A line contains the points (-26, -37) and (-32, -61). What is the slope of the line in simplified form? -3 −14 14 3

Answer:

u = -50

Step-by-step explanation:

2,023 - 548 = 1475

1475/-29.5 = -50

u = -50

check:

-29.5(-50) + 548 = 2,023

   1475 + 548 = 2,023

correct!

By identifying type of sequence we got that recursive definition for the sequence -6, -10, -14, -18... is  

A sequence is collection of numbers with a particular pattern.

Here given sequence is

-6, -10, -14, -18...

\(a_1=-6\)

\(a_2=-10\)

\(a_3=-14\)

\(a_4=-18\)

\(a_2-a_1=-6+-10=-16\)

\(a_3-a_2=-14+-10=-24\)

\(a_4-a_3=-18+-14=-32\)

Hence this is an AP with a = -1 and d = -18

So general term of this AP can be written as

So difference of any consecutive terms is equal to -18

\(a_n-a_{n-1}=-18\)

\(a_n-a_{n-1}+-18\)

By identifying type of sequence we got that recursive definition for the sequence -6, -10, -14, -18... is \(a_n-a_{n-1}+-18\)

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Answer:

0.375

Step-by-step explanation:

The probability of having at least one girl out of 3 children can be calculated as;

P(1 girl, 2 boys) or P(2 girls, 1 boy) or P(3 girls)

Since the P(b) = P(g) = 1/2

Then the probability at any point in time is 1/2 * 1/2 * 1/2 = 1/8

So we have ;

1/8 + 1/8 + 1/8 = 3/8 = 0.375

There are approximately 11.25 cups of granulated sugar in a 5 pound bag.

To determine the number of cups of granulated sugar in a 5 pound bag, we can use the conversion factor of 2.25 cups per pound.

First, we multiply the number of pounds (5) by the conversion factor:

5 pounds * 2.25 cups/pound = 11.25 cups

Therefore, there are approximately 11.25 cups of granulated sugar in a 5 pound bag.

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The equation regarding the algebraic information that represents the total earnings is y = 22x + 125.

From the information that's given, it can be seen that the expression is:

y = 22x + 125

She earned $555 after working for 15 hours. Therefore, the equation to represent the total earnings will be:

y = 22x + 125.

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Answer:

Step-by-step explanation:

the line given is

\(x + 3y = 6\\3y = -x + 6\\y = \frac{-1}{3} (x) + 2\\\)

parallel lines have the same slope

\(y = \frac{-1}{3} (x) + b\\3 = \frac{-1}{3}(5) + b\\\frac{9}{3} = \frac{-5}{3} + b\\ b = \frac{14}{3}\\\)

\(y = \frac{-1}{3} (x) + \frac{14}{3}\)

The equation of line passes through the point (5, 3) will be;

⇒ y = - x/3 + 14/3

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The point on the line are (5, 3).

And, The parallel line is,

⇒ x + 3y = 6

⇒ y = - x/3 + 2

Now,

Since, The equation of line passes through the point (5, 3).

So, We need to find the slope of the line.

Since, The slope of the parallel line is same.

Hence, Slope of the line is,

⇒ y = - x/3 + 2

⇒ m = dy/dx = - 1/3

⇒ m = - 1/3

Thus, The equation of line with slope - 1/3 is,

⇒ y - 3 = - 1/3 (x - 5)

⇒ y - 3 = - 1/3 (x - 5)

⇒ y - 3 = - x/3 + 5/3

⇒ y = - x/3 + 5/3 + 3

⇒ y = - x/3 + 14/3

Therefore, The equation of line passes through the point (5, 3) will be;

⇒ y = - x/3 + 14/3

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Answer:

x=3

CD = 13

Step-by-step explanation:

BE = CD in a parallelogram

1+4x = 5x -2

Subtract 4x from each side

1+4x-4x = 5x-2 -4x

1 = x-2

Add 2 to each side

1+2 = x-2+2

3 =x

The length of CD

CD = 5x-2 = 5*3 -2 = 15-2 = 13

Integrate the density over the disk \(D\) given by

\(D = \{(x,y) ~:~ x^2 + y^2 \le 2^2\}\)

or more conveniently, in polar coordinates by

\(D' = \left\{(r,\theta) ~:~ 0 \le r \le 2 \text{ and } 0\le \theta\le2\pi\right\}\)

Since the density depends on the distance from the origin, we have

\(\rho(r) = \left(1\dfrac{\rm lb}{\mathrm{in}^6}\right)r^3 - \left(2\dfrac{\rm lb}{\mathrm{in}^4}\right)r + 5\dfrac{\rm lb}{\mathrm{in}^3}\)

(Note the units in each coefficient ensure that \(\rho\) is measured in lb/in³.)

