region with a 10-mile radius and a population density of 869 people per square mile.

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Using a moving average of order p = 3, a forecast for time period 6 is 46.

The moving average is a mathematical method for calculating a series of averages using various subsets of the full dataset. It is also known as a rolling average or a running average. The moving average smoothes the underlying data and lowers the noise level, allowing us to visualize the underlying patterns and patterns more readily. In other words, a moving average is a mathematical calculation that employs the average of a subset of data at various time intervals to determine trends, eliminate noise, and better forecast future outcomes. Answer: 46.

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342 = 2, 3, 6, 9

191 = no factors

1235 = 5

40320 = 2, 4, 8

16 = 2, 4, 8

78448 = 2, 4, 8

588 = 2, 4 , 12

67 = no factors

925 = 5

60043 = no factors

3663 = 3, 6

350 = 5

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Answer:

Step-by-step explanation:

n/3 - 2 = 4             Add 2 to both sides

n/3 - 2 + 2 = 4+2    Combine

n/3 = 6                  Multiply both sides by 3

3*n/3 = 6 * 3

n = 18

The equation in the vertex form will be y = (x + b/2a)² - b²/4a² + c/a and the equation in the standard form will be ax² + bx + c = 0.

The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.

Convert the standard equation into a vertex form, then we have

x² + (b/a)x + (c/a) = 0

x² + (b/a)x + b²/4a² - b²/4a² + c/a = 0

(x + b/2a)² - b²/4a² + c/a = 0

Put h = - b/2a and k = - b²/4a² + c/a, where (h, k) be the vertex of the parabola. Then the equation will be

(x - h)² + k = 0

The function written in vertex form will be y = (x - h)² + k and in the standard form will be ax² + bx + c = 0.

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

Work Shown:

m = -5 is the slope

(x1,y1) = (-3,-7) is the point the line goes through

Plug this into the point slope form below and simplify.

y - y1 = m(x - x1)

y - (-7) = -5(x - (-3))

y + 7 = -5(x + 3)

Side note: If we solved for y, we'd get y = -5x - 22 showing that -22 is the y intercept.

x - 3y = 3

Line perpendicular ,is found by formula m•m' = -1

Then first find Slope m = x - term / -y- term = 1/--3 = 1/3

Now find perpendicular slope m' = -1/(1/3) = -3

Following find ,y- intercept b

b = Y - m'X

b = -9 - (-3)•5

. = -9 + 15 = 6

Then ,now write

Y = -3X + 6

Answer is, equation

Y = -3X + 6

Answer:

is 11

Step-by-step explanation:

Answer:

A fraction with non-zero denominators is called a rational number. The number ½ is a rational number because it is read as integer 1 divided by integer 2. All the numbers that are not rational are called irrational.

...

Solved Examples.

Decimal Number Fraction Rational Number

0.09 1/11 yes

√ 3 ? No

The angle 1 can be named as follows:

∠RST

∠TSR

∠S

There are various ways to name an angles. You can name an angle by its vertex, by the three points of the angle (the middle point must be the vertex), or by a letter or number written within the opening of the angle.

Therefore, let's name the angle 1 indicated on the diagram as follows:

Hence, the different ways to name the angle 1 is as follows:

∠RST or ∠TSR

Or

∠S

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The small business will pay approximately $14,280 in interest over the 7-year loan term.

To calculate the interest, we can use the formula for compound interest:

\(\( A = P \times (1 + r/n)^{nt} \)\)

Where:

- A is the final amount (loan + interest)

- P is the principal amount (loan amount)

- r is the interest rate per period (4% in this case)

- n is the number of compounding periods per year (12 for monthly compounding)

- t is the number of years

In this case, the principal amount is $67,000, the interest rate is 4% (or 0.04), the compounding period is monthly (n = 12), and the loan term is 7 years (t = 7).

Substituting these values into the formula, we get:

\(\( A = 67000 \times (1 + 0.04/12)^{(12 \times 7)} \)\)

Calculating the final amount, we find that A ≈ $81,280.

To calculate the interest, we subtract the principal amount from the final amount: Interest = A - P = $81,280 - $67,000 = $14,280.

Therefore, the small business will pay approximately $14,280 in interest over the 7-year loan term.

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Given the exponential function f(x) and the logarithmic function g(x)  the true statement is given as

\(x- > \infty, f (x)- > \infty and g(x) - > \infty\)  Option A.

This is further explained below.

Generally, The exponential function is a kind of mathematical function that may be represented using the notation f(x)=exp or ex. The word, unless otherwise mentioned, usually refers to the function of a real variable that has a positive value; however, it may be extended to complex numbers or applied to other mathematical objects such as matrices or Lie algebras.

In conclusion, the Exponential equation x = ay is defined as analogous to the logarithmic function y = logan. Only when (x = ay), (a > 0), and (a 1) does (y = logan). It is referred to as the logarithmic function of base a. Think about what it implies when the exponential function is inverted: x = ay.

Given the exponential function f(x) and the logarithmic function g(x)  the true statement is given as

\(x- > \infty, f (x)- > \infty and g(x) - > \infty\)  Option A.

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To solve the given problems, we can use the properties of the normal distribution and the provided mean and standard deviation. The probability that the battery life is at least 9.1 hours is 0.179. The probability that the battery life is less than 7.9 hours is 0.179. The time of use that is exceeded with a probability of 0.9 is approximately 9.332 hours.

a. To find the probability that the battery life is at least 9.1 hours, we need to calculate the area under the normal distribution curve to the right of 9.1 hours. This can be done by standardizing the value using the z-score formula:

z = (x - μ) / σ

where x is the value of interest, μ is the mean, and σ is the standard deviation. In this case, x = 9.1 hours, μ = 8.5 hours, and σ = 39 minutes (which is equivalent to 0.65 hours).

Converting the values to a common unit (hours), we have:

z = (9.1 - 8.5) / 0.65 = 0.923

Using a standard normal distribution table or a calculator, we can find the corresponding probability, which is approximately 0.179.

b. To find the probability that the battery life is less than 7.9 hours, we again standardize the value using the z-score formula:

z = (x - μ) / σ

Here, x = 7.9 hours, μ = 8.5 hours, and σ = 0.65 hours.

Calculating the z-score:

z = (7.9 - 8.5) / 0.65 = -0.923

Using the standard normal distribution table or a calculator, we find the corresponding probability for a z-score of -0.923, which is approximately 0.179.

c. To find the time of use that is exceeded with a probability of 0.9, we need to find the z-score that corresponds to a cumulative probability of 0.9. This can be done by looking up the z-score in the standard normal distribution table.

Looking up the z-score for a cumulative probability of 0.9, we find the z-score to be approximately 1.28.

Using the z-score formula:

z = (x - μ) / σ

we have: 1.28 = (x - 8.5) / 0.65

Solving for x, we find: x - 8.5 = 1.28 * 0.65

x - 8.5 = 0.832

x = 8.5 + 0.832

x ≈ 9.332

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The new mixture exists 56.5% peanuts.

The first batch of 9 lb of mixed nuts possesses 40% peanuts.

This means the quantity of peanuts exists:

9 \(*\) 40/100 = 3.6 lb

The second batch of 9 lb of mixed nuts possesses 73% peanuts.

This means the quantity of peanuts exists:

9 \(*\) 73/100 = 6.57 lb

The total quantity of peanuts in the mix exists

3.6 lb + 6.57 lb = 10.17 lb

There exist 9 lb + 9 lb = 18 lb of mix.

Therefore, the percent of peanuts in the mix exists:

10.17 / 18 \(*\) 100 = 56.5%

The new mixture exists 56.5% peanuts.

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