A line has a slope of – 2 and passes through the point ( – 2, – 3). Write its equation in slope-intercept form.

Answer:

Step-by-step explanation:

An arithmetic progression is a list of numbers a1, a2, a3 ………….. an in which each term is obtained by adding a fixed number to the preceding term except the first term.

This fixed number is called the common difference( d ) of the AP. Common difference of an AP will be the difference between any two consecutive terms.

a2= a1+d

a3= a2+d

a4= a3+d

……..

an= an-1+d ………

Each of the numbers in the list is called a term .

Method to find the common difference :

d = a2 - a1 or a3 - a2 or a4 - a3...

General form of an AP.:

a, a+d, a+2d, a+3d…….

Here a is the first term and d is common difference.

General term or nth term of A.P

The general term or nth term of A.P is given by an or tn = a + (n – 1)d, where a = a1 is the first term, d is the common difference and n is the number of term.

SOLUTION :

Given -

A man saved in the first month,in the second month ,in the third month… are 640, 720, 800 .. which forms a sequence(AP).

Here, a1 or t1 = 640 , a2 or t2= 720, a3 or t3 = 800

d = t2 – t1

d= 720- 640

d= 80

tn = a + (n-1) d

t25 = 640 + (25 - 1) 80

t25 = 640 + 24 (80)

t25= 640 + 1920

t25 = 2560

Hence, his Saving will be 2560 in the 25th month.

Hope this helps,from Armax.

Slope of the given graph function is -3/2 while the y-intercept: (0, 1)

What is slope intercept?

Finding the equation of a straight line in the coordinate plane is done using the slope intercept form. The connection that any point's coordinates on the line must satisfy is the equation of a straight line. Any point that is not on the line will not have coordinates that satisfy. The answer to this equation is simple to determine.

To Find :  equation of the line, in slope-intercept form

Solution:

Standard/ general form of equation of line in 2 variables is

Ax + By + C = 0

Slope intercept form is

y = mx + c

intercept form is

x/a  + y/b   = 1

Slope intercept form is

y = mx + c

m = Slope = -3/2

c = y intercept  =  1  

y  = (-3/2)x  + 1

equation of the line, in slope-intercept form is   y  = (-3/2)x  + 1.

Learn more about y-intercept here:

https://brainly.com/question/4015585

#SPJ1

a) Diminishing returns start at x = 1,  where the marginal revenue will be less than the marginal cost

b)At x = 1, the company will earn R(1) = -32 + 6 + 18 + 4 = -4,000 dollars.

c) 0 ≤ x ≤ 25 implies that the Coffee Junction company has the capacity to spend a maximum of 25,000 dollars per month on advertisements.

a) At what level of advertising spending does diminishing returns start?

Diminishing returns refers to a situation when the marginal return on investment decreases as more resources are devoted to it. For instance, in case of Coffee Junction, increasing the advertising expenditure may lead to higher revenue, but the marginal revenue (revenue generated by each additional dollar spent) will gradually decrease.

b) How much revenue will the company earn at that level of advertising spending?

At x = 1, the company will earn R(1) = -32 + 6 + 18 + 4 = -4,000 dollars.

c) What does 0≤x≤25 tell us with respect to this problem?

In this problem, 0 ≤ x ≤ 25 implies that the Coffee Junction company has the capacity to spend a maximum of 25,000 dollars per month on advertisements.

To learn more about marginal cost refer:-

https://brainly.com/question/14923834

#SPJ11

Answer:

After 24 hours, there will be 4191 bacteria present in the culture.