Then the mass (in lb) of the puck is

\(\displaystyle \iint_{D'} r\,\rho(r)\,dr\,d\theta = \int_0^{2\pi} \int_0^2 r (r^3 - 2r + 5) \, dr \, d\theta \\\\ ~~~~~~~~ = 2\pi \int_0^2 (r^4 - 2r^2 + 5r) \, dr \\\\ ~~~~~~~~ = 2\pi \left(\frac{2^5}5 - \frac{2\cdot2^3}3 + \frac{5\cdot2^2}2\right) = \boxed{\frac{332\pi}{15}}\)

Answer:

1230 minutes

Step-by-step explanation:

All you have to do is multiply 20.5 times 60. Since 60 minutes are in an hour and there is 20.5 hours.

*Please mark brainliest answer

Answer:

least to greatest : 7.78    7.778    7.7778   7.7777

Step-by-step explanation:

The local maximum of f(x,y) = 6xy - 4x - 9y - 4x^2 - 4y^2 is 151/7 at the critical point (-43/14, -24/7).

To find the local maximum of f(x,y) = 6xy - 4x - 9y - 4x² - 4y², we need to find the critical points and check their values.

Taking the partial derivative of f with respect to x and y, we get:

fₓ = 6y - 8x - 4

\(f_y\) = 6x - 9 - 8y

Setting both partial derivatives equal to zero, we get:

6y - 8x - 4 = 0

6x - 9 - 8y = 0

Solving for x and y, we get:

x = -43/14

y = -24/7

Therefore, the critical point is (-43/14, -24/7).

To check if this is a local maximum, we need to use the second partial derivative test.

Taking the second partial derivatives of f with respect to x and y, we get:

\(f_{yx}=6\)

\(f_{yy}=-8\)

Evaluating these second partial derivatives at the critical point (-43/14, -24/7), we get:

\(f_{xx} (\frac{-43}{14} ,\frac{-24}{7} )= -8\)

\(f_{xy}(\frac{-43}{14} ,\frac{-24}{7}) =6\)

\(f_{yx}(\frac{-43}{14} ,\frac{-24}{7} )=6\)

\(f_{yy}(\frac{-43}{14} ,\frac{-24}{7} )=-8\)

The discriminant of the second partial derivative test is:

D = \(f_{xx}(\frac{-43}{14} ,\frac{-24}{7}) \times f_{yy}(\frac{-43}{14} ,\frac{-24}{7} ) - f_{xy}(\frac{-43}{14} ,\frac{-24}{7} )^2\)

D = (-8) × (-8) - (6)²

D = 64 - 36

D = 28

Since D is positive and fₓₓ is negative at the critical point, we can conclude that the critical point (-43/14, -24/7) is a local maximum.

f(x,y) = 6xy - 4x - 9y - 4x² - 4y²

\(f(\frac{-43}{14} ,\frac{-24}{7} ) = 6(\frac{-43}{14})(\frac{-24}{7})- 4(\frac{-43}{14})- 9(\frac{-24}{7}) - 4(\frac{-43}{14})^2 - 4(\frac{-24}{7})\)

= 151/7

Therefore, the local maximum of f(x,y) = 6xy - 4x - 9y - 4x² - 4y² is 151/7 at the critical point (-43/14, -24/7).

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At least three functions can be called, including checkweather. The other two functions can be any other functions that the program contains.

The maximum number of functions that can be called when calling the checkweather function depends on the program. If the program contains other functions, then up to three functions can be called, including the checkweather function. When calling the checkweather function, the first function that will be called is the checkweather function itself. After the checkweather function is called, the program will then proceed to call any other functions that have been determined by the program. This means that the maximum number of functions that can be called is at least two, with the checkweather function being one of them.In addition, if the program contains additional functions, then the maximum number of functions that can be called increases to three. For example, if the program contains functions to display the weather forecast, to check the temperature and to generate an alert, then these functions can also be called in addition to the checkweather function. In this case, the maximum number of functions that can be called is three, with the checkweather function still being one of them.

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Answer:

20% of 75 is 15

Answer:

The correct answer is 15.

Step-by-step explanation:

To find 20% of 75, we must multiply 75 by 20%.

75 x 0.20 = 15

Therefore, the correct answer is 15.

Hope this helps! :D

Answer:

A.

