What is the slope and y-intercept of the equation 3(y-2) + 6(x + 1) - 2 = 0?
O A.
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slope = -2, y-intercept =
WIN
OB.
2
slope = 2, y-intercept =
WIN
OC.
slope = -2, y-intercept = -
WIN WIN
OD. slope = 2, y-intercept = -
3
O E slope = -2, y-intercept
=
2.
NI

Answer:

625 students

Step-by-step explanation:

Answer:
Slope is 3/2
y-intercept is (0,-45)

This relationship holds true for all right triangles and is a fundamental property of trigonometry.

The relationship between the sines and cosines of the two acute angles in right triangles is defined by the concept of trigonometric ratios. The sine of an angle is equal to the ratio of the length of the side opposite the angle to the hypotenuse, while the cosine of an angle is equal to the ratio of the length of the side adjacent to the angle to the hypotenuse. The relationship between the sines and cosines can be summarized as follows: the sine of an angle is equal to the cosine of its complement, and the cosine of an angle is equal to the sine of its complement.

This relationship exists because the two acute angles in a right triangle are complementary angles, meaning their sum is equal to 90 degrees. Since the hypotenuse is the longest side in a right triangle and is shared by both angles, the ratio of the length of the side opposite one angle to the hypotenuse is equal to the ratio of the length of the side adjacent to the other angle to the hypotenuse. Therefore, the sine of one angle is equal to the cosine of its complement, and the cosine of one angle is equal to the sine of its complement. This relationship holds true for all right triangles and is a fundamental property of trigonometry.

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Answer: For Jon, buying 3 shirts for $20 can be written as a rate as follows:

The number of shirts Jon buys per dollar spent = 3 shirts / $20 = 3/20 shirts/dollar

For Brenda, recording 76 songs on 4 albums can be written as a rate as follows:

The number of songs Brenda records per album = 76 songs / 4 albums = 19 songs/album

So, the rate of songs Brenda records per album can be written as 19 songs/album.

Step-by-step explanation:

Answer:

The answer is a "Weather occurs because the climate is costantly changing"

Answer:

A (climate is the trend in weather over a long period of time)

Step-by-step explanation:

The value of the double integral ∬R (x^2 - 2y^2) dA, where R is the first quadrant region between the circles of radius 3 and radius 4 centered at the origin, can be calculated as -180π/5.

To evaluate the given integral, we can convert it into polar coordinates. In polar coordinates, x = rcosθ and y = rsinθ. The region R can be described as 3 ≤ r ≤ 4 and 0 ≤ θ ≤ π/2.

Substituting these values into the integral and using the appropriate Jacobian factor, the integral becomes:

∫₀^(π/2) ∫₃⁴ (r^2cos²θ - 2r^2sin²θ) rdrdθ

Simplifying and evaluating the integral, we obtain the result -180π/5.

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Answer:

1164

Step-by-step explanation:

Surface area is the sum of the areas for all the faces. So 20×15= 300 since there is another one like that you multiply that answer by 2. Then 16×12= 192 then repeat and multiply 192 by 2. Then 12×15= 180 and since there is only one you dont multiply it by 2. Now add (192×2) + (300×2) + 192.

384 + 600 + 192 = 1164

The exercise involves finding the product C = AB, where matrix A is given by [2 9] and matrix B is given by [3 6 1]. We need to perform the matrix multiplication to obtain the resulting matrix C.

Let's calculate the matrix product C = AB step by step:

Matrix A has dimensions 2x1, and matrix B has dimensions 1x3. To perform the multiplication, the number of columns in A must match the number of rows in B.

In this case, both matrices satisfy this condition, so the product C = AB is defined.

Calculating AB:

AB = [23 + 912 26 + 94 21 + 95]

[103 + 612 106 + 64 101 + 65]

Simplifying the calculations:

AB = [6 + 108 12 + 36 2 + 45]

[30 + 72 60 + 24 10 + 30]

AB = [114 48 47]

[102 84 40]

Therefore, the product C = AB is:

C = [114 48 47]

[102 84 40]

In summary, the matrix product C = AB, where A = [2 9] and B = [3 6 1], is given by:

C = [114 48 47]

[102 84 40]

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The equation of the function d(t) is d(t) = -2sin(π/2 t) + 5

The function is given as:

d(t) = a * sin(b * t) + d

The bob is 5 cm away from the wall implies that the vertical shift is 5.