Step-by-step explanation:

Initial number of bacteria = 300

amount in 10 hrs = 3 x 300 = 900

time taken = 10 hours

Bacterial growth is exponential, ans so we use the equation

N = N'\(e^{kt}\)

where N is the final amount

N' is the initial amount

k is the growth constant

t is the time

For this first case, we have

900 = 300 x \(e^{k*10}\)

3 = \(e^{10k}\)

take natural log of both sides, we'll have

ln 3 = ln \(e^{10k}\)

1.0986 = 10k

k = 1.0986/10 = 0.10986

using the growth constant above, we calculate for a day which is 24 hours

N = N'\(e^{kt}\)

N = 300 x \(e^{0.10986*24}\)

N = 300 x \(e^{2.637}\)

N = 300 x 13.97

N = 4191 bacteria

Answer

6r^4-330r^3-6300r^2

Step-by-step explanation:

Answer: I think the answer is B

Step-by-step explanation:

Hence, the three numbers are 8, 1, and 3

Answer:

Here is my original puzzle problem:

* * *

There are three coins, each with a different value. The sum of the three coins is 10. The value of the first coin is twice the value of the second coin. The value of the third coin is 1 more than the value of the first coin.

What are the values of the three coins?

_________________

To solve this puzzle, you can use the following steps:

1. Let X be the value of the first coin.

2. Let Y be the value of the second coin.

3. Let Z be the value of the third coin.

4. Set up equations to represent the given information.

5. Solve the equations for X, Y, and Z.

The equations for this puzzle are as follows:

X + Y + Z = 10

X = 2Y

Z = X + 1

Solving these equations, we find that the values of the three coins are X = 4, Y = 2, and Z = 5.

I hope you enjoy this puzzle!

Answer

516,901

Step-by-step explanation:

36,700/7.1%

you have to change the 7.1% to a decimal so its now

36,700/0.071= 516,901.4084507

round it to the nearest whole number is 516,901

Answer:

0

Step-by-step explanation:

Answer:

518

Step-by-step explanation:

Since you are rounding to the nearest whole number.

518.1 would need to be 518.5 or higher to be 519 so anything below that would just round up the 518

Answer:

120

Step-by-step explanation:

Answer: 120

12 x 10 = 120

Answer:

F(1) = - 1

Step-by-step explanation:

F(x) = 2x-3

F(1) = 2(1)-3 (plug in 1 for x because 1=x)

F(1) = 2-3 (multiply 1 and 2)

F(1) = - 1

The final conclusion is that there is sufficient evidence to warrant the rejection of the claim that the population mean is not equal to 65.2.

What is the mean and standard deviation?

The mean and standard deviation are commonly used in various statistical analyses, such as hypothesis testing, probability distributions, and the characterization of data distributions. They provide valuable insights into the central tendency and variability of a dataset, allowing for comparisons and further statistical calculations.

To find the critical value for this test, we need to determine the z-score corresponding to the significance level of α = 0.05. Since this is a two-tailed test, we divide the significance level by 2 to get α/2 = 0.025 for each tail.

Using a standard normal distribution table or a statistical calculator, we find that the z-score corresponding to α/2 = 0.025 is approximately 1.96.

The critical value for this test is ±1.96.

the formula to calculate the test statistic,

test statistic = (sample mean - population mean) / (standard deviation / √(sample size))

Plugging in the given values:

test statistic = (62 - 65.2) / (6.9 / √(42))

≈ -1.742

The test statistic is approximately -1.742.

Since the test statistic falls outside the critical region (which is defined by the critical values ±1.96), we fail to reject the null hypothesis.

The test statistic is not in the critical region.

Therefore, the final conclusion is that there is sufficient evidence to warrant the rejection of the claim that the population mean is not equal to 65.2.

To learn more about the mean and standard deviation visit:

brainly.com/question/475676

#SPJ4

The sum of money shared between Karen and Natasha is $262.50.

Denote the amount of money Karen received as x.

According to the given ratio, Natasha received 5 times the amount Karen received, which is 5x.

we can set up the equation:

5x = x + $210

solve for x

5x - x = $210

4x = $ 210

x = $210 / 4

x = $52.50

Therefore, Karen received $52.50.

the sum of money shared

sum of money shared = Karen's amount + Natasha's amount

sum of money shared = $52.50 + $210

sum of money shared = $262.50

Hence, the sum of money shared between Karen and Natasha is $262.50.