Step-by-step explanation:

If you take -6 and add 12, you first add 6 to make it zero, and have 6 to add after that. This gives you 6* F

Answer:

net loss of 3 degrees

Step-by-step explanation:

we can write this out as an equation. let x represent the temperature when iko woke up.

x+11-14

simplify to get your answer:

x-3

this means that the net loss was 3 degrees over the course of the day.

Answer:

  x = 4 . . . cm

Step-by-step explanation:

You want the measure of the segment CE from external point C to circle O, given several other dimensions of chords and segments in the circle.

As in the attachment, we can extend segment DO across the circle to make diameter DX. Then we can use the relation for chord lengths to find the radius of the circle (r).

Segments of crossing chords have the same product:

  FA·FE = FD·FX

  7·4 = 2·(2r -2) . . . . . use given segment values

  14 = 2r -2 . . . . . . divide by 2

  16 = 2r . . . . . . . add 2

  r = 8 . . . . . . . divide by 2

The radius of the circle is 8 cm.

We can also extend radius EO across the circle to make diameter EY, as shown in the attachment.

The relation involving the product of secant segments can be used to find x:

  CE·CY = CB·CA

  x(x +16) = 5(5+4+7)

  x² +16x = 80 . . . . . . . . simplify

  x² +16x +64 = 144 . . . . . . . add 64 to complete the square

  (x +8)² = 12² . . . . . . . . . write as squares

  x +8 = 12 . . . . . . . . positive square root

  x = 4 . . . . . . . . subtract 8

The value of x is 4.

__

Additional comment

The attachment is accurately drawn.

Bu using mathematical sets Total 200 members of 18-24 year olds did not do any of these three activities last Friday night.

To resolve this issue, we use mathematical sets we can apply the inclusion-exclusion concept.

Let:

A represents the group of adults who watched TV, B represents the group who socialised with peers, and C represents the group who consumed pizza.

The size of the set (AUBUC), which reflects the group of adults who chose not to participate in any of the three activities, should then be determined.

We can determine the sizes of the sets A, B, and C as well as the sizes of their junctions using the information provided:

Using the formulas,

|A| = 173 + 37 + 39 + 36 = 285

|B| = 177 + 39 + 36 + 36 = 288

|C| = 187 + 37 + 36 + 36 = 296

|A∩B| = 39 + 36 = 75

|A∩C| = 37 + 36 = 73

|B∩C| = 36 + 36 = 72

|A∩B∩C| = 36

We can determine the magnitude of (AUBUC)' using the inclusion-exclusion principle in the manner shown below:

|(AUBUC)'| = N - |AUBUC|

= N - (|A| + |B| + |C| - |A∩B| - |A∩C| - |B∩C| + |A∩B∩C|)

= N - (285 + 288 + 296 - 75 - 73 - 72 + 36)

= N - 327

where N represents the overall sample size of adults (N = 527).

The amount of 18 to 24 year olds who chose not to participate in any of the three activities on Friday night is thus:

|(AUBUC)'| = N - 327

= 527 - 327

= 200

Thus, 200 young adults (18 to 24) chose not to participate in any of these three things on Friday night.

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Answer:

\(Slope (m) = -\frac{2}{3}\)

Step-by-step explanation:

To find the slope of the line of the graph, pick any 2 points on the line as your coordinate pairs.

Thus, on the line, let's pick 2 points as our coordinate pairs at:

When x = -6, y = 5 => (-6, 5), and

When x = 3, y = -1 => (3, -1)

Let (-6, 5) be (x1, y1), and (3, -1) be (x2, y2)

\( Slope (m) = \frac{y2 - y1}{x2 - x1} \)

\( Slope (m) = \frac{-1 - 5}{3 - (-6)} \)

\( Slope (m) = \frac{-1 - 5}{3 + 6} \)

\( Slope (m) = \frac{-6}{9} \)

\(Slope (m) = -\frac{2}{3}\)

The area of the figure can be obtained by splitting the figure into smaller components

The area of the irregular figure = Area of A + Area of B + Area of C

Area of A = L X B = 12 x 7 = 84 sq meters

Area of B = L X B = 5 X 8 = 40 sq meters

Area of C = L X B = 5 x 8 = 40 sq meters

Total area = 84 + 40 + 40 = 164 sq meters

Answer:

answer is 2

Step-by-step explanation:

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Answer:

Each wheel has diameter 45cm. James cycles his bicycle in a straight line in the playground. The front wheel makes 15 complete revolutions.

Step-by-step explanation:

tell me if im wrong.........

The explicit rule for the geometric sequence 3, 12, 48,... is:

f(n) = \(3 \times 4^{(n-1)\). B.

The explicit rule for the geometric sequence 3, 12, 48,... need to determine the common ratio, r.

