find the equation of the line passing through the point (2, -4) that is parallel to the line y=3x+2​

Answer:

10

Step-by-step explanation:

We can set up an equation using the information given to us:

x+x-2+6=\(\frac{1}{2}*(x-2)*6\)

Simplify both sides

2x+4=3(x-2)

Distribute the 3 on the right side

2x+4=3(x)-3(2)

2x+4=3x-6

Move like terms to one side

x=10

\(\stackrel{\textit{value of the perimeter in feet}}{(x)+(x-2)+(6)}~~ = ~~\stackrel{\textit{value of the area in }ft^2}{\cfrac{1}{2}\underset{base}{(x-2)}\underset{height}{6}} \\\\\\ 2x+4=3x-6\implies 4=x-6\implies 10=x\)

Answer:5

Step-by-step explanation:

The range of the function g(x) = a[x], where a < 0, is y ≤ 0.

The function f(x) = [x], where [x] represents the greatest integer less than or equal to x, has a range of y ≤ 0. This means that the output of the function f(x) can be any number less than or equal to zero, including negative integers, zero, and non-negative fractions.

Consider the function g(x) = a[x], where a is a negative constant. When we multiply the input x by a the output of the function is also multiplied by a. Since a is negative, the sign of the output is flipped. Moreover, the output is an integer, as [x] is an integer for all x.

Here, the range of the function g(x) = a[x] is y ≤ 0.

This means that the output of the function g(x) can be any negative integer, zero, or any non-positive fraction, as these are the numbers that are less than or equal to zero.

Thus, the range of the function g(x) = a[x], where a < 0, is y ≤ 0.

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The nonlinear- function which represents b(9)=4 is given by b(x)=72/x - 4 .

In mathematics and physics, a nonlinear system is one in which the change in the output is not proportional to the change in the input. Engineers, biologists, physicists, mathematicians, and many other scientists are interested in nonlinear problems since the majority of systems are inherently nonlinear.

Nonlinear function graphs don't resemble lines at all. It contains the formula f(x) = ax + b. Its equation can take any form, with the exception of f(x) = ax + b. The slope of the curve is the same between any two points. The point pairs on the graph do not all have equal slopes.

Of all the given options: the only equations which imply that b(9)=4  are :

i) b(x)=72/x - 4 and  (iv) b(x)=4

Of this two options only the first option is non-linear.

Hence the required option is  b(x)=72/x - 4 .

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Disclaimer:

The missing options are:

i)   b(x) = 72/x - 4

ii) b(x) = √x + 7

iii)b(x)  = 2x+1

iv) b(x) = 4

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Answer:

24 minutes

Step-by-step explanation:

The Dimensions of the wall are given as:

8ft × 5ft = 40ft² or 40 square feet

Step-by-step explanation:

Answer:

24 minutes

Step-by-step explanation:

8 * 5 = 40 ft²

---------------------------

Method I: Use a proportion

x/40 = 45/75

multiply both sides by 40

x = 45/75 * 40

x = 24

24 minutes

---------------------------

Method II: Use the rate

45/75 = 0.6min/ft²

40 * 0.6 = 24

24 minutes

The volumes of the solids are listed below:

Case 4: V = 570 cm³

Case 5: V = 222 cm³

Case 6: V = 378 cm²

Case 7: V = 168 cm³

Case 8: V = 514.8 cm³

Case 9: V = 1.125π m³

Case 10: V = 13.333π cm³

Case 11: V = 1152π cm³

Case 12: V = 10.667π cm³

In this problem we need to determine the volumes of nine solids, the formulas need to determine each volume are listed below:

Prism

V = A · h

Pyramid

V = A · h / 3

Hemisphere

V = (2π / 3) · r³

An eighth of the sphere

V = (π / 6) · r³

Surface areas

Polygon

A = (n · l · a) / 2

Circular sector

A = (α / 180) · π · r²

Triangle

A = w · s / 2

Rectangle

A = w · s

Where:

Case 4

V = 0.5 · (5 cm) · (12 cm) · (19 cm)