Learn more about ratio at

https://brainly.com/question/12024093

#SPJ1

Answer:12

Step-by-step explanation:  55 + 40=95

7 times 12=84

84+1=85

55+40+85=180

The equivalent expressions are:

(30/12)*k + (4/12)*k + 1-  3/4

(34/12)*k - 1/4

So here we have the expression:

(5/2)*k + 1 + (1/3)*k - 3/4

An equivalent expression is an expression that can be rewritten into this one.

If we simplify the expression we will get:

(5/2)*k + (1/3)*k + 1-  3/4

(15/6)*k + (2/6)*k + 1/4

(17/6)*k + 1/4

The equivalent expressions are then:

(30/12)*k + (4/12)*k + 1-  3/4  (this is like our second step).

(34/12)*k - 1/4 (just multiply the fraction by 2 in the denominator and numerator)

Learn more about equivalent expressions at:

https://brainly.com/question/2972832

#SPJ1

The equivalent expressions of 5/2k + 1 + 1/3k - 3/4 are

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

5/2k + 1 + 1/3k - 3/4

Express the fractions to have equal denominators

So, we have

30/12k + 1 + 4/12k - 3/4 ---- this is represented by option (a)

Evaluate the like terms

34/12k + 1/4 ---- this is represented by option (d)

The above are the expressions equivalent to 5/2k + 1 + 1/3k - 3/4

Read more about equivalent expressions at:

https://brainly.com/question/15775046

#SPJ1

Answer: I would suppose 2.

Answer:

Assuming its "Modeling a Water Wheel" from EDGE its

Distance: a= 1/2 b=1 c=3/2

Heights: d=1  e=0  f=-1

Step-by-step explanation:

The solution is, a = 6, b = 7, c = 8, d = 7 and e = 6.

Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.

here, we have,

Let's remember that the complete revolution of the wheel is 360 degrees, and the distance traveled by a complete revolution is the length of the circumference: 2*pi*radius.

The inicial height of the point is 6 ft, and the radius of the wheel is 1 ft.

When the distance traveled is 0, the wheel turned 0 degrees, and the point will be in its inicial position (the lower position of the wheel), which is 6 feet high.

So the height will be a = 6 + 0 = 6 ft

When the distance traveled is pi/2, the wheel turned 90 degrees, and the point will be half the complete height of the wheel, which is 2 feet.

So the height will be b = 6 + 1 = 7 ft

When the distance traveled is pi, the wheel turned 180 degrees, and the point will be at the top of the wheel, which is 2 feet higher than the lower point of the wheel.

So the height will be c = 6 + 2= 8 ft

When the distance traveled is 3pi/2, the wheel turned 270 degrees, and the point will be half the complete height of the wheel, which is 2 feet.

So the height will be d = 6 + 1 = 7 ft

When the distance traveled is 2pi, the wheel turned 360 degrees, and the point will be in its inicial position (the lower position of the wheel), which is 6 feet high.

So the height will be e = 6 + 0 = 6 ft

So the answers are:

a = 6, b = 7, c = 8, d = 7 and e = 6

To earn more on addition click:

brainly.com/question/29560851

#SPJ7

The object in three-dimensional space defined by the equation z = x^2 and the constraint 0 ≤ y ≤ 3 is a parabolic surface that opens upward along the y-axis, bounded between the planes y = 0 and y = 3.

The equation z = x^2 represents a parabolic surface in the x-z plane, with the vertex at the origin. This surface extends infinitely along the x-axis and opens upward. The constraint 0 ≤ y ≤ 3 restricts the object to a specific region in the y-axis direction. This means that the parabolic surface is bounded between the planes y = 0 and y = 3, creating a finite portion of the parabolic surface.