We can do this by dividing any term by the previous term:

r = 12/3

= 48/12

= 4

Now that we know the common ratio can use the formula for the nth term of a geometric sequence:

\(a_n\) = \(a_1 \times r^{(n-1)\)

where:

\(a_n\) is the nth term

\(a_1\) is the first term (3 in this case)

r is the common ratio (4 in this case)

n is the term number

Substituting these values into the formula, we get:

\(a_n\) = \(3 \times 4^{(n-1)\)

So, the explicit rule for the geometric sequence 3, 12, 48,... is:

f(n) = \(3 \times 4^{(n-1)\)

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Answer:

We have the proportion: 8/10 = 100/y

We can solve for y by cross-multiplying.

That is, 8y = 100 * 10 Simplifying the right-hand side, 8y = 1000

Dividing both sides by 8 to solve for y, y = 125

Hence, the value of y is 125.

Finally, we have the expression: y = √80We can simplify this expression by factoring 80 into its prime factors:80 = 2 * 2 * 2 * 2 * 5

Taking the square root of 2 * 2 * 2 * 2, we have:√(2 * 2 * 2 * 2) = 2 * 2 = 4

Therefore, y = 4√5The value of y is 4√5.

Step-by-step explanation:

Hope this helps!! Have a good day/night!!

Answer:

8

Step-by-step explanation:

A is at -6

B is at 2

The distance between the two numbers is 8 Units

The dot product of vectors x and y with magnitudes 5 and 4 units, respectively, is 20 units, indicating that they are parallel to each other and in the same direction.

From the given information, we know that the magnitudes of vectors x and y are 5 and 4 units, respectively, and their dot product is 20 units.

To find the angle between vectors x and y, we can use the formula:

cos(theta) = (x.y) / (|x| * |y|)

Substituting the given values, we get:

cos(theta) = 20 / (5 * 4)
cos(theta) = 1

This implies that the angle between vectors x and y is 0 degrees, which means that they are parallel to each other.

Thus, we can conclude that vectors x and y are parallel and in the same direction.



Given the magnitudes of vectors x and y and their dot product, we can determine their relationship and direction. The dot product is the product of their magnitudes and the cosine of the angle between them. Using this formula, we found that the angle between vectors x and y is 0 degrees, indicating that they are parallel to each other. Therefore, we can conclude that vectors x and y are parallel and in the same direction. This information can be useful in various mathematical and physical applications, such as determining the force required to move an object in a particular direction.



In conclusion, the dot product of vectors x and y with magnitudes 5 and 4 units, respectively, is 20 units, indicating that they are parallel to each other and in the same direction. This information can be useful in various mathematical and physical applications.

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Answer:

f^-1(x)=x/3-1/3

Step-by-step explanation:

Answer:

w >= 5

Step-by-step explanation:

Let's start by defining a variable to represent the number of weeks Maggie needs to save up to buy the hoodie. Let's call this variable "w".

We know that Maggie currently has $30 in her bank account, and she will be making weekly deposits of $10. Therefore, after w weeks, she will have saved up:

$30 + $10w

To purchase the hoodie, Maggie needs at least $75 in her bank account. Therefore, we can write the following inequality:

$30 + $10w >= $75

To solve for w, we can start by subtracting $30 from both sides:

$10w >= $45

Next, we can divide both sides by $10:

w >= 4.5

This means that Maggie needs to save up for at least 4.5 weeks to purchase the hoodie. However, since she cannot save for half a week, we can round up to the nearest whole number, which gives us:

w >= 5

Therefore, Maggie needs to save up for at least 5 weeks to purchase the hoodie.

To graph this inequality on a number line, we can draw a closed circle at 5 (since Maggie needs to save for at least 5 weeks), and shade to the right of the circle (since any value of w greater than or equal to 5 will satisfy the inequality).

The three angles are 44, 54, and 82 degrees. Since two angles (44 and 44 degrees) have the same measure, the triangle is isosceles.

If the measures of the three angles of a triangle are x, x + 10, and 2x - 6, the triangle must be isosceles.

In a triangle, the sum of the angles is always 180 degrees. Therefore, we can set up the equation:

x + (x + 10) + (2x - 6) = 180

Combine the terms:

4x + 4 = 180

Subtract 4 from both sides:

4x = 176

Divide by 4:

x = 44

Now, we can find the measures of the other two angles:

x + 10 = 44 + 10 = 54
2x - 6 = 2(44) - 6 = 88 - 6 = 82

The three angles are 44, 54, and 82 degrees. Since two angles (44 and 44 degrees) have the same measure, the triangle is isosceles.

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