This means that

d = 5

So, we have

d(t) = a * sin(b * t) + 5

The bob reaches the closest point to the wall, which is 3 cm from the wall.

So, the amplitude is

A = 3 - 5

Evaluate

A= -2

So, we have:

d(t) = -2 * sin(b * t) + 5

The period is calculated as:

B = 2π/t

Where

t = (5 + 3)/2

This gives

t = 4

Substitute t = 4 in B = 2π/t

B = 2π/4

Evaluate

B = π/2

So, we have:

d(t) = -2sin(π/2 t) + 5

Hence, the equation of the function d(t) is d(t) = -2sin(π/2 t) + 5

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Answer:

students= 110

adults= 40

Step-by-step explanation:

Step one:

given data

Tickets for students were $2 and tickets for adults were $3.

let students be x

and adults be y

so

2x+3y= 340--------------1

and

x+y= 150--------------------2

from 2

x= 150-y

from 1

2(150-y)+3y= 340

300-2y+3y= 340

collect like terms

y=340-300

y= 40

put y= 40 in 2

x+40=150

x= 150-40

x= 110

Answer:

x.   y

-1---2^-1=1/2

0---0

1----2

2----2*2=4

Step-by-step explanation:

x.   y

-1---2^-1=1/2

0---0

1----2

2----2*2=4

a.  No because P(A | B) ≠ P(A).

b. No because P(A ∩ B) ≠ 0.

c. The probability that neither A nor B takes place is 0.43

The correct answer is: No because P(A | B) ≠ P(A).

The correct answer is: No because P(A ∩ B) ≠ 0.

To calculate the probability that neither A nor B takes place, we need to find the complement of the union of A and B, which is denoted as A' ∩ B'.

The complement of an event A is the probability of the event not occurring, which is equal to 1 - P(A). Thus, the probability that neither A nor B takes place is P(A' ∩ B') = 1 - P(A ∪ B).

To find P(A ∪ B), we can use the inclusion-exclusion principle:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B).

Given that P(A) = 0.54, P(B) = 0.25, and P(A ∩ B) = 0.22, we can substitute these values into the equation:

P(A ∪ B) = 0.54 + 0.25 - 0.22 = 0.57.

Therefore, the probability that neither A nor B takes place is:

P(A' ∩ B') = 1 - P(A ∪ B) = 1 - 0.57 = 0.43.

The probability that neither A nor B takes place is 0.43 (rounded to 2 decimal places).

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When a scatterplot is created from a table of values, the statement that is correct is A.It is possible for two points to have the same x-coordinate and the same y-coordinate.

Scatter plots in mathematics can be considered as the graphs that helps in the establishment of the relationship between two variables in a data-set.

It shoud be noted that this represents data points which can be represented on the two-dimensional plane or on a Cartesian system however there are two variables whereby the independent variable or attribute is plotted on the X-axis,  and the other is plotted on the Y-axis.

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Answer:

1/r^7 + 1/s^12

Step-by-step explanation:

Since there is a negative exponent, the term becomes a fraction. As we do not know the value of the term, it remains in its variable form with a positive exponent

Answer: -x + y = 8

Step-by-step explanation:

So first you are going to want to find the slope of the equation. The equation for that it (y2 - y1)/(x2 - x1) = (10 - 7)/(2 - -1) and that equals 1. So your slope will be 1.

Now you have half of your equation complete, currently it looks like, y = x + b. So we have to find the y intercept. You can do that by plugging in a pair of coordinates into the current equation and solve for b.

Lets plug in (2,10)

10 = 2 + b

10 - 2 = b

b = 8

So now you have your equation in slope intercept form, y = x + 8. Just move the x over to the left side and there is your answer.