In other words, if we visualize the object, we can imagine a three-dimensional shape that resembles a curved sheet or a bowl. The shape widens as it moves away from the y-axis due to the parabolic nature of the equation. The object is confined to the region between the planes y = 0 and y = 3, which limits the extent of the shape along the y-axis. Within this region, the object exists as a solid surface with a varying height in the z-direction, determined by the x-coordinate squared.

Learn more about coordinates here:

https://brainly.com/question/32836021

#SPJ11

Answer:

name the two things they hoped to achieve when they moved into the interior

Decoding Forecast starting at 17:00Z:

Wind:

24014G23KT

Visibility:

5 statute miles

Weather:

Light rain showers

Clouds:

Overcast at 1500 feet

Incomplete report.

The decoded report is:

Location:

KJAX (Jacksonville International Airport)

Date/Time: 10th at 23:20Z

Wind:

00000KT

Visibility:

More than 6 statute miles

Clouds:

Scattered at 3500 feet

Forecast starting at 11:00Z:

Wind:

00000KT

Visibility:

5 statute miles

Weather:

Mist

Clouds:

Broken at 1000 feet, Broken at 2000 feet

Forecast starting at 06:00Z:

Wind:

16003KT

Visibility:

2 statute miles

Weather:

Mist

Clouds:

Broken at 500 feet, Overcast at 1000 feet

Temporary condition between 08:00Z and 12:00Z:

Visibility:

1 statute mile

Weather:

Mist

Clouds:

Overcast at 300 feet

Forecast starting at 14:00Z:

Wind:

20010G18KT

Visibility:

More than 6 statute miles

Weather:

Vicinity showers

Clouds:

Broken at 1500 feet, Overcast at 2500 feet

For similar questions on Decoding

https://brainly.com/question/29168785

#SPJ11

Answer:

6

Step-by-step explanation:

Answer:

4140°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 25 , then

sum = 180° × 23 = 4140°

Answer:

8 visits

Step-by-step explanation:

x=# of visits
100=40+7.5x
60=7.5x
x=8

hope this helps :)

Answer:

A

tyler has a points card for a movie theater.

he receives 75 rewards points just for signing up.

• he earns 10.5 points for each visit to the movie theater.

he needs 180 points for a free movie ticket.

.

a

how many visits must tyler make to earn a free movie ticket?

Step-by-step explanation: hqwediywydgwq78d

The value of the surface integral is `8(5√5 - 2√2 - 1)/15`.

The surface integral can be evaluated by first calculating the surface area element `dS` of the cone with given parametric equations. `dS` is obtained by finding the cross product of the partial derivatives of `x(u,v), y(u,v)`, and `z(u,v)` with respect to `u` and `v`.

Then, the surface integral can be calculated by integrating the product of `xyz` and `dS` over the surface `S`. Here's how to evaluate the surface integral:

Given that `S` is the cone with parametric equations `x=ucos(v), y=usin(v), z=u`, `0≤u≤2`, `0≤v≤2π`.

The surface area element `dS` of the cone is given by: `dS = |r_u × r_v| du dv`where `r(u, v) = `.

Then, the partial derivatives of `r(u, v)` with respect to `u` and `v` are:`r_u = ` and `r_v = <-u sin(v), u cos(v), 0>`

Thus, the surface area element `dS` can be calculated as:

dS = |r_u × r_v| du dv= |<-u cos(v), -u sin(v), u>| du dv= u √(1+u²) du dv

Therefore, the surface integral ∬S xyz dS can be evaluated as follows:

`∬S xyz dS`=`∬(xyz) (u√(1+u²)) du dv` `(` using dS above `)``

= ∫(0 to 2π) [ ∫(0 to 2) [ ∫(0 to u) (u cos(v) * u sin(v) * u) u √(1+u²) du ] dv ]`

=` ∫(0 to 2π) [ ∫(0 to 2) [ u^5/5 * cos(v) * sin(v) * √(1+u²)/2 ] dv ] du`

(using the formula `∫cosθsinθdθ = (sin²θ)/2`)`

= ∫(0 to 2π) [ ∫(0 to 2) [ u^5/10 * sin(2v) * √(1+u²) ] dv ] du`

(simplifying further using `sin(2v) = 2sin(v)cos(v)`)