V = 570 cm³

Case 5

V = [0.5 · (3 cm) · (7 cm) + (15 cm) · (3 cm)] · (4 cm)

V = 222 cm³

Case 6

V = 0.5 · (7 cm) · (9 cm) · (12 cm)

V = 378 cm²

Case 7

V = [(5 cm) · (4 cm) + (12 cm) · (3 cm)] · (3 cm)

V = 168 cm³

Case 8

V = (1 / 3) · [0.5 · 6 · (6 cm) · (5.2 cm)] · √[(17.3 cm)² - (5.2 cm)²]

V = 514.8 cm³

Case 9

V = π · [(1.25 m)² - (1 m)²] · (2 m)

V = 1.125π m³

Case 10

V = (60 / 360) · π · (12 cm) · (20 cm) / 3

V = 13.333π cm³

Case 11

V = (2π / 3) · (12 cm)³

V = 1152π cm³

Case 12

V = (π / 6) · (4 cm)³

V = 10.667π cm³

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The Solution:

We are required to find the sum of

This also means that we should simplify

Therefore, the correct answer is option 2

Answer:

P = 0.3511

Explanation:

Using the equation for the binomial distribution, we get that the probability can be calculated as:

Where nCx is calculated as:

So, n is the total number of bats, x is the number of hits and p is the probability of getting a hit. So, replacing n = 4, x = 2 and p = 0.41, we get:

Therefore, the answer is P = 0.3511

The value of the expression 2x/3 ÷ 3x/2 when x ≠ 0 is 4/9.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

2x/3 ÷ 3x/2 when x ≠ 0.

This can be written as,

= (2x/3) x (2/3x)

= 2/3 x 2/3

= 4/9

Thus,

The value of the expression is 4/9.

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The required sample size of the given value is 577.

What is margin of error?

The formula to calculate the sample size  :-

n = (p(1-p)((Zα/₂)/E)²

Given :  Estimated proportion  p = 0.60

Margin of error : E = 0.04

Significance level : α = 1-0.95 = 0.05

Critical value : Zα/₂ = 1.96

Now, the required sample size will be :-

n = (0.60)(0.11)(1.96/0.04)²

= 6.6 * (0.0784)²

= 0.57744

Hence, the required minimum sample size of the given is 577.

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Answer:

\(x=\dfrac{32}{15}\)

Answer:

The 12 magnets for $34.68 as the unit price is lower.

Step-by-step explanation:

→ Find the cost per magnet for 12

34.86 ÷ 12 = $2.89

→ Find the cost per magnet for 3

9.57 ÷ 3 = $3.19

Answer:

2000

Step-by-step explanation:

1 kilogram is 100 grams therefore 2 kilo grams is equal to 2000 grams

The word kilo means thousand in Greek and i think French

:)

Answer:

2,000 grams :)

The segment lengths are given as follows:

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The theorem is expressed as follows:

c² = a² + b².

In which:

Considering the geometric mean theorem, the triangle has bases of 7 and 14 - 7 = 7, hence the altitude BD is given as follows:

BD² = 7 x 7

BD² = 7²

BD = 7.

The segment BC is the hypotenuse of a right triangle of two sides with length 7, hence:

(BC)² = 7² + 7²

\(BC = \sqrt{2 \times 49}\)

\(BC = 7\sqrt{2}\)

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Answer:

x = 65

Step-by-step explanation:

the sum of the interior angles of a quadrilateral = 360°

sum the angles and equate to 360

x + 95 + 118 + 82 = 360

x + 295 = 360 ( subtract 295 from both sides )

x = 65

A statement which is the most complete valid conclusion about the relationship between weight and fuel efficiency include the following: D. For every 100-pound increase in car weight, we expect to see a 1.11 mpg decrease in fuel efficiency.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + c

Where:

Based on the information provided about the car's weights and fuel efficiencies, a reasonable value for the slope (m) of the regression line is equal to -1.11.

In this context, we can logically conclude that for every 100-pound increase in car weight, there would be a 1.11 mpg decrease in fuel efficiency because the slope is negative.