-x + y = 8

Answer: all of them

Step-by-step explanation:

Rational numbers are represented as dividing two integers, which is a fraction or decimal. Therefore, the numbers stated (134, 49, 9, etc.) are rational numbers since they are all whole numbers.

The system of equations associated with the augmented matrix [6 3 6 -2 -4 -9] is 6x + 3y + 6z = -2 and -4x - 9y + z = -9. The system of equations associated with the augmented matrix [3 2 1 11; 2 1 3 15; 0 2 -1 -2] is 3x + 2y + z = 11, 2x + y + 3z = 15 and -2x + 4y - z = -2.

For the first augmented matrix, the system of equations would be

6x + 3y + 6z = -2

-4x - 9y + z = 1

The coefficients of x, y, and z can be found in the first three columns of the matrix, and the constants are in the last column. The system of equations can be written by using these coefficients and constants.

For the second augmented matrix, the system of equations would be

3x + 2y + z = 11

2x + y + 3z = 15

-2x + 4y - z = -2

Again, the coefficients of x, y, and z can be found in the first three columns, and the constants are in the last column. The system of equations can be written using these coefficients and constants.

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--The given question is incomplete, the complete question is given

"Write the system of equations associated with each augmented matrix. Do not solve. 6 3 6 -2 -4 -9 1) a) 6x 3y  [ 3 2 1 11 [2 1 3 15. 02 42 -1 -2 3 15 "--

The labor hours required for the eighth satellite are calculated to be 51,200 based on a learning curve value of 0.5120 and an expected improvement curve of 80%.

The learning curve concept suggests that as the cumulative production doubles, the labor hours required to produce each unit decrease by a certain percentage. In this case, the learning curve value for the eighth unit is given as 0.5120, which means that the labor hours needed for the eighth satellite is 51.20% of the labor hours required for the first unit.

To calculate the actual number of labor hours, we multiply the learning curve value by the total labor hours required for the first unit. Given that the total labor hours for the first unit is 100,000, we can calculate the labor hours for the eighth satellite as follows: 0.5120 * 100,000 = 51,200.

Therefore, based on the given learning curve value and the expected improvement curve of 80%, the number of labor hours for the eighth satellite is determined to be 51,200.

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The value of the given and completed expression in this problem is

-1

Combined operations are defined as a set of operations applied to the same problem, for example addition, subtraction, multiplication, are frequently used in arithmetic polynomials.

In this case we have an arithmetic polynomial.

We complete the expression as follows:

1 + 2 - 3 + 4 - 5

We group the positive terms on one side and negative terms on the other:

The value of the expression (1 + 2 - 3 + 4 - 5) is -1

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Using the properties of Isosceles Triangle we get that When the line containing the vertex of an isosceles triangle is drawn from the vertex angle perpendicular to the base, it bisects the vertex angle and the base.

Based on the length of the sides of the triangle, there are three types of equilateral triangles . , isosceles triangle, unequal triangle. An isosceles triangle is a triangle with two sides of equal length and corresponding angles are equal.

Statement : -

Let ABC be an isosceles triangle such that AB=AC.

Let AD be the bisector of ∠A.

we have to prove:- BD=DC

Proof :-

In △ABD&△ACD

AB=AC(∵△ABC is an isosceles triangle)

∠BAD=∠CAD(∵AD is the bisector of ∠A)

AD=AD (Common)

By S.A.S.(side angle side)

△ABD≅△ACD

By corresponding parts of congruent triangles-

⇒BD=DC

Hence proved that the perpendicular drawn from the vertex angle to the base bisect the vertex angle and base.

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Complete question:

Prove that if a line containing a vertex of an isosceles triangle is perpendicular drawn from the vertex angle to the base bisect the vertex angle and the base.

Answer:It is not possible

Step-by-step explanation: It is not possible because we need 12 plot to solve for an accurate mean but there is only 11 data which is impossible.

The rate of increase of the side of a square is 8.5 cm/sec. To find the rate of increase of the perimeter, we can use the formula for the perimeter of a square and differentiate it with respect to time. The rate of increase of the perimeter is therefore 34 cm/sec.