=` 8 ∫(0 to 2) [ u^5/10 √(1+u²) ] du`=` 8/15 [ (1+u²)^(5/2) - 1 ]

[from 0 to 2]`=` 8/15 [ (5√5 - 2√2) - 1 ]`

=` 8/15 (5√5 - 2√2 - 1)`

=` 8(5√5 - 2√2 - 1)/15`

Know more about the surface integral

https://brainly.com/question/28171028

#SPJ11

A transversal line intersects two parallel lines a and b with values of corresponding angles congruent pairs of corresponding angles are (1, 5), (4, 8), (3, 7), and (2, 6).

∠1 ≅ ∠5 (corresponding angle theorem)

∠7 ≅ ∠5 (vertical angle theorem)

∠1 ≅ ∠7 (Transitive property of congruence)

Complete question is at the end of solution.

As per the given data, a transversal line intersects two parallel lines a and b.

The values of corresponding angles congruent pairs of corresponding angles are (1, 5), (4, 8), (3, 7), and (2, 6)

Line a is parallel to line b.

Therefore,

a ║ b

Let's prove ∠1 ≅ ∠7

Hence,

∠1 ≅ ∠5 (corresponding angle theorem)

Corresponding angles are the angles that are formed in matching corners or corresponding corners with the transversal when two parallel lines are cut by the traversal.

∠7 ≅ ∠5 (vertical angle theorem)

Vertical angles theorem or vertically opposite angles theorem:

According to the theorem, two opposing vertical angles that are created when two lines cross one other are always equal.

Vertical angles are the angles formed when two lines intersect each other.

∠1 ≅ ∠7 (Transitive property of congruence)

Transitive property of congruence: If two lines, angles, or triangles are congruent with one another, then the first line, angle, or triangle is congruent with the second, third, or fourth line, angle, or triangle.

For more questions on angles and parallel lines

https://brainly.com/question/27987060

#SPJ4

The given statement states that a transversal line intersects two parallel lines, a and b, with corresponding angle congruent pairs of (1, 5), (4, 8), (3, 7), and (2, 6). The proof uses the corresponding angles theorem, vertical angles theorem, and transitive property of congruence to show that the angles are congruent.

Given 2. Corresponding angles theorem 3. Vertical angles theorem 4. Transitive property of congruence Reasons: 1. The transversal line intersects two parallel lines a and b with values of corresponding angles congruent pairs of (1, 5), (4, 8), (3, 7), and (2, 6). 2. If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. 3. If two angles are vertical angles, then they are congruent. 4. If two angles are congruent to the same angle, then they are congruent to each other.

The given statement states that a transversal line intersects two parallel lines, a and b, with corresponding angle congruent pairs of (1, 5), (4, 8), (3, 7), and (2, 6). The proof uses the corresponding angles theorem, vertical angles theorem, and transitive property of congruence to show that the angles are congruent.

Learn more about angle here

https://brainly.com/question/28451077

#SPJ4

Answer:

1/250

Step-by-step explanation:

5^-3 × 2^-1

5^-3 = 1/5^3 = 1/125

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

so 5^-3 × 2^-1 means 1/125 × 1/2

= 1/125 × 1/2

= 1/250

Answer:

  (-1, -5)

Step-by-step explanation:

Each point on a graph is the ordered pair (x, f(x)). Then the point M(-1 -3) is the ordered pair (-1, f(-1)) where f(-1) = -3.

A point on the shifted graph will be ...

  (x, f(x) -2)

Then for x = -1, the point is ...

  (-1, f(-1) -2) = (-1, -3 -2) = (-1, -5)

The minimum on the shifted curve is M'(-1, -5).

_____

Additional comment

f(x) is the y-coordinate of a point on a graph. Then f(x) -2 is the y-coordinate shifted down 2 units.