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Complete Question:

Suppose we have a collection of cars, we measure their weights and fuel efficiencies, and generate the following graph of the data.

Note: automobile fuel efficiency is often measured in mpg (miles that the car can be driven per one gallon of gas).

For this data set, X represents the weight of each car in hundreds of pounds, and Y represents the predicted fuel efficiency of each car in miles per gallon (mpg). A reasonable value for the slope of the regression line is -1.11.

Which of the following statements is the most complete valid conclusion about the relationship between weight and fuel efficiency?

A. Heavier cars tend to have lower mpg ratings.

B. For every 100-pound increase in car weight, we expect to see a 1.11 mpg increase in fuel efficiency.

C. For every 1-pound increase in car weight, we expect to see a 1.11 mpg decrease in fuel efficiency.

D. For every 100-pound increase in car weight, we expect to see a 1.11 mpg decrease in fuel efficiency.

The area of the poster in inches is,

⇒ A = 4 inches²

We have to given that;

A rectangular poster is 50 centimeters long and 25 centimeters wide.

Here, 1 centimeter is approximately 0.4 inches

Hence, Lenght = 50 cm

Lenght = 50 x 0.4

            = 2 inches

Width = 25 cm

          = 25 x 0.4

           = 1 inches

Thus, The area of the poster in inches is,

⇒ A = 1 x 4

⇒ A = 4 inches²

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Answer:

37

Step-by-step explanation:

we have the system of equations

Equate the functions f(x) and g(x)

Apply property of logarithms

Apply the definition of logarithm

With 99% confidence that the true difference lies between 0.1316 and 0.2694.

A 99% confidence interval for the difference in average SAT scores between coached and uncoached students can be constructed using the data above.

The confidence interval is calculated as (mean of coached students - mean of uncoached students) +/- (2 * standard error of the difference in means).

The mean of coached students is (0.3098 + 0.3399 + 0.219 + 0.0798) / 4 = 0.2155, and the mean of uncoached students is (0.0046 + 0.0248) / 2 = 0.0147. The standard error of the difference in means can be calculated as the square root of ((0.2155(1-0.2155)/4) + (0.0147(1-0.0147)/2)).

The confidence interval is then (0.2155 - 0.0147) +/- (2 * 0.0347) = 0.201 +/- 0.0694, or (0.1316, 0.2694). This indicates that, on average, coached students gain 0.201 points more than uncoached students, with 99% confidence that the true difference lies between 0.1316 and 0.2694.

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Answer:

-4.1

Step-by-step explanation:

5.7-9.8= -4.1

Answer:

2/3

Step-by-step explanation:

Find two points

(0,-2) and (3,0)

Using the slope formula

m = (y2-y1)/(x2-x1)

   = (0- -2)/(3-0)

  = (0+2)/(3-0)

   = 2/3

Answer:

\(\frac{2}{3}\)

Step-by-step explanation:

From the graph, we can see the line passes through the points (3,0) and (0,-2).

The slope of a line, \(m\), that passes through points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \(m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}\)

Let \((x_1,y_1)\implies (3,0)\) and \((x_2,y_2)\implies (0,-2)\).

The slope of the line that passes through these points is:

\(m=\frac{-2-0}{0-3}=\frac{-2}{-3}=\boxed{\frac{2}{3}}\)

Answer:

Given the information you provided, we can model cellular phone usage over time with an exponential growth model. An exponential growth model follows the equation:

`y = a * b^(x - h) + k`

where:

- `y` is the quantity you're interested in (cell phone usage),

- `a` is the initial quantity (34 million in 1995),

- `b` is the growth factor (1.22, representing 22% growth per year),

- `x` is the time (the year),

- `h` is the time at which the initial quantity `a` is given (1995), and

- `k` is the vertical shift of the graph (0 in this case, as we're assuming growth starts from the initial quantity).

So, our specific model becomes:

`y = 34 * 1.22^(x - 1995)`

To find the cellular usage in 2003, we plug 2003 in for x:

`y = 34 * 1.22^(2003 - 1995)`

Calculating this out will give us the cellular usage in 2003.