Let's denote the side length of the square as s and the perimeter as P. The formula for the perimeter of a square is P = 4s. We are given that the side length is increasing at a rate of 8.5 cm/sec. Therefore, we can express the rate of change of the side length as ds/dt = 8.5 cm/sec.

To find the rate of increase of the perimeter, we differentiate the perimeter formula with respect to time:

dP/dt = d/dt (4s)

Using the chain rule, we have:

dP/dt = 4(ds/dt)

Substituting the given rate of change of the side length, we get:

dP/dt = 4(8.5) = 34 cm/sec

Hence, the rate of increase of the perimeter of the square is 34 cm/sec.

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Given:

Total produce = 80 liters

15% Acid solution and 25% acid solution

Find-:

How many litres of each

Explanation-:

Let

Total 80 litres

eq(2) - 3eq(1) is:

So, the value of "y" is:

So x is 40

Then,

Square tile with measure of each side is 16inches have area equals to 1652 centimeters( round off to nearest square centimeters).

As given in the question,

Measure of each side length of a square tile = 16 inches

Conversion

1 inch = 2.54 centimeters

16 inches = ( 16 × 2.54 )centimeters

                = 40.64centimeters

Area of a square tile is :

= ( Side length ) × ( Side length)

= (40.64) × (40.64)

= 1651.6096 centimeters

= 1652 centimeters ( round off to nearest square centimeters)

Therefore, the area of a square tile with given measure of each side is equal to 1652 centimeters ( round off to nearest square centimeters).

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Parallel lines are defined as lines that do not intersect or meet at any point in a plane. They are always parallel and equidistant from one another.

What is answer parallel line?

In geometry, parallel lines can be defined as two lines in the same plane that are at equal distance from each other and never meet. They can be both horizontal and vertical.

Parallel lines are two lines in the same plane that are equal distance apart and never intersect.

Real-world parallel line examples include railroad tracks, sidewalk edges, street markings, zebra crossings, the surface of pineapple and strawberry fruit, staircases and railings, and so on.

Parallel lines are lines in a plane that never meet, no matter how far they are extended. The distance between the parallel lines is constant because they never meet.

Parallel lines are defined as lines that do not intersect or meet at any point in a plane. They are always parallel and equidistant from one another.

these are 8 parallel lines

2x+3y = 6

2x+3y = 4

2x+3y = 1

2x+3y = 2

2x+3y = 3

2x+3y = 8

2x+3y = 7

2x+3y = 5

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The population of the city after one year nearest to the whole number is 289,440.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

The exponent is given as

y = a(b)ˣ

The number of inhabitants in the city increments by 0.5% each year. In the event that the current year's populace is 288,000.

The exponential equation is given as,

y = 288,000 · (1 + 0.005)ˣ

y = 288,000 · (1.005)ˣ

Then the population of the city after one year is calculated as,

y = 288,000 · (1.005)¹

y = 288,000 · (1.005)

y = 289,440

The number of inhabitants in the city following one year closest to the entire number is 289,440.

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The equation of a line is y = -3/4x. so, y = -3/4x is the correct answer.

What is the line of the equation?

The equation of the line is an algebraic form of representing the set of points, which together form a line in a coordinate system.

(0,0) and (4,-3) are the given points.

so,

slope = (-3-0)/(4-0) = -3/4

Now,

y = mx + b

or, 0 = -3/4 * 0 + b

or, 0 = 0 + b

so, b = 0

Now,

y = mx + b

or, y = -3/4x + 0

y = -3/4x

Hence, the equation of a line is y = -3/4x. so, y = -3/4x is the correct answer.

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Part (a)

Let one of the angles be \(\theta\). After solving for all of the other angles using the triangle sum theorem, we see that \(\triangle CDA \sim \triangle BDC \sim \triangle BCA\).

Part (b)

\(\frac{BD}{BC}=\frac{BC}{CA}, \frac{DA}{DC}=\frac{DC}{DB}\)