Let's calculate this:

`y = 34 * 1.22^(2003 - 1995)`

So,

`y = 34 * 1.22^8`

Calculating the above expression gives us:

`y ≈ 97.97` million.

So, the cellular phone usage in 2003, according to this model, is approximately 98 million.

To find the mass of the lamina, we need to integrate the density function over region D. The density function is given by? (x, y) = 7ky, where k is a constant. The region D is bounded by y = \((1 ? x^2)\)  and y = 0, and the limits of integration are \(0 < = y < = (1 - x^2)\) .

So, the mass of the lamina is:

\(m = ∫∫?(x, y) dx dy = ∫∫ 7ky dx dy\\= 7k ∫∫ y dx dy = 7k * ∫ (1 - x^2) dy dx\\= 7k * ∫(0 to 1 - x^2) y dy\\= 7k * (1/2 * ∫(0 to 1 - x^2) y^2 dy)\\= 7k * (1/2 * [y^3/3] evaluated at y = (1-x^2) and y=0)\\= 7k * (1/2 * [((1-x^2)^3/3] - 0))= 7k * (1/2 * (1/3 - x^6))\)

To find the center of mass (x bar, y bar) of the lamina, we need to find the x and y coordinates of the center of mass.

The x-coordinate is given by

\((x bar) = 1/m * ∫∫ x ?(x, y) dx dy = 1/m * ∫∫ x * 7ky dx dy \\= 7k * ∫ (x * y) dx dy\\= 7k * (x * 1/2 * ∫(0 to 1 - x^2) y^2 dy)\\= 7k * (x * 1/2 * [y^3/3] evaluated at y = (1-x^2) and y=0)\\= 7k * (x * (1/2 * (1/3 - x^6))\\The y-coordinate is given by\\(y bar) = 1/m * ∫∫ y ?(x, y) dx dy = 1/m * ∫∫ y * 7ky dx dy= 7k * ∫ (y^2) dx dy\\= 7k * (1/3 * ∫(0 to 1 - x^2) y^3 dy)\\= 7k * (1/3 * [y^4/4] evaluated at y = (1-x^2) and y=0)\\= 7k * (1/3 * (1/4 - x^6/2))\)

It's worth noting that the mass and center of mass of the lamina depend on the constant k, which is not specified in the problem.

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The given form to expand is (2x-4)^7

and we need to find the coefficient of x^3.

The binomial formula is

where n is a positive integer and a, b are real numbers, and 0 < r ≤ n

Substituting the values a = 2x, b = -4, n = 7 and r = 4

Then we have,

Now the coefficient of x^3 will be

Hence, the coefficient will be 71680.

Answer:

hi please upload the photo so we can help :)

Answer:

A:12p^3r and D:54p^3

Step-by-step explanation:

The equation of the line that passes through (4, 3) and (-4, -1) is y = -x/2 + 5. So, correct option is A.

To find the equation of the line that passes through two given points, we use the slope-intercept form of a linear equation, which is:

y = mx + b

where m is the slope of the line and b is the y-intercept.

First, we need to find the slope of the line using the two given points. The formula for finding slope between two points is:

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

Substituting the given points into the formula, we get:

m = (-1 - 3) / (-4 - 4) = -4/8 = -1/2

Now we know the slope, we can use one of the given points (4, 3) and substitute the slope into the slope-intercept form of the equation and solve for b.

y = mx + b

3 = (-1/2)(4) + b

3 = -2 + b

b = 5

Therefore, the equation of the line that passes through (4, 3) and (-4, -1) is:

y = -x/2 + 5

So, correct option is A.

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Complete question is:

What is the equation of the line that passes through (4, 3) and (-4, -1)?

Choices:

y = -x/2 + 5

y=2x+7

y=x/2 +1

y= -x/2 +7

Answer:

145

Step-by-step explanation:

You told me 0-o

Answer:

After 4 weeks, she has $145 dollars left in her bank account.

Step-by-step explanation:

Week 1 = 225 - 20 = 205

Week 2 = 205 - 20 = 185

Week 3 = 185 - 20 = 165

Week 4 = 165 - 20 = 145